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@@ -0,0 +1,1295 @@
+1
+00:00:05,250 --> 00:00:07,890
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,890 --> 00:00:10,650
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:10,650 --> 00:00:15,990
+أهله وصحبه أجمعين هذه هي المحاضرة رقم 23 مساق 
+
+4
+00:00:15,990 --> 00:00:20,050
+تحليل اقتراني أو تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:20,050 --> 00:00:25,670
+الإسلامية قسم الرياضيات للماجستير اليوم هنحكي عن
+
+6
+00:00:25,670 --> 00:00:30,550
+ثلاثة ثمانية اللي هو representation of functional
+
+7
+00:00:30,550 --> 00:00:36,850
+on Hilbert spaces اللي بدنا نسويه إنه اللي هو عادة 
+
+8
+00:00:36,850 --> 00:00:40,770
+لما الناس يقول لك بدأ أعمل تمثيل لشغلها بوسط شغلها 
+
+9
+00:00:40,770 --> 00:00:44,970
+أكيد اللي بده يعملها الشغل الجديد اللي يعملها أحد
+
+10
+00:00:44,970 --> 00:00:48,730
+عمرين إما تكون أسهل أو إما تكون يعني الصيغة اللي 
+
+11
+00:00:48,730 --> 00:00:51,990
+بده يعملها بتستخدم في أمور أخرى حتى لو كانت معقدة
+
+12
+00:00:52,240 --> 00:00:56,220
+ماشي الحال الآن هذه لحسن الحظ أنا بقى أنا هيك وجهة 
+
+13
+00:00:56,220 --> 00:00:59,340
+نظري أن احنا بدنا نروح باتجاه اللي هو ناخد ال
+
+14
+00:00:59,340 --> 00:01:04,440
+functional ونوصله إلى صيغة معينة الصيغة سهلة اللي 
+
+15
+00:01:04,440 --> 00:01:06,640
+هو بالكتب اللي هو ال functional بصورة inner 
+
+16
+00:01:06,640 --> 00:01:09,720
+product يعني أي linear functional يعني ده اللي 
+
+17
+00:01:09,720 --> 00:01:13,080
+linear functional بدك تكتبها على صورة ايش بتساوي 
+
+18
+00:01:13,080 --> 00:01:16,020
+inner product و inner product لطيف يعني و الناس 
+
+19
+00:01:16,020 --> 00:01:19,720
+بتحب تتعامل معه نيجي الآن نيجي اللي هي أول نظرية 
+
+20
+00:01:19,720 --> 00:01:23,920
+بنحكي فيها اللي هي دي النظرية Riesz theorem بقول لك
+
+21
+00:01:23,920 --> 00:01:27,400
+every bounded linear functional on a Hilbert space
+
+22
+00:01:28,290 --> 00:01:31,710
+H can be represented in terms of inner product
+
+23
+00:01:31,710 --> 00:01:36,390
+يعني كل linear functional اللي هو of Hilbert space 
+
+24
+00:01:36,390 --> 00:01:39,610
+كان بيه ايش ما له بنقدر نكتبها على صورة inner 
+
+25
+00:01:39,610 --> 00:01:43,830
+product بالظبط لو F bounded linear functional بقدر
+
+26
+00:01:43,830 --> 00:01:46,730
+أقول لك أكتب لك F of X بيساوي ال inner product بين X
+
+27
+00:01:46,730 --> 00:01:52,330
+و Z حيث Z depends on F اللي بتحكي عنها أكيد لأن كل 
+
+28
+00:01:52,330 --> 00:01:55,070
+واحدة بده يكونها Z معينة والـ F is uniquely
+
+29
+00:01:55,070 --> 00:01:59,210
+determined by F with norm كمان هيطلع norm الـ Z
+
+30
+00:01:59,210 --> 00:02:03,490
+هذا هو normية norm الـ F هذه النظرية اللي عندنا
+
+31
+00:02:03,490 --> 00:02:07,600
+ماشي الحال اطلع خلينا نشوف ال proof الشيء الذي يظهر
+
+32
+00:02:07,600 --> 00:02:10,880
+في حالة f يتساوي 0 هو حالة الـ Z لأنه على طول 
+
+33
+00:02:10,880 --> 00:02:14,280
+تلاقي الـ Z يتساوي 0 بيصير f of x يتساوي x و 0
+
+34
+00:02:14,280 --> 00:02:17,760
+بيصير الهي الهي الهي الهي الهي الهي الهي الهي الهي
+
+35
+00:02:17,760 --> 00:02:18,600
+الهي الهي الهي الهي الهي الهي الهي الهي الهي الهي
+
+36
+00:02:18,600 --> 00:02:19,440
+الهي الهي الهي الهي الهي الهي الهي الهي الهي الهي
+
+37
+00:02:19,440 --> 00:02:21,680
+الهي الهي الهي الهي الهي الهي الهي الهي الهي الهي
+
+38
+00:02:21,680 --> 00:02:22,240
+الهي الهي الهي الهي ال
+
+39
+00:02:27,870 --> 00:02:32,850
+بما أن F لا تساوي صفر إذا يعني ما فيش حاجة تقول لي
+
+40
+00:02:32,850 --> 00:02:37,230
+إن كل العناصر هتروح للصفر يعني ال null F مش هيكون 
+
+41
+00:02:37,230 --> 00:02:40,330
+ال H اللي هو ال null space ال null space هو عبارة
+
+42
+00:02:40,330 --> 00:02:44,690
+عن super zero مدان فيه صورة مش صفر إذا أكيد ما له
+
+43
+00:02:44,690 --> 00:02:48,840
+ال null F في شمالها مش كل ال H كاملة طيب لكن احنا 
+
+44
+00:02:48,840 --> 00:02:52,540
+قبل هيك قلنا N of S from null space is a closed
+
+45
+00:02:52,540 --> 00:02:55,980
+subspace of H طيب ماذا يعمل closed subspace لـ H 
+
+46
+00:02:55,980 --> 00:02:59,440
+ده الأمور حلوة في الدنيا بالصحيحة إذا من theorem
+
+47
+00:02:59,440 --> 00:03:04,080
+3.3.4 بقدر أكتب H اللي هي ال complete على صورة
+
+48
+00:03:04,080 --> 00:03:07,240
+closed subspace N of S و ال orthogonal complement
+
+49
+00:03:07,240 --> 00:03:11,580
+له اللي هو N of F أي orthogonal كتبت على صورة 
+
+50
+00:03:11,580 --> 00:03:17,890
+direct sum من الـ H طبعا هنا ال N of F مش H إذا ال
+
+51
+00:03:17,890 --> 00:03:21,770
+N of F Orthogonal مش صفر إذا ال N of F Orthogonal
+
+52
+00:03:21,770 --> 00:03:25,330
+ليسوا صفر فما دام هيك ما دام مش صفر إذا بقدر
+
+53
+00:03:25,330 --> 00:03:29,830
+أجي اللي هو Z not لا تساوي صفر و Z not وين موجودة 
+
+54
+00:03:29,830 --> 00:03:35,340
+في ال N of F Orthogonal طيب طيب الآن منها هذه بدي
+
+55
+00:03:35,340 --> 00:03:38,820
+أصنع اللي بدي .. اللي بدي أصل لمين للـ z اللي فوق 
+
+56
+00:03:38,820 --> 00:03:42,220
+ماشي الحالة بواسطة هذه و بواسطة ال F اللي هي اللي 
+
+57
+00:03:42,220 --> 00:03:46,380
+عندي المعتار الآن صارت عندي z note بين إيديا و ال
+
+58
+00:03:46,380 --> 00:03:52,340
+F عندي معتار بقول لك 6 الآن أو اللي هو ركب التركيبة 
+
+59
+00:03:52,340 --> 00:03:57,880
+التالية ضرب ل z note في F of X X arbitrary fixed
+
+60
+00:03:57,880 --> 00:04:02,800
+point و X في مين في أفه في Z note و حاصل الطرح سميه
+
+61
+00:04:02,800 --> 00:04:06,980
+مين هنا V و مقصودة أن هذي هذي Z note وهنا X وهنا X 
+
+62
+00:04:06,980 --> 00:04:10,790
+وهنا Z note مقصودة على الطرح Where X is an arbitrary
+
+63
+00:04:10,790 --> 00:04:16,690
+element in H since F is linear إذا لو جيت حسبت ال
+
+64
+00:04:16,690 --> 00:04:21,290
+F of V هذي بيصير عدد بتطلع براها فبيصير F of Z0 في 
+
+65
+00:04:21,290 --> 00:04:25,310
+F of X و هذي بيصير عدد بتطلع برا ال F بيصير ناقص F 
+
+66
+00:04:25,310 --> 00:04:29,250
+of X في F of Z0 حصلت رحلنا ايش بيساوي؟ بيساوي 0
+
+67
+00:04:29,250 --> 00:04:34,370
+صارت ال V هذه اللي اخترتها هذه where موجودة في ال
+
+68
+00:04:34,370 --> 00:04:39,200
+null في ال null of F إذا صارت الـ V عمودية على مين؟
+
+69
+00:04:39,200 --> 00:04:41,400
+على الـ Z note اللي هي اللي موجودة في الـ N of 
+
+70
+00:04:41,400 --> 00:04:45,160
+orthogonal إذا صار عندي مدام عمودية عليها إذا صار
+
+71
+00:04:45,160 --> 00:04:48,580
+عندي ال inner product بين ال V و Z note صفر ال V 
+
+72
+00:04:48,580 --> 00:04:52,380
+حقق اللي قيمتها اللي هي Z note و F of X ناقص X في
+
+73
+00:04:52,380 --> 00:04:56,640
+F و Z note و Z note استخدم خلاص ال inner product و
+
+74
+00:04:56,640 --> 00:05:00,460
+طلع لي هدولة برا و ارتب لي اياه فبيصير F of X في Z note
+
+75
+00:05:00,460 --> 00:05:04,770
+و Z يعني هادي مع هادي ناقص هادي مع هادي بيصير عندي F 
+
+76
+00:05:04,770 --> 00:05:09,190
+of X في Z0 و Z ناقص اللي هي F of Z0 بتطلع و X و
+
+77
+00:05:09,190 --> 00:05:13,770
+مين و Z0 معي الآن صار عندي أي واجهة عندها دي
+
+78
+00:05:13,770 --> 00:05:18,970
+صارت عندي هذا المقدار بيساوي صفر أنقل لي هذا على 
+
+79
+00:05:18,970 --> 00:05:23,890
+الطرف الثاني ماشي الحال و اجمع لي اللي هو على Z و
+
+80
+00:05:23,890 --> 00:05:28,450
+Z0 فبيصير F of X ايش هتساوي اللي هو هذا المقدار على
+
+81
+00:05:28,450 --> 00:05:32,890
+Z و Z0 بيصير اللي هي F of Z0 على Z و Z0 في X و مين
+
+82
+00:05:32,890 --> 00:05:39,340
+و Z0 واضح معي
+
+83
+00:05:39,340 --> 00:05:43,760
+يا جماعة إذا F of X صارت عبارة عن F of Z note على 
+
+84
+00:05:43,760 --> 00:05:47,920
+Z of Z note في X of Z note واضحة اتها و بيساوي الآن 
+
+85
+00:05:47,920 --> 00:05:52,300
+دخليها دي على بعيد عشان بتاخد Z أنا بتلاحظ ال Z
+
+86
+00:05:52,300 --> 00:05:57,900
+فبيصير X of F of Z note على اللي هو Z note و Z note
+
+87
+00:05:57,900 --> 00:06:04,490
+و norm و Z note ماشي الآن عندي X was arbitrary إذا 
+
+88
+00:06:04,490 --> 00:06:07,530
+لو اجينا اخذنا صارت الآن F of X بالساوية القيمة
+
+89
+00:06:07,530 --> 00:06:12,350
+هذه هذه صارت بين إيديا مبنية ال Z note وهذه بين 
+
+90
+00:06:12,350 --> 00:06:18,270
+إيديا ماشي الحال كل هذه كل هذه هي اللي سميه لي إياها
+
+91
+00:06:18,270 --> 00:06:23,910
+Z إذا صار عندي الآن حصلنا F of X بالساوية X ومين
+
+92
+00:06:23,910 --> 00:06:30,620
+و Z هاي واحد الآن بدي أثبت لك اللي هو عندي بدي أثبت لك 
+
+93
+00:06:30,620 --> 00:06:33,420
+أنه وحيدة وبعدين بدي أثبت لك norm هذه بيسوي norm مين
+
+94
+00:06:33,420 --> 00:06:36,760
+الـ z خلّيني واحدة واحدة to prove the uniqueness
+
+95
+00:06:36,760 --> 00:06:40,840
+of z suppose that there are z واحد and z اتنين 
+
+96
+00:06:40,840 --> 00:06:44,940
+such that f of x بيساوي x و z واحد و f of x بيساوي x
+
+97
+00:06:44,940 --> 00:06:48,940
+و z اتنين وهذه سهلة for all x المتناشر إذا جيب هنا
+
+98
+00:06:48,940 --> 00:06:51,440
+دولة جانب بعض و اترحى من بعض بيطلع من ساوي صفر 
+
+99
+00:06:51,440 --> 00:06:56,950
+اترحى انش هيكون x و z واحد ناقص z اتنين الآن عندي
+
+100
+00:06:56,950 --> 00:07:00,570
+هذا الكلام صحيح لكل x والتي موجودة في الـ H مضمنها
+
+101
+00:07:00,570 --> 00:07:06,770
+هي z1-z2 في الـ H إذا صار z1-z2 إذا z1-z2 بيساوي 0
+
+102
+00:07:06,770 --> 00:07:10,370
+إذا ال norm هنا بيساوي 0 إذا z1 بيساوي z2 وهذا
+
+103
+00:07:10,370 --> 00:07:13,890
+بيثبت ال uniqueness الآن أنزلوا شوية، أنزلوا، 
+
+104
+00:07:13,890 --> 00:07:18,510
+أنزلوا، بنرجع نثبت مين الآن عندي اللي هو norm F
+
+105
+00:07:18,510 --> 00:07:25,890
+بيساوي norm z، norm F بيساوي norm الـ z احنا
+
+106
+00:07:25,890 --> 00:07:29,890
+قلنا f of x ايش هتساوي ال inner product بين x و z 
+
+107
+00:07:29,890 --> 00:07:34,110
+صح ولا لأ؟ لأن خدوا لي ال absolute value للجهتين أو 
+
+108
+00:07:34,110 --> 00:07:38,530
+ال modulus هذا بشوارز ال quality بيصير أصغر أو 
+
+109
+00:07:38,530 --> 00:07:44,190
+يساوي norm ال x في norm الـ z لأن اجمعوا لي
+
+110
+00:07:44,190 --> 00:07:46,170
+الجهتين على norm ال x اللي هي ال xات اللي بيساوي
+
+111
+00:07:46,170 --> 00:07:52,230
+نش صفر فبيصير f of x على norm الـ x أصغر أو يساوي norm 
+
+112
+00:07:52,230 --> 00:07:55,730
+مين الـ z صارت هذه upper bound لهذه إذا أكيد ال
+
+113
+00:07:55,730 --> 00:07:57,730
+suprem لهادي أصغر أو يساوي هذه اللي هو اللي is upper
+
+114
+00:07:57,730 --> 00:08:03,410
+bound إذا ال suprem لهادي over x element أتش و x 
+
+115
+00:08:03,410 --> 00:08:08,810
+لا تساوي صفر بيصير عندي هذا كله اسمه مين norm ال F 
+
+116
+00:08:08,810 --> 00:08:12,950
+إذا صار norm ال F أصغر أو يساوي مين norm ال Z هاي واحدة 
+
+117
+00:08:12,950 --> 00:08:18,170
+الآن الاتجاه الثاني الاتجاه الثاني خدوا الآن عندي 
+
+118
+00:08:18,170 --> 00:08:27,860
+F of X بيساوي ايش يا جماعة X و Z صح ولا لأ؟ لأن
+
+119
+00:08:27,860 --> 00:08:33,220
+F of Z ايش بيساوي اللي هي ال inner product بين Z و مين 
+
+120
+00:08:33,220 --> 00:08:46,220
+و Z صح ويساوي مين norm Z تربيع بايش الحال عند 
+
+121
+00:08:46,220 --> 00:08:50,110
+norm ال F أكيد اللي عندي absolute value of f of z
+
+122
+00:08:50,110 --> 00:08:55,790
+بيساوي norm الـ z تربيع صح ولا لأ؟ باين هاه؟ باين 
+
+123
+00:08:55,790 --> 00:09:04,090
+هاه؟ هذه الآن أكبر أو يساوي اللي هو norm of f of z
+
+124
+00:09:04,090 --> 00:09:05,830
+من norm of f نفسها
+
+125
+00:09:09,670 --> 00:09:14,410
+ماشي الحال عند norm ال F أصغر أو يساوي norm ال ..
+
+126
+00:09:14,410 --> 00:09:20,810
+ال .. الأكبر آسف شو هو هذي اللي هي ال supremum norm ال 
+
+127
+00:09:20,810 --> 00:09:25,470
+F supremum وهذه نقطة منها بيصير norm ال F أكبر 
+
+128
+00:09:25,470 --> 00:09:29,630
+أو يساوي norm ال Z هي أكبر أو يساوي norm ال Z وهي أصغر 
+
+129
+00:09:29,630 --> 00:09:34,290
+أو يساوي norm ال Z من التنتين مع بعض اشملها معايا
+
+130
+00:09:34,290 --> 00:09:37,670
+يا جماعة هاد norm ال F أصغر أو يساوي و هاد norm ال F 
+
+131
+00:09:37,670 --> 00:09:40,770
+أكبر أو يساوي التنتين مع بعض اللي هو بيصير norm ال F 
+
+132
+00:09:40,770 --> 00:09:47,010
+يساوي norm ال Z يلا اللي بعدها نيجي الآن لما هاد
+
+133
+00:09:47,010 --> 00:09:47,770
+المم سهلة 
+
+134
+00:09:50,440 --> 00:09:54,320
+ف V1 و W .. مش عارف ايش كتبتها اصلا V2 و W for all 
+
+135
+00:09:54,320 --> 00:09:58,980
+W in inner product space X then V1 بيساوي V2 in
+
+136
+00:09:58,980 --> 00:10:02,180
+particular V1 و W بيساوي 0 for all W المتن X 
+
+137
+00:10:02,180 --> 00:10:06,100
+implies that V1 بيساوي مين؟ صفر هذا exercise بسيط
+
+138
+00:10:06,100 --> 00:10:13,320
+يعني .. طب و في أثناء البرهان اللي برهنّاها اللي
+
+139
+00:10:13,320 --> 00:10:28,520
+قبل وشوية هنشوفها عند ما أعطيني V1 و V2 و V1
+
+140
+00:10:28,520 --> 00:10:32,800
+و V2 في ال X بقول إذا كان هذا بيساوي ذاك معناته V1 
+
+141
+00:10:32,800 --> 00:10:36,700
+بساوة V2 فكي ترجله هذا على الجهة الثانية بيصيح V1 نقص
+
+142
+00:10:36,700 --> 00:10:40,680
+V2 و W عملتها قبل شوية بساوة سفر هذا لكل W من ضمن
+
+143
+00:10:40,680 --> 00:10:47,340
+هم مين V1 نقص V2 لأن V1 نقص V2 و V1 نقص V2 بساوة 
+
+144
+00:10:47,340 --> 00:10:52,160
+سفر أو منه اللي هو V1 بساوة V2 لأنه ال norm التربيعي
+
+145
+00:10:52,160 --> 00:10:55,800
+بساوة سفر لأن V1 بساوة V2 إلى اللي بعدها حالة خاصة
+
+146
+00:10:55,800 --> 00:11:00,730
+منها إذا كانت V1 و W بساوة سفر لكل W في ال X إذا
+
+147
+00:11:00,730 --> 00:11:04,530
+سأكون من ضمن الـ W V1 يصبح V1 و V1 بالساعة وسفر و
+
+148
+00:11:04,530 --> 00:11:06,370
+V1 بالساعة وسفر وهو المطلوب
+
+149
+00:11:11,800 --> 00:11:16,200
+حكينا كان عن ال linear .. اطلع لفوق شوية حكينا عن
+
+150
+00:11:16,200 --> 00:11:20,000
+ال linear functional الآن عرفنا احنا قبل هيك ال
+
+151
+00:11:20,000 --> 00:11:23,900
+bilinear بتكون linear في الجهتين اه يعني function
+
+152
+00:11:23,900 --> 00:11:25,800
+of two variables بتكون linear في الأولى و linear
+
+153
+00:11:25,800 --> 00:11:29,120
+في الثانية sesquilinear بتكون linear في الأولى و
+
+154
+00:11:29,120 --> 00:11:31,880
+الثانية conjugate linear يعني مش linear .. زي اللي
+
+155
+00:11:31,880 --> 00:11:34,980
+انار ال product .. زي اللي بنار ال product الـ
+
+156
+00:11:34,980 --> 00:11:37,860
+Linear Product Linear في الأولى لكن في الـ Inter
+
+157
+00:11:37,860 --> 00:11:40,560
+الثانية هي إيش ماله Conjugate Linear لما يطلع يطلع
+
+158
+00:11:40,560 --> 00:11:44,180
+يبقى إيش و Conjugate فعشان هيك بنسميه Sesquilinear
+
+159
+00:11:44,180 --> 00:11:49,300
+إذا نقول بالظبط إيش اللي بتحكيه هذا بقول الآن let
+
+160
+00:11:49,300 --> 00:11:53,920
+X and Y be vector spaces over a field K تنين over
+
+161
+00:11:53,920 --> 00:11:59,420
+the same field لأن a sesquilinear form أو
+
+162
+00:11:59,420 --> 00:12:04,320
+sesquilinear functional H هو عبارة عن ده لمن X
+
+163
+00:12:04,320 --> 00:12:09,700
+cross Y لمين للـ scalar field تبع حينكي إيش بيحقق؟
+
+164
+00:12:09,700 --> 00:12:14,240
+بيحقق إنه linear في الأولى و conjugate linear في
+
+165
+00:12:14,240 --> 00:12:19,920
+الثانية، ماشي؟ إيش يعني أنه لكل X1 و X2 و X في الـ
+
+166
+00:12:19,920 --> 00:12:24,280
+X و Y1 و Y2 نقوله بـ Y و كل Scale as Alpha Beta
+
+167
+00:12:24,280 --> 00:12:31,360
+تحقق مالي H of X1 زائد X2 و Y بتساوي H of X1 و Y
+
+168
+00:12:31,360 --> 00:12:36,440
+زائد H of X2 و Y زي ال inner product الآن اتشوف x و
+
+169
+00:12:36,440 --> 00:12:39,720
+y واحد زي إضاءة y اتنين بالساوية اتشوف x واحد و y
+
+170
+00:12:39,720 --> 00:12:44,960
+واحد زي اتشوف x و y اتنين اللي نهار اتعادى بس لأن
+
+171
+00:12:44,960 --> 00:12:47,280
+لما ندخل ال scalar بصير أنا conjugate و أنا مش
+
+172
+00:12:47,280 --> 00:12:50,620
+conjugate لأن H في Alpha X و Y بيسوي Alpha H X و Y
+
+173
+00:12:50,620 --> 00:12:53,800
+إذا ال linear صارت في ال entry الأول في ال entry
+
+174
+00:12:53,800 --> 00:12:57,020
+الثاني بتطلع بيه conjugate يعني اللي هو conjugate
+
+175
+00:12:57,020 --> 00:13:01,720
+linear هذا كله مع بعض بنسميه Sesquilinear لو لو
+
+176
+00:13:01,720 --> 00:13:06,200
+كانت K بيتساوي R ال above بنسميه إيش ماله bilinear
+
+177
+00:13:06,200 --> 00:13:08,800
+لأن مافيش حاجة اسمها conjugate حيصير إيش ماله اللي
+
+178
+00:13:08,800 --> 00:13:11,900
+هو ال conjugate هو نفسه في حالة ال real
+
+179
+00:13:14,640 --> 00:13:19,060
+أطلع لفوق، بدنا نعرف الـ Normally, if X and Y are
+
+180
+00:13:19,060 --> 00:13:22,940
+normed spaces, then is C أكبر من 0 such that for
+
+181
+00:13:22,940 --> 00:13:26,660
+all X element in X and all Y element in Y، احسبلي
+
+182
+00:13:26,660 --> 00:13:30,720
+الـabsolute value of H of X وY، ماشي؟ الـabsolute
+
+183
+00:13:30,720 --> 00:13:35,790
+value of H of X وY، لأ مش حسب، بدنا نعرف إن X وY
+
+184
+00:13:35,790 --> 00:13:39,170
+هم مجموعات عادية وكان هناك C أكبر من 0 إذا كان
+
+185
+00:13:39,170 --> 00:13:42,770
+عندي
+
+186
+00:13:42,770 --> 00:13:46,190
+H بX وY أصغر سواء C في عادية X وعادية Y إذا كان
+
+187
+00:13:46,190 --> 00:13:52,100
+هذا حدث إذا كان هذا حدث بنسميه H is bounded and the
+
+188
+00:13:52,100 --> 00:13:55,980
+number normal h نفس اللي قمناها قبل اللي هو
+
+189
+00:13:55,980 --> 00:13:59,680
+supremum لهذا المقدار على norm ال X و norm ال Y ال
+
+190
+00:13:59,680 --> 00:14:02,580
+Xات اللي بيساوي نش سفر و ال Yات اللي بيساوي نش سفر
+
+191
+00:14:02,580 --> 00:14:06,700
+أو ال supremum عليهم نفسهم ال H of X و Y و هدول
+
+192
+00:14:06,700 --> 00:14:11,520
+نوماتهم إيش بيساوي بيساوي واحد الآن هذا بسميه اللي
+
+193
+00:14:11,520 --> 00:14:14,680
+هو norm sesquilinear اللي هو H
+
+194
+00:14:18,360 --> 00:14:22,520
+الآن واضح أنه لو جيت أخدت ال H في X و Y هتصير
+
+195
+00:14:22,520 --> 00:14:25,140
+الأصغر يساوي Norm ال H في Norm ال X في Norm ال Y
+
+196
+00:14:25,140 --> 00:14:30,740
+لأنه هذه Norm ال H أكبر أو يساوي هذا على هذا لأن
+
+197
+00:14:30,740 --> 00:14:34,410
+Norm ال H هي ال supremum فأكيد H و في x و y أصغر
+
+198
+00:14:34,410 --> 00:14:38,870
+سواء Norm H في Norm x في Norm y for all x و
+
+199
+00:14:38,870 --> 00:14:42,310
+y عندي the inner product is sesquilinear and
+
+200
+00:14:42,310 --> 00:14:46,210
+bounded و هذا طبعا أخدناه هو ولا مش هو كله أخدناه
+
+201
+00:14:46,210 --> 00:14:49,530
+أنه أصلا هو اللي قلنا عنه مثال عالمين على ال
+
+202
+00:14:49,530 --> 00:14:55,530
+sesquilinear طيب نيجي للنظرية الأخيرة عندنا اطلع
+
+203
+00:14:55,530 --> 00:14:59,610
+لفظ الآن الـ Riesz Representation Theorem زي
+
+204
+00:14:59,610 --> 00:15:03,370
+الأولى تبع الـ Linear Functional بدنا نعمل لنين؟
+
+205
+00:15:03,370 --> 00:15:06,830
+لأ اللي هو Sesquilinear Form أو Sesquilinear
+
+206
+00:15:06,830 --> 00:15:09,490
+Functional اللي أنا بقوله إذا الـ Riesz
+
+207
+00:15:09,490 --> 00:15:12,910
+Representation Theorem ليه اتقدش واحد؟ أنا اتقدش
+
+208
+00:15:12,910 --> 00:15:17,520
+اتنين مالهن الـ Hilbert spaces كاملة يعني over a
+
+209
+00:15:17,520 --> 00:15:23,440
+field يعني K and H من H واحد cross H اتنين لعند K
+
+210
+00:15:23,440 --> 00:15:28,320
+فرضي أنه احنا a bounded Sesquilinear form then H
+
+211
+00:15:28,320 --> 00:15:32,100
+can be written or has a representation H of X وY
+
+212
+00:15:32,100 --> 00:15:35,300
+إيش بتساوي برضه بدأت يطبع على صورة inner
+
+213
+00:15:35,300 --> 00:15:41,430
+product اللي هي Sx دالة في الـ H واحد والـ Y where S
+
+214
+00:15:41,430 --> 00:15:44,870
+من H واحد لعند H اتنين function من H واحد لعند H
+
+215
+00:15:44,870 --> 00:15:50,490
+اتنين الآن is a bounded linear operator ماشي
+
+216
+00:15:50,490 --> 00:15:55,410
+moreover Norm S اللي هو حيساو الـH و الـS is
+
+217
+00:15:55,410 --> 00:15:58,790
+uniquely determined by H and has the Norm اللي هو
+
+218
+00:15:58,790 --> 00:16:01,430
+Norm الـS بيساوي Norm الـH إذا نفس الأولى، نفس
+
+219
+00:16:01,430 --> 00:16:07,370
+النص تقريبا بس بما يلائم اللي هو من الـH اللي هي
+
+220
+00:16:07,370 --> 00:16:10,630
+الـ Sesquilinear form اللي عندي إذا الآن ال
+
+221
+00:16:10,630 --> 00:16:13,610
+Sesquilinear form can be written as an inner
+
+222
+00:16:13,610 --> 00:16:17,490
+product هذا اللي هذا و الكتابة اللي هي أشمالها
+
+223
+00:16:17,490 --> 00:16:26,450
+وحيدة اطلع لفوق الآن بدنا نحصل على ال S ونحصل على
+
+224
+00:16:26,450 --> 00:16:31,170
+ال H as inner product بين ال S X وY ونثبت إن Norm
+
+225
+00:16:31,170 --> 00:16:37,010
+S هو Norm H واحدة Consider الآن f of x y conjugate
+
+226
+00:16:37,010 --> 00:16:43,030
+which is linear in y لأنها
+
+227
+00:16:43,030 --> 00:16:46,290
+كانت لحالها بدون ال conjugate اللي هي linear في
+
+228
+00:16:46,290 --> 00:16:50,870
+الأولى و conjugate linear في الثانية لما أخدناها
+
+229
+00:16:50,870 --> 00:16:54,910
+صارت اللي هي linear في مين في ال y خلينا نثبت x و
+
+230
+00:16:54,910 --> 00:16:58,610
+نشتغل على مين و كأنها صارت هذه function f of x y
+
+231
+00:16:58,610 --> 00:17:02,870
+function في مين بس في y و x arbitrary لكن fixed
+
+232
+00:17:03,740 --> 00:17:07,680
+الآن إذا هذه صارت عبارة عن linear function in Y
+
+233
+00:17:07,680 --> 00:17:12,180
+الشكل اللي بدي استخدمه من نظرية قبل شوية اللي كانت
+
+234
+00:17:12,180 --> 00:17:15,720
+.. اللي هي تحكي عن من لجيلها inner product بواسطة
+
+235
+00:17:15,720 --> 00:17:20,660
+مين اللي هتكون F linear، ماشي؟ إذا now for any
+
+236
+00:17:20,660 --> 00:17:25,220
+fixed x element in H we have a by theorem 381
+
+237
+00:17:25,220 --> 00:17:29,880
+اللي أخدناها to get a unique Z element in H2 that
+
+238
+00:17:29,880 --> 00:17:35,940
+depends on X لأن احنا أخدنا الآن ثبتنا X صارت عند
+
+239
+00:17:35,940 --> 00:17:40,880
+H of X معينة و Y واخدناها كونتجة صارت function في
+
+240
+00:17:40,880 --> 00:17:46,880
+مين في Y يعني حتاخد من H2 وترمي في مين في K في
+
+241
+00:17:46,880 --> 00:17:50,590
+ال scalar field ماشي الحال إلى أن أنا بحكي عن X
+
+242
+00:17:50,590 --> 00:17:55,810
+محددة بين ديها هذه الآن صارت linear في ال Y مدام
+
+243
+00:17:55,810 --> 00:17:59,290
+linear في ال Y إذا بقدر ألاقي حسب النظرية اللي قبل
+
+244
+00:17:59,290 --> 00:18:02,350
+وشوية بلاقي Z بحيث أن هذه بتساوي ال inner product
+
+245
+00:18:02,350 --> 00:18:05,670
+بين اللي هو ال Y و ال Z أو ال Z و ال Y ماشي الحال
+
+246
+00:18:06,490 --> 00:18:10,530
+طيب هذه لمن؟ لـ X المحددة هذه إذا كل X هجي لها من؟
+
+247
+00:18:10,530 --> 00:18:13,910
+Z معينة آه لأن ما أضمنش كل .. هذه احنا حكيت عن X
+
+248
+00:18:13,910 --> 00:18:17,470
+معينة لو غيرت ال X هجي Z تاني وهكذا إذا صارت اللي
+
+249
+00:18:17,470 --> 00:18:21,910
+هي ال Z هذه بتعتمد على من؟ على ال X اللي عنده طيب
+
+250
+00:18:21,910 --> 00:18:28,200
+إذا وكأنه صح بده يصير ده لأ الآن نقلنا to get a
+
+251
+00:18:28,200 --> 00:18:32,180
+unique Z وحيدة element in h2 that depends on x
+
+252
+00:18:32,180 --> 00:18:36,380
+element in h1 such that h of x,y هذه الـ function
+
+253
+00:18:36,380 --> 00:18:40,360
+اللي عندي f of a كنا نسميها f of y بتساوي ال y و
+
+254
+00:18:40,360 --> 00:18:44,060
+ال z اللي لجيتها، معايا؟ لكن ال z تعتمد عالميا على
+
+255
+00:18:44,060 --> 00:18:49,400
+x for all y element in h2 and so رجع الأمور لنصابها
+
+256
+00:18:49,400 --> 00:18:52,940
+بيصير h of x و y بتساوي ال inner product أخدت
+
+257
+00:18:52,940 --> 00:18:55,920
+ال conjugate له الجهتين أخدت ال conjugate له هذه و ال
+
+258
+00:18:55,920 --> 00:19:00,120
+conjugate له هذه هذي رجعت لنفسها و هذي صارت z و y ماشي
+
+259
+00:19:00,120 --> 00:19:05,100
+الحال hence الآن الاسم h واحد أدش اتنين إيش هي
+
+260
+00:19:05,100 --> 00:19:08,940
+given by مين زي ما قولنا كل x بتلاقي لها مين z as
+
+261
+00:19:08,940 --> 00:19:13,200
+x إيش بتساوي z is an operator and h of x و y
+
+262
+00:19:13,200 --> 00:19:17,840
+بتساوي اللي هو Z و Y اللي سميتها دي إيش ما لها S X
+
+263
+00:19:17,840 --> 00:19:24,560
+and for عندي أثبتت إنه أتشوف X و Y بيساوي S X و Y
+
+264
+00:19:24,560 --> 00:19:28,480
+بدنا الآن نثبت إنه هذه الأس اللي لقيناها is linear
+
+265
+00:19:28,480 --> 00:19:35,550
+ماشي طيب خدوا الآن for all x1 و x2 in element h1 و
+
+266
+00:19:35,550 --> 00:19:39,530
+y element in h2 and all scalars α احسبلي الآن ال
+
+267
+00:19:39,530 --> 00:19:44,430
+inner product S α x1 زائد x2 و y بتساوي حسب اللي ..
+
+268
+00:19:44,430 --> 00:19:49,330
+اللي عرفته فوق حسب اللي أوجدته هان إيش هيساوي H of
+
+269
+00:19:49,330 --> 00:19:55,550
+اللي هي α x .. هيها من Sxy بيساوي H of xy ماشي
+
+270
+00:19:55,550 --> 00:20:02,620
+الآن S of α x1 زائد x2 و y بيساوي H هيها بعد هذه of α
+
+271
+00:20:02,620 --> 00:20:08,220
+X1 زائد X2 أو Y Y ساوي الـ H ما هي Sesquilinear
+
+272
+00:20:08,220 --> 00:20:12,620
+اللي هنا في الأولى إذا تطلع الـ Alpha H of X1 Y زائد
+
+273
+00:20:12,620 --> 00:20:18,600
+H of X2 X2 أو Y هذه اللي هي مين بتمثل اللي هي
+
+274
+00:20:18,600 --> 00:20:24,760
+Alpha في S X1 أو Y وهذه بتمثل مين الثانية H of X2
+
+275
+00:20:24,760 --> 00:20:31,320
+اللي هي عبارة عن S X2 ومين أو Y من هذا التعريف الآن
+
+276
+00:20:31,320 --> 00:20:39,000
+صار عندي اللي هو S α X1 زائد X2 و Y بيساوي هذا
+
+277
+00:20:39,000 --> 00:20:43,880
+المقدار ماشي رجعوهم لبعض هيك في ال inner product
+
+278
+00:20:43,880 --> 00:20:48,380
+inner product هي Y و هي Y مظبوط هذه بندخلها هنا و
+
+279
+00:20:48,380 --> 00:20:53,280
+بنجمع هذه اللي هذه بيصير α S X1 و S X2 و Y صار هذا
+
+280
+00:20:53,280 --> 00:20:57,160
+المقدار بيساوي هذا المقدار لكل Y حسب النظرية اللي 
+
+281
+00:20:57,160 --> 00:21:03,300
+قبله شوية لما قلنا اللي هو V1 و V2 و W متساويات
+
+282
+00:21:03,300 --> 00:21:07,960
+دائما إذا لازم اللي هو الـ V1 سوى V2 هذه و هذه
+
+283
+00:21:07,960 --> 00:21:11,980
+بساوي هذه و هذه لكل Y إذا اللي جوا هذا بساوي اللي 
+
+284
+00:21:11,980 --> 00:21:15,860
+جوا هذا إذا أصبح بايلمة تلاتة تمانين قبل بشوية
+
+285
+00:21:15,860 --> 00:21:20,740
+هيطلع S of Alpha X واحد زايد X اتنين بسوء Alpha S
+
+286
+00:21:20,740 --> 00:21:25,840
+X واحد زايد S X اتنين وهذه تعني أن الـ S is linear
+
+287
+00:21:25,840 --> 00:21:30,720
+الآن نثبت الـ boundedness إذا كانت S بتساوي صفر
+
+288
+00:21:30,720 --> 00:21:34,880
+then it is bounded automatically ما أنتم عارفين إذا
+
+289
+00:21:34,880 --> 00:21:38,460
+كانت الـ S لا تساوي صفر then احسبلي الـ norm
+
+290
+00:21:38,460 --> 00:21:43,050
+الـ H إيش بيساوي الـ supremum للـ h of x و y اللي هو
+
+291
+00:21:43,050 --> 00:21:46,890
+ليش h of x و y بيساوي Sxy ع Normal x في Normal y
+
+292
+00:21:46,890 --> 00:21:50,510
+ماشي الحال وشيل الـ Xات طبعا over الـ Xات و الـ Yات
+
+293
+00:21:50,510 --> 00:21:54,390
+اللي مش صفر هذه أكيد أكبر أو يساوي الـ supremum للـ
+
+294
+00:21:54,390 --> 00:21:59,130
+S x و للـ S x Normal x و Normal S x x limiting h1 ليش 
+
+295
+00:21:59,130 --> 00:22:03,330
+هذه أكبر يساوي هذه لأن هذه المجموعة هذه المجموعة
+
+296
+00:22:03,330 --> 00:22:08,150
+اللي موخوذة على كل الـ inner product S X و Y وهذه 
+
+297
+00:22:08,150 --> 00:22:11,770
+المجموعة هذه المجموعة بتحتوي هذه لأنها حالة خاصة 
+
+298
+00:22:11,770 --> 00:22:17,270
+من هذهك بس على خدة الـ Y التي عصورة من S X فأكيد الـ
+
+299
+00:22:17,270 --> 00:22:20,170
+supremum الكبيرة أكبر أو يساوي الـ supremum
+
+300
+00:22:20,170 --> 00:22:25,770
+الصغيرة كمجموعات الآن هذه الآن بتساوي بتعمل اختصارات
+
+301
+00:22:25,770 --> 00:22:29,170
+هذه مع هذه فبصير supremum للـ S X ع Normal X
+
+302
+00:22:29,170 --> 00:22:34,790
+فاهمين؟ اه و يساوي هذه اصلا تعريف مين تعريف Normal 
+
+303
+00:22:34,790 --> 00:22:41,430
+S إذا صارت Normal H أكبر أو يساوي Normal الـ S
+
+304
+00:22:41,430 --> 00:22:49,010
+إذا Normal H أكبر أو يساوي norm الـ S يعني مكاني 
+
+305
+00:22:49,010 --> 00:22:54,090
+بقولي الـ S صارت bounded طيب ناخد الجهة الثانية 
+
+306
+00:22:54,090 --> 00:22:57,670
+hence S is bounded and Normal H أكبر يساوي Normal
+
+307
+00:22:57,670 --> 00:23:02,490
+H but Normal H إيش بيساوي الـ supremum S X was Y ع
+
+308
+00:23:02,490 --> 00:23:07,070
+Normal X Normal Y وهذا أصغر أو يساوي الـ Supremum،
+
+309
+00:23:07,070 --> 00:23:11,230
+بتاخد مين الآن؟ الـ Schwarz inequality الآن هذه نفسها
+
+310
+00:23:11,230 --> 00:23:14,250
+absolute value لها أصغر أو يساوي Norm هذه في Norm 
+
+311
+00:23:14,250 --> 00:23:17,070
+هذه، لذا الـ supremum على هذه هيكون أصغر أو يساوي
+
+312
+00:23:17,070 --> 00:23:21,580
+الـ supremum على هذه إن هدولة هدى أكبر أو يساوي هدى
+
+313
+00:23:21,580 --> 00:23:25,500
+ما هي الآن اقوم بالاختصارات هدى مح هدى فبصير SX
+
+314
+00:23:25,500 --> 00:23:29,380
+على مين على الـ X وهى Norm بيهن الـ S إذا صارت Norm 
+
+315
+00:23:29,380 --> 00:23:33,420
+الـ H أصغر أو يساوي Norm الـ S التنتين مع بعض Norm 
+
+316
+00:23:33,420 --> 00:23:38,990
+الـ H إيش بيساوي Norm الـ S نثبت إنه الوحيد To prove
+
+317
+00:23:38,990 --> 00:23:41,510
+the uniqueness, suppose that there is a linear
+
+318
+00:23:41,510 --> 00:23:46,610
+operator T تاني من H1 إلى H2 بحيث أن Hxy بيساوي 
+
+319
+00:23:46,610 --> 00:23:51,610
+Sxy الأولاني و بيساوي Txy الأولاني بفرضنا جديد for 
+
+320
+00:23:51,610 --> 00:23:55,670
+all x element in H1 و all y element in H2 إذاً by
+
+321
+00:23:55,670 --> 00:23:59,750
+لمّا طلعت الـ 82 لقبل بشوية مزام هذا بيساوي هذا 
+
+322
+00:23:59,750 --> 00:24:02,730
+لكل الوايات اللي في الدنيا إذاً هذه بتساوي هذه لكل
+
+323
+00:24:02,730 --> 00:24:06,510
+الـ Xات وهذا يعني أن T بتساوي S معناته S is unique
+
+324
+00:24:06,510 --> 00:24:09,150
+وبارك الله فيكم وإلى لقاء آخر
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/2kTCGkbdyVU.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/2kTCGkbdyVU.srt
new file mode 100644
index 0000000000000000000000000000000000000000..aae361f04563d00bcadc03c618c961c9af741fee
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/2kTCGkbdyVU.srt
@@ -0,0 +1,375 @@
+1
+00:00:05,500 --> 00:00:07,980
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,980 --> 00:00:10,740
+والصلاة والسلام على سيدنا محمد وعلى آله وصحبه
+
+3
+00:00:10,740 --> 00:00:15,440
+جميعًا هذه هي المحاضرة رقم 12 مساق تحليل اقتراني
+
+4
+00:00:15,440 --> 00:00:19,000
+أو تحليل دالي لطلاب وطالبات الجامعة الإسلامية
+
+5
+00:00:19,000 --> 00:00:24,620
+ماجستير الرياضيات إن شاء الله هنحكي اليوم عن اللي
+
+6
+00:00:24,620 --> 00:00:28,340
+هو section قصير وسريع اللي هو 2.6 linear
+
+7
+00:00:28,340 --> 00:00:31,400
+operators المفروض هذا يكون أنتم يعني خليني أقول
+
+8
+00:00:31,400 --> 00:00:36,200
+عارفينه من الجبر الخطي ولكن حبيت أن أحكيه على أساس
+
+9
+00:00:36,200 --> 00:00:39,100
+أنه نذكركم فيه على الأقل يعني ونشوف ال notations
+
+10
+00:00:39,100 --> 00:00:42,300
+اللي بدنا نستخدمها عشان اللي هو للمرات القادمة
+
+11
+00:00:43,210 --> 00:00:48,330
+Definition: A linear operator T is a mapping such 
+
+12
+00:00:48,330 --> 00:00:53,070
+that عندي بنقول عن T إنه Linear operator إذا بحقق
+
+13
+00:00:53,070 --> 00:00:56,590
+أولًا domain D of T of T is a vector
+
+14
+00:00:56,590 --> 00:01:00,090
+space and the range R of T lies in a vector space
+
+15
+00:01:00,090 --> 00:01:04,740
+over the same field. ثانيًا على نفس ال field. For all
+
+16
+00:01:04,740 --> 00:01:08,500
+x و y limited in D of T and all scalars α, T(x + 
+
+17
+00:01:08,500 --> 00:01:15,060
+y) = T(x) + T(y) and T(αx) = αT(x) اللي 
+
+18
+00:01:15,060 --> 00:01:20,140
+بالظبط اللي هو عندي بكل سهولة T من عند domain of T
+
+19
+00:01:20,810 --> 00:01:26,490
+لعند x أو لعند y هذا اللي هو عبارة عن اللي هي
+
+20
+00:01:26,490 --> 00:01:33,850
+domain of T نفسه lies بعملني اللي هو vector space 
+
+21
+00:01:33,850 --> 00:01:39,930
+vector space و ال range إيه له هذا اللي هو lies in
+
+22
+00:01:39,930 --> 00:01:42,830
+a vector space يعني Y vector space و D of T vector
+
+23
+00:01:42,830 --> 00:01:50,290
+space domain of T الآن ثانيًا شرط أن نكون ناشمال هنا
+
+24
+00:01:50,290 --> 00:01:53,990
+over the same field لأنه عشان نسميه Linear لازم
+
+25
+00:01:53,990 --> 00:01:59,590
+يكون T(αx + y) = αTx + Ty
+
+26
+00:01:59,590 --> 00:02:07,090
+أو زي ما قلنا أن T(x + y) = Tx + Ty
+
+27
+00:02:07,090 --> 00:02:12,670
+بالإضافة T(αx) = αTx هذولا مع بعض أو 
+
+28
+00:02:12,670 --> 00:02:16,710
+هذا التنين اللي هو T بنقول عنه linear لاحظ ليش
+
+29
+00:02:16,710 --> 00:02:18,810
+هو بيقول over the same field بس هذي اللي بتحكيها
+
+30
+00:02:18,810 --> 00:02:21,790
+ليش التنين over the same field يعني هذا لازم يكون
+
+31
+00:02:21,790 --> 00:02:27,900
+over ℝ مثلاً وهذا over ℝ لأنه .. لأنه الآن .. عشان
+
+32
+00:02:27,900 --> 00:02:29,760
+ال .. هذه اللي .. ال .. ال .. ال .. ال .. ال 
+
+33
+00:02:29,760 --> 00:02:30,500
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+34
+00:02:30,500 --> 00:02:31,500
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+35
+00:02:31,500 --> 00:02:34,340
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+36
+00:02:34,340 --> 00:02:35,940
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+37
+00:02:35,940 --> 00:02:37,300
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+38
+00:02:37,300 --> 00:02:39,440
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+39
+00:02:39,440 --> 00:02:42,980
+.. ال ..
+
+40
+00:02:42,980 --> 00:02:44,800
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+41
+00:02:44,800 --> 00:02:50,850
+.. ال .. ما هي α وين في ال .. في ال .. في ال
+
+42
+00:02:50,850 --> 00:02:54,590
+complex وهذه over ℝ مش ذابطة هنا مع بعض فلازم يكون
+
+43
+00:02:54,590 --> 00:02:59,270
+التنين أشماله over the same field. طيب اللي قال ال
+
+44
+00:02:59,270 --> 00:03:02,570
+null space أو ال kernel كله نقول عنه في أحيانًا ال
+
+45
+00:03:02,570 --> 00:03:05,990
+N of T إيش بيساوي؟ هي عبارة عن كل ال x من ال
+
+46
+00:03:05,990 --> 00:03:11,370
+domain of T اللي صورها إيش بتساوي الصفر هذه اللي 
+
+47
+00:03:11,370 --> 00:03:15,960
+بنسميها أشماله ال null space. نيجي لبعض النظريات
+
+48
+00:03:15,960 --> 00:03:19,220
+النظرية الأولى هذه طبعًا نظرية من الجبر الخطي
+
+49
+00:03:19,220 --> 00:03:24,100
+وبرهانها لكم لأنه شغلات بسيطة ومش وخلينا نقول
+
+50
+00:03:24,100 --> 00:03:28,080
+متطلب سابق للمادة أكثر من إنها هي المادة. Let T
+
+51
+00:03:28,080 --> 00:03:33,320
+be a linear operator, then لأن لو T linear operator
+
+52
+00:03:33,320 --> 00:03:38,480
+معناته range of T نفسه إيش هيطلع vector space وإذا
+
+53
+00:03:38,480 --> 00:03:41,180
+كان ال dimension للـ T بيساوي N هيكون ال dimension
+
+54
+00:03:41,180 --> 00:03:44,960
+لل range of T اللي هو ال .. ال .. ال .. ال range
+
+55
+00:03:44,960 --> 00:03:50,360
+أصغر أو يساوي مين؟ أصغر أو يساوي N، ال N null space
+
+56
+00:03:50,360 --> 00:03:53,860
+نفسه هيطلعلي برضه vector space. مبرهنه سهلة يعني
+
+57
+00:03:53,860 --> 00:03:57,800
+مبرهنة جبر خطي عاديات ما .. مافيش فيه مشكلة عشان
+
+58
+00:03:57,800 --> 00:04:01,920
+هيك left to the reader. ال .. ال theorem الثاني. Let X
+
+59
+00:04:01,920 --> 00:04:06,120
+and Y be vector spaces, both real or إيه شماله هنا،
+
+60
+00:04:06,120 --> 00:04:09,360
+both complex. التنين يا ريال يا إما يا complex.
+
+61
+00:04:09,360 --> 00:04:14,550
+لت يعني التنين over the same field. Let T from domain of 
+
+62
+00:04:14,550 --> 00:04:17,130
+T لعند Y be a linear operator with domain of T
+
+63
+00:04:17,130 --> 00:04:20,210
+subset من مين؟ من ال X اللي هو عبارة عن vector
+
+64
+00:04:20,210 --> 00:04:24,730
+space and range of T subset من مين؟ من Y. Then T from
+
+65
+00:04:24,730 --> 00:04:27,950
+inverse من R of T لعند D of T exists if and only
+
+66
+00:04:27,950 --> 00:04:31,550
+if Tx = 0 implies مين؟ x = 0 يعني
+
+67
+00:04:31,550 --> 00:04:34,900
+نبي نكون one to one. Tx = 0 تقع تقع تقع
+
+68
+00:04:34,900 --> 00:04:36,440
+تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع
+
+69
+00:04:36,440 --> 00:04:37,740
+تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع
+
+70
+00:04:37,740 --> 00:04:44,660
+تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع
+
+71
+00:04:44,660 --> 00:04:47,540
+تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع
+
+72
+00:04:47,540 --> 00:04:48,100
+تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع
+
+73
+00:04:48,100 --> 00:04:57,900
+تقع تقع تقع تقع تقع تقع تقع
+
+74
+00:04:57,900 --> 00:05:03,320
+تق
+
+75
+00:05:03,900 --> 00:05:08,780
+واضح؟ طيب إذا كان ال dimension لـ T بيساوي N و T
+
+76
+00:05:08,780 --> 00:05:12,020
+inverse exist إذا ال dimension ل domain of T إيش
+
+77
+00:05:12,020 --> 00:05:16,860
+هيساوي؟ ال dimension لمين؟ لل R of T ماشي الحال
+
+78
+00:05:16,860 --> 00:05:20,800
+إذا كان ال dimension ل domain of T بيساوي N و T
+
+79
+00:05:20,800 --> 00:05:24,000
+inverse exist صارت بين ال domain و T أصلاً و ال
+
+80
+00:05:24,000 --> 00:05:26,980
+range of T one to one onto أصلاً هيكون ال dimension
+
+81
+00:05:26,980 --> 00:05:30,340
+ل domain of T هو نفس ال dimension لمين؟ لل range
+
+82
+00:05:30,340 --> 00:05:34,440
+of T برضه ال .. ال .. left to the reader اللي هو
+
+83
+00:05:34,440 --> 00:05:42,040
+جابته الخطي بحت. نيجي الآن لنظرية اللمم الأخيرة. Let X,
+
+84
+00:05:42,220 --> 00:05:46,480
+Y and Z be vector spaces and let T من X لعند Y and
+
+85
+00:05:46,480 --> 00:05:49,520
+S من عند Y لعند Z be a combination of
+
+86
+00:05:49,520 --> 00:05:54,990
+functions. إذا كان T اللي هو bijective و Linear
+
+87
+00:05:54,990 --> 00:05:59,010
+Operators يعني اثنين وانت وانت و Linear
+
+88
+00:05:59,010 --> 00:06:01,970
+عشان يقدر يعرف يعرف إيش ال inverse بده يجيب ال
+
+89
+00:06:01,970 --> 00:06:06,970
+inverse, then S T inverse exist و ال S T inverse
+
+90
+00:06:06,970 --> 00:06:10,610
+بيساوي إيش؟ T inverse composite S inverse. طبعًا S في
+
+91
+00:06:10,610 --> 00:06:13,490
+T هنا composition يعني S composition T لكل inverse
+
+92
+00:06:13,490 --> 00:06:15,950
+هو عبارة عن T inverse composition من مين؟ لل S
+
+93
+00:06:15,950 --> 00:06:18,610
+inverse و هذا برضه left to the reader و هيك بتكون
+
+94
+00:06:18,610 --> 00:06:21,430
+خلصت المحاضرة و السلام عليكم ورحمة الله وبركاته
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/2kTCGkbdyVU_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/2kTCGkbdyVU_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ca3edc991a76a407c650a6fd96111255523e5aaa
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/2kTCGkbdyVU_raw.srt
@@ -0,0 +1,392 @@
+1
+00:00:05,500 --> 00:00:07,980
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,980 --> 00:00:10,740
+والصلاة والسلام على سيدنا محمد وعلى آله والصحابي
+
+3
+00:00:10,740 --> 00:00:15,440
+الجماعين هذه هي المحاضرة رقم 12 مساق تحليل إقتراني
+
+4
+00:00:15,440 --> 00:00:19,000
+أو تحليل دالي طلاب وطالبات الجامعة الإسلامية
+
+5
+00:00:19,000 --> 00:00:24,620
+ماجستير الرياضياتان شاء الله هنحكي اليوم عن اللي
+
+6
+00:00:24,620 --> 00:00:28,340
+هو section قصير وسريع اللي هو اتنين ستة linear
+
+7
+00:00:28,340 --> 00:00:31,400
+operators المفروض هذا يكون انتوا يعني خليني اقول
+
+8
+00:00:31,400 --> 00:00:36,200
+عارفينه من الجبر الخطي ولكن حبيت ان احكيه على اساس
+
+9
+00:00:36,200 --> 00:00:39,100
+انه نذكركم فيه على اقل يعني ونشوف ال notations
+
+10
+00:00:39,100 --> 00:00:42,300
+اللي بدنا نستخدمها عشان اللي هو للمرات القادمة
+
+11
+00:00:43,210 --> 00:00:48,330
+definition a linear operator T is a mapping such
+
+12
+00:00:48,330 --> 00:00:53,070
+that عندي بنقول عن T إنه linear operator إذا بحقق
+
+13
+00:00:53,070 --> 00:00:56,590
+مالي أول حاجة ال domain D of T of T is a vector
+
+14
+00:00:56,590 --> 00:01:00,090
+space and the range R of T lies in a vector space
+
+15
+00:01:00,090 --> 00:01:04,740
+over the same field اتنين على نفس ال fieldFor all
+
+16
+00:01:04,740 --> 00:01:08,500
+x و y limited in D of T and all scalars α T x زائد
+
+17
+00:01:08,500 --> 00:01:15,060
+y بيسوا T x زائد T y and T α x بيسوا α T x اللي
+
+18
+00:01:15,060 --> 00:01:20,140
+بالظبط اللي هو عندي بكل سهولة T من عند domain of T
+
+19
+00:01:20,810 --> 00:01:26,490
+لعند X أو لعند Y هذا اللي هو عبارة عن اللي هي
+
+20
+00:01:26,490 --> 00:01:33,850
+domain of T نفسه lies بعملني اللي هو vector space
+
+21
+00:01:33,850 --> 00:01:39,930
+vector space و ال range إيه له هذا اللي هو lies in
+
+22
+00:01:39,930 --> 00:01:42,830
+a vector space يعني Y vector space و D of T vector
+
+23
+00:01:42,830 --> 00:01:50,290
+space domain of Tالان اتنين شرط ان نكون ناشمال هنا
+
+24
+00:01:50,290 --> 00:01:53,990
+over the same field لأنه عشان نسميه Linear لازم
+
+25
+00:01:53,990 --> 00:01:59,590
+يكون T of Alpha X زائد Y بساوية Alpha TX زائد TY
+
+26
+00:01:59,590 --> 00:02:07,090
+او زي ما قلنا ان TX زائد Y بساوية TX زائد TY
+
+27
+00:02:07,090 --> 00:02:12,670
+بالاضافة T Alpha X بساوية Alpha TXهذولا مع بعض او
+
+28
+00:02:12,670 --> 00:02:16,710
+هذا التنين اللي هو C يان بنقول عنه linear لاحظ ليش
+
+29
+00:02:16,710 --> 00:02:18,810
+هو بيقول over the same field بس هذي اللي بتحكيها
+
+30
+00:02:18,810 --> 00:02:21,790
+ليش التنين over the same field يعني هذا لازم يكون
+
+31
+00:02:21,790 --> 00:02:27,900
+over R مثلا وهذا over Rلأنه .. لأنه الآن .. عشان
+
+32
+00:02:27,900 --> 00:02:29,760
+ال .. هذه اللي .. ال .. ال .. ال .. ال .. ال .. ال
+
+33
+00:02:29,760 --> 00:02:30,500
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+34
+00:02:30,500 --> 00:02:30,500
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+35
+00:02:30,500 --> 00:02:31,500
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+36
+00:02:31,500 --> 00:02:34,340
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+37
+00:02:34,340 --> 00:02:35,940
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+38
+00:02:35,940 --> 00:02:37,300
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+39
+00:02:37,300 --> 00:02:39,440
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+40
+00:02:39,440 --> 00:02:39,440
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+41
+00:02:39,440 --> 00:02:42,980
+.. ال ..
+
+42
+00:02:42,980 --> 00:02:42,980
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+43
+00:02:42,980 --> 00:02:42,980
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+44
+00:02:42,980 --> 00:02:44,800
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+45
+00:02:44,800 --> 00:02:50,850
+.. ال .. الما هي Alpha وين في ال .. في ال .. في ال
+
+46
+00:02:50,850 --> 00:02:54,590
+complex وهذه over R مش ذابطة هنا مع حد فلازم يكون
+
+47
+00:02:54,590 --> 00:02:59,270
+التنين اشماله over the same field طيب اللي قال ال
+
+48
+00:02:59,270 --> 00:03:02,570
+null space او ال kernel كله نقول عنه في احيانا ال
+
+49
+00:03:02,570 --> 00:03:05,990
+N of T ايش بيساوي؟ هي عبارة عن كل ال Excel من ال
+
+50
+00:03:05,990 --> 00:03:11,370
+domain of T اللي صورها ايش بتساوي السفر هذه اللي
+
+51
+00:03:11,370 --> 00:03:15,960
+بنسميها اشمالها ال null spaceنيدي لبعض النظريات
+
+52
+00:03:15,960 --> 00:03:19,220
+النظرية الأولى هذه طبعا نظرية من الجبر الخطي
+
+53
+00:03:19,220 --> 00:03:24,100
+وبرهانها لكم لإنه شغلات بسيطة ومش وخلينا نقول
+
+54
+00:03:24,100 --> 00:03:28,080
+متطلب سابق للمادة أكثر من إنها هي المادة let T
+
+55
+00:03:28,080 --> 00:03:33,320
+بيقى linear operator then لأن لو T linear operator
+
+56
+00:03:33,320 --> 00:03:38,480
+معناته range of T نفسه إيش هيطلع vector spaceوإذا
+
+57
+00:03:38,480 --> 00:03:41,180
+كان ال dimension للـ T بيساوي N هيكون ال dimension
+
+58
+00:03:41,180 --> 00:03:44,960
+لل range of T اللي هو ال .. ال .. ال .. ال range
+
+59
+00:03:44,960 --> 00:03:50,360
+أصغر أو يساوي مين أثر أو يساوي N ال N null space
+
+60
+00:03:50,360 --> 00:03:53,860
+نفسه هيطلعيش مرضه vector space مبرهين انسهلات يعني
+
+61
+00:03:53,860 --> 00:03:57,800
+مبرهين جبر خط عاديات ما .. مافيش فيه مشكلة عشان
+
+62
+00:03:57,800 --> 00:04:01,920
+هيك left to the reader ال .. ال theorem التانيلت X
+
+63
+00:04:01,920 --> 00:04:06,120
+and Y be vector spaces, both real or إيه شمال هين،
+
+64
+00:04:06,120 --> 00:04:09,360
+both complex، التنين، يا الريال يا إياش يا كمplex،
+
+65
+00:04:09,360 --> 00:04:14,550
+لت يعني التنين over the same fieldلت من domain of
+
+66
+00:04:14,550 --> 00:04:17,130
+T لعند Y بي a linear operator with domain of T
+
+67
+00:04:17,130 --> 00:04:20,210
+subset من مين من ال X اللي هو عبارة عن vector
+
+68
+00:04:20,210 --> 00:04:24,730
+space and range of T subset من مين من Y then T من
+
+69
+00:04:24,730 --> 00:04:27,950
+inverse من R of T لعند E of T exists if and only
+
+70
+00:04:27,950 --> 00:04:31,550
+if ال T X بساوة سفر implies مين X بساوة سفر يعني
+
+71
+00:04:31,550 --> 00:04:34,900
+نبقى ناخر one to oneTX بتساوة و سفرة تقع تقع تقع
+
+72
+00:04:34,900 --> 00:04:36,440
+تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع
+
+73
+00:04:36,440 --> 00:04:37,740
+تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع
+
+74
+00:04:37,740 --> 00:04:44,660
+تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع
+
+75
+00:04:44,660 --> 00:04:47,540
+تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع
+
+76
+00:04:47,540 --> 00:04:48,100
+تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع
+
+77
+00:04:48,100 --> 00:04:57,900
+تقع تقع تقع تقع تقع تقع تقع
+
+78
+00:04:57,900 --> 00:05:03,320
+تق
+
+79
+00:05:03,900 --> 00:05:08,780
+واضح؟ طيب إذا كان ال dimension لـ T بيساوي N و T
+
+80
+00:05:08,780 --> 00:05:12,020
+inverse exist إذا ال dimension ل domain of T إيش
+
+81
+00:05:12,020 --> 00:05:16,860
+هيساوي؟ ال dimension لمين؟ لل R of T ماشي الحال
+
+82
+00:05:16,860 --> 00:05:20,800
+إذا كان ال dimension ل domain of T بيساوي N و T
+
+83
+00:05:20,800 --> 00:05:24,000
+inverse exist صارت بين ال domain و T أصلا و ال
+
+84
+00:05:24,000 --> 00:05:26,980
+range of T one to one onto أصلا هيكون ال dimension
+
+85
+00:05:26,980 --> 00:05:30,340
+ل domain of T هو نفس ال dimension لمين؟ لل range
+
+86
+00:05:30,340 --> 00:05:34,440
+of Tبرضه ال .. ال .. left to the reader اللي هو
+
+87
+00:05:34,440 --> 00:05:42,040
+جابه الخط بحت نيجي لان لنظرية اللمم الأخيرة let X,
+
+88
+00:05:42,220 --> 00:05:46,480
+Y and Z be vector spaces and let T من X لعند Y and
+
+89
+00:05:46,480 --> 00:05:49,520
+S من عند Y لعند B لعند Z بده يعمل combination of
+
+90
+00:05:49,520 --> 00:05:54,990
+functions إذا كان T اللي هوBijective و Linear
+
+91
+00:05:54,990 --> 00:05:59,010
+Operators يعني اتنين وانت وان وانت واش و Linear
+
+92
+00:05:59,010 --> 00:06:01,970
+عشان يقدر يعرف يعرف ايش ال inverse بده يجيب ال
+
+93
+00:06:01,970 --> 00:06:06,970
+inverse then S T inverse exist و ال S T inverse
+
+94
+00:06:06,970 --> 00:06:10,610
+بيساوي ايش T inverse composite S inverse طبعا S في
+
+95
+00:06:10,610 --> 00:06:13,490
+T هنا composition يعني S composition T لكل inverse
+
+96
+00:06:13,490 --> 00:06:15,950
+هو عبارة عن T inverse composition من مين لل S
+
+97
+00:06:15,950 --> 00:06:18,610
+inverse و هذا برضه left to the reader و هيك بتكون
+
+98
+00:06:18,610 --> 00:06:21,430
+خلصت المحاضرة و السلام عليكم و رحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/4GZHS19Cyqk.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/4GZHS19Cyqk.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ab7a9bcf441c3d202e1bc55cd5fa1d9a8bf62cfb
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/4GZHS19Cyqk.srt
@@ -0,0 +1,1775 @@
+1
+00:00:05,040 --> 00:00:07,760
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,760 --> 00:00:10,580
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:10,580 --> 00:00:16,840
+أهله وصحبه أجمعين المحاضرة رقم 17 مساق تحليل 
+
+4
+00:00:16,840 --> 00:00:20,560
+اقتراني أو تحليل دالي طلاب وطالبات الجامعة 
+
+5
+00:00:20,560 --> 00:00:25,590
+الإسلامية ماجستير رياضيات أحنا المحاضرة الماضية 
+
+6
+00:00:25,590 --> 00:00:29,830
+أنهينا Chapter 2 اللي هو Normed Spaces الآن بدنا 
+
+7
+00:00:29,830 --> 00:00:35,410
+ندخل للحلقة اللي داخل Normed Spaces اللي هي Inner 
+
+8
+00:00:35,410 --> 00:00:41,050
+Product Space ومن ثم الشيء المكتمل منه اسمه 
+
+9
+00:00:41,050 --> 00:00:45,880
+Hilbert Space الثلاثه واحد اللي هو تحت عنوان inner
+
+10
+00:00:45,880 --> 00:00:49,960
+product space و Hilbert space الكلام يعني هذا أنا 
+
+11
+00:00:49,960 --> 00:00:53,160
+بتذكّر أعطيته في الجبر الخطي الجبر الخطي للطلاب
+
+12
+00:00:53,160 --> 00:00:56,940
+الجبر الخطي 2 كنا نعطيه في الجامعة الـ inner 
+
+13
+00:00:56,940 --> 00:00:59,740
+product space وحتى الـ Hilbert space حكينا فيه يعني 
+
+14
+00:00:59,740 --> 00:01:04,300
+زي ما قلنا في البداية عنده اللي هو topological 
+
+15
+00:01:04,300 --> 00:01:09,800
+spaces وفي داخله اللي هو metric spaces وفي داخله
+
+16
+00:01:09,800 --> 00:01:14,260
+اللي هو Normed Spaces ومن ثم اليوم بنحكي عن اللي 
+
+17
+00:01:14,260 --> 00:01:18,100
+هو Inner Product Spaces أو اللي هو المكتمل منه الـ
+
+18
+00:01:18,100 --> 00:01:21,720
+Hilbert Spaces وأنفلّ عليه اللي هو الـR تربيع
+
+19
+00:01:21,720 --> 00:01:26,580
+والـC تربيع والـC والـR إلى آخره وكل ما يتعلق بهذه
+
+20
+00:01:26,580 --> 00:01:29,600
+الأمور اللي احنا مشتغلّين فيها في حياتنا فخلينا احنا
+
+21
+00:01:29,600 --> 00:01:32,740
+نبدأ الآن اللي هو نعرف شو معناه Inner Product
+
+22
+00:01:34,300 --> 00:01:39,080
+الحديث الآن خلّيني أقول أقرب إلى الشيء الجبري ومن 
+
+23
+00:01:39,080 --> 00:01:42,320
+ثمّ بندخل إلى اللي هو ندخل الـ topology أو الـ
+
+24
+00:01:42,320 --> 00:01:46,780
+norm اللي بتولد من الـ inner product an inner
+
+25
+00:01:46,780 --> 00:01:49,960
+product space is a vector space إذا احنا شغلنا
+
+26
+00:01:49,960 --> 00:01:52,520
+over vector space زي ما كنا نشتغل في normed space
+
+27
+00:01:52,520 --> 00:01:56,100
+اللي هي أرضيتنا vector space with an inner product
+
+28
+00:01:56,100 --> 00:01:58,780
+defined on X يعني inner product space هو عبارة عن
+
+29
+00:01:58,780 --> 00:02:01,320
+vector space معرف عليه حاجة اسمها inner product
+
+30
+00:02:02,200 --> 00:02:05,820
+ماشي الآن a Hilbert space is a complete inner
+
+31
+00:02:05,820 --> 00:02:08,920
+product space الـ Hilbert space هو اسمه complete
+
+32
+00:02:08,920 --> 00:02:14,420
+inner product وكأنه من تحت بطن بقول لكم إنّ الـ inner
+
+33
+00:02:14,420 --> 00:02:17,540
+product بيعمل topology هو في الواقع الـ inner
+
+34
+00:02:17,540 --> 00:02:21,800
+product بيعمل norm مباشرة والـ norm بيعمل اللي هو
+
+35
+00:02:21,800 --> 00:02:25,240
+اللي هي topology وبيسير عندنا اللي هي أو بيعمل
+
+36
+00:02:25,240 --> 00:02:29,830
+metric space و ثم بيعملنا topology الحديث عن الـ
+
+37
+00:02:29,830 --> 00:02:34,090
+part أو complete inner product space اللي هو مبرّر
+
+38
+00:02:34,090 --> 00:02:37,630
+لأنّ an inner product لأنّ شو معناه inner product on 
+
+39
+00:02:37,630 --> 00:02:41,310
+X is a mapping of X cross X onto the scalar field
+
+40
+00:02:41,310 --> 00:02:46,210
+K of X such that يحقق مالي إذا الـ inner product الـ
+
+41
+00:02:46,210 --> 00:02:51,340
+inner product ما هو الـ inner product عبارة عن دالة
+
+42
+00:02:51,340 --> 00:02:56,880
+من اللي هو X across X من X across X هي الدالة دي
+
+43
+00:02:56,880 --> 00:02:59,400
+بس ده الروج اللي برهزها ده الروج اللي أقف ده مضايق
+
+44
+00:02:59,400 --> 00:03:02,960
+منها لعند الـ scalar field mean كي الـ scalar field
+
+45
+00:03:02,960 --> 00:03:08,860
+اللي أمامي حسب اللي هو الـ field اتبع من الـ X اللي
+
+46
+00:03:08,860 --> 00:03:13,780
+نفسها يا real يا إما يا complex يحقق الشروط 
+
+47
+00:03:13,780 --> 00:03:18,660
+الآتية اللي هو التعميم عموما هو للـ dot product
+
+48
+00:03:18,660 --> 00:03:24,280
+اللي بيكونوا ياخدوا في المتجهات شوفوا الآن الـ X
+
+49
+00:03:24,280 --> 00:03:31,120
+زائد Y والـ Z بيساوي X وZ زائد mean Y وZ يعني و
+
+50
+00:03:31,120 --> 00:03:37,560
+كأنه linear in the first entry ماشي؟ الآن طبعا هذه 
+
+51
+00:03:37,560 --> 00:03:40,780
+دالة زي ما قلنا دالة من X cross X هذا من الـ X 
+
+52
+00:03:40,780 --> 00:03:45,090
+الأولى وهذا من X الثانية ماشي الآن الـ alpha x
+
+53
+00:03:45,090 --> 00:03:49,410
+بيساوي الـ alpha بتطلع منه الجريب alpha في x و mean
+
+54
+00:03:49,410 --> 00:03:54,310
+و y إذا و كأنه مش additive بس linear كاملة في اللي
+
+55
+00:03:54,310 --> 00:03:58,870
+هو the first entry الآن x و y بيساوي الـ y و x ايش 
+
+56
+00:03:58,870 --> 00:04:02,390
+ما لها conjugate يعني لما بدك ايش علاقة الـ x و y
+
+57
+00:04:02,390 --> 00:04:07,130
+بيه اللي هي y و x اللي هي هذه conjugate لهذه ماشي
+
+58
+00:04:07,130 --> 00:04:11,510
+الحال طيب the complex conjugate of a y و x لو كان
+
+59
+00:04:11,510 --> 00:04:14,310
+ريال بيصير ايش مالهم هو الـ conjugate ولادك زي بعض
+
+60
+00:04:14,310 --> 00:04:20,410
+بيصير نفسه بيساوي معايا ايه الآن X و X هيطلع ريال
+
+61
+00:04:20,410 --> 00:04:25,230
+هيطلع أكبر أو يساوي صفر و X و X بيساوي صفر إذا و 
+
+62
+00:04:25,230 --> 00:04:30,110
+فقط X ايش مالها تساوي ايش صفر بعد شوية حلاجة هذا
+
+63
+00:04:30,110 --> 00:04:32,290
+هو اللي بيطلع اللي بيولد لنا norm أو بيطلع لنا 
+
+64
+00:04:32,290 --> 00:04:36,630
+norm ايه الآن اطلع لفوق an inner product on X
+
+65
+00:04:36,630 --> 00:04:42,760
+defines a norm الادعاء كان التالي الآن الـ product
+
+66
+00:04:42,760 --> 00:04:47,480
+هذا بنقدر منه نعرف منه norm الـ norm كيف بتعرفه
+
+67
+00:04:47,480 --> 00:04:50,880
+على الـ X اللي هو عبارة عن norm الـ X بيساوي هذا جول
+
+68
+00:04:50,880 --> 00:04:54,380
+الأكبر شو صفر فالجذر التابع هو مشروع فبتاخد الجذر
+
+69
+00:04:54,380 --> 00:04:59,820
+التابع له هذا هيعمل ليه norm يعني هيحقق لكل شروط
+
+70
+00:04:59,820 --> 00:05:05,260
+norm اللي احنا بنعرفها أو تحقيقها مش صعب and a 
+
+71
+00:05:05,260 --> 00:05:08,740
+metric on X والمتريك ما دام جبنا norm نجيب metric 
+
+72
+00:05:08,740 --> 00:05:12,880
+المتريك ايش هو المسافة بين X و Y هو عبارة عن norm
+
+73
+00:05:12,880 --> 00:05:16,000
+X minus Y عرفناها زمان هذه اللي هي عبارة حسب
+
+74
+00:05:16,000 --> 00:05:18,060
+التعريف اللي فوق يبقى عبارة عن جذر التربيع للـ
+
+75
+00:05:18,060 --> 00:05:23,160
+inner product بين X minus Y و X minus Y الآن الـ
+
+76
+00:05:23,160 --> 00:05:27,620
+inner product spaces are normed spaces لأنّ جبناها
+
+77
+00:05:27,620 --> 00:05:33,140
+من وين الـ norm هذا اللي جبناها جبناها من مين؟ من
+
+78
+00:05:33,140 --> 00:05:37,240
+inner product صار كل inner product يجيب له نور فالـ
+
+79
+00:05:37,240 --> 00:05:40,400
+inner product spaces are normed spaces لكن الـ 
+
+80
+00:05:40,400 --> 00:05:43,680
+normed spaces مش شرط يكون شمالين inner product
+
+81
+00:05:43,680 --> 00:05:55,740
+spaces وحناخد بعد شوية مثلاً Hilbert spaces هم 
+
+82
+00:05:55,740 --> 00:06:00,940
+بنخّ الاسباس الآن بعض الخواص الأخرى اللي بنستقيها من
+
+83
+00:06:00,940 --> 00:06:07,520
+الخواص اللي فوق واستقاها سهل for all x, y and z
+
+84
+00:06:07,520 --> 00:06:11,700
+in an inner product space and an scalar α لو جيت 
+
+85
+00:06:11,700 --> 00:06:18,120
+حسبت α x زائد y و z بيساوي اللي هو α في x و z زائد
+
+86
+00:06:18,120 --> 00:06:22,460
+y و z فبنعملنا خطوتين أول شي Alpha X ككلّ واحدة و
+
+87
+00:06:22,460 --> 00:06:26,460
+Z زاد Y على Z من الخاصية الأولى والـ Alpha بتطلّحها
+
+88
+00:06:26,460 --> 00:06:28,960
+من الخاصية الثانية X و Y بتطلع اللي هي بالشكل هذه
+
+89
+00:06:28,960 --> 00:06:33,480
+الآن هذه X و Alpha Y لما تطلع من اللي بعيد بتطلع
+
+90
+00:06:33,480 --> 00:06:37,220
+من الـ conjugate كيف بجيبها Alpha X و Alpha Y 
+
+91
+00:06:37,220 --> 00:06:41,680
+بتساوي اللي هو Alpha Y و X conjugate الآن من
+
+92
+00:06:41,680 --> 00:06:46,290
+الخاصية اللي بقى بنتجيب الخاصية هل جيت X و α y
+
+93
+00:06:46,290 --> 00:06:49,890
+بيساوي الخاصية الثالثة أظنّ أنّه بتساوي الـ conjugate
+
+94
+00:06:49,890 --> 00:06:54,430
+لها α y و x صح ولا لأ الآن الـ alpha بتطلع من
+
+95
+00:06:54,430 --> 00:07:01,230
+الجريم مباشرة بيساوي الـ alpha في الـ y و x وكلّ
+
+96
+00:07:01,230 --> 00:07:05,070
+ما له الـ conjugate الـ alpha conjugate هذه في هذه
+
+97
+00:07:05,070 --> 00:07:08,790
+بتطلع أنّ alpha conjugate في الـ y و x conjugate
+
+98
+00:07:08,790 --> 00:07:13,450
+ماشي هذه اللي هي بتساوي الـ alpha conjugate في x و 
+
+99
+00:07:13,450 --> 00:07:19,450
+y ما هو المطلوب طيب إذا الآن عندي هذه اللي هي سهلة 
+
+100
+00:07:19,450 --> 00:07:24,110
+نيجي للي بعيدها هذه برضه اللي عملناها نيجي للي
+
+101
+00:07:24,110 --> 00:07:27,450
+بعيدها هذه بناء على الحالتين اللي فوق أو الحالة
+
+102
+00:07:27,450 --> 00:07:29,930
+هذه والـ Linearية الأولى والـ Additiveية الأولى
+
+103
+00:07:29,930 --> 00:07:34,750
+X و Alpha Y زائد Z بتساوي اللي هو Alpha conjugate
+
+104
+00:07:34,750 --> 00:07:40,730
+Alpha conjugate XY زائد اللي هو Y X ومين وZ الآن
+
+105
+00:07:40,730 --> 00:07:46,140
+بعملها conjugation بتصير هذه عبارة عن α y زائد z و
+
+106
+00:07:46,140 --> 00:07:49,660
+x conjugate وإن جريبه بعملها زي اللي ملّمنت اللي 
+
+107
+00:07:49,660 --> 00:07:52,340
+فوق وبتطلع وتضال تحت الـ conjugate وبعدين 
+
+108
+00:07:52,340 --> 00:07:55,740
+برجعّولها للأصل فاهمين؟ ما فيش داعي أنّ أعملها سوى
+
+109
+00:07:55,740 --> 00:08:00,340
+نفس اللي هي اللي عاملة إذا وكأنه اللي هو في الجريب 
+
+110
+00:08:00,340 --> 00:08:03,630
+في الجريب في الـ inter الجريب linear في الـ .. في
+
+111
+00:08:03,630 --> 00:08:06,590
+الـ .. في الـ .. في الـ .. في الجريب .. في ال ..
+
+112
+00:08:06,590 --> 00:08:10,450
+في البعيد مش linear خلّينا نقول conjugate linear
+
+113
+00:08:10,450 --> 00:08:13,590
+ده صح التعبير يعني بتطلع من برا الألف ألف 
+
+114
+00:08:13,590 --> 00:08:17,850
+conjugate أما الـ additive additive additive فاهمين؟
+
+115
+00:08:17,850 --> 00:08:21,650
+لأنّ the inner product is sesquilinear بناء عن اللي
+
+116
+00:08:21,650 --> 00:08:25,570
+حكيته ايش معنى sesquilinear؟ linear in the first 
+
+117
+00:08:25,570 --> 00:08:30,990
+factor and conjugate linear in the second factor 
+
+118
+00:08:30,990 --> 00:08:36,070
+وكأنه بيقولّي احنا بنعرف الـ sesquilinear أصلاً هو
+
+119
+00:08:36,070 --> 00:08:42,170
+عبارة عن ايش؟ إنّ عدالة من X cross X بترمي في كده
+
+120
+00:08:42,170 --> 00:08:45,390
+إنّ لو كانت في الأولى Linear وفي الثاني يكون Digit
+
+121
+00:08:45,390 --> 00:08:47,670
+Linear بنسمّي اللي هي الدالة في هذه الحالة
+
+122
+00:08:47,670 --> 00:08:52,170
+Sesquilinear Function ماشي الآن مثال على
+
+123
+00:08:52,170 --> 00:08:55,030
+Sesquilinear اللي هو inner product inner product
+
+124
+00:08:55,030 --> 00:08:58,370
+إذا Sesquilinear الـ general حكيته وده inner
+
+125
+00:08:58,370 --> 00:09:01,410
+product ducked مثال عليه الآن نيجي للـ 
+
+126
+00:09:01,410 --> 00:09:07,150
+parallelogram equality اللي هي Fx is an inner
+
+127
+00:09:07,150 --> 00:09:15,530
+product space ضمن for all x of y element in x هيكون
+
+128
+00:09:15,530 --> 00:09:17,950
+عندي normal x زائد y تربيع زائد normal x minus y
+
+129
+00:09:17,950 --> 00:09:21,270
+تربيع بيساوي 2 for normal x تربيع زائد normal mean
+
+130
+00:09:21,270 --> 00:09:26,610
+الـ y تربيع البرهانة
+
+131
+00:09:26,610 --> 00:09:30,870
+سهلة خلّيني أعمل لكم إياها نحسب لكم إياها عشان تتعلموا 
+
+132
+00:09:30,870 --> 00:09:33,150
+.. خلّيني أقول ندّرق على الحسابات وبعدين تصير 
+
+133
+00:09:33,150 --> 00:09:38,450
+الشغلات هذه إليكم على السريع هنيجي اللي هو normal
+
+134
+00:09:38,450 --> 00:09:45,190
+x زائد y norm x زائد y الكل تربيع زائد norm x minus y
+
+135
+00:09:45,190 --> 00:09:54,710
+x minus y الكل تربيع عندي
+
+136
+00:09:54,710 --> 00:10:00,870
+اللي هو لو كان المستطيل هذا هاي الـ vector هذا x
+
+137
+00:10:01,980 --> 00:10:06,200
+والـ vector هذا Y هذا ايش شماله؟ هذا X زائد Y
+
+138
+00:10:06,200 --> 00:10:12,140
+مظبوط هذا الآن Y بالشكل هذا وهذا اللي هو X بالشكل 
+
+139
+00:10:12,140 --> 00:10:19,620
+هذا الآن اللي بيسكر في الاتجاه المخالف اللي هو
+
+140
+00:10:19,620 --> 00:10:24,140
+سلبهم فبيصير هذا طول هذا زي الطول الثاني بيساوي هذا
+
+141
+00:10:24,140 --> 00:10:28,280
+زائد هذا زائد هذا ماشي فطول فعشان هيك بيسموها
+
+142
+00:10:28,280 --> 00:10:32,440
+program law طيب شوفوا صلى الله عليه وسلم الحسابات 
+
+143
+00:10:32,440 --> 00:10:37,480
+لأن نيجي للحسابات نيجي للحسابات ويساوي X زائد Y و
+
+144
+00:10:37,480 --> 00:10:40,280
+X زائد Y هذا الـ inner product .. الـ X زائد Y  الکتر
+
+145
+00:10:40,280 --> 00:10:43,700
+بيه اتعرفنا الـ inner product و .. و .. و مع الـ law
+
+146
+00:10:43,700 --> 00:10:50,160
+زائد X minus Y و X minus Y بنفكل الآن ويساوي X مع
+
+147
+00:10:50,160 --> 00:10:59,160
+الـ X فاهمين؟ و X مع الـ Y و الـ y مع الـ x و الـ y مع
+
+148
+00:10:59,160 --> 00:11:08,080
+الـ y تحتيها الـ x مع الـ x اه لأن الـ x مع ناقص y
+
+149
+00:11:08,080 --> 00:11:13,660
+بطلع النقص برا تسيي الـ x و الـ y فاهمين؟ و لأن خلاص
+
+150
+00:11:13,660 --> 00:11:18,040
+من الـ x مع التنتين لأن ناقص y ناقص y مع الـ x بطلع
+
+151
+00:11:18,040 --> 00:11:22,880
+ناقص y مع الـ x و ناقص Y معاه ناقص Y ناقصين بيطلعين
+
+152
+00:11:22,880 --> 00:11:25,880
+بيطلعين زائد ناقص واحد ناقص واحد بيطلع من برا ناقص
+
+153
+00:11:25,880 --> 00:11:32,680
+واحد نفسه و ناقص واحد نفسه نفسه نفسه نفسه نفسه
+
+154
+00:11:32,680 --> 00:11:37,380
+نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه
+
+155
+00:11:37,380 --> 00:11:37,580
+نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه
+
+156
+00:11:37,580 --> 00:11:37,640
+نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه
+
+157
+00:11:37,640 --> 00:11:45,080
+نفسه نفسه نفسه نفسه نفسه نفسه 
+
+158
+00:11:45,080 --> 00:11:54,920
+نفس اللي هي هذه البرنامج equality is true الان
+
+159
+00:11:54,920 --> 00:12:01,620
+شوفوا الان بس هذا كلام مهم انت باهم if x is an
+
+160
+00:12:01,620 --> 00:12:05,940
+inner product space عشان نفهم النص كويس لإن
+
+161
+00:12:05,940 --> 00:12:09,800
+استعمالته مهمة if x is an inner product space إذا 
+
+162
+00:12:09,800 --> 00:12:13,920
+كان عند inner product space مضمون مية في المية
+
+163
+00:12:13,920 --> 00:12:19,650
+then for all x هذه متحققة الان الـ Contraposition
+
+164
+00:12:19,650 --> 00:12:23,810
+لها لو مش متحققة مش هيكون inner product space
+
+165
+00:12:23,810 --> 00:12:28,870
+وكأنها tool أو أداة لإثبات إن الـ space اللي عندك
+
+166
+00:12:28,870 --> 00:12:33,110
+ماله مش inner product إنه نجيب اللي هو vectors
+
+167
+00:12:33,110 --> 00:12:36,870
+بحيث إنه هذا لا يساوي هذا كل سنة من تسلميه ميكونش
+
+168
+00:12:36,870 --> 00:12:39,770
+اللي هو main inner product يعني الـ normed space
+
+169
+00:12:39,770 --> 00:12:46,040
+ليس مولد من inner product definition Element X in
+
+170
+00:12:46,040 --> 00:12:48,820
+an inner product space X is said to be orthogonal
+
+171
+00:12:48,820 --> 00:12:54,360
+to Y إذا كان الـ inner product بين X وY بساوية 0 و
+
+172
+00:12:54,360 --> 00:12:57,160
+كنا نكتب X أرثجونال لـ Y بساوية 100 لما كنا نعمل
+
+173
+00:12:57,160 --> 00:12:59,700
+زمان في الـ .. في الـ .. في الـ vectors العادية لما
+
+174
+00:12:59,700 --> 00:13:02,900
+يكون عندي اللي هو اللي بنقول عن الـ .. الـ .. الـ ..
+
+175
+00:13:02,900 --> 00:13:04,940
+الـ vector عمودي على التاني إذا كان اللي هو الـ
+
+176
+00:13:04,940 --> 00:13:08,600
+inner product بينهم مش بساوية 0 ماشي الحال الآن
+
+177
+00:13:08,600 --> 00:13:13,080
+هذا بنسميه orthogonal elements وعنا علم كامل في الـ
+
+178
+00:13:13,080 --> 00:13:16,200
+orthogonality فيه حتى مش في الـ inner product سر
+
+179
+00:13:16,200 --> 00:13:21,430
+نعرف الـ orthogonality في الـ north spaces في الـ
+
+180
+00:13:21,430 --> 00:13:27,810
+north اه اه طبعا في الـ inner and product طبعا بشكل
+
+181
+00:13:27,810 --> 00:13:34,100
+معين FA و PR subsets of X بنقول إن X عمودية على Y
+
+182
+00:13:34,100 --> 00:13:36,660
+إذا كانت X عمودية على كل element منها على نصره
+
+183
+00:13:36,660 --> 00:13:39,560
+يعني X ارتجون على كل element يعني الـ inner product
+
+184
+00:13:39,560 --> 00:13:42,600
+بين X و أي element في الـ A بيساوي صفر بنقول two
+
+185
+00:13:42,600 --> 00:13:45,240
+sets عموديات على بعض إذا كان كل element هنا عمودي
+
+186
+00:13:45,240 --> 00:13:48,140
+على ثاني يعني الـ inner product بين A وB بيساوي صفر
+
+187
+00:13:48,140 --> 00:13:52,480
+لكل A وB كل A المتن A وB المتن B اطلع لفوق كلام
+
+188
+00:13:52,480 --> 00:13:55,660
+جميل وسهل الان included in space around is a
+
+189
+00:13:55,660 --> 00:13:57,700
+Hilbert space with inner product defined by inner
+
+190
+00:13:57,700 --> 00:14:00,700
+product بين x و y بسبب summation x i i في مين في
+
+191
+00:14:00,700 --> 00:14:04,320
+Gamma I الان هو هذا عبارة زي ما قلنا قبل شوية
+
+192
+00:14:04,320 --> 00:14:08,160
+عبارة عن الـ x و الـ y عبارة عن تعميم لمين للـ dot
+
+193
+00:14:08,160 --> 00:14:11,020
+product الـ dot product زي ما قلنا لو جينا في الـ R
+
+194
+00:14:11,020 --> 00:14:14,980
+تنين اللي كنا لو كان الـ vector A بيساوي x i زائد y
+
+195
+00:14:14,980 --> 00:14:19,220
+j و B بيساوي x prime i زائد y prime j إيش بيكون الـ
+
+196
+00:14:19,220 --> 00:14:22,740
+dot product A dot B عبارة عن x في x prime زائد y
+
+197
+00:14:22,740 --> 00:14:26,670
+في y prime الان هذا إذا اللي معرفه هنا ما هو اللي
+
+198
+00:14:26,670 --> 00:14:29,430
+عبارة عن تعميم للـ inner product للـ dot product
+
+199
+00:14:29,430 --> 00:14:32,610
+اللي احنا بنعرفه في الأصل في الـ calculus gene هذا
+
+200
+00:14:32,610 --> 00:14:35,370
+هيعمل inner product كيف ده يثبت إنه inner product
+
+201
+00:14:35,370 --> 00:14:38,190
+بثبت إنه inner product إنه بيحقق الشروط اللي عندي
+
+202
+00:14:38,190 --> 00:14:41,150
+الاربعة او الخمسة اللي موجودة عندي الان كيف معرفي
+
+203
+00:14:41,150 --> 00:14:43,350
+إنه احنا X اللي هي إكساية واحد إكساية اتنين إكساية
+
+204
+00:14:43,350 --> 00:14:46,070
+تلتة وتلتة إكساية وY بيساوي Gamma واحد Gamma اتنين
+
+205
+00:14:46,070 --> 00:14:48,810
+Gamma تلتة Gamma and عناصر في الأرقام الـ inner
+
+206
+00:14:48,810 --> 00:14:51,330
+product بيانين اللي هو الـ entry الأول زي ما عملنا
+
+207
+00:14:51,330 --> 00:14:54,020
+في الـ .. في الـ .. في الـ .. في الـ ..في الـ .. الـ
+
+208
+00:14:54,020 --> 00:14:57,820
+vector اللي هو الـ dot .. الـ dot من الـ vectors اللي
+
+209
+00:14:57,820 --> 00:15:01,120
+بنعرفها في الـ calculus gene اللي هو xi واحد ماجاما
+
+210
+00:15:01,120 --> 00:15:03,640
+واحد زاد xi اتنين ماجاما اتنين لما اصل xi ان جاما
+
+211
+00:15:03,640 --> 00:15:07,220
+ان هذا بيعمل الـ inner product الـ الـ inner product
+
+212
+00:15:07,220 --> 00:15:10,120
+بيقول لي اللي هو induce the norm الـ norm اللي
+
+213
+00:15:10,120 --> 00:15:14,020
+بيطلع منه x و x زي ما احنا عارفين اللي هو x و x
+
+214
+00:15:14,020 --> 00:15:17,720
+اللي هو ده بيطلع norm تربيع بيصير Xi I في Xi I
+
+215
+00:15:17,720 --> 00:15:21,760
+بيصير Xi I تربيع إذن بيصير نورم الـ X لحاله اللي
+
+216
+00:15:21,760 --> 00:15:24,120
+هو الجدر التربيعي لهذا اللي هو Xi I تربيعه اللي هو
+
+217
+00:15:24,120 --> 00:15:28,460
+الـ norm اللي احنا عارفينه في القرآن وهذا أثبتناه
+
+218
+00:15:28,460 --> 00:15:31,840
+في المرة الماضية إن إيش ماله هذا بيعمل لي complete
+
+219
+00:15:31,840 --> 00:15:36,780
+normed space إذن الـ inner product اللي ولد هذا الـ
+
+220
+00:15:36,780 --> 00:15:39,720
+norm هو complete يعني بمعنى آخر الـ inner product
+
+221
+00:15:39,720 --> 00:15:45,160
+مع هذا is a Hilbert space ومش هيك وبنطلع منه الـ
+
+222
+00:15:45,160 --> 00:15:49,120
+Metrical تالي DXY بيساوي الـ norm للـ X minus Y اللي
+
+223
+00:15:49,120 --> 00:15:53,560
+هو هذا XII نقص غامعي تربيع لكل إيه شماله لكل نص
+
+224
+00:15:53,560 --> 00:15:58,280
+وهذا برضه أثبتنا عبارة عن Metric على اللي هو الـ
+
+225
+00:15:58,280 --> 00:16:00,400
+space الأخرى يعني هي أول من التالي يلا اللي بعد
+
+226
+00:16:02,630 --> 00:16:05,790
+الان الـ Unitary space نفس اللي توّى نفس اللي توّى
+
+227
+00:16:05,790 --> 00:16:07,770
+الـ Unitary space اللي هو الكمبليكس بدل الـ R اللي
+
+228
+00:16:07,770 --> 00:16:11,410
+هي الـ UNC الان بس بدنا ناخد بعين الاعتبار ان الـ
+
+229
+00:16:11,410 --> 00:16:14,770
+inner product هيصير ايش ماله الـ Psi I في الـ
+
+230
+00:16:14,770 --> 00:16:17,850
+conjugate تبع حاجة ده مش فيه في الـ conjugate سواء
+
+231
+00:16:17,850 --> 00:16:21,080
+ما I اللي هو conjugate الان هذا لما صار في الـ
+
+232
+00:16:21,080 --> 00:16:25,320
+conjugate لما بتحسب الـ X و الـ X فبصير Xi I في Xi I
+
+233
+00:16:25,320 --> 00:16:29,200
+conjugate فبتطلع الموضوع للتربيع ماشي الحال فبصير
+
+234
+00:16:29,200 --> 00:16:34,120
+الان الـ norm اللي هو عبارة عن جدر التربيع لـ X و X
+
+235
+00:16:34,120 --> 00:16:38,850
+بساوة الـ summation هذا لكل أص نص هذا بيصير اللي جوا
+
+236
+00:16:38,850 --> 00:16:41,850
+زي ما تقولنا المدرس تربيع أس نص اللي هو الـ norm
+
+237
+00:16:41,850 --> 00:16:45,050
+اللي احنا عارفينه من الاصل على الـ CN واحنا عارفين
+
+238
+00:16:45,050 --> 00:16:47,330
+ان الـ norm على الـ CN is complete اذا هذا الـ inner
+
+239
+00:16:47,330 --> 00:16:50,670
+product عملي complete normed space اللي هو هيطلع
+
+240
+00:16:50,670 --> 00:16:53,530
+عليه في الهش ماله complete inner product space
+
+241
+00:16:53,530 --> 00:16:58,270
+يعني Hilbert space و الـ metric تبعه دي x و y نفس
+
+242
+00:16:58,270 --> 00:17:01,530
+اللي قبل بشوية summation x I I نبسغام I تربيع اللي
+
+243
+00:17:01,530 --> 00:17:04,330
+كل أس نص عاملة واحدة عند N لكل الـ X و الـ Y
+
+244
+00:17:04,330 --> 00:17:09,100
+الموجودة في الـ CN اللي بعده الان اول مرة نحكي عن
+
+245
+00:17:09,100 --> 00:17:14,570
+حاجة اسمها L2VAB قبل هيك عرفنا نورم نورم اللي هو
+
+246
+00:17:14,570 --> 00:17:17,990
+نورم الـ X كفانكشن لما أخدنا الـ space of all
+
+247
+00:17:17,990 --> 00:17:20,210
+continuous functions الـ space of all continuous
+
+248
+00:17:20,210 --> 00:17:24,730
+functions X تربيع of T DT كل إيش ماله أص نص هذا
+
+249
+00:17:24,730 --> 00:17:28,470
+اللي هو خليني نقول نورم اللي عرفناه قبل هيك قلنا
+
+250
+00:17:28,470 --> 00:17:31,430
+هذا النورم إيش ماله مش complete بيعملليش complete
+
+251
+00:17:31,430 --> 00:17:34,230
+space و جبنا الرسمات و جبناكم مثال و قلنا مش
+
+252
+00:17:34,230 --> 00:17:39,010
+complete الان اكملوا احنا و قلنا قبل هيك أنه أنا
+
+253
+00:17:40,730 --> 00:17:43,970
+متريك الـ space أو any normed space can be
+
+254
+00:17:43,970 --> 00:17:50,010
+completed الكمبليشن اللي هو الكمبليشن اللي هو
+
+255
+00:17:50,010 --> 00:17:51,810
+الكمبليشن اللي هو الكمبليشن اللي هو الكمبليشن اللي
+
+256
+00:17:51,810 --> 00:17:52,270
+هو الكمبليشن اللي هو الكمبليشن اللي هو الكمبليشن
+
+257
+00:17:52,270 --> 00:17:52,770
+اللي هو الكمبليشن اللي هو الكمبليشن اللي هو
+
+258
+00:17:52,770 --> 00:17:54,290
+الكمبليشن اللي هو الكمبليشن اللي هو الكمبليشن اللي
+
+259
+00:17:54,290 --> 00:17:55,150
+هو الكمبليشن اللي هو الكمبليشن اللي هو الكمبليشن
+
+260
+00:17:55,150 --> 00:17:55,210
+اللي هو الكمبليشن اللي هو الكمبليشن اللي هو
+
+261
+00:17:55,210 --> 00:17:56,030
+الكمبليشن اللي هو الكمبليشن اللي هو الكمبليشن اللي
+
+262
+00:17:56,030 --> 00:17:57,710
+هو الكمبليشن اللي هو الكمبليشن اللي هو الكمإذا ال
+
+263
+00:17:57,710 --> 00:18:02,010
+L of 2 of A وB the completion of the space of all
+
+264
+00:18:02,010 --> 00:18:05,630
+continuous real valid functions on A وB with norm
+
+265
+00:18:05,630 --> 00:18:09,450
+defined بهذا عند الـ inner product في هذه الحالة
+
+266
+00:18:09,450 --> 00:18:12,750
+مين هو هناخده الـ inner product هو عبارة عن الـ X of
+
+267
+00:18:12,750 --> 00:18:16,770
+T في مين في Y of T من A لعند B لو بداش تشغل على الـ
+
+268
+00:18:16,770 --> 00:18:20,230
+C باخد بس الـ conjugate ماشي الحال سمونا احنا بنحكي
+
+269
+00:18:20,230 --> 00:18:24,030
+عالمين على الـ R لأنه على فترة من A لعند B و بترمي
+
+270
+00:18:24,030 --> 00:18:29,140
+برضه في R لو جيت أخدت اللي هو الـ norm من هنا X و X
+
+271
+00:18:29,140 --> 00:18:32,320
+هتطلع X of T و Y of T مضربات في بعض X of T و X of
+
+272
+00:18:32,320 --> 00:18:36,020
+T بتصير تربيع الان و هذا norm تربيع فبتطلع أقلص نص
+
+273
+00:18:36,020 --> 00:18:39,540
+فعلا هذا الـ inner بولد الـ norm هذا إذا هذا عبارة
+
+274
+00:18:39,540 --> 00:18:43,560
+عن inner product space اللي قالته الان على اللي هي
+
+275
+00:18:43,560 --> 00:18:46,780
+هذه اللي هي الـ continuous ده حالها مش complete لكن
+
+276
+00:18:46,780 --> 00:18:51,380
+لما حكيناها بصورة عامة على الـ completion إيش ماله
+
+277
+00:18:51,380 --> 00:18:55,960
+صار complete أي سؤال؟ طيب، قل لبعدي The function X
+
+278
+00:18:55,960 --> 00:18:58,640
+of T can be accepted to be complex-valid وزي ما
+
+279
+00:18:58,640 --> 00:19:01,300
+قلت أن A و B and the corresponding inner product
+
+280
+00:19:01,300 --> 00:19:04,960
+is a norm لأن الـ inner product بين X و Y هي نفسها 
+
+281
+00:19:04,960 --> 00:19:07,800
+بس بتنحط conjugate و الـ norm في هذه الحالة بتطلع
+
+282
+00:19:07,800 --> 00:19:12,360
+أشماله modulus تربيع الكل أس نص و then L2 of A و B
+
+283
+00:19:12,360 --> 00:19:15,640
+becomes the completion of the space of all
+
+284
+00:19:15,640 --> 00:19:19,760
+continuous complex-valued functions يعني بترمي في
+
+285
+00:19:19,760 --> 00:19:23,000
+الـ complex تاخد من الفترة a و b لكن غير متهيأش في
+
+286
+00:19:23,000 --> 00:19:26,520
+الـ complex on a و b corresponding to this norm in
+
+287
+00:19:26,520 --> 00:19:32,080
+each case real or complex L2 is a Hilbert space
+
+288
+00:19:32,080 --> 00:19:35,440
+لأن L2 في a و b إذا ما له و إيش ما له Hilbert space
+
+289
+00:19:35,440 --> 00:19:43,050
+الـ space L2 الـ L2 برضه Hilbert space هذا الـ
+
+290
+00:19:43,050 --> 00:19:48,390
+Hilbert space of all functions الـ two big
+
+291
+00:19:48,390 --> 00:19:51,330
+integrable functions هذا الـ Hilbert space مقابل
+
+292
+00:19:51,330 --> 00:19:55,330
+له الـ two الهو of .. اللي بنسميه sequence space
+
+293
+00:19:55,330 --> 00:19:58,310
+Hilbert sequence space أو اللي بيسموه classical
+
+294
+00:19:58,310 --> 00:20:01,850
+Hilbert space يعني اللي أصلا هو .. يعني سمي الجثة
+
+295
+00:20:01,850 --> 00:20:06,740
+كلها على علب هو يعني This space is a Hilbert space
+
+296
+00:20:06,740 --> 00:20:10,000
+with inner product اللي هو زي بي قبل بشوية inner
+
+297
+00:20:10,000 --> 00:20:13,260
+product بين X Y بيصير X I I في القمة I conjugate
+
+298
+00:20:13,260 --> 00:20:16,440
+بس I من عند واحد مش لأن في حالة الأران إلى ما
+
+299
+00:20:16,440 --> 00:20:20,940
+لنهاية هذا بيعمل inner product و هيحقق الشروط كلها
+
+300
+00:20:21,220 --> 00:20:25,640
+Norm هو نورم التبع للـ L2 زمان إيش هو نورم الـ X؟
+
+301
+00:20:25,640 --> 00:20:28,360
+اللي هو هذا X و X بيصير هذا تربيع و هذا أس نص اللي
+
+302
+00:20:28,360 --> 00:20:32,000
+هو نورم اللي في الـ L2 الأصلي فبكون عند ال inner
+
+303
+00:20:32,000 --> 00:20:34,760
+product هذا هو اللي ولد ال .. ال .. ال norm اللي
+
+304
+00:20:34,760 --> 00:20:38,940
+احنا عارفينه اللي أثبتنا عنه أن الـ L2 is a
+
+305
+00:20:38,940 --> 00:20:44,500
+complete normed space ماشي الحال و بيكون اللي هو
+
+306
+00:20:44,500 --> 00:20:48,220
+هذا inner product space السؤال الآن أنت حكيت عن
+
+307
+00:20:48,220 --> 00:20:54,540
+الـ L2 طب الـ LB و الـ B لا تساوي 2 هل هذا
+
+308
+00:20:54,540 --> 00:20:58,420
+inner product space هذا أحد الأمثلة اللي عندنا
+
+309
+00:20:58,420 --> 00:21:04,260
+بيكون normed space لكن مش البرت space أو مش inner
+
+310
+00:21:04,260 --> 00:21:08,900
+أو مش مش لا يمكن اللي هو ان نولده من inner product
+
+311
+00:21:08,900 --> 00:21:17,030
+ده مشوفأطلع فوق This space with B لـ 99 و 2 is not
+
+312
+00:21:17,030 --> 00:21:21,790
+an inner product space hence أكيد is not a Hilbert
+
+313
+00:21:21,790 --> 00:21:25,290
+space مين اللي بدو يثبت لنا اللي قبل شوية ال
+
+314
+00:21:25,290 --> 00:21:29,150
+parallelogram equality الآن البراجرام equality بيقول لي
+
+315
+00:21:29,150 --> 00:21:32,630
+if x is a normed space then it satisfies
+
+316
+00:21:32,630 --> 00:21:35,910
+الـ parallelogram equality الآن بدنا نثبت ان هذه غير
+
+317
+00:21:35,910 --> 00:21:39,690
+متساوية جيبلي مثال هيوغو جايبلك مثال حلو هيك وسريع
+
+318
+00:21:39,690 --> 00:21:43,150
+consider x بتساوي 1 1 وصفر كلين التاني y
+
+319
+00:21:43,150 --> 00:21:47,120
+بيساوي 1 وناقص 1 والباقي صفاربقولك اجمعلي
+
+320
+00:21:47,120 --> 00:21:49,960
+هذا مع هذا هذا مع هذا بيصير 2 و هدولة بيصير
+
+321
+00:21:49,960 --> 00:21:53,420
+صفر و الباقي صفر اترحل من بعض 1 نفس 1 صفر و
+
+322
+00:21:53,420 --> 00:21:56,080
+هد بيصير 1 نفس 1 بيصير 2 ماشي و الباقي
+
+323
+00:21:56,080 --> 00:21:59,480
+صفر الآن بيصير عبارة عن normal x زائد y عبارة عن
+
+324
+00:21:59,480 --> 00:22:02,620
+2 و صفر و صفر و صفر لكل تربيع normal زائد
+
+325
+00:22:02,620 --> 00:22:06,480
+التاني صفر و 2 و صفر و صفر لكل تربيع نورم هذا
+
+326
+00:22:06,480 --> 00:22:09,780
+اللي هو عبارة عن جديش و أنا وين قاعد في ال pيه
+
+327
+00:22:09,780 --> 00:22:13,800
+اللي هو summation تربيع و بعدين باخده اللي هو اللي
+
+328
+00:22:13,800 --> 00:22:18,060
+هو بدون قصر بيقول القصر اللي عندي 1 على pيه لكن
+
+329
+00:22:18,060 --> 00:22:23,020
+احنا مااخده ليهاش نورم تربيع بيصير عندي هذا 2 في 2
+
+330
+00:22:23,020 --> 00:22:27,180
+بقى 4 بيطلع 4 و هذا التاني 2 في 2 هيطلع برضه إيش
+
+331
+00:22:27,180 --> 00:22:30,620
+4 أربعة أربعة 8 تعرفوا كيف احنا بنحسب
+
+332
+00:22:30,620 --> 00:22:36,820
+النورم summation xi i أس p الكل أس 1 على
+
+333
+00:22:36,820 --> 00:22:40,740
+2 طيب
+
+334
+00:22:40,740 --> 00:22:44,300
+but
+
+335
+00:22:44,300 --> 00:22:50,100
+2 في Normal X تربيع زائد Normal Y تربيع بيساوي ال
+
+336
+00:22:50,100 --> 00:22:52,980
+Normal X اللي هو عبارة عن 1 1 والباقي صفر
+
+337
+00:22:52,980 --> 00:22:58,140
+والتاني 1 ناقص 1 والباقي صفر ماشي الحال طيب
+
+338
+00:22:58,140 --> 00:23:04,100
+شوفوا الآن الأولاني اللي هو عبارة عن ال .. اللي
+
+339
+00:23:04,100 --> 00:23:10,120
+عندي Y ساوي 2 فيه هذا قيمته اللي هو عبارة عن
+
+340
+00:23:10,120 --> 00:23:16,560
+الـ summation اللي هو 1 انتوا إيش ال .. ال .. ال
+
+341
+00:23:16,560 --> 00:23:21,720
+..
+
+342
+00:23:21,720 --> 00:23:27,880
+عشان عندي X بيساوي xi 1 xi 2 إلى ما يعني
+
+343
+00:23:27,880 --> 00:23:34,000
+انها هي normal X بساوية summation xi i أس p
+
+344
+00:23:34,000 --> 00:23:38,360
+كله 1 على مين على p صح ولا لأ طيب الآن
+
+345
+00:23:38,360 --> 00:23:46,080
+ساوي الآن عندي الـ X عندي أنا 1 1 1 1
+
+346
+00:23:46,080 --> 00:23:51,180
+والباقي مين صفر بنحسبلها الـ norm ل 1 1
+
+347
+00:23:51,180 --> 00:23:57,720
+والباقي صفر ويساوي الـ summation الأولاني هد أس p
+
+348
+00:23:57,720 --> 00:24:04,660
+1 مظبوط زائد الثاني 1 لأن 1 أس p هو 1،
+
+349
+00:24:04,660 --> 00:24:08,380
+مظبوط؟ الآن زائد الباقي صفر، هذا يكون أس p
+
+350
+00:24:08,380 --> 00:24:15,080
+ويساوي 2 أس p 1 على p، ماشي؟ هذا norm الـ X mean،
+
+351
+00:24:15,080 --> 00:24:21,500
+norm الـ X تربيع، بيصير لأن 2 في 1 و 1 و 1 اللي هي
+
+352
+00:24:21,500 --> 00:24:25,840
+2 في .. هاد 2 برا، هاد برا برا خالص، بحسب p، 2
+
+353
+00:24:25,840 --> 00:24:29,620
+في X تربيع زي Y تربيع الآن هذه اللي جوا 2
+
+354
+00:24:29,620 --> 00:24:32,000
+أس p لكل تربيع و الثاني 2 أس p لكل تربيع هدولة 
+
+355
+00:24:32,000 --> 00:24:35,340
+مجموحين بيساوي اللي هو عبارة عن
+
+356
+00:24:35,340 --> 00:24:39,340
+هدولة 2 اه دلوقتي طبعا بيصير 2 على p
+
+357
+00:24:39,340 --> 00:24:42,440
+2 على p 2 وهي في 2 بيصير 4 في
+
+358
+00:24:42,440 --> 00:24:45,780
+2 أقصى 2 على p هذه مش ممكن تصير 8
+
+359
+00:24:45,780 --> 00:24:49,140
+إلا في حالة الـ B إيش بتساوي 2 يعني في حالة
+
+360
+00:24:49,140 --> 00:24:52,640
+الـ L2 و الـ B لا تساوي 2 إذا هذه أكيد مالها
+
+361
+00:24:52,640 --> 00:24:56,330
+بتساويش 8 وها دي طبعا x زائد y اللي هي عبارة عن
+
+362
+00:24:56,330 --> 00:25:00,310
+2 وشفر وشفر بس 2 أس p أس 1 على p بيصير
+
+363
+00:25:00,310 --> 00:25:04,690
+2 و تربيع بيصير 4 فاهمين؟ فعلا إذا صارت
+
+364
+00:25:04,690 --> 00:25:07,850
+الـ parallelogram law is not satisfied إذا الـ قلبي is not a
+
+365
+00:25:07,850 --> 00:25:13,440
+Hilbert space اللي بعته اللي بعته مثال آخر اللي هو
+
+366
+00:25:13,440 --> 00:25:17,840
+الـ space of all continuous functions space C of A
+
+367
+00:25:17,840 --> 00:25:22,620
+و B this space is not an inner product space hence
+
+368
+00:25:22,620 --> 00:25:25,460
+is not Hilbert space طبعا الـ continuous functions
+
+369
+00:25:25,460 --> 00:25:29,080
+هذه الأولاني
+
+370
+00:25:29,080 --> 00:25:34,190
+الـ norm اللي عليها الـ integration الآن هذا الـ norm
+
+371
+00:25:34,190 --> 00:25:37,910
+تبعه مين؟ اللي هو الـ maximum اللي الـ norm عليه
+
+372
+00:25:37,910 --> 00:25:43,630
+maximum مش هيعمل inner product خد الآن خد لك two
+
+373
+00:25:43,630 --> 00:25:48,550
+functions مش هيحققن الـ parallelogram له X of T
+
+374
+00:25:48,550 --> 00:25:51,950
+بيساوي 1 و Y of T اللي هو ثابتة و Y of T linear
+
+375
+00:25:51,950 --> 00:25:55,210
+اللي هي عبارة عن T على B minus A ناقص A على B
+
+376
+00:25:55,210 --> 00:25:59,260
+minus A اللي هي عبارة عن دالة اللي هي إيش خطية شوف
+
+377
+00:25:59,260 --> 00:26:02,320
+الآن on the closed interval mean J اللي هي J
+
+378
+00:26:02,320 --> 00:26:05,500
+بتساوي إيش A و B وده بدي تشتغل على الـ 0 1 بينما
+
+379
+00:26:06,500 --> 00:26:09,180
+كانت تجيب مثال على النساء بس احنا بدنا C و V و A و
+
+380
+00:26:09,180 --> 00:26:15,220
+B in general خد الآن هذه الدالة خطية متصلة وهذه
+
+381
+00:26:15,220 --> 00:26:18,260
+الدالة ثابتة متصلة إذا أنا أكيد الـ X و الـ Y مالهم
+
+382
+00:26:18,260 --> 00:26:22,300
+دوال موجودات في الـ C و V و A و B ونورم الأولى نورم
+
+383
+00:26:22,300 --> 00:26:25,480
+الأولى الـ maximum للـ 1 1 نورم الثانية الـ
+
+384
+00:26:25,480 --> 00:26:29,380
+maximum للـ T minus A و B minus A لما تتراوح بين الـ
+
+385
+00:26:29,380 --> 00:26:34,740
+A و بين مين الـ B ماشي هذا الـ T تزايد للدالة هذا
+
+386
+00:26:34,740 --> 00:26:39,900
+تزايدية لأن T على B minus A موجبة وهذه كانت ثابت
+
+387
+00:26:39,900 --> 00:26:44,680
+زائد ثابت اه ماشي الحال فالآن أعلى قيمة لها عند
+
+388
+00:26:44,680 --> 00:26:48,900
+مين عند اللي هي T بتساوي B واقع القيمة عند الأولى
+
+389
+00:26:48,900 --> 00:26:54,360
+ليه لها تزايدية فإذا القيمة القصوى لها عند B يعني
+
+390
+00:26:54,360 --> 00:26:58,290
+B minus A على B minus A ويساويهاش 1 الـ X زائد Y
+
+391
+00:26:58,290 --> 00:27:02,250
+بيساوي الـ maximum للـ X اللي هي 1 والـ Y هيها
+
+392
+00:27:02,250 --> 00:27:06,350
+يجمعوها لبعض هذه طبعا ثابتة وهذه الـ maximum اللي
+
+393
+00:27:06,350 --> 00:27:09,470
+هي جديش 1 يعني كلها على بعض هذه بتكون الـ
+
+394
+00:27:09,470 --> 00:27:12,790
+maximum اللي هي عندك بيساوي B ويساوي جديش 2
+
+395
+00:27:13,410 --> 00:27:18,490
+الآن X-Y هي 1 ناقص هذه بيصير الآن هذه اللي هي
+
+396
+00:27:18,490 --> 00:27:21,110
+الـ maximum اللي عند مين عند الـ A مش عند الـ B ده
+
+397
+00:27:21,110 --> 00:27:24,690
+لا تنقصيها لأنها صارت بنضربها بناقص فالآن هذه بيصير
+
+398
+00:27:24,690 --> 00:27:29,130
+عندي الـ maximum عند T بتساوي الـ maximum بيصير عند
+
+399
+00:27:29,130 --> 00:27:33,510
+T بتساوي A اللي هي A-A على B-A يعني بتساوي إيش؟
+
+400
+00:27:33,510 --> 00:27:38,560
+1 فاهمين طيب إذا صار عندي حسبنا اللي هو النورمات
+
+401
+00:27:38,560 --> 00:27:42,040
+كلها لو جيت ضربت 2 في normal X تربيع زائد normal Y
+
+402
+00:27:42,040 --> 00:27:45,600
+تربيع هذا 1 و هذا 1 اللي هو 1 و 1
+
+403
+00:27:45,600 --> 00:27:48,640
+2 في 2 بيطلع 4 لكن هذا تربيع زائد هذا
+
+404
+00:27:48,640 --> 00:27:52,320
+تربيع هي الأولاني 2 تربيع بيطلع 4 و هذا
+
+405
+00:27:52,320 --> 00:27:55,420
+التاني 1 تربيع بيطلع 5 الـ 4 مش الـ 5 أكيد
+
+406
+00:27:55,420 --> 00:27:59,740
+إذا مش متحققة إذا الـ space اللي عندي is not an
+
+407
+00:27:59,740 --> 00:28:00,080
+inner
+
+408
+00:28:07,850 --> 00:28:15,270
+Remark الأخيرة حسبت Remark 1 for any x و y in a
+
+409
+00:28:15,270 --> 00:28:20,470
+real inner product space الحكي في واحد عالمين على
+
+410
+00:28:20,470 --> 00:28:23,850
+real inner product space أن الـ inner product بين x
+
+411
+00:28:23,850 --> 00:28:27,270
+و y بيساوي ربع في normal x زائد y لكل تربيع ناقص x
+
+412
+00:28:27,270 --> 00:28:31,550
+ناقص y لكل تربيع للفرقان X Y in the complex inner
+
+413
+00:28:31,550 --> 00:28:36,710
+product space الآن الـ real تبعه هذا الـ HD هذا
+
+414
+00:28:36,710 --> 00:28:40,170
+المكان inner product بيساوي هذا اللي فوق و الـ
+
+415
+00:28:40,170 --> 00:28:44,070
+imaginary عبارة عن ربع الـ X زائد iY و الـ X ناقص
+
+416
+00:28:44,070 --> 00:28:48,990
+main iY الكتر بيعمل شغل حسابات بحت يعني بتيجي
+
+417
+00:28:48,990 --> 00:28:54,610
+بتاخد تحسب هذا تحسب هذاهيطلع عندك اللي هو المقدار
+
+418
+00:28:54,610 --> 00:28:59,810
+اللي هو بيطلع عندك بيساوي 4 الريال part لل X و Y
+
+419
+00:28:59,810 --> 00:29:03,010
+هذا في حالة الكمبيوتر في حالة الريال بيطلع هذا
+
+420
+00:29:03,010 --> 00:29:09,290
+أحسبلكم واحدة والتانية زيها عشان برضه ليطمئنوا 
+
+421
+00:29:09,290 --> 00:29:19,930
+قلوبكم أنا بقلبي مطمئن عليها طيب شوفوا صلوا على
+
+422
+00:29:19,930 --> 00:29:24,590
+النبي عليه الصلاة والسلام عندي الـ inner product 
+
+423
+00:29:24,590 --> 00:29:34,750
+اللي هي norm الـ X زائد Y الكل تربيع ناقص norm الـ X
+
+424
+00:29:34,750 --> 00:29:38,650
+ناقص Y الكل تربيع، صح؟  بساوي الـ inner product لل
+
+425
+00:29:38,650 --> 00:29:44,470
+X زائد Y و X زائد Y ناقص الـ X ناقص Y و X ناقص Y
+
+426
+00:29:44,470 --> 00:29:49,630
+معايا يا جماعة، اه؟ و يساوي الفك هذه الأولى بساوي 
+
+427
+00:29:49,630 --> 00:30:00,830
+X و X زائد X و Y زائد Y و X زائد Y و Y أي واحدة
+
+428
+00:30:00,830 --> 00:30:06,050
+تنتج ثلاثة ايه الرابعة اللي بعيدها ناقص X و X
+
+429
+00:30:06,050 --> 00:30:14,150
+ناقص بيصير زائد X و Y لأن X و ناقص Y ناقص ناقص
+
+430
+00:30:14,150 --> 00:30:24,640
+اللي هي ناقص Y و Y ثلاثة ناقص زائد Y أو X طيب هدولة
+
+431
+00:30:24,640 --> 00:30:31,480
+مع بعض لأ هدولة مع بعض و هدولة مع بعض ضل بساوي
+
+432
+00:30:31,480 --> 00:30:43,980
+اثنين في X و Y زائد اثنين Y و X صح؟ و يساوي و
+
+433
+00:30:43,980 --> 00:30:54,590
+يساوي اثنين في X و Y زائد XY conjugate هذا الآن 
+
+434
+00:30:54,590 --> 00:30:57,590
+العدد زائد ال conjugate له بطلع اللي هو اثنين 
+
+435
+00:30:57,590 --> 00:31:05,340
+الريال أي العدد a زائد ib بنضيف له a ناقص ib لو 
+
+436
+00:31:05,340 --> 00:31:10,600
+ضفناها مع بعض إيش بطلع اثنين الريال فبصير عندي هذا
+
+437
+00:31:10,600 --> 00:31:16,540
+بسوء اثنين الريال part للـ X و Y اللي هو في اثنين
+
+438
+00:31:16,540 --> 00:31:22,060
+بيصير معله أربعة ريال part فبصير عندي اللي هو هذا 
+
+439
+00:31:22,960 --> 00:31:29,680
+هذا ناقص هذا في ربع بطلع الريال برضه لو كان ريال
+
+440
+00:31:29,680 --> 00:31:35,440
+لو كان ريال بكون أصلا اللي هو هذا صفر فبكون الـ X
+
+441
+00:31:35,440 --> 00:31:39,540
+و الـ Y هو نفسه الـ Y و الـ X فبصير الأولى يشملها
+
+442
+00:31:39,540 --> 00:31:43,760
+automatic الأخيرة similarly احسبها دي هتطلعولها
+
+443
+00:31:43,760 --> 00:31:47,600
+أربعة في الـ imaginary برضه مبارك الله فيكم و إلى
+
+444
+00:31:47,600 --> 00:31:48,380
+لقاء آخر
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/9LHmh6ZbiLE.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/9LHmh6ZbiLE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..707970f708ddde34055c00ff37e7ff6a494d8942
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/9LHmh6ZbiLE.srt
@@ -0,0 +1,1482 @@
+1
+00:00:05,110 --> 00:00:07,690
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,690 --> 00:00:10,410
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:10,410 --> 00:00:16,970
+آله وصحبه أجمعين هذه المحاضرة الخامسة مساق تحليل 
+
+4
+00:00:16,970 --> 00:00:19,910
+دالي أو تحليل اقتراني لطلاب وطالبات الجامعة
+
+5
+00:00:19,910 --> 00:00:24,700
+الإسلامية ماجستير رياضيات هنا المرة الماضية اللي هو 
+
+6
+00:00:24,700 --> 00:00:28,780
+في المحاضرة السابعة اللي هو chapter واحد والآن
+
+7
+00:00:28,780 --> 00:00:31,460
+بدنا ندخل لـ chapter اثنين اللي هو normal spaces
+
+8
+00:00:31,460 --> 00:00:35,480
+and banach spaces حكينا في الأول عن metric spaces
+
+9
+00:00:35,480 --> 00:00:39,450
+والآن بنحكي عن اللي هو الـ banach spaces احنا قلنا 
+
+10
+00:00:39,450 --> 00:00:42,650
+فيه topological spaces وفيه في داخله اللي هو الـ
+
+11
+00:00:42,650 --> 00:00:45,610
+metric spaces يعني كل metric spaces أو topological
+
+12
+00:00:45,610 --> 00:00:49,490
+spaces لكن العكس ليس صحيح ممكن نلاقي 
+
+13
+00:00:49,490 --> 00:00:52,490
+topological spaces مش metric spaces الآن بدنا نيجي على 
+
+14
+00:00:52,490 --> 00:00:57,720
+اللي هو احنا اللي هو بعد ما أخذنا الـ Topological
+
+15
+00:00:57,720 --> 00:01:03,020
+Spaces اللي هو عندنا الـ Metric Spaces في داخله 
+
+16
+00:01:03,020 --> 00:01:06,340
+وفيه في داخله اللي الآن هناخد مين الـ Normed
+
+17
+00:01:06,340 --> 00:01:09,860
+Spaces والشابتر الثالث هناخد في داخله اللي هو الـ
+
+18
+00:01:09,860 --> 00:01:15,220
+Hilbert Spaces يعني كل هيكلة اللي هو عندك كل 
+
+19
+00:01:15,220 --> 00:01:19,400
+Hilbert Norm وكل Normed Metric وكل Metric
+
+20
+00:01:19,400 --> 00:01:23,860
+Topological لكن الرجوع في أمثلة بتقول لأ ليس شرطًا
+
+21
+00:01:24,290 --> 00:01:28,130
+طيب إذا هذه هي الصورة العامة وفي داخل الـ الـ space 
+
+22
+00:01:28,130 --> 00:01:31,410
+الـ الـ space اللي احنا بنشتغل عليه الـ R والـ R تربيع و
+
+23
+00:01:31,410 --> 00:01:35,050
+R تكعيب اللي هو الـ Herbert spaces ومن ثم هتكون 
+
+24
+00:01:35,050 --> 00:01:39,790
+اللي هو كل اللي فوق متحققة فيه اللي هو الـ space 
+
+25
+00:01:39,790 --> 00:01:42,210
+اللي احنا بنشتغل فيه في الـ calculus وفي الـ 
+
+26
+00:01:43,370 --> 00:01:46,850
+المعادلة التفاضلية في الاحتكاكات والآخرين طيب
+
+27
+00:01:46,850 --> 00:01:51,250
+صلّينا وسلمنا نيجي نشوف معناتها الاثنين واحد 
+
+28
+00:01:51,250 --> 00:01:55,110
+اللي هو مقدمة عن vector spaces طبعًا هذه background
+
+29
+00:01:55,110 --> 00:01:57,330
+موجودة من الأصل عند الواحد من الـ baccalaureate
+
+30
+00:01:57,330 --> 00:02:02,730
+ما أعرفش الـ vector space الآن normed space بنخ
+
+31
+00:02:02,730 --> 00:02:07,960
+space إذا بتتذكروا الـ metric space بنى على ست 6
+
+32
+00:02:07,960 --> 00:02:12,160
+عليها إيهاش metric دي لأ لأ احنا بدنا ندخل الآن
+
+33
+00:02:12,160 --> 00:02:16,300
+لعمليات الجبرية يعني الـ X نفسها مش مجرد اللي هو
+
+34
+00:02:16,300 --> 00:02:19,740
+نقول والله هذا عبارة عن عن 6 ونحط عليها metric لأ
+
+35
+00:02:19,740 --> 00:02:25,730
+بدها تكون الـ X نفسها فيه هي vector space بحط مبني على 
+
+36
+00:02:25,730 --> 00:02:29,750
+vector space وبعرف عليه اللي هو حاجة اسمها norm
+
+37
+00:02:29,750 --> 00:02:33,510
+norm في الواقع الثالث هو تعميم للـ absolute value 
+
+38
+00:02:33,510 --> 00:02:39,110
+اللي عندنا أو الـ absolute value حالة خاصة منه
+
+39
+00:02:39,110 --> 00:02:43,910
+definition a normed space X is a vector space with
+
+40
+00:02:43,910 --> 00:02:49,250
+a norm defined on it الـ normed space هو عبارة عن
+
+41
+00:02:49,250 --> 00:02:52,830
+vector space X لما نعرف عليه اللي هو ده اللي
+
+42
+00:02:52,830 --> 00:02:57,810
+بنسميها norm نشوف ايه الشروط الآن بـ normed space هو
+
+43
+00:02:57,810 --> 00:03:02,980
+complete normed space الـ Complete in the metric
+
+44
+00:03:02,980 --> 00:03:05,980
+defined by the norm يعني الـ Completeness لأن احنا 
+
+45
+00:03:05,980 --> 00:03:09,420
+أخدنا الـ Completeness with respect to metric بعد
+
+46
+00:03:09,420 --> 00:03:12,300
+شوية هنشوف أنه اللي هو الـ Completeness تبع الـ
+
+47
+00:03:12,300 --> 00:03:15,900
+normed space with the metric اللي بنسميه induced 
+
+48
+00:03:15,900 --> 00:03:19,700
+by the norm يعني اللي اتولد منه من الـ norm اللي
+
+49
+00:03:19,700 --> 00:03:23,590
+عندنا طيب هل جيتوا تفهموا ايش اللي بقوله؟ لأن a norm
+
+50
+00:03:23,590 --> 00:03:28,770
+on a real or complex vector space X is a real
+
+51
+00:03:28,770 --> 00:03:33,110
+valued function on X with whose value at an X is
+
+52
+00:03:33,110 --> 00:03:35,790
+denoted by norm X which has the following
+
+53
+00:03:35,790 --> 00:03:39,950
+properties يعني الآن بتتعرفوا على النورم النورم ما هو
+
+54
+00:03:39,950 --> 00:03:45,250
+اللي عبارة عن دالة من X لعند اللي هو R positive
+
+55
+00:03:45,250 --> 00:03:52,710
+اتحاد مين الـ 0 تحقق ما يليه إنه F of X هي رمزنا برمز 
+
+56
+00:03:52,710 --> 00:03:57,930
+||X|| إذا الدالة اللي بنحكي عنها هي ||X||
+
+57
+00:03:57,930 --> 00:04:01,830
+تحقق الشروط التالية الشرط الأول إنها تكون أكبر أو 
+
+58
+00:04:01,830 --> 00:04:06,370
+يساوي 0 طبيعي الشرط الثاني انها تساوي صفر if and
+
+59
+00:04:06,370 --> 00:04:11,250
+only if x ايش منها بتساوي صفر الشرط الثالث الـ norm
+
+60
+00:04:11,250 --> 00:04:14,030
+من الـ α في x بساوي الـ absolute value من الـ
+
+61
+00:04:14,030 --> 00:04:17,230
+α في الـ norm من الـ x أو المدلس من الـ α في
+
+62
+00:04:17,230 --> 00:04:20,190
+norm من الـ x حسب الـ α الـ scale هذا الـ scale من 
+
+63
+00:04:20,190 --> 00:04:22,950
+الـ α اللي هو أنا بحكي عن vector space vector
+
+64
+00:04:22,950 --> 00:04:26,470
+space إذا في الأرضية اللي هو الـ R أو الـ C الـ R أو
+
+65
+00:04:26,470 --> 00:04:30,580
+الـ C اللي بشتغل فيه بس الخاصية الرابعة هي
+
+66
+00:04:30,580 --> 00:04:33,760
+Triangling Quality ||X + Y|| أصغر من ||X||
+
+67
+00:04:33,760 --> 00:04:39,220
+زائد ||Y|| لكل X و Y Vectors و α Scalar إذا 
+
+68
+00:04:39,220 --> 00:04:44,320
+اتحققت الشروط الأربع هذه بنسميه norm مع هذا الـ 
+
+69
+00:04:44,320 --> 00:04:48,300
+vector space بنسميه norm of this space
+
+70
+00:04:52,340 --> 00:04:57,460
+بعض الملاحظات المهمة a norm on X defines a metric
+
+71
+00:04:57,460 --> 00:05:01,520
+D on X في الواقع أنا بقدر أجيب من الـ norm metric
+
+72
+00:05:01,520 --> 00:05:07,300
+كيف بعرفه؟ باجي بقول المسافة بين X و Y بدها عنصر
+
+73
+00:05:07,300 --> 00:05:12,360
+بسوا ||X − Y|| لو جيت على الشروط الأربع
+
+74
+00:05:12,360 --> 00:05:15,800
+تبعات الـ metric هتلاقيها automatically متحققة
+
+75
+00:05:15,800 --> 00:05:18,840
+ايش هالشروط الـ metric أول شيء d(X, Y) أكبر أو يساوي
+
+76
+00:05:18,840 --> 00:05:24,060
+0 وهذا أكبر بشروط النورم الشرط الثاني ||X − Y||
+
+77
+00:05:24,060 --> 00:05:31,300
+= 0 if and only if يعني d(X, Y) = 0
+
+78
+00:05:31,300 --> 00:05:35,160
+if and only if ||X − Y|| = 0 if and
+
+79
+00:05:35,160 --> 00:05:38,940
+only if حسب اللي هي الخاصية الأولى في الـ norm اللي
+
+80
+00:05:38,940 --> 00:05:42,720
+هو X ناقص Y = 0 اللي هو if and only if X ايش
+
+81
+00:05:42,720 --> 00:05:47,590
+بتساوي Y إذا الشرط الثاني للمتريك متحقق الشرط اللي هو
+
+82
+00:05:47,590 --> 00:05:52,790
+الثالث الـ distance بين الـ X والـ Y بيساوي ||X − Y||
+
+83
+00:05:52,790 --> 00:05:58,530
+ماشي اللي هو نفسه بيساوي ||Y − X||
+
+84
+00:05:58,530 --> 00:06:03,070
+اللي هو بيساوي الـ distance بين 
+
+85
+00:06:03,070 --> 00:06:07,990
+الـ X والـ Y آسف الـ Y والـ X الـ symmetry إذا الشرط 
+
+86
+00:06:07,990 --> 00:06:11,030
+الرابع اللي هو الـ Triangling Quality برضه 
+
+87
+00:06:11,030 --> 00:06:14,950
+Automatic بتطلع اللي هي ايش الشرط الرابع؟ إن ||X
+
+88
+00:06:14,950 --> 00:06:21,490
+− Y|| اللي هو بيساوي ||X − Y|| بالـ
+
+89
+00:06:21,490 --> 00:06:25,910
+Triangling Quality تبعت الـ norm أصغر أو يساوي ||X 
+
+90
+00:06:25,910 --> 00:06:32,410
+− Z|| زائد ||Z − Y|| اللي هي بساوي d(X,
+
+91
+00:06:32,410 --> 00:06:37,660
+Z) زائد d(Z, Y) إذا الـ triangle inequality برضه
+
+92
+00:06:37,660 --> 00:06:41,920
+متحققة لأن هذا فعلاً metric إذا اللي هو أنا بقدر 
+
+93
+00:06:41,920 --> 00:06:46,260
+أجيب من الـ norm أو أولد من الـ norm metric وهذا الـ
+
+94
+00:06:46,260 --> 00:06:52,500
+normed space بنسميه the metric space induced by
+
+95
+00:06:52,500 --> 00:06:58,260
+the norm اللي مذكورة طيب هذه الملاحظة الأولى and
+
+96
+00:06:58,260 --> 00:07:00,760
+called the metric induced by the norm. Hence,
+
+97
+00:07:00,960 --> 00:07:04,640
+among the spaces and benefit spaces ايش هتكون؟
+
+98
+00:07:04,640 --> 00:07:09,100
+Metric spaces لكن العكس مش صحيح جدًا وهنجيب بعد
+
+99
+00:07:09,100 --> 00:07:14,070
+شوية مثال نيجي الآن لـ .. اللي هي الـ .. الـ
+
+100
+00:07:14,070 --> 00:07:17,710
+equality اللي أمامنا for all x y limited x لـ
+
+101
+00:07:17,710 --> 00:07:20,430
+| ||X|| − ||Y|| | أصغر أو يساوي 
+
+102
+00:07:20,430 --> 00:07:23,910
+||X − Y|| وهنا سؤال بندوبه عادة في
+
+103
+00:07:23,910 --> 00:07:26,490
+الـ calculus طلاب الـ calculus بنشيل .. بنشيل
+
+104
+00:07:26,490 --> 00:07:29,170
+العصيتين اللي هي عصيتين ونحط عصة واحدة للـ absolute
+
+105
+00:07:29,170 --> 00:07:34,510
+value والبرهان نفس الأسلوب بالظبط زي ما بنبرهن في 
+
+106
+00:07:34,510 --> 00:07:40,140
+الـ calculus بنقول احنا ||X|| بالـ Triangle
+
+107
+00:07:40,140 --> 00:07:45,160
+Inequality أصغر أو يساوي ||X − Y|| زائد ||Y|| بالـ
+
+108
+00:07:45,160 --> 00:07:48,820
+Triangle Inequality اللي قبل بشوية إذا
+
+109
+00:07:48,820 --> 00:07:53,860
+صار عندي ||X|| − ||Y|| أصغر أو يساوي ||X 
+
+110
+00:07:53,860 --> 00:07:58,660
+− Y|| مظبوط؟ لأن Similarly بدل ما تبدأ بـ X
+
+111
+00:07:58,660 --> 00:08:03,420
+تبدأ بـ Y ||Y|| أصغر أو يساوي ||X − Y|| 
+
+112
+00:08:03,420 --> 00:08:09,380
+فاهمين؟ زائد ||X|| Triangle inequality ضفت الـ X 
+
+113
+00:08:09,380 --> 00:08:14,720
+وطرحت الـ X هذه بيصير ||Y|| − ||X||
+
+114
+00:08:14,720 --> 00:08:21,440
+أصغر أو يساوي ||X − Y|| هذه وهذه ضلبت هذه
+
+115
+00:08:21,440 --> 00:08:27,380
+بسالب بيصير عندي أضرب هذه بسالب بيصير ناقص أو عندي
+
+116
+00:08:27,380 --> 00:08:32,910
+||X|| − ||Y|| أكبر أو يساوي −||X
+
+117
+00:08:32,910 --> 00:08:40,690
+− Y|| هذه مع هذه بتعطيك ||X|| − ||Y||
+
+118
+00:08:40,690 --> 00:08:45,970
+أصغر أو يساوي ||X − Y|| وأكبر أو يساوي −||X
+
+119
+00:08:45,970 --> 00:08:50,030
+− Y|| بالثاني وهذه بتعطيني الـ absolute value 
+
+120
+00:08:50,030 --> 00:08:55,990
+أصغر أو يساوي ||X|| − ||Y|| كلام سهل جدًا
+
+121
+00:08:55,990 --> 00:08:59,330
+اللي هو الملاحظة الثانية the norm is continuous
+
+122
+00:08:59,330 --> 00:09:03,730
+يعني الـ norm نفسه is a continuous function بمعنى
+
+123
+00:09:03,730 --> 00:09:08,170
+آخر اللي هو لما الـ X ترسل لـ ||X|| اللي هي 
+
+124
+00:09:08,170 --> 00:09:13,730
+بنسميها continuous mapping من الـ X لعند مين؟ لعند
+
+125
+00:09:13,730 --> 00:09:17,490
+الـ R شوفوا كيف نثبت إنها continuous mapping أو
+
+126
+00:09:17,490 --> 00:09:22,050
+continuous function شوفوا
+
+127
+00:09:23,350 --> 00:09:28,530
+الدالة اللي عندنا اللي هي مين نسميها F من اللي هو
+
+128
+00:09:28,530 --> 00:09:33,330
+الـ X لعند مين؟ طبعًا الـ X والـ metric تبعها الـ
+
+129
+00:09:33,330 --> 00:09:37,170
+induced by the norm لعند الـ R positive اتحاد مين
+
+130
+00:09:37,170 --> 00:09:42,050
+الـ zero ممكن نثبت إنها اللي هو continuous أنا جانب
+
+131
+00:09:42,050 --> 00:09:45,830
+ايش احنا بنقول كيف نثبت رايحة وين هي دي فعلاً في الـ
+
+132
+00:09:45,830 --> 00:09:48,210
+topology تبعنا تبع الـ video الـ topology يعني الـ 
+
+133
+00:09:48,210 --> 00:09:54,710
+net F(X) لما X تروح لـ X0 هذه طبعًا X تروح لـ X0
+
+134
+00:09:54,710 --> 00:10:00,590
+اللي هو نقول في الـ metric تبعد لـ more بتساوي F(
+
+135
+00:10:00,590 --> 00:10:06,190
+X0) يعني for every ε > 0 there exists δ
+
+136
+00:10:06,190 --> 00:10:10,360
+بقول أنا = ε such that لما X تروح للـ X0 ايش
+
+137
+00:10:10,360 --> 00:10:14,380
+معناته؟ إن ||X − X0|| يكون أصغر من
+
+138
+00:10:14,380 --> 00:10:19,800
+ε أو من δ يعطيك || اللي هو دي بيصير F
+
+139
+00:10:19,800 --> 00:10:23,860
+(X) − ε اللي هي || من |  اللي هو
+
+140
+00:10:23,860 --> 00:10:28,470
+|F(X) − F(X0)|
+
+141
+00:10:28,470 --> 00:10:33,070
+بتتواصلها تكون أصغر من مين؟ من الـ absolute هذه مين هي
+
+142
+00:10:33,070 --> 00:10:39,450
+بساوية absolute value؟ f of x هي norm الـx ناقص
+
+143
+00:10:39,450 --> 00:10:45,590
+norm الـx0 هذه الآن من الملاحظة اللي جابلها أصغر
+
+144
+00:10:45,590 --> 00:10:52,090
+أو يساوي norm الـ X ناقص X0 ومن هنا أصغر من دلتا
+
+145
+00:10:52,090 --> 00:10:56,550
+اللي أنا مختار دلتا إيه بتساوي اهو المفروض إذا
+
+146
+00:10:56,550 --> 00:11:01,770
+صارت الـ norm إيه شمالها is a continuous function
+
+147
+00:11:01,770 --> 00:11:06,030
+طيب، اللي بعد الـ
+
+148
+00:11:06,030 --> 00:11:10,270
+median examples اللي هم ناخدهم في العالمين على 
+
+149
+00:11:10,270 --> 00:11:16,350
+metric spaces كلها مثبتة يعني مافيش إيش يثبتهالآن
+
+150
+00:11:16,350 --> 00:11:19,830
+الـ Euclidean space are N Unitary space CN هدولة
+
+151
+00:11:19,830 --> 00:11:22,570
+تبعتنا اللي قبل شوية كنا نعملهم إيش؟ Metric 
+
+152
+00:11:22,570 --> 00:11:27,450
+Spaces These are Banach Spaces كل نسبة ناهم
+
+153
+00:11:27,450 --> 00:11:31,450
+completed Complete Metric Spaces with respect to
+
+154
+00:11:31,450 --> 00:11:36,930
+their نوع اللي هي Metrics With norm norm X بيساوي
+
+155
+00:11:36,930 --> 00:11:39,750
+الـ summation XII كل تربيع I من واحد لـ N كل
+
+156
+00:11:39,750 --> 00:11:46,860
+إشماله نصهذا إثباته إنه norm سهل تثبته norm بشكل
+
+157
+00:11:46,860 --> 00:11:51,920
+سريع مشابه لما أثبتناها قبل this norm induce the
+
+158
+00:11:51,920 --> 00:11:56,020
+metric هذا الـ norm إيش معله بولد الـ metric التالي
+
+159
+00:11:56,020 --> 00:11:59,720
+دي x y بيساوي norm الـ x minus y و سوصة هذا الـ norm
+
+160
+00:11:59,720 --> 00:12:03,200
+هيه بيولد metric معين نشوف أشهر الـ metric هذا
+
+161
+00:12:03,200 --> 00:12:06,180
+بيساوي الـ summation x i i minus gamma i تربيع x i
+
+162
+00:12:06,180 --> 00:12:10,870
+i تبع الـ x أو تبع الـ y من gamma iطب ما هذا الـ
+
+163
+00:12:10,870 --> 00:12:13,810
+metric اللي هتبع زمان الـ metric الأولاني إذا صار
+
+164
+00:12:13,810 --> 00:12:16,990
+الـ norm هذا بولد نفس الـ metric اللي أنا أثبتت إنه
+
+165
+00:12:16,990 --> 00:12:22,130
+complete metric space إذا صار عندي الآن الـ space
+
+166
+00:12:22,130 --> 00:12:26,110
+هذا under this norm اللي وولد نفس الـ metric is a
+
+167
+00:12:26,110 --> 00:12:31,690
+complete metric space إذا صار بنخ SPS والآن إثباته
+
+168
+00:12:31,690 --> 00:12:35,690
+الـ norm أكبر أو يساوي صفر والآن اللي هو بيساوي
+
+169
+00:12:35,690 --> 00:12:38,150
+صفر if and only if X بيساوي صفر كله على طول من هنا
+
+170
+00:12:38,150 --> 00:12:43,130
+وبعدين اللي هي الـ scalar norm الـ alpha X بيساوي الـ
+
+171
+00:12:43,130 --> 00:12:48,830
+summationبنعملكم إياها هذه مادلة بس جديدة بقى
+
+172
+00:12:48,830 --> 00:12:53,590
+الباقي اللي الـ triangles هي Normal Alpha X X بتساوي
+
+173
+00:12:53,590 --> 00:12:59,370
+X I واحد لعندك X I N الآن الـ Alpha X بتساوي اللي
+
+174
+00:12:59,370 --> 00:13:03,430
+هي Alpha X I واحد لعند الـ Alpha X I N هذه بتساوي
+
+175
+00:13:03,430 --> 00:13:09,550
+معايا اه So summation Alpha اللي هي X I I تربيع
+
+176
+00:13:09,550 --> 00:13:16,560
+الكل أص نص I من واحد لعند الـ N ماشي الحال
+
+177
+00:13:21,850 --> 00:13:26,170
+طيب هو يساوي هذا الـ alpha بيطلع من جوا بيطلع اللي
+
+178
+00:13:26,170 --> 00:13:28,830
+هو alpha تربيع بيطلع برا الـ alpha تربيع و نص بيطلع
+
+179
+00:13:28,830 --> 00:13:30,830
+من الـ alpha then بيطلع الـ absolute value of alpha
+
+180
+00:13:30,830 --> 00:13:35,630
+في الـ summation xi i تربيع الكل أص نص من عند واحد
+
+181
+00:13:35,630 --> 00:13:39,210
+لعند ان و هذا عبارة عنه يساوي alpha absolute value
+
+182
+00:13:39,210 --> 00:13:42,530
+of alpha for normal x إذا اللي هي هذه برضه متحققة
+
+183
+00:13:42,530 --> 00:13:46,360
+و و و الأخرى الـ Triangling Collision هي نفس اللي
+
+184
+00:13:46,360 --> 00:13:50,480
+عملناها في الـ Matrix العادي طيب اطلع لفوق الآن
+
+185
+00:13:50,480 --> 00:13:55,640
+عند الـ space الثاني هو الـ LB space طبعًا هو هذا الـ
+
+186
+00:13:55,640 --> 00:14:02,120
+RN نفسه vector space الـ RN vector space الـ LB برضه
+
+187
+00:14:02,120 --> 00:14:05,670
+vector space الـ Vector Space بيحقق شروط الـ Vector
+
+188
+00:14:05,670 --> 00:14:11,070
+Space كلها و الجمع اللي بين عناصره هو جمع بين
+
+189
+00:14:11,070 --> 00:14:15,630
+Sequences عادية Alpha I و Gamma I بيصير Alpha I
+
+190
+00:14:15,630 --> 00:14:18,690
+زائد Gamma I و مجموحين واحد الأخرى عملية الجمع
+
+191
+00:14:18,690 --> 00:14:20,910
+الخاصة مع الـ Scalar Multiplication اللي عادي اللي
+
+192
+00:14:20,910 --> 00:14:24,230
+هو Born Twice فاهمين اللي بحكيه؟ يعني أنا بقول
+
+193
+00:14:24,230 --> 00:14:29,110
+Alpha في X كيف نضربها Alpha في الأولى؟ زي ما عملت
+
+194
+00:14:29,110 --> 00:14:33,270
+قبل شوية الـ point twice اللي هو multiplication هذا
+
+195
+00:14:33,270 --> 00:14:36,970
+بعمله vector space بالقلبي القلبي vector space لو
+
+196
+00:14:36,970 --> 00:14:40,990
+عرفت عليه الـ norm التالي هيطلع normed space و الـ
+
+197
+00:14:40,990 --> 00:14:43,450
+metric اللي بيطلعه الـ norm هو الـ metric تبعنا اللي
+
+198
+00:14:43,450 --> 00:14:46,450
+استخدمناه و أثبتنا فيه complete قبل بشوية فبكون
+
+199
+00:14:46,450 --> 00:14:50,550
+عندي إشمله عبارة عن complete normed space إذا هيطلع
+
+200
+00:14:50,550 --> 00:14:55,810
+عندي Banach space إذاً هذا المجلد هو مجلد Banach مع norm
+
+201
+00:14:55,810 --> 00:15:00,330
+مخصصة بي norm الـ X بيساوي ثميتي من XI بي الكل اس
+
+202
+00:15:00,330 --> 00:15:05,550
+واحد على بي هيا لان لما نحتاج طول من الـ metric هذا
+
+203
+00:15:05,550 --> 00:15:10,530
+النورم يدفع الـ metric DXY بيساوي norm الـ X minus Y
+
+204
+00:15:11,520 --> 00:15:16,860
+و إي ساوي هذا هو نفس الـ metric الأصلي إذا عندي الـ
+
+205
+00:15:16,860 --> 00:15:20,000
+metric هذا عملني الـ lpb space وهذا الـ metric اللي
+
+206
+00:15:20,000 --> 00:15:23,800
+جيناه المتولد من الـ norm اللي عندي إذا الـ norm
+
+207
+00:15:23,800 --> 00:15:28,260
+اللي عندي complete اللي هو بيعمل complete اللي هو
+
+208
+00:15:28,260 --> 00:15:30,940
+normed space يعني بيعمل Banach space
+
+209
+00:15:33,850 --> 00:15:39,110
+نفس القصة الـ space من هو هذا الـ infinity الـ
+
+210
+00:15:39,110 --> 00:15:42,070
+space الـ infinity برضه عناصرها bounded sequences
+
+211
+00:15:42,070 --> 00:15:45,530
+و هو هيعمل vector space ليش هيعمل vector space
+
+212
+00:15:45,530 --> 00:15:48,250
+اللي هو under الـ addition اللي هو الـ pointwise
+
+213
+00:15:48,250 --> 00:15:49,990
+addition تبع الـ sequence و الـ scalar
+
+214
+00:15:49,990 --> 00:15:53,430
+multiplication برضه pointwise إذن هيطلع عند هذا الـ
+
+215
+00:15:53,430 --> 00:15:56,590
+infinity vector space بشروط اللي بدأنا بنعرفها في
+
+216
+00:15:56,590 --> 00:16:01,670
+الجبر الخطي الآن هذا بدأ عرف عليه metric الـ metric
+
+217
+00:16:01,670 --> 00:16:05,150
+اللي بدأ عرفه as if norm الـ norm يعرفه norm
+
+218
+00:16:05,150 --> 00:16:09,470
+supernormal xii تبع الـ x الـ super normal هي واضح
+
+219
+00:16:09,470 --> 00:16:13,050
+إن هذا الـ norm هيطلع ليه metric dxy بساعة norm x
+
+220
+00:16:13,050 --> 00:16:16,050
+minus y اللي هو عبارة عن الـ super norm الأولاني
+
+221
+00:16:16,050 --> 00:16:18,530
+يعني نفس الـ metric اللي اشتغلنا عليه و أثبتنا إن
+
+222
+00:16:18,530 --> 00:16:22,770
+الـ infinity is .. is إيش ماله complete واضح ها إذا
+
+223
+00:16:22,770 --> 00:16:27,250
+صار عندي الـ infinity is Banach space يعني complete
+
+224
+00:16:27,250 --> 00:16:32,890
+normed spaceأي سؤال ولا مسرع ما سهل الكلام
+
+225
+00:16:32,890 --> 00:16:38,090
+ماعليكم لا بيض ولا شفطة طيب صلّى الله عليه الصلاة
+
+226
+00:16:38,090 --> 00:16:44,850
+والسلام الـ space الـ space اللي عند c of a و b اللي
+
+227
+00:16:44,850 --> 00:16:48,950
+هو the continuous functions اللي هو عالميا على
+
+228
+00:16:48,950 --> 00:16:54,370
+الفترة a و b اللي قبل بشوية الآن الحمال norm يولد
+
+229
+00:16:54,370 --> 00:16:58,970
+نفس اللي هو اللاجنين اللي هو الـ metric اللي تبقى
+
+230
+00:16:58,970 --> 00:17:03,480
+الـ maximum ماذا يعني هذا؟ this space is Banach
+
+231
+00:17:03,480 --> 00:17:06,680
+space و الـ norm defined by الـ norm من هو الـ
+
+232
+00:17:06,680 --> 00:17:10,240
+maximum norm الـ X بيساوي الـ maximum لـ X of T، T
+
+233
+00:17:10,240 --> 00:17:13,900
+Elemental J هذا هيعملني norm of this space كامل،
+
+234
+00:17:13,900 --> 00:17:16,620
+تدربوا في البيت أنتم، تخشوه و تطلعوا بعض لجوهتك،
+
+235
+00:17:16,620 --> 00:17:23,000
+هذا كيف تطلع هذا البرمجة يدعم البرمجة DXY بيساوي
+
+236
+00:17:23,000 --> 00:17:24,820
+البرمجة DXY بيساوي البرمجة DXY بيساوي البرمجة DXY
+
+237
+00:17:24,820 --> 00:17:34,580
+بيساوي البرمجة DXY بيساوي
+
+238
+00:17:34,580 --> 00:17:41,320
+البرمجة الآن اللي حكينا عنه قبل بشوية incomplete
+
+239
+00:17:41,320 --> 00:17:44,780
+metric space بالرغم إن هو the space of continuous
+
+240
+00:17:44,780 --> 00:17:49,500
+functions لكن under this metric يعني على المعيار
+
+241
+00:17:49,500 --> 00:17:52,460
+هذا تبع الـ metric شوفوا مع اختلاف المعايير الدنيا
+
+242
+00:17:52,460 --> 00:17:57,600
+هيك أصلا إخن في المعيار بيصير كل الأمور بتختلف فلإن
+
+243
+00:17:57,600 --> 00:18:01,480
+أنت خلفت المعيار اللي عليه بدك تجيس أو تبني أو كده
+
+244
+00:18:01,480 --> 00:18:04,360
+أو تعمل limit أو تعمل continuity تبعتك و تعمل الـ
+
+245
+00:18:04,360 --> 00:18:07,380
+.. هو كيف أعمل limits إحنا و continuous functions
+
+246
+00:18:07,380 --> 00:18:09,740
+و differentiability و كده كل اللي لازم يكون فيه
+
+247
+00:18:09,740 --> 00:18:12,600
+اللي هو عايش topology لإن الـ topology هذا أخلفته
+
+248
+00:18:12,600 --> 00:18:14,800
+من إيش لا إيش خلاص بيختلف بيصير الـ space اختلف
+
+249
+00:18:15,300 --> 00:18:19,820
+اختلفت .. اختلفت بيصير .. بيصير حتى إنه .. إنه
+
+250
+00:18:19,820 --> 00:18:23,600
+متحقق خاصية الاكتمال أو ما يتحققش لأنه .. و هذا
+
+251
+00:18:23,600 --> 00:18:28,040
+خاصية الاكتمال تعتمد على إيش؟ على خاصية topology
+
+252
+00:18:28,040 --> 00:18:31,600
+اللي هي على الـmetric نفسه لأنه تعتمد على
+
+253
+00:18:31,600 --> 00:18:34,380
+الـconvergence و إن الـCauchy sequence تكون
+
+254
+00:18:34,380 --> 00:18:37,530
+convergence والـ Cauchy Sequence أو الـ Convergence
+
+255
+00:18:37,530 --> 00:18:41,090
+أصلًا هي ما يمكن أن نتحدث عنها بدون Metric إذا
+
+256
+00:18:41,090 --> 00:18:44,370
+الأساسي فيها إن هو وجود Metric أو وجود Topology أو
+
+257
+00:18:44,370 --> 00:18:47,990
+وجود إن هو Norm عشان هي ما اختلف الـ Norm أو ما
+
+258
+00:18:47,990 --> 00:18:51,870
+اختلف الـ Topology بيصير المقالات مختلفة صار الـ
+
+259
+00:18:51,870 --> 00:18:55,370
+continuous function قبل بشوية مش complete وكل
+
+260
+00:18:55,370 --> 00:18:58,310
+continuous function complete طب هنا ماشي لأن هنا
+
+261
+00:18:58,310 --> 00:19:01,150
+norm هنا اختلف عن الـ norm هنا واضح الدنيا كيف
+
+262
+00:19:01,150 --> 00:19:07,270
+ناشيها؟ طيب الأمور القليلة هذه مهمة الـ space X of
+
+263
+00:19:07,270 --> 00:19:11,010
+R continuous real valued functions on J with norm
+
+264
+00:19:11,010 --> 00:19:14,310
+defined by norm X بيساوي الـ integration 0 1 X of T
+
+265
+00:19:14,310 --> 00:19:17,810
+DT إذا أنا أخدت الـ norm من هنا الـ integration is an
+
+266
+00:19:17,810 --> 00:19:23,160
+incomplete metric space لإن هذا النورم بيولد لي
+
+267
+00:19:23,160 --> 00:19:28,220
+norm DXY بيساوي norm X-Y اللي هو الـ metric اللي
+
+268
+00:19:28,220 --> 00:19:31,280
+جابه قبل بشوية أثبتناه إنه مش complete إذا صار
+
+269
+00:19:31,280 --> 00:19:36,220
+عندي هذا is a non-Banach space أو is a non-normed space
+
+270
+00:19:36,220 --> 00:19:40,670
+which is not complete أنا non يعني Banach space
+
+271
+00:19:40,670 --> 00:19:44,270
+خليني نقول إن non هنا بس بأنفي فيها الـ
+
+272
+00:19:44,270 --> 00:19:47,390
+completeness ما بديش أقول non Banach لإنه وسيلكون
+
+273
+00:19:47,390 --> 00:19:51,370
+نفيها قد يكون من هنا جاية أو من هنا لأ لأ اللي
+
+274
+00:19:51,370 --> 00:19:56,810
+بقصد فيها إن هو التعبير الأدق incomplete normed space
+
+275
+00:19:56,810 --> 00:20:03,640
+طيب صلّع لنا بالأساس دي اللي رسمتها قبل شوية الـ
+
+276
+00:20:03,640 --> 00:20:08,640
+topological space جواته اللي هو metric جواته
+
+277
+00:20:08,640 --> 00:20:14,290
+normed الآن الـ normed الـ Non-metric الـ Metric مش
+
+278
+00:20:14,290 --> 00:20:17,110
+شرط يكون Non-Doha مثال بدي أجيب لكم الـ Metric
+
+279
+00:20:17,110 --> 00:20:23,870
+اللي اخذناه في المحاضرات السابقة مش هيكون مولّج من
+
+280
+00:20:23,870 --> 00:20:29,290
+أي Norm في عندي الآن لمّة هي اللي بتشرّعلي الإثبات 
+
+281
+00:20:29,290 --> 00:20:34,630
+هذا اللي هي Translation Invariance بتقول لي a
+
+282
+00:20:34,630 --> 00:20:36,150
+metric space D
+
+283
+00:20:39,590 --> 00:20:44,910
+induced by a norm on space X satisfies the
+
+284
+00:20:44,910 --> 00:20:48,590
+following يعني بيقول لي لو كان عندكم metric space
+
+285
+00:20:48,590 --> 00:20:54,410
+مولد من norm لازم يحقق ما يلي، ما حققش معناته 
+
+286
+00:20:54,410 --> 00:21:00,650
+metricك مش مولد من norm ماشي الآن a metric space D
+
+287
+00:21:00,650 --> 00:21:08,750
+مولد من norm لازم يحقق واحد اثنين، الخاصية الأولى أن
+
+288
+00:21:08,750 --> 00:21:12,530
+d(x, y) + d(y, z) = d(x, z)
+
+289
+00:21:12,530 --> 00:21:19,290
+و مين أو أي هذه الخاصية بس متحققة لو كان ال metric
+
+290
+00:21:19,290 --> 00:21:22,410
+مولد 
+
+291
+00:21:22,410 --> 00:21:28,070
+منه أكيد هتتحقق، الآن لو كان ال metric مولد من ال
+
+292
+00:21:28,070 --> 00:21:32,070
+norm برضه هيكون d(αx, αy) بسبب شروط value Alpha في
+
+293
+00:21:32,070 --> 00:21:36,230
+d(x, y) لكل x, y اللي أنت نفسك فيه والألفة شمالها scalar 
+
+294
+00:21:36,230 --> 00:21:40,670
+ماشي الحالة لأن بمعنى لو هذه الخاصية غير متحققة
+
+295
+00:21:40,670 --> 00:21:43,890
+معناته ال metric تبعك مش مولد من ال norm لأنه لو
+
+296
+00:21:43,890 --> 00:21:46,930
+مولد من ال norm لازم ياش تحققها نفس الشيء الثانية
+
+297
+00:21:46,930 --> 00:21:52,950
+عشان تعرفوا فائدتها اللي اثبتها سهل كثير d(x, a) زي دي
+
+298
+00:21:52,950 --> 00:21:57,710
+و y زي دي، إيش بيساوي؟ لأن ال norm لهذه ناقص هذه، x
+
+299
+00:21:57,710 --> 00:22:00,190
+زي دي - a ناقص y زي دي - a ويساوي ال norm من ال x
+
+300
+00:22:00,190 --> 00:22:05,610
+minus y ويساوي اللي هو المسافة بين مين؟ x و y، إذا نزيح
+
+301
+00:22:05,610 --> 00:22:10,500
+شوية الجهتين، المقطعين، x و y، وناخد المسافة بينهم، 
+
+302
+00:22:10,500 --> 00:22:14,340
+مش هتفرق، هدف وين؟ هدف وين؟ أنتو، زي ما بيقولوا،
+
+303
+00:22:14,340 --> 00:22:17,560
+our mind restricted to ℝ، احنا هيك أصلاً مركبة،
+
+304
+00:22:17,560 --> 00:22:20,500
+لكن، الآن هذا الكلام بيحكي عن وين، فعلاً، بس ال
+
+305
+00:22:20,500 --> 00:22:24,720
+norm space، يعني هذا الكلام ليس شرط من أنه يتحقق
+
+306
+00:22:24,720 --> 00:22:28,620
+وين، في ال metric space in general، أو في ال .. في
+
+307
+00:22:28,620 --> 00:22:32,580
+ال .. في ال .. ال topological spaces، لو ترجمنا 
+
+308
+00:22:32,580 --> 00:22:34,580
+هذا الكلام بواسطة Norm and South Spaces، اللي هو 
+
+309
+00:22:34,580 --> 00:22:37,630
+matrix، لأن ما فيش متركز فيه، مش شرط يكون في متركز
+
+310
+00:22:37,630 --> 00:22:43,990
+في ال topology، فاهمين ما أقول هو؟ طيب، d(αx, 
+
+311
+00:22:43,990 --> 00:22:48,150
+αy) بيساوي المعاملة ال αx ناقص αy
+
+312
+00:22:48,150 --> 00:22:50,390
+وبيساوي ال |α| نوع x وبيساوي
+
+313
+00:22:50,390 --> 00:22:54,690
+|α| في d(x, y)، هذا بس متحقق أو
+
+314
+00:22:54,690 --> 00:22:57,670
+مديش أقول بس، مديش أقول بس هذا لو كان ال metric
+
+315
+00:22:57,670 --> 00:23:01,800
+induced by the norm هيتحقق فعلاً لأنه ليش بقول
+
+316
+00:23:01,800 --> 00:23:04,880
+ما تقولش بس لأنه أصلاً ممكن ألاقي اللي هو مش metric
+
+317
+00:23:04,880 --> 00:23:10,780
+spaces لكن بتحقق هذه، مش non-spaces لكن بتحقق هذه 
+
+318
+00:23:12,250 --> 00:23:17,930
+واطلع لفوق space S، ال S مين هو؟ إذا بتذكروا ال
+
+319
+00:23:17,930 --> 00:23:25,750
+space of all sequences بغض النظر بغض 
+
+320
+00:23:25,750 --> 00:23:29,050
+النظر عن إيش ال sequence بيقول لي bounded
+
+321
+00:23:29,050 --> 00:23:33,490
+convergence لأ لأ أنا بأخذ اللي هو space of مين؟ of
+
+322
+00:23:33,490 --> 00:23:42,680
+sequences طيب نشوف هذا ال space هذا اخذناه الآن دعنا 
+
+323
+00:23:42,680 --> 00:23:46,860
+نكون ال vector space من كل التجارب مع مترة بيكس
+
+324
+00:23:46,860 --> 00:23:52,040
+و y بسوء كده vector space of all continuous
+
+325
+00:23:52,040 --> 00:23:56,440
+sequences سيعمل limiters إذا كان الأل الأفينية
+
+326
+00:23:56,440 --> 00:24:00,200
+يعمل metric space فهو يعمل metric space والأل الفينية
+
+327
+00:24:00,200 --> 00:24:03,540
+يعمل metric space فهو يعمل metric space أسف vector space
+
+328
+00:24:03,540 --> 00:24:06,900
+ال .. ال .. ال .. الاشي لل .. العليات اللي هي ال
+
+329
+00:24:06,900 --> 00:24:09,200
+pointwise addition و ال pointwise scalar
+
+330
+00:24:09,200 --> 00:24:14,860
+multiplication sequences عادية، إذا S عبارة عن
+
+331
+00:24:14,860 --> 00:24:18,800
+vector space of all sequences بس هذا احنا عرفنا
+
+332
+00:24:18,800 --> 00:24:22,300
+عليه metric قبل هيك و بعيداً عن vector space عرفنا
+
+333
+00:24:22,300 --> 00:24:24,500
+metric أن المسافة بين x و y بيساوي ال summation x
+
+334
+00:24:24,500 --> 00:24:28,240
+i - y i على 2، ساي إذا بتذكروا في واحد
+
+335
+00:24:28,240 --> 00:24:31,080
+زيادة x i - y i كده، وقلنا إيه؟ ما حطينا هذا عشان نضمن 
+
+336
+00:24:31,080 --> 00:24:35,360
+أن ال series زي دي دايمًا شمالها converges ماشي لأن
+
+337
+00:24:35,360 --> 00:24:38,020
+هذا المقدار اللي فوق هيكون أصغر أو يساوي واحد، اه
+
+338
+00:24:38,020 --> 00:24:40,900
+فبيصير هذا المقدار دايمًا أصغر أو يساوي نص، معناته
+
+339
+00:24:40,900 --> 00:24:45,420
+مضمون اللي هو يعني بيكون converged لإنه ال geometry
+
+340
+00:24:45,420 --> 00:24:47,520
+accessories 1/2 are converged و ال
+
+341
+00:24:47,520 --> 00:24:51,590
+comparison test الآخر أنتو عارفين طيب، فرانكس بيساوي
+
+342
+00:24:51,590 --> 00:24:57,150
+x i و y i بيساوي γy n، show that this metric
+
+343
+00:24:57,150 --> 00:25:01,670
+can't be obtained from a norm اثبت أن هذا إيش ماله؟
+
+344
+00:25:01,670 --> 00:25:07,110
+مش ممكن يحصل عليه من ال norm اللي هو اثبت واحدة من
+
+345
+00:25:07,110 --> 00:25:10,230
+الخاصية التامة بتتحقق مش كل سنة، أنتو سالمين بيكون
+
+346
+00:25:10,230 --> 00:25:14,190
+مش induced by the norm الآن let alpha be scalar 
+
+347
+00:25:14,190 --> 00:25:17,290
+such that ال |α| شمالها أبعد مثلاً 
+
+348
+00:25:17,290 --> 00:25:20,170
+لألفا اللي بتساوي 1 عشان الألفا اللي بتساوي
+
+349
+00:25:20,170 --> 00:25:24,150
+1 ال |α| بيحققن بيحققن بيحققن، أنا 
+
+350
+00:25:24,150 --> 00:25:30,510
+بدي أجيب إشي ما بيحققش معانا؟ معانا؟ إن أنا أقول به
+
+351
+00:25:30,510 --> 00:25:35,150
+αx و αy بيساوي ال summation ال α
+
+352
+00:25:35,150 --> 00:25:38,430
+x من ال αx i و ال αy i، αγ i
+
+353
+00:25:38,430 --> 00:25:41,830
+كـ sequence فبيصير |αx i - αγ i| على 2 x i على 1 زي αx i زي αy
+
+354
+00:25:41,830 --> 00:25:45,790
+γ i مثلًا هي ال sequence αx وهي ال
+
+355
+00:25:45,790 --> 00:25:51,010
+sequence αy، الآن هذا بيساوي خد هذا absolute
+
+356
+00:25:51,010 --> 00:25:55,560
+value برة وهذه 2 i وهذه طلّعها برة، واضح واضح
+
+357
+00:25:55,560 --> 00:26:00,180
+واضح أنه بقدرش اللي هو أقول أن هذا بيساوي من
+
+358
+00:26:00,180 --> 00:26:04,460
+|α| في هذه يعني أنا بقدرش أن أجي
+
+359
+00:26:04,460 --> 00:26:07,280
+أقول والله خد هذا |α| وطير هذا 
+
+360
+00:26:07,280 --> 00:26:10,660
+وطير هذا هذا الأولاني إيش ما البطل يساوي هذا، واضح
+
+361
+00:26:10,660 --> 00:26:15,080
+فاهمي اللي بحكي اه؟ ويساوي اللي هو
+
+362
+00:26:15,080 --> 00:26:18,680
+ 
+363
+00:26:39,460 --> 00:26:45,810
+بمعنى آخر، بمعنى آخر الآن من الملاحظات اللي قبل بشوية
+
+364
+00:26:45,810 --> 00:26:50,310
+مستحيل يكون ال metric هذا induced by norm by the
+
+365
+00:26:50,310 --> 00:26:55,010
+norm والملاحظة الأخيرة the above example shows
+
+366
+00:26:55,010 --> 00:27:01,890
+that the metric in space need not be normed spaces
+
+367
+00:27:01,890 --> 00:27:11,600
+اه قلها أن لأ عندي بيصير اللي هو ماشي اللي هو عند
+
+368
+00:27:11,600 --> 00:27:15,600
+ال topological بحتوي على ال metric و ال metric
+
+369
+00:27:15,600 --> 00:27:19,920
+بحتوي على ال norm و ال norm بحتوي على ال Hilbert و
+
+370
+00:27:19,920 --> 00:27:23,300
+ال Hilbert بحتوي على ال ℝ و ال ℂ ليس شرطًا والله
+
+371
+00:27:23,300 --> 00:27:24,200
+يعطيكم العافية 
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/9LHmh6ZbiLE_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/9LHmh6ZbiLE_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..55e6156b6dde13cd0b786ab9e73a1d7121d928aa
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/9LHmh6ZbiLE_raw.json
@@ -0,0 +1 @@
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168.81, "end": 169.07, "word": " عبارة", "probability": 0.9908447265625}, {"start": 169.07, "end": 169.25, "word": " عن", "probability": 0.99462890625}, {"start": 169.25, "end": 169.49, "word": " vector", "probability": 0.9697265625}, {"start": 169.49, "end": 169.95, "word": " space", "probability": 0.95263671875}, {"start": 169.95, "end": 170.29, "word": " X", "probability": 0.98388671875}], "temperature": 1.0}, {"id": 9, "seek": 17935, "start": 170.91, "end": 179.35, "text": "لما نعرف عليه اللي هو ده اللي بنسميها non نشوف ايه الشروطة الان بمخ space هو complete non-space", "tokens": [1211, 15042, 8717, 3615, 28480, 47356, 13672, 1829, 31439, 11778, 3224, 13672, 1829, 44945, 38251, 1829, 11296, 2107, 8717, 8592, 38688, 1975, 1829, 3224, 25124, 32887, 9566, 3660, 2423, 7649, 4724, 2304, 9778, 1901, 31439, 3566, 2107, 12, 24824], "avg_logprob": -0.3320312574505806, "compression_ratio": 1.2982456140350878, "no_speech_prob": 1.2516975402832031e-06, "words": [{"start": 170.91, "end": 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"word": " الخاصية", "probability": 0.8095703125}, {"start": 1507.49, "end": 1507.77, "word": " التامة", "probability": 0.7146809895833334}, {"start": 1507.77, "end": 1508.29, "word": " بتتحقق", "probability": 0.91318359375}, {"start": 1508.29, "end": 1508.45, "word": " مش", "probability": 0.93359375}, {"start": 1508.45, "end": 1508.61, "word": " كل", "probability": 0.92626953125}, {"start": 1508.61, "end": 1508.77, "word": " سنة", "probability": 0.9479166666666666}, {"start": 1508.77, "end": 1508.93, "word": " انت", "probability": 0.624267578125}, {"start": 1508.93, "end": 1509.43, "word": " سالمين", "probability": 0.8310546875}, {"start": 1509.43, "end": 1510.23, "word": " بيكون", "probability": 0.7391764322916666}, {"start": 1510.23, "end": 1510.71, "word": " مش", "probability": 0.9453125}, {"start": 1510.71, "end": 1511.19, "word": " induced", "probability": 0.337646484375}, {"start": 1511.19, "end": 1511.47, "word": " by", "probability": 0.9765625}, {"start": 1511.47, "end": 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"probability": 0.95068359375}, {"start": 1515.45, "end": 1515.79, "word": " أفعى", "probability": 0.559814453125}, {"start": 1515.79, "end": 1516.29, "word": " شمالها", "probability": 0.8109130859375}, {"start": 1516.29, "end": 1516.91, "word": " ابعد", "probability": 0.7232666015625}, {"start": 1516.91, "end": 1517.29, "word": " مثلا", "probability": 0.871826171875}, {"start": 1517.29, "end": 1517.69, "word": " لألفات", "probability": 0.815185546875}, {"start": 1517.69, "end": 1517.79, "word": " اللي", "probability": 0.904541015625}, {"start": 1517.79, "end": 1518.13, "word": " بتساوي", "probability": 0.912841796875}, {"start": 1518.13, "end": 1518.49, "word": " واحد", "probability": 0.979248046875}, {"start": 1518.49, "end": 1519.35, "word": " عشان", "probability": 0.93505859375}, {"start": 1519.35, "end": 1519.81, "word": " الألفات", "probability": 0.9036458333333334}, {"start": 1519.81, "end": 1519.87, "word": " اللي", "probability": 0.98486328125}, {"start": 1519.87, "end": 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1549.79, "end": 1550.91, "word": " وهي", "probability": 0.92431640625}, {"start": 1550.91, "end": 1551.01, "word": " ال", "probability": 0.9033203125}, {"start": 1551.01, "end": 1551.43, "word": " sequence", "probability": 0.9794921875}, {"start": 1551.43, "end": 1551.75, "word": " Alpha", "probability": 0.9892578125}, {"start": 1551.75, "end": 1552.03, "word": " Y", "probability": 0.56396484375}], "temperature": 1.0}, {"id": 71, "seek": 157868, "start": 1553.44, "end": 1578.68, "text": "الان هذا بيساوي خد هذا absolute value برا وهذه اتنين I وهذه طلحها برا واضح واضح واضح انه بقدرش اللي هو اقول ان هذا بيساوي من absolute value لألفة في هذه يعني انا بقدرش ان اجي اقول والله خد هذا absolute value لألفة وطير هذا وطير هذا هذا الأولاني ايش ما الببطل يساوي هذا واضح فاهمي اللي بحكي اه؟ ويساوي اللي هو", "tokens": [6027, 7649, 23758, 4724, 1829, 3794, 995, 45865, 16490, 3215, 23758, 8236, 2158, 4724, 23557, 37037, 24192, 1975, 2655, 1863, 9957, 286, 37037, 24192, 23032, 1211, 5016, 11296, 4724, 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0.9326171875}, {"start": 1554.04, "end": 1554.68, "word": " بيساوي", "probability": 0.81318359375}, {"start": 1554.68, "end": 1555.2, "word": " خد", "probability": 0.850830078125}, {"start": 1555.2, "end": 1555.34, "word": " هذا", "probability": 0.7255859375}, {"start": 1555.34, "end": 1555.56, "word": " absolute", "probability": 0.86474609375}, {"start": 1555.56, "end": 1555.82, "word": " value", "probability": 0.98876953125}, {"start": 1555.82, "end": 1556.16, "word": " برا", "probability": 0.797119140625}, {"start": 1556.16, "end": 1556.88, "word": " وهذه", "probability": 0.5008544921875}, {"start": 1556.88, "end": 1557.14, "word": " اتنين", "probability": 0.77740478515625}, {"start": 1557.14, "end": 1557.38, "word": " I", "probability": 0.70849609375}, {"start": 1557.38, "end": 1557.64, "word": " وهذه", "probability": 0.79052734375}, {"start": 1557.64, "end": 1558.04, "word": " طلحها", "probability": 0.8260498046875}, {"start": 1558.04, "end": 1558.38, "word": " برا", 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"probability": 0.831298828125}, {"start": 1567.86, "end": 1568.4, "word": " خد", "probability": 0.98046875}, {"start": 1568.4, "end": 1568.7, "word": " هذا", "probability": 0.95849609375}, {"start": 1568.7, "end": 1569.02, "word": " absolute", "probability": 0.904296875}, {"start": 1569.02, "end": 1569.3, "word": " value", "probability": 0.98681640625}, {"start": 1569.3, "end": 1569.82, "word": " لألفة", "probability": 0.8963623046875}, {"start": 1569.82, "end": 1570.4, "word": " وطير", "probability": 0.8251953125}, {"start": 1570.4, "end": 1570.66, "word": " هذا", "probability": 0.76318359375}, {"start": 1570.66, "end": 1570.98, "word": " وطير", "probability": 0.9801432291666666}, {"start": 1570.98, "end": 1571.3, "word": " هذا", "probability": 0.97705078125}, {"start": 1571.3, "end": 1571.94, "word": " هذا", "probability": 0.88671875}, {"start": 1571.94, "end": 1572.54, "word": " الأولاني", "probability": 0.9271240234375}, {"start": 1572.54, "end": 1572.72, "word": " ايش", "probability": 0.6553548177083334}, {"start": 1572.72, "end": 1572.88, "word": " ما", "probability": 0.51904296875}, {"start": 1572.88, "end": 1573.38, "word": " الببطل", "probability": 0.755340576171875}, {"start": 1573.38, "end": 1573.7, "word": " يساوي", "probability": 0.9722900390625}, {"start": 1573.7, "end": 1574.08, "word": " هذا", "probability": 0.97314453125}, {"start": 1574.08, "end": 1575.08, "word": " واضح", "probability": 0.9503580729166666}, {"start": 1575.08, "end": 1576.06, "word": " فاهمي", "probability": 0.6468505859375}, {"start": 1576.06, "end": 1576.08, "word": " اللي", "probability": 0.975830078125}, {"start": 1576.08, "end": 1576.38, "word": " بحكي", "probability": 0.9849853515625}, {"start": 1576.38, "end": 1577.1, "word": " اه؟", "probability": 0.642578125}, {"start": 1577.1, "end": 1577.72, "word": " ويساوي", "probability": 0.855859375}, {"start": 1577.72, "end": 1578.42, "word": " اللي", "probability": 0.96337890625}, {"start": 1578.42, "end": 1578.68, "word": " هو", "probability": 0.98486328125}], "temperature": 1.0}, {"id": 72, "seek": 160344, "start": 1599.46, "end": 1603.44, "text": "بمعنى أخر بمعنى أخر", "tokens": [3555, 2304, 3615, 1863, 7578, 5551, 34740, 4724, 2304, 3615, 1863, 7578, 5551, 34740], "avg_logprob": -0.3447916587193807, "compression_ratio": 1.1666666666666667, "no_speech_prob": 1.0251998901367188e-05, "words": [{"start": 1599.4599999999998, "end": 1600.86, "word": "بمعنى", "probability": 0.7052978515625}, {"start": 1600.86, "end": 1601.54, "word": " أخر", "probability": 0.5162353515625}, {"start": 1601.54, "end": 1602.68, "word": " بمعنى", "probability": 0.88564453125}, {"start": 1602.68, "end": 1603.44, "word": " أخر", "probability": 0.936767578125}], "temperature": 1.0}, {"id": 73, "seek": 162731, "start": 1603.81, "end": 1627.31, "text": "الان من الممال اللي قبل بشوية مستحيل يكون ال metric هذا induced by main by the norm والملاحظة الأخيرة the above example shows that the metric in space need not be normed spaces اه قلها ان لأ عندي بيصير اللي هو", "tokens": [6027, 7649, 9154, 9673, 2304, 6027, 13672, 1829, 12174, 36150, 4724, 8592, 2407, 10632, 3714, 14851, 5016, 26895, 7251, 30544, 2423, 20678, 23758, 33991, 538, 2135, 538, 264, 2026, 16070, 2304, 15040, 5016, 19913, 3660, 16247, 9778, 48923, 264, 3673, 1365, 3110, 300, 264, 20678, 294, 1901, 643, 406, 312, 2026, 292, 7673, 1975, 3224, 12174, 1211, 11296, 16472, 5296, 10721, 18871, 16254, 4724, 1829, 9381, 13546, 13672, 1829, 31439], "avg_logprob": -0.31294013412905414, "compression_ratio": 1.4820512820512821, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 1603.81, "end": 1604.27, "word": "الان", "probability": 0.71337890625}, {"start": 1604.27, "end": 1604.51, "word": " من", "probability": 0.65576171875}, {"start": 1604.51, "end": 1604.95, "word": " الممال", "probability": 0.4933268229166667}, {"start": 1604.95, "end": 1605.07, "word": " اللي", "probability": 0.533447265625}, {"start": 1605.07, "end": 1605.25, "word": " قبل", "probability": 0.96435546875}, {"start": 1605.25, "end": 1605.81, "word": " بشوية", "probability": 0.8646240234375}, {"start": 1605.81, "end": 1606.83, "word": " مستحيل", "probability": 0.9342041015625}, {"start": 1606.83, "end": 1607.23, "word": " يكون", "probability": 0.980712890625}, {"start": 1607.23, "end": 1607.41, "word": " ال", "probability": 0.88330078125}, {"start": 1607.41, "end": 1607.69, "word": " metric", "probability": 0.451416015625}, {"start": 1607.69, "end": 1608.07, "word": " هذا", "probability": 0.63525390625}, {"start": 1608.07, "end": 1608.55, "word": " induced", "probability": 0.66162109375}, {"start": 1608.55, "end": 1608.87, "word": " by", "probability": 0.94140625}, {"start": 1608.87, "end": 1609.33, "word": " main", "probability": 0.299560546875}, {"start": 1609.33, "end": 1610.07, "word": " by", "probability": 0.5556640625}, {"start": 1610.07, "end": 1610.31, "word": " the", "probability": 0.8125}, {"start": 1610.31, "end": 1610.75, "word": " norm", "probability": 0.95263671875}, {"start": 1610.75, "end": 1612.37, "word": " والملاحظة", "probability": 0.8770345052083334}, {"start": 1612.37, "end": 1612.75, "word": " الأخيرة", "probability": 0.95849609375}, {"start": 1612.75, "end": 1612.95, "word": " the", "probability": 0.31787109375}, {"start": 1612.95, "end": 1613.19, "word": " above", "probability": 0.9521484375}, {"start": 1613.19, "end": 1613.89, "word": " example", "probability": 0.9755859375}, {"start": 1613.89, "end": 1615.01, "word": " shows", "probability": 0.828125}, {"start": 1615.01, "end": 1615.69, "word": " that", "probability": 0.939453125}, {"start": 1615.69, "end": 1616.25, "word": " the", "probability": 0.77978515625}, {"start": 1616.25, "end": 1616.67, "word": " metric", "probability": 0.92919921875}, {"start": 1616.67, "end": 1617.03, "word": " in", "probability": 0.48291015625}, {"start": 1617.03, "end": 1618.09, "word": " space", "probability": 0.78759765625}, {"start": 1618.09, "end": 1618.61, "word": " need", "probability": 0.77490234375}, {"start": 1618.61, "end": 1619.09, "word": " not", "probability": 0.96044921875}, {"start": 1619.09, "end": 1619.67, "word": " be", "probability": 0.9296875}, {"start": 1619.67, "end": 1620.89, "word": " normed", "probability": 0.669921875}, {"start": 1620.89, "end": 1621.89, "word": " spaces", "probability": 0.515625}, {"start": 1621.89, "end": 1622.99, "word": " اه", "probability": 0.4248046875}, {"start": 1622.99, "end": 1623.21, "word": " قلها", "probability": 0.6592610677083334}, {"start": 1623.21, "end": 1623.37, "word": " ان", "probability": 0.6787109375}, {"start": 1623.37, "end": 1623.97, "word": " لأ", "probability": 0.7010498046875}, {"start": 1623.97, "end": 1625.23, "word": " عندي", "probability": 0.66015625}, {"start": 1625.23, "end": 1626.07, "word": " بيصير", "probability": 0.83837890625}, {"start": 1626.07, "end": 1626.95, "word": " اللي", "probability": 0.96142578125}, {"start": 1626.95, "end": 1627.31, "word": " هو", "probability": 0.99267578125}], "temperature": 1.0}, {"id": 74, "seek": 164420, "start": 1629.92, "end": 1644.2, "text": "ماشي اللي هو عند ال topological بحتوى على ال metric و ال metric بحتوى على ال norm و ال norm بحتوى على ال Hilbert و ال Hilbert بحتوى على ال R و ال U ليس شرطا و الله يعطيكوا العافية", "tokens": [2304, 33599, 1829, 13672, 1829, 31439, 43242, 2423, 1192, 4383, 4724, 33753, 2407, 7578, 15844, 2423, 20678, 4032, 2423, 20678, 4724, 33753, 2407, 7578, 15844, 2423, 2026, 4032, 2423, 2026, 4724, 33753, 2407, 7578, 15844, 2423, 19914, 4290, 4032, 2423, 19914, 4290, 4724, 33753, 2407, 7578, 15844, 2423, 497, 4032, 2423, 624, 32239, 3794, 13412, 2288, 9566, 995, 4032, 21984, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632], "avg_logprob": -0.20946558489315753, "compression_ratio": 1.8503401360544218, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 1629.92, "end": 1630.52, "word": "ماشي", "probability": 0.6627604166666666}, {"start": 1630.52, "end": 1630.86, "word": " اللي", "probability": 0.771240234375}, {"start": 1630.86, "end": 1631.1, "word": " هو", "probability": 0.96875}, {"start": 1631.1, "end": 1631.6, "word": " عند", "probability": 0.87255859375}, {"start": 1631.6, "end": 1632.1, "word": " ال", "probability": 0.642578125}, {"start": 1632.1, "end": 1633.12, "word": " topological", "probability": 0.724853515625}, {"start": 1633.12, "end": 1633.78, "word": " بحتوى", "probability": 0.807861328125}, {"start": 1633.78, "end": 1634.04, "word": " على", "probability": 0.89697265625}, {"start": 1634.04, "end": 1634.74, "word": " ال", "probability": 0.91064453125}, {"start": 1634.74, "end": 1635.14, "word": " metric", "probability": 0.83203125}, {"start": 1635.14, "end": 1635.3, "word": " و", "probability": 0.56005859375}, {"start": 1635.3, "end": 1635.34, "word": " ال", "probability": 0.853515625}, {"start": 1635.34, "end": 1635.6, "word": " metric", "probability": 0.9296875}, {"start": 1635.6, "end": 1636.08, "word": " بحتوى", "probability": 0.98046875}, {"start": 1636.08, "end": 1636.3, "word": " على", "probability": 0.92236328125}, {"start": 1636.3, "end": 1636.84, "word": " ال", "probability": 0.88916015625}, {"start": 1636.84, "end": 1637.94, "word": " norm", "probability": 0.386474609375}, {"start": 1637.94, "end": 1638.14, "word": " و", "probability": 0.81201171875}, {"start": 1638.14, "end": 1638.22, "word": " ال", "probability": 0.9013671875}, {"start": 1638.22, "end": 1638.4, "word": " norm", "probability": 0.94580078125}, {"start": 1638.4, "end": 1638.82, "word": " بحتوى", "probability": 0.9771728515625}, {"start": 1638.82, "end": 1638.92, "word": " على", "probability": 0.8994140625}, {"start": 1638.92, "end": 1639.0, "word": " ال", "probability": 0.99267578125}, {"start": 1639.0, "end": 1639.44, "word": " Hilbert", "probability": 0.6461181640625}, {"start": 1639.44, "end": 1639.92, "word": " و", "probability": 0.91943359375}, {"start": 1639.92, "end": 1639.96, "word": " ال", "probability": 0.9306640625}, {"start": 1639.96, "end": 1640.22, "word": " Hilbert", "probability": 0.956298828125}, {"start": 1640.22, "end": 1640.64, "word": " بحتوى", "probability": 0.98583984375}, {"start": 1640.64, "end": 1640.72, "word": " على", "probability": 0.90087890625}, {"start": 1640.72, "end": 1640.76, "word": " ال", "probability": 0.91162109375}, {"start": 1640.76, "end": 1640.96, "word": " R", "probability": 0.82421875}, {"start": 1640.96, "end": 1641.08, "word": " و", "probability": 0.919921875}, {"start": 1641.08, "end": 1641.18, "word": " ال", "probability": 0.359375}, {"start": 1641.18, "end": 1641.42, "word": " U", "probability": 0.0811767578125}, {"start": 1641.42, "end": 1642.06, "word": " ليس", "probability": 0.92041015625}, {"start": 1642.06, "end": 1642.56, "word": " شرطا", "probability": 0.94140625}, {"start": 1642.56, "end": 1643.04, "word": " و", "probability": 0.60400390625}, {"start": 1643.04, "end": 1643.3, "word": " الله", "probability": 0.93701171875}, {"start": 1643.3, "end": 1643.8, "word": " يعطيكوا", "probability": 0.89765625}, {"start": 1643.8, "end": 1644.2, "word": " العافية", "probability": 0.95166015625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1644.92475, "duration_after_vad": 1607.2662499999976}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/9LHmh6ZbiLE_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/9LHmh6ZbiLE_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a86fcf2bebbc1a253c82fb33e5fddc62bf4c07b5
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/9LHmh6ZbiLE_raw.srt
@@ -0,0 +1,1484 @@
+1
+00:00:05,110 --> 00:00:07,690
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,690 --> 00:00:10,410
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,410 --> 00:00:16,970
+آله وصحبه أجمعين هذه المحاضرة الفامنة مساق تحليل
+
+4
+00:00:16,970 --> 00:00:19,910
+دالي أو تحليل اقتراني لطلاب وطالبات الجامعة
+
+5
+00:00:19,910 --> 00:00:24,700
+الإسلامية ماجستير رياضيةهنا المرة الماضية اللى هو
+
+6
+00:00:24,700 --> 00:00:28,780
+في المحاضرة السابعة اللى هو chapter واحد والان
+
+7
+00:00:28,780 --> 00:00:31,460
+بدنا ندخل ل chapter اتنين اللى هو normal spaces
+
+8
+00:00:31,460 --> 00:00:35,480
+and banach spaces حكينا في الأول عن metric spaces
+
+9
+00:00:35,480 --> 00:00:39,450
+والان بنحكي عن اللى هو ال banach spacesأحنا قلنا
+
+10
+00:00:39,450 --> 00:00:42,650
+فيه topological spaces وفيه في داخله اللي هو ال
+
+11
+00:00:42,650 --> 00:00:45,610
+metric spaces يعني كل metric spaces او topological
+
+12
+00:00:45,610 --> 00:00:49,490
+spaces او لكن العكس ليس صحيح ممكن نلاقي
+
+13
+00:00:49,490 --> 00:00:52,490
+topological spaces مش metric spaces الان ديين على
+
+14
+00:00:52,490 --> 00:00:57,720
+اللي هو احنا اللي هو بعد ما أخدناالـ Topological
+
+15
+00:00:57,720 --> 00:01:03,020
+Spaces اللي هو عندنا الـ Metric Spaces في داخله
+
+16
+00:01:03,020 --> 00:01:06,340
+وفيه في داخله اللي الآن هناخد مين الـ Normed
+
+17
+00:01:06,340 --> 00:01:09,860
+Spaces والشبطن الثالث هناخد في داخله اللي هو الـ
+
+18
+00:01:09,860 --> 00:01:15,220
+Hilbert Spaces يعني كل هيكة اللي هو عندك كل
+
+19
+00:01:15,220 --> 00:01:19,400
+Hilbert Norm وكل Normed Metric وكل Metric
+
+20
+00:01:19,400 --> 00:01:23,860
+Topological لكن الرجوع في أمثلة بتقول لأ ليس شرطة
+
+21
+00:01:24,290 --> 00:01:28,130
+طيب إذا هذه هي الصورة العامة و في داخل ال ال space
+
+22
+00:01:28,130 --> 00:01:31,410
+ال ال space اللي احنا بنشتغل عليه ال R و R تربيع و
+
+23
+00:01:31,410 --> 00:01:35,050
+R تقعيب اللي هو ال Herbert spaces و من ثم هتكون
+
+24
+00:01:35,050 --> 00:01:39,790
+اللي هو كل اللي فوق متحققة فيه اللي هو ال space
+
+25
+00:01:39,790 --> 00:01:42,210
+اللي احنا بنشتغل فيه في ال calculus و في ال
+
+26
+00:01:43,370 --> 00:01:46,850
+المعادلة التفاضلية في الاحتبانات و الاخرين طيب
+
+27
+00:01:46,850 --> 00:01:51,250
+صلّعنا بلس والسلام نيجي نشوف معنات الاتنين واحد
+
+28
+00:01:51,250 --> 00:01:55,110
+اللي هو مقدمة عن vector spaces طبعا هذه background
+
+29
+00:01:55,110 --> 00:01:57,330
+موجودة من الأصل عند الواحد من ال baccalaureate
+
+30
+00:01:57,330 --> 00:02:02,730
+ماعرفش ال vector space الآن northern space بنخ
+
+31
+00:02:02,730 --> 00:02:07,960
+space إذا بتتذكروا ال metric space بنى على ست6
+
+32
+00:02:07,960 --> 00:02:12,160
+عليها إيهاش metric دي لأ لأ احنا بدنا ندخل الآن
+
+33
+00:02:12,160 --> 00:02:16,300
+لعمليات الجبرية يعني ال X نفسها مش مجرد اللي هو
+
+34
+00:02:16,300 --> 00:02:19,740
+نقول والله هذا عبارة عن عن 6 ونحط عليها metric لأ
+
+35
+00:02:19,740 --> 00:02:25,730
+بديكون ال X نفسها فيه هي vector spaceبحط مبني على
+
+36
+00:02:25,730 --> 00:02:29,750
+vector space و بعرف عليه اللي هو حاجة اسمها norm
+
+37
+00:02:29,750 --> 00:02:33,510
+norm في الواقع التالت هو تعميم لل absolute value
+
+38
+00:02:33,510 --> 00:02:39,110
+اللي عندنا أو ال absolute value حالة خاصة منه
+
+39
+00:02:39,110 --> 00:02:43,910
+definition a normed space X is a vector space with
+
+40
+00:02:43,910 --> 00:02:49,250
+a norm defined on it ال normed space هو عبارة عن
+
+41
+00:02:49,250 --> 00:02:52,830
+vector space Xلما نعرف عليه اللي هو ده اللي
+
+42
+00:02:52,830 --> 00:02:57,810
+بنسميها non نشوف ايه الشروطة الان بمخ space هو
+
+43
+00:02:57,810 --> 00:03:02,980
+complete non-spaceالـ Complete in the metric
+
+44
+00:03:02,980 --> 00:03:05,980
+defined by the norm يعني الـ Completeness لأن أحنا
+
+45
+00:03:05,980 --> 00:03:09,420
+أخدنا الـ Completeness with respect to metric بعد
+
+46
+00:03:09,420 --> 00:03:12,300
+شوية هنشوف أنه اللي هو الـ Completeness تبع الـ
+
+47
+00:03:12,300 --> 00:03:15,900
+normed space with the metric اللي بنسميه induced
+
+48
+00:03:15,900 --> 00:03:19,700
+by the norm يعني اللي اتولد منه من ال norm اللي
+
+49
+00:03:19,700 --> 00:03:23,590
+عندنا طيب هل جيه تفهموا إيش اللي بقوله؟لأن a norm
+
+50
+00:03:23,590 --> 00:03:28,770
+on a real or complex vector space X is a real
+
+51
+00:03:28,770 --> 00:03:33,110
+valued function on X with whose value at an X is
+
+52
+00:03:33,110 --> 00:03:35,790
+denoted by norm X which has the following
+
+53
+00:03:35,790 --> 00:03:39,950
+properties يعني الآن تتعرفي النورم النورم ما هو
+
+54
+00:03:39,950 --> 00:03:45,250
+اللي عبارة عن دالة من X لعند اللي هو R positive
+
+55
+00:03:45,250 --> 00:03:52,710
+اتحادمين الـ0 تحقق ما يليهإنه F of X هي رمزنا برمز
+
+56
+00:03:52,710 --> 00:03:57,930
+Normal X إذا دمتنا اللي بنحكي عنها هي Normal X
+
+57
+00:03:57,930 --> 00:04:01,830
+تحقق الشروط التالية الشرط الأول إنها تكون أكبر أو
+
+58
+00:04:01,830 --> 00:04:06,370
+يساوي 0 طبيعيالشرط الثاني انها تساوي صفر if and
+
+59
+00:04:06,370 --> 00:04:11,250
+only if x ايش منها بتساوي صفر الشرط الثالث ال norm
+
+60
+00:04:11,250 --> 00:04:14,030
+من ال alpha في x بساوي ال absolute value من ال
+
+61
+00:04:14,030 --> 00:04:17,230
+alpha في ال norm من ال x او المدلس من ال alpha في
+
+62
+00:04:17,230 --> 00:04:20,190
+norm من ال x حسب ال alpha ال scale هذا ال scale من
+
+63
+00:04:20,190 --> 00:04:22,950
+ال alpha اللي هو انا بحكي عن vector space vector
+
+64
+00:04:22,950 --> 00:04:26,470
+space اذا في الارضية اللي هو ال R او ال C ال R او
+
+65
+00:04:26,470 --> 00:04:30,580
+ال C اللي بشتغل فيه بسالخاصية الرابعة هي
+
+66
+00:04:30,580 --> 00:04:33,760
+Triangling Quality Normal X زي Y أصغر من Normal X
+
+67
+00:04:33,760 --> 00:04:39,220
+زي Normal Y لكل X و Y Vectors و Alpha Scalar إذا
+
+68
+00:04:39,220 --> 00:04:44,320
+اتحققت الشروط الأربع هذه بنسميه norm مع هذا ال
+
+69
+00:04:44,320 --> 00:04:48,300
+vector space بنسميه norm of this space
+
+70
+00:04:52,340 --> 00:04:57,460
+بعض الملاحظات المهمة a norm on X defines a metric
+
+71
+00:04:57,460 --> 00:05:01,520
+D on X في الواقع انا بقدر اجيب من ال norm metric
+
+72
+00:05:01,520 --> 00:05:07,300
+كيف بعرفه؟ باجي بقول المسافة بين X و Y بده عنصر
+
+73
+00:05:07,300 --> 00:05:12,360
+بسوء norm X ناقص من Y لو جيت على الشروط الأربعة
+
+74
+00:05:12,360 --> 00:05:15,800
+تبعات ال metric هتلاقيها automatic اشمالها متحققة
+
+75
+00:05:15,800 --> 00:05:18,840
+ايش هالشروط ال metric اول شي دي X و Y أكبر او سوى
+
+76
+00:05:18,840 --> 00:05:24,060
+0وهذا أكبر بشروط النورم الشرط الثاني Normal X
+
+77
+00:05:24,060 --> 00:05:31,300
+minus Y بساوي 0 if and only if يعني DX وY بساوي 0
+
+78
+00:05:31,300 --> 00:05:35,160
+if and only if Normal X minus Y بساوي 0 if and
+
+79
+00:05:35,160 --> 00:05:38,940
+only if حسب اللي هي الخاصية الأولى في ال norm اللي
+
+80
+00:05:38,940 --> 00:05:42,720
+هو X ناطس Y بساوي 0 اللي هو if and only if X إيش
+
+81
+00:05:42,720 --> 00:05:47,590
+بتساوي إذا الشرط التاني للمتريك متحققالشرط اللي هو
+
+82
+00:05:47,590 --> 00:05:52,790
+الثالث ال distance بين ال X و ال Y بيساوي نورم ال
+
+83
+00:05:52,790 --> 00:05:58,530
+X minus Y ماشي اللي هو نفسه بيساوي نورم المين ال Y
+
+84
+00:05:58,530 --> 00:06:03,070
+minus إيش minus X اللي هو بيساوي ال distance بين
+
+85
+00:06:03,070 --> 00:06:07,990
+ال X و ال Y آسف ال Y و ال X ال symmetry إذا الشرط
+
+86
+00:06:07,990 --> 00:06:11,030
+الرابعاللي هو الـ Triangling Quality برضه
+
+87
+00:06:11,030 --> 00:06:14,950
+Automatic بتطلع اللي هي إيش الشرط الرابع؟ ان نورم
+
+88
+00:06:14,950 --> 00:06:21,490
+ال X دي X و Y اللي هو بساوة نورم ال X minus Y بال
+
+89
+00:06:21,490 --> 00:06:25,910
+Triangling Quality تبعت ال norm أصغر وسوء، نورم ال
+
+90
+00:06:25,910 --> 00:06:32,410
+X minus Z زاد نورم ال Z minus Y اللي هي بساوة دي X
+
+91
+00:06:32,410 --> 00:06:37,660
+و Zزا دي زد OI إذا ال triangle inequality برضه
+
+92
+00:06:37,660 --> 00:06:41,920
+متحققة لأن هذا فعلا metric إذا اللي هو أنا بقدر
+
+93
+00:06:41,920 --> 00:06:46,260
+أجيب من ال norm أو أولد من ال norm metric و هذا ال
+
+94
+00:06:46,260 --> 00:06:52,500
+normed space بتسميه the metric space induced by
+
+95
+00:06:52,500 --> 00:06:58,260
+the norm اللي مذكورة طيب هذه الملاحظة الأولىand
+
+96
+00:06:58,260 --> 00:07:00,760
+called the metric induced by the norm. Hence,
+
+97
+00:07:00,960 --> 00:07:04,640
+among the spaces and benefit spaces ايش هتكون؟
+
+98
+00:07:04,640 --> 00:07:09,100
+Metric spaces لكن العكس مش صحيح جدًا و هنجيب بعد
+
+99
+00:07:09,100 --> 00:07:14,070
+شوية مثالييجي الآن لـ .. اللي هي الـ .. الـ
+
+100
+00:07:14,070 --> 00:07:17,710
+equality اللي أمامنا for all x y limited x لـ
+
+101
+00:07:17,710 --> 00:07:20,430
+absolute value لـ normal x ناقص normal y أصغر شويه
+
+102
+00:07:20,430 --> 00:07:23,910
+لـ normal الـ x minus y وهنا سؤال بندوبه عادة في
+
+103
+00:07:23,910 --> 00:07:26,490
+الـ calculus طلاب الـ calculus بنشيل .. بنشيل
+
+104
+00:07:26,490 --> 00:07:29,170
+العصيتين اللي هي عصيتين ونحط عصة عصها لـ absolute
+
+105
+00:07:29,170 --> 00:07:34,510
+value والبرهانة نفس الأسلوب بالظبط زي ما بنبرهن في
+
+106
+00:07:34,510 --> 00:07:40,140
+الـ calculus بنقول احنا normal xبالـ Triangle
+
+107
+00:07:40,140 --> 00:07:45,160
+Inquality أصغر أشهر نورم الـ X ناقص Y زائد نورمين
+
+108
+00:07:45,160 --> 00:07:48,820
+الـ Y بالـ Triangle Inquality اللي قبل بشوية إذا
+
+109
+00:07:48,820 --> 00:07:53,860
+صار عندي نورم الـ X ناقص نورم الـ Y أصغر أشهر نورم
+
+110
+00:07:53,860 --> 00:07:58,660
+الـ X ناقص Y، مظبوط؟ لأن Similarly بدل مبدأ بـ X
+
+111
+00:07:58,660 --> 00:08:03,420
+بتبدأ بـ Y نورم الـ Y أصغر أشهر نورم الـ X minus Y
+
+112
+00:08:03,420 --> 00:08:09,380
+فاهمين؟زائد norm ال X Triangling equality ضفت ال X
+
+113
+00:08:09,380 --> 00:08:14,720
+و طرحت ال X هذي بيصير norm ال Y ناقص norm ال X
+
+114
+00:08:14,720 --> 00:08:21,440
+أصغر يساوي norm ال X minus Y هذي و هذي ضلبت هذي
+
+115
+00:08:21,440 --> 00:08:27,380
+بسالب بيصير عندي اضم هذي بسالب بيصير ناقص او عندي
+
+116
+00:08:27,380 --> 00:08:32,910
+norm ال Xنقص Normal Y أكبر أفشاوي ناقص Normal X
+
+117
+00:08:32,910 --> 00:08:40,690
+minus Y هذه مع هذه بتعطيك Normal X ناقص Normal Y
+
+118
+00:08:40,690 --> 00:08:45,970
+أصغر أفشاوي Normal X ناقص Y وأكبر أفشاوي Normal X
+
+119
+00:08:45,970 --> 00:08:50,030
+minus Y بالثانب وهذه بتعطيني ال absolute value
+
+120
+00:08:50,030 --> 00:08:55,990
+أصغر أفشاوي Normal X minus Normal Y كلام سهلفنجي
+
+121
+00:08:55,990 --> 00:08:59,330
+اللي هو الملاحظة التانية the norm is continuous
+
+122
+00:08:59,330 --> 00:09:03,730
+يعني ال norm نفسه is a continuous function بمعنى
+
+123
+00:09:03,730 --> 00:09:08,170
+آخر اللي هو لما ال X ترسل ل norm ال X اللي هي
+
+124
+00:09:08,170 --> 00:09:13,730
+بنسميها continuous mapping من ال X لعند مين لعند
+
+125
+00:09:13,730 --> 00:09:17,490
+ال R شوفوا كيف نثبت إنها continuous mapping أو
+
+126
+00:09:17,490 --> 00:09:22,050
+continuous function شوفوا
+
+127
+00:09:23,350 --> 00:09:28,530
+الدالة اللي عنده اللي هي مين نسميها F من اللي هو
+
+128
+00:09:28,530 --> 00:09:33,330
+ال X لعند مين طبعا ال X و ال metric تبعها ال
+
+129
+00:09:33,330 --> 00:09:37,170
+induced by the norm لعند ال R positive اتحاد مين
+
+130
+00:09:37,170 --> 00:09:42,050
+ال zero ممكن نثبت انها اللي هو continuous انا جانب
+
+131
+00:09:42,050 --> 00:09:45,830
+ايش احنا بنقول كيف نثبت رايحة وين هي دي فعلا في ال
+
+132
+00:09:45,830 --> 00:09:48,210
+topology تبعنا تبع ال video ال topology يعني ال
+
+133
+00:09:48,210 --> 00:09:54,710
+netF of X لما X تروح ل X0 هذي طبعا X تروح ل X0
+
+134
+00:09:54,710 --> 00:10:00,590
+اللي هو نقوين في ال metric تبعد ل more بتساوي F of
+
+135
+00:10:00,590 --> 00:10:06,190
+X0 يعني for every Y أكبر من 0 there exists Delta
+
+136
+00:10:06,190 --> 00:10:10,360
+بقول أنا بساوي Y such thatلما X تروح للـ X0، إيش
+
+137
+00:10:10,360 --> 00:10:14,380
+معناته؟ إنه نورم الـ X minus X0 يكون أصغر من
+
+138
+00:10:14,380 --> 00:10:19,800
+إبسلون أو من دلتا، يعطيك نورم، اللي هو دي بيصير F
+
+139
+00:10:19,800 --> 00:10:23,860
+of X نقصة في Y، اللي هي نورما من Absolute value،
+
+140
+00:10:23,860 --> 00:10:28,470
+اللي هو Absolute value للـ F of Xناقص f of x0
+
+141
+00:10:28,470 --> 00:10:33,070
+بيتواصلها تكون أصغر من مين؟ من أبسلوت هذه مين هي
+
+142
+00:10:33,070 --> 00:10:39,450
+بساوية absolute value؟ f of x هي نورم الـx ناقص
+
+143
+00:10:39,450 --> 00:10:45,590
+نورم الـx0 هذه الآن من الملاحظة اللي جابلها أصغر
+
+144
+00:10:45,590 --> 00:10:52,090
+أو يساويnorm الـ X ناقص X0 ومن هنا أصغر من دلتا
+
+145
+00:10:52,090 --> 00:10:56,550
+اللي أنا مختار دلتا إيه بتساوي اهو المفروض إذا
+
+146
+00:10:56,550 --> 00:11:01,770
+صارت ال norm إيه شماله is a continuous function
+
+147
+00:11:01,770 --> 00:11:06,030
+طيب، اللي بعد ال
+
+148
+00:11:06,030 --> 00:11:10,270
+median examples اللي هم ناخدهم في العالمين على
+
+149
+00:11:10,270 --> 00:11:16,350
+metric spaces كلها مثبتة يعني مافيش إيش يثبتهمالآن
+
+150
+00:11:16,350 --> 00:11:19,830
+الـ Euclidean space are N Unitary space CN هدولة
+
+151
+00:11:19,830 --> 00:11:22,570
+تبعتنا اللي قبل شوية كنا نعملهم إيه إيش؟ Metric
+
+152
+00:11:22,570 --> 00:11:27,450
+Spaces These are Banach Spaces كل نسبة ناهم
+
+153
+00:11:27,450 --> 00:11:31,450
+completed Complete Metric Spaces with respect to
+
+154
+00:11:31,450 --> 00:11:36,930
+their نوع اللي هي Metrics With norm norm X بساوي
+
+155
+00:11:36,930 --> 00:11:39,750
+ال summation XII كل تربية I من واحد لديه N كل
+
+156
+00:11:39,750 --> 00:11:46,860
+إشماله نصهذا إثباته إنه نورم سهل تثبته نورم بشكل
+
+157
+00:11:46,860 --> 00:11:51,920
+سريع مشابه لما أثبتناها قبل this norm induce the
+
+158
+00:11:51,920 --> 00:11:56,020
+metric هذا النورم إيش معله بولد ال metric التالي
+
+159
+00:11:56,020 --> 00:11:59,720
+دي x y بيساوي نورم ال x minus y و سوصة هذا النورم
+
+160
+00:11:59,720 --> 00:12:03,200
+هيه بيولد metric معين نشوف أشهر ال metric هذا
+
+161
+00:12:03,200 --> 00:12:06,180
+بيساوي ال summation x i i minus gamma i تربيع x i
+
+162
+00:12:06,180 --> 00:12:10,870
+i تبع ال x أو تبع ال y من gamma iطب ما هذا ال
+
+163
+00:12:10,870 --> 00:12:13,810
+metric اللي هتبع زمان ال metric الأولاني إذا صار
+
+164
+00:12:13,810 --> 00:12:16,990
+ال norm هذا بولد نفس ال metric اللي انا أثبتت انه
+
+165
+00:12:16,990 --> 00:12:22,130
+complete metric space إذا صار عندي الآن ال space
+
+166
+00:12:22,130 --> 00:12:26,110
+هذا under this norm اللي وولد نفس ال metric is a
+
+167
+00:12:26,110 --> 00:12:31,690
+complete metric spaceإذا صار بنخ SPS والان إثباته
+
+168
+00:12:31,690 --> 00:12:35,690
+ال norm أكبر أوي يساوي سفر والان اللي هو بيساوي
+
+169
+00:12:35,690 --> 00:12:38,150
+سفر if and only if X بيساوي سفر كله على طول من هنا
+
+170
+00:12:38,150 --> 00:12:43,130
+وبعدين اللي هي ال scalar norm ال alpha X بيساوي ال
+
+171
+00:12:43,130 --> 00:12:48,830
+summationبنعملكم إياها هذه مادلة بس جديدة بقى
+
+172
+00:12:48,830 --> 00:12:53,590
+الباق اللي ال triangles هي Normal Alpha X X بتساوي
+
+173
+00:12:53,590 --> 00:12:59,370
+X I واحد لعندك X I N الان ال Alpha X بتساوي اللي
+
+174
+00:12:59,370 --> 00:13:03,430
+هي Alpha X I واحد لعند ال Alpha X I N هذه بتساوي
+
+175
+00:13:03,430 --> 00:13:09,550
+معايا اه So summation Alpha اللي هي X I I تربيع
+
+176
+00:13:09,550 --> 00:13:16,560
+الكل أص نص I من واحد لعند ال Nماشي الحال
+
+177
+00:13:21,850 --> 00:13:26,170
+طيب هو يساوي هذا ال alpha بيطلع من جوا بيطلع اللي
+
+178
+00:13:26,170 --> 00:13:28,830
+هو alpha تربيه بيطلع برا ال alpha تربيه و نص بيطلع
+
+179
+00:13:28,830 --> 00:13:30,830
+من ال alpha then بيطلع ال absolute value of alpha
+
+180
+00:13:30,830 --> 00:13:35,630
+في ال summation xi i تربيه الكل أص نص من عند واحد
+
+181
+00:13:35,630 --> 00:13:39,210
+لعند ان و هذا عبارة عنه يساوي alpha absolute value
+
+182
+00:13:39,210 --> 00:13:42,530
+of alpha for normal x اذا اللي هي هذه برضه متحققة
+
+183
+00:13:42,530 --> 00:13:46,360
+و و و الاخرىالـ Triangling Collision هي نفس اللي
+
+184
+00:13:46,360 --> 00:13:50,480
+عملناها في الـ Matrix العادي طيب اطلع لفوق الان
+
+185
+00:13:50,480 --> 00:13:55,640
+عند ال space التاني هو ال LB space طبعا هو هذا ال
+
+186
+00:13:55,640 --> 00:14:02,120
+RN نفسه vector space ال RN vector space ال LB برضه
+
+187
+00:14:02,120 --> 00:14:05,670
+vector spaceالـ Vector Space بيحقق شروط الـ Vector
+
+188
+00:14:05,670 --> 00:14:11,070
+Space كلها و الجمع اللي بين عناصره هو جمع بين
+
+189
+00:14:11,070 --> 00:14:15,630
+Sequences عادية Alpha I و Gamma I بيصير Alpha I
+
+190
+00:14:15,630 --> 00:14:18,690
+زائد Gamma I و مجموحين واحد الأخرى عملية الجمع
+
+191
+00:14:18,690 --> 00:14:20,910
+الحادة مع الـ Scalar Multiplication اللي عادي اللي
+
+192
+00:14:20,910 --> 00:14:24,230
+هو Born Twice فاهمين اللي بحكيه؟يعني أنا بقول
+
+193
+00:14:24,230 --> 00:14:29,110
+Alpha في X كيف نضربها Alpha في الأولى؟ زي ما عملت
+
+194
+00:14:29,110 --> 00:14:33,270
+قبل شوية ال point twice اللي هو multiplication هذا
+
+195
+00:14:33,270 --> 00:14:36,970
+بعمله vector space بالقلبي القلبي vector space لو
+
+196
+00:14:36,970 --> 00:14:40,990
+عرفت عليه ال norm التالي هيطلع non despase و ال
+
+197
+00:14:40,990 --> 00:14:43,450
+metric اللي بيطلعه ال norm هو ال metric تبعنا اللي
+
+198
+00:14:43,450 --> 00:14:46,450
+استخدمناه و أثبتنا فيه complete قبل بشوية فبكون
+
+199
+00:14:46,450 --> 00:14:50,550
+عندي أشمله عبارة عن complete non despase إذا حيطلع
+
+200
+00:14:50,550 --> 00:14:55,810
+عندي بنخ spaceإذاً هذا المجلد هو مجلد بنخ مع نورم
+
+201
+00:14:55,810 --> 00:15:00,330
+مخصصة بي نورم ال X بيساوي ثميتي من XI بي الكل اس
+
+202
+00:15:00,330 --> 00:15:05,550
+واحد على بي هيا لان لما نحتاج طول من الميطرك هذا
+
+203
+00:15:05,550 --> 00:15:10,530
+النورم يدفع الميطرك DXY بيساوي نورم ال X minus Y
+
+204
+00:15:11,520 --> 00:15:16,860
+وإي ساوي هذا هو نفس ال metric الأصلي إذا عندي ال
+
+205
+00:15:16,860 --> 00:15:20,000
+metric هذا عملني ال b space وهذا ال metric اللي
+
+206
+00:15:20,000 --> 00:15:23,800
+جيناه المتولد من ال norm اللي عندي إذا ال norm
+
+207
+00:15:23,800 --> 00:15:28,260
+اللي عندي complete اللي هو بيعمل complete اللي هو
+
+208
+00:15:28,260 --> 00:15:30,940
+normed space يعني بيعمل بنخ space
+
+209
+00:15:33,850 --> 00:15:39,110
+نفس القصة الـ space من هو هذا الـ infinity الـ
+
+210
+00:15:39,110 --> 00:15:42,070
+space الـ infinity برضه عناصر و bounded sequences
+
+211
+00:15:42,070 --> 00:15:45,530
+و هو هيعمل vector space ليش هيعمل vector space
+
+212
+00:15:45,530 --> 00:15:48,250
+اللي هو under ال addition اللي هو ال pointwise
+
+213
+00:15:48,250 --> 00:15:49,990
+addition تبع ال sequence و ال scalar
+
+214
+00:15:49,990 --> 00:15:53,430
+multiplication برضه pointwise إذن هيطلع عند هذا ال
+
+215
+00:15:53,430 --> 00:15:56,590
+infinity vector space بشروط اللي بدأنا بنعرفها في
+
+216
+00:15:56,590 --> 00:16:01,670
+الجبر الخطي الآن هذا بدأ عرف عليه metric ال metric
+
+217
+00:16:01,670 --> 00:16:05,150
+اللي بدأ عرفهas if norm ال norm يعرفه norm
+
+218
+00:16:05,150 --> 00:16:09,470
+supernormal xii تبع ال x ال super normal هى واضح
+
+219
+00:16:09,470 --> 00:16:13,050
+ان هذا ال norm هيطلع ليه metric dxy بساعة norm x
+
+220
+00:16:13,050 --> 00:16:16,050
+minus y اللى هو عبارة عن ال super norm الأولانى
+
+221
+00:16:16,050 --> 00:16:18,530
+يعنى نفس ال metric اللى اشتغلنا عليه و أثبتنا ان
+
+222
+00:16:18,530 --> 00:16:22,770
+ال infinity is .. is ايش ماله complete واضح ها إذا
+
+223
+00:16:22,770 --> 00:16:27,250
+صار عند ال ال infinity is ابنخ space يعني complete
+
+224
+00:16:27,250 --> 00:16:32,890
+normed spaceأي شؤال و لا مسرع ما السهل الكلام
+
+225
+00:16:32,890 --> 00:16:38,090
+ماعلكم لا بيض ولا شفطة طيب صلى الله عليه الصلاة
+
+226
+00:16:38,090 --> 00:16:44,850
+والسلام ال space ال space اللي عند c of a و b اللي
+
+227
+00:16:44,850 --> 00:16:48,950
+هو the continuous functions اللي هو عالميا على
+
+228
+00:16:48,950 --> 00:16:54,370
+الفترة a و b اللي قبل بشوية الان الحمال norm يولد
+
+229
+00:16:54,370 --> 00:16:58,970
+نفس اللي هو اللاجنين اللي هو ال metric اللي تبقى
+
+230
+00:16:58,970 --> 00:17:03,480
+ال maximumماذا يعني هذا؟ this space is أبناءك
+
+231
+00:17:03,480 --> 00:17:06,680
+space و ال norm defined by ال norm من هو ال
+
+232
+00:17:06,680 --> 00:17:10,240
+maximum نورم ال X بيساوي ال maximum ل X of T، T
+
+233
+00:17:10,240 --> 00:17:13,900
+Elemental J هذا هيعملني norm of this space كامل،
+
+234
+00:17:13,900 --> 00:17:16,620
+تدربوا في البيت انتوا، تخشوه و تطلعوا بعض لجوهتك،
+
+235
+00:17:16,620 --> 00:17:23,000
+هذا كيف تطلعهذا البرمجة يدعم البرمجة DXY بيساوي
+
+236
+00:17:23,000 --> 00:17:24,820
+البرمجة DXY بيساوي البرمجة DXY بيساوي البرمجة DXY
+
+237
+00:17:24,820 --> 00:17:34,580
+بيساوي البرمجة DXY بيساوي
+
+238
+00:17:34,580 --> 00:17:41,320
+البرمجةالان اللي حكينا عنه قبل بشوية incomplete
+
+239
+00:17:41,320 --> 00:17:44,780
+metric space بالرغم ان هو the space of continuous
+
+240
+00:17:44,780 --> 00:17:49,500
+functions لكن under this metric يعني على المعيار
+
+241
+00:17:49,500 --> 00:17:52,460
+هذا تبع ال metric شوفوا مع اختلاف المعيامات الدنيا
+
+242
+00:17:52,460 --> 00:17:57,600
+هيك أصلاإخن في المعيار بيصير كل الأمور بتختلف فلإن
+
+243
+00:17:57,600 --> 00:18:01,480
+انت خلفت المعيار اللي عليه بدك تجيس أو تبني أو كده
+
+244
+00:18:01,480 --> 00:18:04,360
+أو تعمل limit أو تعمل continuity تبعتك و تعمل ال
+
+245
+00:18:04,360 --> 00:18:07,380
+.. هو كيف اعمل limits احنا و continuous functions
+
+246
+00:18:07,380 --> 00:18:09,740
+و differentiability و كده كل اللي لازم يكون فيه
+
+247
+00:18:09,740 --> 00:18:12,600
+اللي هو عايش topology لإن ال topology هذا أخلفته
+
+248
+00:18:12,600 --> 00:18:14,800
+من إيش لا إيش خلاص بيختلف بيصير ال space اختلف
+
+249
+00:18:15,300 --> 00:18:19,820
+اختلفت .. اختلفت بيصير .. بيصير حتى هو انه .. انه
+
+250
+00:18:19,820 --> 00:18:23,600
+متحقق خاصية الاكتمال او مايتحققش لأنه .. و هذا
+
+251
+00:18:23,600 --> 00:18:28,040
+خاصية الاكتمال تعتمد على ايهاش؟ على خاصية تبوليجية
+
+252
+00:18:28,040 --> 00:18:31,600
+اللي هي على الـmetric نفسه لإنه تعتمد على
+
+253
+00:18:31,600 --> 00:18:34,380
+الـconvergence وانه الـCauchy sequence تكون
+
+254
+00:18:34,380 --> 00:18:37,530
+convergenceوالـ Cauchy Sequence أو الـ Convergence
+
+255
+00:18:37,530 --> 00:18:41,090
+أصلا هي ما يمكن أن نتحدث عنها بدون Metric إذا
+
+256
+00:18:41,090 --> 00:18:44,370
+الأساسي فيها أن هو وجود Metric أو وجود Tomology أو
+
+257
+00:18:44,370 --> 00:18:47,990
+وجود أن هو Norm عشان هي ما اختلف ال Norm أو ما
+
+258
+00:18:47,990 --> 00:18:51,870
+اختلف ال Tomology بصير المقالات مختلفة صار ال
+
+259
+00:18:51,870 --> 00:18:55,370
+continuous function قبل بشوية مش complete وكل
+
+260
+00:18:55,370 --> 00:18:58,310
+continuous function complete طب هنا ماشي لأن هنا
+
+261
+00:18:58,310 --> 00:19:01,150
+norm هنا اختلف عن ال norm هنا واضح الدنيا كيف
+
+262
+00:19:01,150 --> 00:19:07,270
+ناشيها؟ طيبالأمور القليلة هذه مهمة الـ space X of
+
+263
+00:19:07,270 --> 00:19:11,010
+R continuous real valued functions on J with norm
+
+264
+00:19:11,010 --> 00:19:14,310
+defined by norm X بسواق ال integration 0 1 X of T
+
+265
+00:19:14,310 --> 00:19:17,810
+DT إذا أنا أخدت النوم من هنا ال integration is an
+
+266
+00:19:17,810 --> 00:19:23,160
+incomplete metric space لإن هذاالنورم بيولد لي
+
+267
+00:19:23,160 --> 00:19:28,220
+نورم DXY بيسوي نورم X-Y اللي هو الـ metric اللي
+
+268
+00:19:28,220 --> 00:19:31,280
+جابه قبل بشوية أثبتناه إنه مش complete إذا صار
+
+269
+00:19:31,280 --> 00:19:36,220
+عندي هذا is a non-bamach space أو is a non-despace
+
+270
+00:19:36,220 --> 00:19:40,670
+which is not completeأنا non يعني بانخ space
+
+271
+00:19:40,670 --> 00:19:44,270
+خلّيني نقول ان non هنا بس بأنفي فيها ال
+
+272
+00:19:44,270 --> 00:19:47,390
+completeness مابديش أقول non بانخ لإنه وسيلكون
+
+273
+00:19:47,390 --> 00:19:51,370
+نفيها قد يكون من هنا جاية أو من هنا لأ لأ اللي
+
+274
+00:19:51,370 --> 00:19:56,810
+بقصد فيها ان هو التعبير الأدق incomplete non space
+
+275
+00:19:56,810 --> 00:20:03,640
+طيب صلّع لنا بالأساس دي اللي ورسمتها قبل شويةالـ
+
+276
+00:20:03,640 --> 00:20:08,640
+topological space جواته اللي هو metric جواته
+
+277
+00:20:08,640 --> 00:20:14,290
+normed الان ال normedالـ Non-metric الـ Metric مش
+
+278
+00:20:14,290 --> 00:20:17,110
+شرط يكون Non-Dohaي مثال بدي أجيبلكم الـ Metric
+
+279
+00:20:17,110 --> 00:20:23,870
+اللي أخدناه في المحاضرات السابقة مش هيكون مولّج من
+
+280
+00:20:23,870 --> 00:20:29,290
+أي نوم في عندي الآن لمّة هي اللي بتشرّعلي الإثبات
+
+281
+00:20:29,290 --> 00:20:34,630
+هذا اللي هي Translation Invariance بتقولّي a
+
+282
+00:20:34,630 --> 00:20:36,150
+metric space D
+
+283
+00:20:39,590 --> 00:20:44,910
+induced by a norm around space X satisfies the
+
+284
+00:20:44,910 --> 00:20:48,590
+following يعني بيقول ليه لو كان عندكم metric space
+
+285
+00:20:48,590 --> 00:20:54,410
+مولد من norm لازم يحقق ما يليه ماحققش معناته
+
+286
+00:20:54,410 --> 00:21:00,650
+metricك مش مولد من norm ماشي الان a metric space D
+
+287
+00:21:00,650 --> 00:21:08,750
+مولد من normلازم يحقق واحد اتنين الخاصية الاولى ان
+
+288
+00:21:08,750 --> 00:21:12,530
+دي اكس زايد ايه ودي ايه زايد ايه بيساوي دي اكس
+
+289
+00:21:12,530 --> 00:21:19,290
+ومين او ايه هذه الخاصية بس متحققة لو كان ال metric
+
+290
+00:21:19,290 --> 00:21:22,410
+مولد
+
+291
+00:21:22,410 --> 00:21:28,070
+منهم اكيد هتتحققالان لو كان ال metric مولد من ال
+
+292
+00:21:28,070 --> 00:21:32,070
+norm برضه هيكون D α X α Y بسبب شجوط value Alpha في
+
+293
+00:21:32,070 --> 00:21:36,230
+D XY لكل XY اللي انت نفسي والألفة أشمالها scalar
+
+294
+00:21:36,230 --> 00:21:40,670
+ماشي الحالة لأن بمعنى لو هذه الخاصية غير متحققة
+
+295
+00:21:40,670 --> 00:21:43,890
+معناته ال metric تبعك مش مولد من ال norm لأنه لو
+
+296
+00:21:43,890 --> 00:21:46,930
+مولد من ال norm لازم ياش تحققها نفس الاشي التانية
+
+297
+00:21:46,930 --> 00:21:52,950
+عشان تعرفوا فيدتها اللي اثبتها سهل كتيردى x زي دي
+
+298
+00:21:52,950 --> 00:21:57,710
+و y زي دي ايش بيساوي لان ال norm لهذه ناقص هذه x
+
+299
+00:21:57,710 --> 00:22:00,190
+زي دي a ناقص y زي دي a ويساوي ال norm من ال x
+
+300
+00:22:00,190 --> 00:22:05,610
+minus y ويساوي اللى المسافة بين مين x و y اذا نزيح
+
+301
+00:22:05,610 --> 00:22:10,500
+شويةالجهتين، المقطين، X وY، وناخد المسافر بينهم،
+
+302
+00:22:10,500 --> 00:22:14,340
+مش هتفرج، هدف وين؟ هدف وين؟ انتوا، زي ما بيقول،
+
+303
+00:22:14,340 --> 00:22:17,560
+our mind restricted to R، احنا هيك اصلا مركبة،
+
+304
+00:22:17,560 --> 00:22:20,500
+لكن، الان هذا الكلام بيحكي عن وين، فعلا، بس ال
+
+305
+00:22:20,500 --> 00:22:24,720
+North Space، يعني هذا الكلام ليس شرط من انه يتحقق
+
+306
+00:22:24,720 --> 00:22:28,620
+وين، في ال metric space in general، او في ال .. في
+
+307
+00:22:28,620 --> 00:22:32,580
+ال .. في ال .. ال topological spaces، لو ترجمنا
+
+308
+00:22:32,580 --> 00:22:34,580
+هذا الكلام بواسط North and South Spaces، اللي هو
+
+309
+00:22:34,580 --> 00:22:37,630
+Matrix،لأن مافيش متركز فيه، مش شرط يكون فيه متركز
+
+310
+00:22:37,630 --> 00:22:43,990
+في الـ Topology فاهمين ما أقول هو؟ طيب، D Alpha X
+
+311
+00:22:43,990 --> 00:22:48,150
+و Alpha Y بيساوي المعاملة الـ Alpha X ناقص Alpha Y
+
+312
+00:22:48,150 --> 00:22:50,390
+وبيساوي الـ Absolute Value Alpha نوع X وبيساوي
+
+313
+00:22:50,390 --> 00:22:54,690
+Absolute Value Alpha في D X و Y هذا بس متحقق أو
+
+314
+00:22:54,690 --> 00:22:57,670
+مديش أقول بس، مديش أقول بس هذا لو كان الـ Metric
+
+315
+00:22:57,670 --> 00:23:01,800
+induced by the norm هيتحققفعلا لأنه ليش بقول
+
+316
+00:23:01,800 --> 00:23:04,880
+ماتقولش بس لأنه أصلا ممكن ألاجي اللي هو مش metric
+
+317
+00:23:04,880 --> 00:23:10,780
+spaces لكن بتحقق هذه مش non-spaces لكن بتحقق هذه
+
+318
+00:23:12,250 --> 00:23:17,930
+واطلع لفوق space S الـ S مين هو إذا بتذكروا الـ
+
+319
+00:23:17,930 --> 00:23:25,750
+space of all sequences بغض النظر بغض
+
+320
+00:23:25,750 --> 00:23:29,050
+النظر عن إيش ال sequence بيقولي bounded
+
+321
+00:23:29,050 --> 00:23:33,490
+convergence لأ لأ أنا بأخد اللي هو space of مين of
+
+322
+00:23:33,490 --> 00:23:42,680
+sequences طيب نشوف هذا ال space هذا خدناهالآن دعنا
+
+323
+00:23:42,680 --> 00:23:46,860
+نكون الـ vector space من كل التجارب مع مترة بيكس
+
+324
+00:23:46,860 --> 00:23:52,040
+واي بسوء كده vector space of all continuous
+
+325
+00:23:52,040 --> 00:23:56,440
+sequences سيعمل limiters إذا كان الأل الافينية
+
+326
+00:23:56,440 --> 00:24:00,200
+يعمل متر كسباس فهو يعمل متر كسباس والأل الفينية
+
+327
+00:24:00,200 --> 00:24:03,540
+يعمل متر كسباس فهو يعمل متر كسباس أسف vector space
+
+328
+00:24:03,540 --> 00:24:06,900
+ال .. ال .. ال .. الاشي لل .. العليات اللي هي ال
+
+329
+00:24:06,900 --> 00:24:09,200
+pointwise addition وال pointwise scalar
+
+330
+00:24:09,200 --> 00:24:14,860
+multiplicationسيكوانسيز عادية اذا S عبارة عن
+
+331
+00:24:14,860 --> 00:24:18,800
+vector space of all sequences بس هذا احنا عرفنا
+
+332
+00:24:18,800 --> 00:24:22,300
+عليه metric قبل هيك و بعيدا عن vector space عرفنا
+
+333
+00:24:22,300 --> 00:24:24,500
+metric ان المسافة بين X و Y بيساوي ال summation X
+
+334
+00:24:24,500 --> 00:24:28,240
+I I نقص جمع I على اتنين ساي اذا بتذكروا في واحد
+
+335
+00:24:28,240 --> 00:24:31,080
+زياد X I I كده و قلنا ايه ما حطينا هذا عشان نضمن
+
+336
+00:24:31,080 --> 00:24:35,360
+ان ال series Z دي دايما شمالها convergesماشي لأن
+
+337
+00:24:35,360 --> 00:24:38,020
+هذا المقدار اللي فوق هيكون اصغر او شاوي واحد اه
+
+338
+00:24:38,020 --> 00:24:40,900
+فبصير هذا المقدار دايما اصغر او شاوي نص معناته
+
+339
+00:24:40,900 --> 00:24:45,420
+مضمون اللي هو يعني بكون converged لإنه ال geometry
+
+340
+00:24:45,420 --> 00:24:47,520
+accessories واحد على اتنين are converged و ال
+
+341
+00:24:47,520 --> 00:24:51,590
+comparison test الاخر انتوا عارفين طيبفرانكس بيسوي
+
+342
+00:24:51,590 --> 00:24:57,150
+xii and y بيسوي gamma yns show that this metric
+
+343
+00:24:57,150 --> 00:25:01,670
+can't be obtained from a norm اثبت ان هذا ايش ماله
+
+344
+00:25:01,670 --> 00:25:07,110
+مش ممكن يحصل عليه من ال norm اللي هو اثبت واحدة من
+
+345
+00:25:07,110 --> 00:25:10,230
+الخاصية التامة بتتحقق مش كل سنة انت سالمين بيكون
+
+346
+00:25:10,230 --> 00:25:14,190
+مش induced by the normالآن let alpha be scalar
+
+347
+00:25:14,190 --> 00:25:17,290
+such that الـ absolute value أفعى شمالها ابعد مثلا
+
+348
+00:25:17,290 --> 00:25:20,170
+لألفات اللي بتساوي واحد عشان الألفات اللي بتساوي
+
+349
+00:25:20,170 --> 00:25:24,150
+واحد الـ absolute value بيحققن بيحققن بيحققن أنا
+
+350
+00:25:24,150 --> 00:25:30,510
+بدي أجيب إشي ما بيحققش معانا معانا؟إن أنا أقول بيه
+
+351
+00:25:30,510 --> 00:25:35,150
+Alpha X و Alpha Min Y بيساوي ال summation ال Alpha
+
+352
+00:25:35,150 --> 00:25:38,430
+X من ال Alpha Xi I وال Alpha I Alpha Gamma I
+
+353
+00:25:38,430 --> 00:25:41,830
+كسيكونس فبيصير absolute value Alpha Xi minus Alpha
+
+354
+00:25:41,830 --> 00:25:45,790
+Gamma I على 2Xi على 1 زي Alpha Xi I زي Alpha Min
+
+355
+00:25:45,790 --> 00:25:51,010
+Gamma I مثهوم هي ال sequence Alpha X وهي ال
+
+356
+00:25:51,010 --> 00:25:55,560
+sequence Alpha Yالان هذا بيساوي خد هذا absolute
+
+357
+00:25:55,560 --> 00:26:00,180
+value برا وهذه اتنين I وهذه طلحها برا واضح واضح
+
+358
+00:26:00,180 --> 00:26:04,460
+واضح انه بقدرش اللي هو اقول ان هذا بيساوي من
+
+359
+00:26:04,460 --> 00:26:07,280
+absolute value لألفة في هذه يعني انا بقدرش ان اجي
+
+360
+00:26:07,280 --> 00:26:10,660
+اقول والله خد هذا absolute value لألفة وطير هذا
+
+361
+00:26:10,660 --> 00:26:15,080
+وطير هذا هذا الأولاني ايش ما الببطل يساوي هذا واضح
+
+362
+00:26:15,080 --> 00:26:18,680
+فاهمي اللي بحكي اه؟ ويساوي اللي هو
+
+363
+00:26:39,460 --> 00:26:45,810
+بمعنى أخر بمعنى أخرالان من الممال اللي قبل بشوية
+
+364
+00:26:45,810 --> 00:26:50,310
+مستحيل يكون ال metric هذا induced by main by the
+
+365
+00:26:50,310 --> 00:26:55,010
+norm والملاحظة الأخيرة the above example shows
+
+366
+00:26:55,010 --> 00:27:01,890
+that the metric in space need not be normed spaces
+
+367
+00:27:01,890 --> 00:27:11,600
+اه قلها ان لأ عندي بيصير اللي هوماشي اللي هو عند
+
+368
+00:27:11,600 --> 00:27:15,600
+ال topological بحتوى على ال metric و ال metric
+
+369
+00:27:15,600 --> 00:27:19,920
+بحتوى على ال norm و ال norm بحتوى على ال Hilbert و
+
+370
+00:27:19,920 --> 00:27:23,300
+ال Hilbert بحتوى على ال R و ال U ليس شرطا و الله
+
+371
+00:27:23,300 --> 00:27:24,200
+يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/CRLpGXH9NAM_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/CRLpGXH9NAM_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d7a6b40360f8722023e9106f3c0285fcca1c9631
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/CRLpGXH9NAM_postprocess.srt
@@ -0,0 +1,3012 @@
+1
+00:00:05,060 --> 00:00:07,820
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,820 --> 00:00:10,740
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,740 --> 00:00:16,160
+آله وصحبه أجمعين هذه المحاضرة رقم 22 مساب تحليل
+
+4
+00:00:16,160 --> 00:00:18,960
+اقتراني او تحليل دالي طلاب طالبات الجامعة
+
+5
+00:00:18,960 --> 00:00:22,440
+الإسلامية مجلسية الرياضيات اليوم وصلنا لعند او
+
+6
+00:00:22,440 --> 00:00:26,530
+اليوم هنحكي في هذه المحاضرة على تلاتة ستةاللي هي
+
+7
+00:00:26,530 --> 00:00:30,470
+تحت عنوان Total Orthonormal Sets and Sequences
+
+8
+00:00:30,470 --> 00:00:34,130
+احنا حكينا عن الـ Orthonormal Sets و Orthonormal
+
+9
+00:00:34,130 --> 00:00:38,070
+Sequences الآن الفكرة في الـ Total Orthonormal
+
+10
+00:00:38,070 --> 00:00:42,950
+Sets and Sequences احنا
+
+11
+00:00:42,950 --> 00:00:49,330
+بدنا نبحث عن set انها من خلالها نجيب ال space كله
+
+12
+00:00:49,880 --> 00:00:55,760
+كل space يعني ما كأنه مشابه لعمل اللي هي roughly
+
+13
+00:00:55,760 --> 00:00:59,600
+هذا الكلام مشابه لعمل ال bases في حالة اللي هو في
+
+14
+00:00:59,600 --> 00:01:02,480
+ال finite dimensional case في حالة ال finite
+
+15
+00:01:02,480 --> 00:01:05,140
+dimensional case اللي بتجيب ال space اللي هو اللي
+
+16
+00:01:05,140 --> 00:01:08,060
+انتوا عارفين ال bases انه على طول اللي هو linearly
+
+17
+00:01:08,060 --> 00:01:12,120
+independent independentlinearly independent معناته
+
+18
+00:01:12,120 --> 00:01:16,500
+يعني ان هي بمعنى اخر انه اقتصادي انه انا مابحطش اش
+
+19
+00:01:16,500 --> 00:01:21,480
+زيادة بقدر اجيبه منهم الجزء الثاني انه بعمل span و
+
+20
+00:01:21,480 --> 00:01:25,820
+بعمل كل space الان في حالة ال infinite dimensional
+
+21
+00:01:25,820 --> 00:01:29,600
+في ال separable الأمور كمان أبسط شوية في حالة ال
+
+22
+00:01:29,600 --> 00:01:34,740
+non separable spacesبصير الأمور حتى شغل فيها شوية
+
+23
+00:01:34,740 --> 00:01:39,720
+أعقد احنا هنشتغل بما ي .. خلانا نقول بما يناسبنا
+
+24
+00:01:39,720 --> 00:01:44,460
+في ال course هذا يعني اللي هيعمل ال .. العمل هذا
+
+25
+00:01:44,460 --> 00:01:48,480
+اللي هو انه من خلاله انه هحنحاول نجيب ال space او
+
+26
+00:01:48,480 --> 00:01:51,600
+اللي حصل عن ال space رفلي هذا الكلام اللي هو حاجة
+
+27
+00:01:51,600 --> 00:01:57,100
+اسمها total orthonormal setالمرة الفاترة حكينا عن
+
+28
+00:01:57,100 --> 00:01:59,640
+ال orthonormal set اليوم ده نحكي عن ال total اللي
+
+29
+00:01:59,640 --> 00:02:03,800
+هي هتعمل هذا العمل خلينا نيجي نطلع على اللي هو شو
+
+30
+00:02:03,800 --> 00:02:06,760
+معناته ال definition أو شو ال definition ل ال
+
+31
+00:02:06,760 --> 00:02:09,280
+total set أو ال issue و بعدين نيجي ل اللي هو ال
+
+32
+00:02:09,280 --> 00:02:12,950
+orthonormal اللي احنا عارفينهالـ Total set أو الـ
+
+33
+00:02:12,950 --> 00:02:16,610
+Fundamental set هي عبارة ان a norm of this base X
+
+34
+00:02:16,610 --> 00:02:19,170
+في أي نوم of this base in general احنا بس شغلنا
+
+35
+00:02:19,170 --> 00:02:22,810
+هيكون في الهيلبرغ is a subset M عبارة عن مجموعة ZM
+
+36
+00:02:22,810 --> 00:02:27,370
+of X whose span is dense in X يعني بس المطلوب منها
+
+37
+00:02:27,370 --> 00:02:31,450
+ان سبانها .. سبان .. بقول على room total .. اذا
+
+38
+00:02:31,450 --> 00:02:37,080
+كان سبانللأم closure بيساوي مين كل space X فهذه
+
+39
+00:02:37,080 --> 00:02:41,880
+الحالة بنسمي اللي هي الست أم إيه شمالها is total
+
+40
+00:02:44,210 --> 00:02:48,210
+الان a total orthonormal set هي بتكون total في نفس
+
+41
+00:02:48,210 --> 00:02:51,370
+الوجه ايه اشمالها orthonormal يعني الجهتين وال
+
+42
+00:02:51,370 --> 00:02:55,590
+orthonormal انتوا عارفين شو معناه orthonormal ال
+
+43
+00:02:55,590 --> 00:02:59,630
+inner product بين كلتين تان مختلفتين سفر وبين
+
+44
+00:02:59,630 --> 00:03:04,270
+الواحدة ونفسها عبارة عن واحد اطلع لفوق الان بعض
+
+45
+00:03:04,270 --> 00:03:10,150
+الملاحظات عندي الملاحظتين اللي عندي أمورهمخلّينا
+
+46
+00:03:10,150 --> 00:03:14,090
+نقول مقدور عليها وفي إشي يعني trivial في حالة ال
+
+47
+00:03:14,090 --> 00:03:17,610
+finite dimensional والتانية اللي هي في حالة ال non
+
+48
+00:03:17,610 --> 00:03:20,910
+separable هذا خارج نطاق شغلنا فإحنا الملاحظات
+
+49
+00:03:20,910 --> 00:03:24,550
+تانية اللي هنحكيهن بشكل أساسي يعني اللي هو برهان
+
+50
+00:03:24,550 --> 00:03:27,230
+هنا الجزء الأول ال trivial اللي هو بما يتعلق بال
+
+51
+00:03:27,230 --> 00:03:30,730
+finite dimensional والتاني بده شوية شغل بتعلق
+
+52
+00:03:30,730 --> 00:03:33,710
+بنظرية اللي خدناها اللي هناخدهن إيش هنا الملاحظات
+
+53
+00:03:33,710 --> 00:03:38,990
+تانية؟In every Hilbert space hatch لأن انا انا
+
+54
+00:03:38,990 --> 00:03:42,250
+قاعد بده اروح باتجاه ان هو هذا ال total earth is
+
+55
+00:03:42,250 --> 00:03:47,680
+normal setهي اللي هتجيبلي ال space فعليها هسمي ال
+
+56
+00:03:47,680 --> 00:03:51,220
+dimension زي ما بنسمي ال dimension على ال ال bases
+
+57
+00:03:51,220 --> 00:03:55,180
+في الحالة اللي هي ال finite dimensional هنحن بنسمي
+
+58
+00:03:55,180 --> 00:03:57,700
+ال bases اللي هو ال dimension اللي هنا على حسب
+
+59
+00:03:57,700 --> 00:04:00,660
+اللي هو ال total orthonormal set اللي عندك انتبهش
+
+60
+00:04:00,660 --> 00:04:03,800
+بقول in every Hilbert space H ل H سوا سفر there
+
+61
+00:04:03,800 --> 00:04:07,680
+exists a total orthonormal set يعني مضمون انه اي
+
+62
+00:04:07,680 --> 00:04:10,500
+Hilbert space H سوا ال finite dimension في حالة ال
+
+63
+00:04:10,500 --> 00:04:14,180
+finite اللي هو ال basesماقياش بتثبيت أنه يكون اللي
+
+64
+00:04:14,180 --> 00:04:17,940
+هي ال norm لكل واحدة بساوي واحد ال .. ال .. ال ..
+
+65
+00:04:17,940 --> 00:04:20,680
+الحالة ال inseparable حالة ال non inseparable
+
+66
+00:04:20,680 --> 00:04:23,680
+انسوها مش .. مش مديعنة الحالة ال inseparable اللي
+
+67
+00:04:23,680 --> 00:04:28,700
+هو فيه hint عليها في .. في الكتابأي Hilbert space
+
+68
+00:04:28,700 --> 00:04:35,220
+H مضمون له total orthonormal set هاي واحد اتنين كل
+
+69
+00:04:35,220 --> 00:04:38,160
+ال total orthonormal set في ال Hilbert space H
+
+70
+00:04:38,160 --> 00:04:40,760
+لايه تساوي سفر اي Hilbert space ال total
+
+71
+00:04:40,760 --> 00:04:43,240
+orthonormal set لهم كلهين have the same
+
+72
+00:04:43,240 --> 00:04:46,960
+cardinality يعني اللي هو زي في حالة ال bases اللي
+
+73
+00:04:46,960 --> 00:04:50,820
+هي نفس العدد هي the same cardinality لخوف انها
+
+74
+00:04:50,820 --> 00:04:55,680
+تكون ايه اش ما لها infinite number of elementsالان
+
+75
+00:04:55,680 --> 00:04:59,100
+بناء عليه مدام كله نلهم نفس ال cardinality هذه ال
+
+76
+00:04:59,100 --> 00:05:01,200
+cardinality اللي لهم هي اللي بنسميها ال diamonds
+
+77
+00:05:01,200 --> 00:05:05,400
+شلمين لل Hilbert space اللي بنحكي عنه where the
+
+78
+00:05:05,400 --> 00:05:08,220
+cardinality of the total orthonormal sit in a
+
+79
+00:05:08,220 --> 00:05:12,140
+Hilbert space أشلس أو شفر الآن هذا اللي هي الأولى
+
+80
+00:05:12,140 --> 00:05:16,130
+اللي هي اللي بدها ال hint للبرهانةWhere the
+
+81
+00:05:16,130 --> 00:05:18,670
+cardinality of the total orthonormal set in
+
+82
+00:05:18,670 --> 00:05:23,570
+Hilbert 3H0900 is called the Hilbert dimension or
+
+83
+00:05:23,570 --> 00:05:25,990
+orthogonal dimension of H
+
+84
+00:05:36,100 --> 00:05:38,960
+ملاقى باسيس مايكونش هيك الأمر في الـ Final
+
+85
+00:05:38,960 --> 00:05:42,080
+Dimension لك اذا H بتساوي سفر الـ Hilbert
+
+86
+00:05:42,080 --> 00:05:47,240
+Dimension اللي نعرفه هو الـ Zero اللي هو الـ
+
+87
+00:05:47,240 --> 00:05:53,060
+Dimension له بروف left to the reader اللي فيه هند
+
+88
+00:05:53,060 --> 00:05:57,080
+في الكتاب الجزء
+
+89
+00:05:57,080 --> 00:06:00,520
+اللي هو الـ separable اللي المطلوب نيجي للنظرية
+
+90
+00:06:00,520 --> 00:06:06,320
+اللي عندناأطلع لفوق شوية ايوة هنا وقفت بقول لي let
+
+91
+00:06:06,320 --> 00:06:09,820
+m be a subset of an inner product space X ماشي
+
+92
+00:06:09,820 --> 00:06:14,950
+الحالعندي M subset من مين؟ من inner product مش ال
+
+93
+00:06:14,950 --> 00:06:18,870
+part space inner product بلزم يشتر بها then الشرط
+
+94
+00:06:18,870 --> 00:06:25,030
+الأول if M is total in X then X element in X and X
+
+95
+00:06:25,030 --> 00:06:28,350
+عموديه على X implies X ايش بتساوي؟ بتساوي سفر هذا
+
+96
+00:06:28,350 --> 00:06:31,310
+كله على بعض شو معناه انه لما تكون X في X و X
+
+97
+00:06:31,310 --> 00:06:34,770
+عموديه على M لازم يعطيني ان X بتساوي سفر يعني
+
+98
+00:06:34,770 --> 00:06:38,830
+وكأني بدي اقول اللي هي بدل هذه كلها ان M
+
+99
+00:06:38,830 --> 00:06:43,370
+orthogonal بساوي 0 بسإن كل X عمودي على M هيطلع إيش
+
+100
+00:06:43,370 --> 00:06:48,010
+بس؟ هو السفر يعني و كأني بقول إن M Orthogonal هو
+
+101
+00:06:48,010 --> 00:06:51,970
+Zero يعني لو كانت M Total in X then M Orthogonal
+
+102
+00:06:51,970 --> 00:06:56,830
+بساوة Zero الآن الجزء الثاني إذا كانت X Complete
+
+103
+00:06:56,830 --> 00:07:01,190
+يعني Hilbert Space بمعنى آخر و if the condition
+
+104
+00:07:01,190 --> 00:07:06,270
+اللي هو M Orthogonal بساوة Zero is satisfied then
+
+105
+00:07:06,270 --> 00:07:12,880
+M إيش هتطلع Total Set in X ماشي الحالةالبرهان بقى
+
+106
+00:07:12,880 --> 00:07:18,240
+فيه أخدنا المرة الفاتة نظرية في حالة الـ H H اللي
+
+107
+00:07:18,240 --> 00:07:22,700
+هي Hilbert space وكأس بكون عندي M orthogonal و M
+
+108
+00:07:22,700 --> 00:07:27,000
+subset منها أخدناها بتيصير M orthogonal بساوة Zero
+
+109
+00:07:27,000 --> 00:07:35,060
+if and only if M أو لسبان لـ M is dense in mean in
+
+110
+00:07:35,060 --> 00:07:41,450
+H أخدناها المرة الماضية أهدف عن استخدامهاالكلام
+
+111
+00:07:41,450 --> 00:07:47,410
+هذا عبارة عن إعادة صياغة لهذه النظرية تقريبا اللي
+
+112
+00:07:47,410 --> 00:07:52,770
+هو بلغة ال total لأن ال total عرفناها إيش ماله، ال
+
+113
+00:07:52,770 --> 00:07:55,870
+span ل ال omicron بساوي إيش، ال space، ال space
+
+114
+00:07:55,870 --> 00:08:01,710
+كلهنجي الآن البرهن لت H بي the completion of X
+
+115
+00:08:01,710 --> 00:08:04,250
+لإنه عشان .. ليش أخدتش completion لل X؟ لإنه أنا
+
+116
+00:08:04,250 --> 00:08:08,110
+بدأ أستخدم نيل النظرية هذه اللي هي بتعتمد على إياش
+
+117
+00:08:08,110 --> 00:08:12,350
+إنه تكون H عبارة عن ال part space وإحنا ضمنين إنه
+
+118
+00:08:12,350 --> 00:08:17,770
+product إيه له completion، ال completion بتكون X
+
+119
+00:08:17,770 --> 00:08:21,780
+then Cماحنا عارفين لما نركبنا اللي هو عملنا ال
+
+120
+00:08:21,780 --> 00:08:25,160
+completion بتكون ال X dense فيه then X can be
+
+121
+00:08:25,160 --> 00:08:29,580
+regarded ممكن تعتبر as a subspace of H which is
+
+122
+00:08:29,580 --> 00:08:34,960
+dense in مين in H طيب however M نفسها is total in
+
+123
+00:08:34,960 --> 00:08:38,800
+X مازال total in X إذا ال closure إلها with
+
+124
+00:08:38,800 --> 00:08:43,480
+respect to X هي .. السباق .. أسف .. السباق لل M ال
+
+125
+00:08:43,480 --> 00:08:46,760
+closure إلها with respect to X هي سوى مين ال X
+
+126
+00:08:46,760 --> 00:08:50,770
+dense فيهاوالـ X نفسها أصلاً زنس في الـ H فبكون
+
+127
+00:08:50,770 --> 00:08:54,410
+نسبان للـ M closure with respect to H هيطلع برضه
+
+128
+00:08:54,410 --> 00:08:58,970
+مين H فبتكون it is zens in مين in H إذا صار هذا
+
+129
+00:08:58,970 --> 00:09:03,090
+متحقق إذا أكيد ال M Orthogonal إيش هتساوي؟ هتساوي
+
+130
+00:09:03,090 --> 00:09:06,610
+سفر إذا M Orthogonal هذا من لمّا إيش اللي بحكيت
+
+131
+00:09:06,610 --> 00:09:11,890
+عنها ديك اسمها ليه لمّا تلاتة تلاتة سبعة اللي
+
+132
+00:09:11,890 --> 00:09:17,620
+بعدها مباشرةخلّي بس نزلت شوية عشان نشوف النص اللي
+
+133
+00:09:17,620 --> 00:09:21,620
+بعدها إذا كانت X Complete يعني X is Hilbert space
+
+134
+00:09:21,620 --> 00:09:27,080
+و M Orthogonal بساوي 0 من هذه مباشرة مباشرة هيكون
+
+135
+00:09:27,080 --> 00:09:32,120
+اللي هو ال M Orthogonal إيش بتساوي؟ و هذي Span
+
+136
+00:09:32,120 --> 00:09:36,120
+Closure بتساوي H متكافئتين إذا على طول بنستخدمها
+
+137
+00:09:36,120 --> 00:09:40,980
+لهذه بصير عندي الآن H Complete و M Orthogonal Zero
+
+138
+00:09:40,980 --> 00:09:45,490
+إذا عليه طلعتعلى طول لسبان كلوجر ايش بيساوي بيساوي
+
+139
+00:09:45,490 --> 00:09:49,430
+ال H لسبان كلوجر بيساوي H شو معناته M is total
+
+140
+00:09:49,430 --> 00:09:57,670
+واضحة طيب اللي قلته يا جماعة انه بما انه X
+
+141
+00:09:57,670 --> 00:10:03,160
+completeو M Orthogonal بتساوي سفر إذا بواسط تهاد
+
+142
+00:10:03,160 --> 00:10:08,120
+النظرية أنه مادامة M Orthogonal Zero بتطلع ل Span
+
+143
+00:10:08,120 --> 00:10:11,180
+ل M closure إيش بيساوي إتش يعني Span ل M between
+
+144
+00:10:11,180 --> 00:10:18,090
+Mين إتش يعني M is total هي عرفنا ب totalالنظرية
+
+145
+00:10:18,090 --> 00:10:25,550
+تلاتة ستة تلاتة تلاتة
+
+146
+00:10:25,550 --> 00:10:32,840
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتةالـ
+
+147
+00:10:32,840 --> 00:10:37,260
+orthonormal set M in a Hilbert space H is total in
+
+148
+00:10:37,260 --> 00:10:41,740
+H if and only if الbar θ ال equality بتصير يعني ال
+
+149
+00:10:41,740 --> 00:10:44,000
+summation بدل ما كانت بيصير ده تكون اي شمالها
+
+150
+00:10:44,000 --> 00:10:48,420
+بيكون بيصير ال summation لل X وال E K تربيع K over
+
+151
+00:10:48,420 --> 00:10:52,380
+K بيسووا من Normal X تربيع for all X المتناجح إذا
+
+152
+00:10:52,380 --> 00:10:58,910
+بتتذكروا المرة الماضيةقلنا بس على جهة هنا هذه اللي
+
+153
+00:10:58,910 --> 00:11:01,510
+هو ال terms اللي جوا ال for real series هذول
+
+154
+00:11:01,510 --> 00:11:05,750
+coefficients هذولة كلهين is far ماعدا countable
+
+155
+00:11:05,750 --> 00:11:08,990
+number منهم قلنا ال countable number هو اللي بتكون
+
+156
+00:11:08,990 --> 00:11:12,030
+اللي هي ممكن تكون non-zero element لكن كل الباقي
+
+157
+00:11:12,030 --> 00:11:15,910
+إيش ماله يعني مش فارقة معايا في الآخر هذه over k
+
+158
+00:11:15,910 --> 00:11:20,260
+لو كانت uncountable اللي هي العدادبظل اللي هي
+
+159
+00:11:20,260 --> 00:11:24,780
+الاشي اللي فيهه قيمة عددية غير الـ Zero بيكون فعلا
+
+160
+00:11:24,780 --> 00:11:29,580
+هو أيش ماله countable طيب هذا على جهة بس الان بدنا
+
+161
+00:11:29,580 --> 00:11:32,480
+ناخد الاتجاه الأول و بعدين الاتجاه الثاني أول
+
+162
+00:11:32,480 --> 00:11:36,500
+اتجاه بيقوللي بدنا .. الآن عندي .. بدنا نثبت انه ا
+
+163
+00:11:36,500 --> 00:11:37,700
+.. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا
+
+164
+00:11:37,700 --> 00:11:37,920
+.. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا
+
+165
+00:11:37,920 --> 00:11:38,120
+.. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا
+
+166
+00:11:38,120 --> 00:11:39,440
+.. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا
+
+167
+00:11:39,440 --> 00:11:39,520
+.. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا
+
+168
+00:11:39,520 --> 00:11:41,580
+.. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا
+
+169
+00:11:41,580 --> 00:11:42,100
+.. ا ..
+
+170
+00:11:45,630 --> 00:11:50,550
+if and only if اللي هو normal X تربيع بساوية الـ
+
+171
+00:11:50,550 --> 00:11:53,770
+summation لأ اللي هي الـ Fourier coefficients دولة
+
+172
+00:11:53,770 --> 00:12:00,170
+A over K اللي أنا بدي أفترض الآن اللي هو بدي أثبت
+
+173
+00:12:00,170 --> 00:12:05,710
+الآن عشان أثبت اللي هو الاتجاه هذايعني بدي أبدأ
+
+174
+00:12:05,710 --> 00:12:09,390
+بهذا و أصل لهذا، ماشي؟ يعني بدي أقول suppose هذا
+
+175
+00:12:09,390 --> 00:12:13,410
+متحقق و أصل لهذا عشان أثبتها هذه بدي أثبتها by
+
+176
+00:12:13,410 --> 00:12:16,510
+contraposition يعني بدي أفترض أن الـM is not total
+
+177
+00:12:16,510 --> 00:12:20,870
+و أصل لهذه معناته أن هذه بيصير تؤدي لهذه إذا الآن
+
+178
+00:12:20,870 --> 00:12:27,430
+if suppose that M is not total ماشي؟ مدام مش total
+
+179
+00:12:28,800 --> 00:12:33,960
+إذا الـ M .. اللي احنا قلنا لو كانت M total M
+
+180
+00:12:33,960 --> 00:12:37,080
+total اللي هو معناته اللي .. اللي هو بتكون M
+
+181
+00:12:37,080 --> 00:12:41,340
+أرثجون الأشمال،ها Zero ماشي، مدامت M .. و هذه F
+
+182
+00:12:41,340 --> 00:12:45,260
+and F، أشتغلنا قدّيها تاني إذا كانت M is not
+
+183
+00:12:45,260 --> 00:12:47,540
+total، اللي من ال theorem اللي قبل بشوية، تلاتة،
+
+184
+00:12:47,540 --> 00:12:52,920
+ستة اتنين، B، هيكون عندي أكيد في اللي هو الـ M
+
+185
+00:12:52,920 --> 00:12:57,950
+أرثجون المش Zeroإذا بمعنى أخر بلاقي X إيش معناه M
+
+186
+00:12:57,950 --> 00:13:01,050
+Orthogonal مش Zero يعني في X في ال M Orthogonal
+
+187
+00:13:01,050 --> 00:13:06,270
+مقله عمودي على ال M و بيسويش سفر إذا there is X
+
+188
+00:13:06,270 --> 00:13:10,030
+element لأتش و X لاته ساوى سفر and X Orthogonal
+
+189
+00:13:10,030 --> 00:13:15,510
+لمين؟ لل M هذا امسكوا فيه then صار عند X و EK
+
+190
+00:13:15,510 --> 00:13:22,740
+بيساوى سفر لكل EK element من M هو نفسه مش سفرطيب
+
+191
+00:13:22,740 --> 00:13:28,140
+إذا hence ال summation ل X و EK تربيع over K كله
+
+192
+00:13:28,140 --> 00:13:32,160
+نفسه هيساوي سفر و مش هيساوي من norm X تربيعه إن X
+
+193
+00:13:32,160 --> 00:13:36,380
+نفسه مش zero إذا صار عندي ال contraposition تحققت
+
+194
+00:13:36,380 --> 00:13:39,540
+إنه لو كانت هذه مش total هتأدي هذا وهذا معناه أن
+
+195
+00:13:39,540 --> 00:13:43,960
+هذا يؤدي هذا therefore if ال summation بيساوي كذا
+
+196
+00:13:43,960 --> 00:13:48,840
+for all اللي هي X المتناش then M اسمها is total in
+
+197
+00:13:48,840 --> 00:13:57,340
+H و converselyالان بدأ افترض انه M is total واصل
+
+198
+00:13:57,340 --> 00:14:02,720
+للمساواة دي اللي ال بارسيفال مالها متحققة لاحظوا
+
+199
+00:14:02,720 --> 00:14:08,400
+ما هي اللي الان suppose that M is total in H وخد X
+
+200
+00:14:08,400 --> 00:14:12,600
+be any element in M in H في arbitrary لكن fixed
+
+201
+00:14:12,600 --> 00:14:16,060
+عشان اثبت لكم انه نور متربية بساوي ال summation
+
+202
+00:14:16,060 --> 00:14:21,540
+اللي عندها طيب صلى الله عليه الصلاة والسلامالان
+
+203
+00:14:21,540 --> 00:14:25,540
+الـ Range of all its non-zero Fourier coefficients
+
+204
+00:14:25,540 --> 00:14:30,220
+in a sequence X و E1 و X و E2 و الى اخرها و بقدر
+
+205
+00:14:30,220 --> 00:14:33,400
+اعمل هيك حتى لو كانت uncountable ليش؟ لان قبل شوية
+
+206
+00:14:33,400 --> 00:14:38,440
+قلتلكم اللي هي الـ non-zero منهااللي هي حاجة تكون
+
+207
+00:14:38,440 --> 00:14:42,420
+countable هم اللي بيعملوا هنا arrangement إذا الأن
+
+208
+00:14:42,420 --> 00:14:46,480
+هدول اللي اختارتهم من هنا اللي هم مش سفر فبصير
+
+209
+00:14:46,480 --> 00:14:50,120
+عندي X و E واحد و X و E اتنين إلى مالة نهاية اللي
+
+210
+00:14:50,120 --> 00:14:55,830
+هي أعملت .. أحطيتهم في sequenceوإذا كان في نايت
+
+211
+00:14:55,830 --> 00:14:59,210
+خلاص من كتب ال X و X و Y أحد و X و Y اتنين و X و Y
+
+212
+00:14:59,210 --> 00:15:04,710
+انتصار اذا ر مكتوب في حركة محددة إذا كان هناك عدد
+
+213
+00:15:04,710 --> 00:15:05,610
+منهم فقط في نايت
+
+214
+00:15:09,690 --> 00:15:14,930
+واضح طيب الان define y by الان هاي الألداء اللي
+
+215
+00:15:14,930 --> 00:15:20,290
+بتوصلني للي بديها الان خليني أن أعرف y بواسطة y
+
+216
+00:15:20,290 --> 00:15:23,250
+بالسواء و ال summation x و ek ek كامن عند واحد إلى
+
+217
+00:15:23,250 --> 00:15:28,030
+مين إلى مال نهاية طيب شو سميلي هذه واحدة لأن بعد
+
+218
+00:15:28,030 --> 00:15:34,350
+شوية أرجعلها أنا بعرف أن أم اشمالها is orthonormal
+
+219
+00:15:34,350 --> 00:15:39,540
+set مدام orthonormal setthen for every ej
+
+220
+00:15:39,540 --> 00:15:45,280
+occurring in one اللي هي الاج اللي في واحد اللي هي
+
+221
+00:15:45,280 --> 00:15:49,120
+واحد لما أخدنا ال summation هذا over k فيه جزئين
+
+222
+00:15:49,120 --> 00:15:53,240
+جزء منه اللي هو عملتله arranging اللي هو xe واحد
+
+223
+00:15:53,240 --> 00:15:57,120
+إلى آخرهم وهدولة اللي هي non-zero elements والجزء
+
+224
+00:15:57,120 --> 00:16:02,020
+الثاني منهم خلّينا نسميه v و ال v هذا ايش مالوسفار
+
+225
+00:16:02,020 --> 00:16:06,470
+ماشي الحال طيب اوبتيجي الآن عملنا arrangement
+
+226
+00:16:06,470 --> 00:16:11,230
+since M is orthonormal then for every EJ occurring
+
+227
+00:16:11,230 --> 00:16:15,790
+in one اللي عملنا لها arrangement we have X minus
+
+228
+00:16:15,790 --> 00:16:19,770
+Y و EJ ال X ال arbitrator ال botfix اللي خدناها في
+
+229
+00:16:19,770 --> 00:16:24,990
+الأول هي عليها الشغل طيب بتساوي X و EJ ناقص Y مين
+
+230
+00:16:24,990 --> 00:16:30,200
+و EJو يساوي X و EJ زي ما هي ناقص هذه ناقص ال
+
+231
+00:16:30,200 --> 00:16:35,740
+summation X و EK في EK و EJ الان عندنا كل هين
+
+232
+00:16:35,740 --> 00:16:40,460
+هيتسفر مع ده EJ ايش مع EJ لإن هو orthonormal إذا
+
+233
+00:16:40,460 --> 00:16:44,940
+صار عند هذا X EJ و هذا X EJ إذا إيش هيساوي؟ هيساوي
+
+234
+00:16:44,940 --> 00:16:50,060
+سفر إذا أثبت لكم الآن X minus Y و EJ بساوي سفر لكل
+
+235
+00:16:50,060 --> 00:16:54,940
+واحدة من العائلة الأولى هذه نيجي الآن ناخدلأن for
+
+236
+00:16:54,940 --> 00:16:59,100
+all V elements in M not occurring in one يعني اللي
+
+237
+00:16:59,100 --> 00:17:01,140
+ما حصلت .. اللي ما أخدناهنش منها .. نحنا قلنا
+
+238
+00:17:01,140 --> 00:17:04,680
+جزأناها جزءين الجزء اللي بيسفرن هو الجزء السفر
+
+239
+00:17:04,680 --> 00:17:08,080
+اللي بيسفرنش هو الجزء السفر هذا أخدنا ال V ال
+
+240
+00:17:08,080 --> 00:17:12,180
+element in M اللي بيعملني سفر we have .. اللي هي
+
+241
+00:17:12,180 --> 00:17:16,520
+طبعا ال V هذي مش هذا ال V اللي هو اللي بيعمله سفر
+
+242
+00:17:16,520 --> 00:17:20,360
+اللي هي .. اللي هو X و V اللي هو أياش مستوى سفر
+
+243
+00:17:20,360 --> 00:17:27,640
+فاهمين عليها أه؟عشان تكون الأمور واضحة اذا we have
+
+244
+00:17:27,640 --> 00:17:32,320
+x و v بيساوي سفر so that احسبني برضه ال x minus y
+
+245
+00:17:32,320 --> 00:17:37,440
+و mean و ال v ايش حيسوي x و v ناقص اللي هو ال
+
+246
+00:17:37,440 --> 00:17:41,260
+summation اللي هو y عبارة عن x و ek و ek و mean و
+
+247
+00:17:41,260 --> 00:17:46,780
+v برضه نفس الجثة ال v ولا واحدة من هدول أصلاأه إذا
+
+248
+00:17:46,780 --> 00:17:49,020
+.. إذا صار عند ال inner product بينه إيش ماله
+
+249
+00:17:49,020 --> 00:17:54,580
+بساوي سفر وهذا أصلا عند X و EK و EK في V هيطلع
+
+250
+00:17:54,580 --> 00:17:59,420
+القيمة كل مرة سفر إذا صار عند X minus Y و V بساوي
+
+251
+00:17:59,420 --> 00:18:05,400
+سفر يعني بمعنى آخر X minus Y وكل العناصر اللي في M
+
+252
+00:18:05,400 --> 00:18:08,860
+سواء العصورة هذه أو العصورة هذه صار ال inner
+
+253
+00:18:08,860 --> 00:18:12,200
+product بينهم سفر يعني X minus Y إيش صارت عمودية
+
+254
+00:18:12,200 --> 00:18:17,720
+على ال Mما دام X minus Y عمودية على الـ M و الـ M
+
+255
+00:18:17,720 --> 00:18:21,360
+however M is totally matched then by لمّة ثلاثة
+
+256
+00:18:21,360 --> 00:18:25,120
+سبعة اتنين هيطلع عند .. كان عند الـ M ارتجونالاش
+
+257
+00:18:25,120 --> 00:18:28,760
+بساوة سفر دي ما هي مهمة و قالش اتمنى في الأول إذا
+
+258
+00:18:28,760 --> 00:18:31,720
+صار عند ال X minus Y اللي موجود هان هيساوة سفر
+
+259
+00:18:31,720 --> 00:18:36,740
+معناته صارت ال X بتساوة من .. بتساوة Y لأن هذا
+
+260
+00:18:36,740 --> 00:18:40,460
+هتوصلنا للي بديها خد و حسن norm ال X سار بيعيش
+
+261
+00:18:40,460 --> 00:18:43,550
+بساوة ال inner product بين ال X و ال Xاللي هو Y و
+
+262
+00:18:43,550 --> 00:18:47,590
+Y صارت ميهم؟ ساوى إيه دلها؟ الان Y إيش بتساوي ال
+
+263
+00:18:47,590 --> 00:18:51,070
+inner product لأ فاهمين ال summation هذا و ال
+
+264
+00:18:51,070 --> 00:18:53,950
+summation نفسه هذا الان بنطلع ال two summations
+
+265
+00:18:53,950 --> 00:18:57,350
+برا صارت هذه معهودة عندنا القول هذا اللي من بعيد
+
+266
+00:18:57,350 --> 00:19:01,490
+هيطلع conjugate و هذا هيكون عادي و هيظل EK و مين و
+
+267
+00:19:01,490 --> 00:19:07,330
+EM كل اللي عندي هنا هيتصفر summation مع ده عند ال
+
+268
+00:19:07,330 --> 00:19:10,990
+K بتساوي مين بتساوي M يعني هيصير ال summation بس
+
+269
+00:19:10,990 --> 00:19:15,810
+على مينعلى واحدة منهم اللي نسميها K وهذا واحد
+
+270
+00:19:15,810 --> 00:19:18,930
+ولقينا ال product بين التنتين اللي زي بعض الواحدة
+
+271
+00:19:18,930 --> 00:19:22,110
+و ال conjugate إلها بيصير المضلة السربيع فبصير
+
+272
+00:19:22,110 --> 00:19:27,090
+عنده Normal X السربيع بساوية هذه و هو المطلوب طيب
+
+273
+00:19:27,090 --> 00:19:35,710
+نيجي نشوف نظرية 364 ايش النظرية بتقول نقول نظرية
+
+274
+00:19:35,710 --> 00:19:40,780
+let H be a Hilbert space thenالجزئين الجزئ الأول
+
+275
+00:19:40,780 --> 00:19:44,220
+اللي هو if H is separable هذا بتساعدنا أصلا في
+
+276
+00:19:44,220 --> 00:19:48,000
+برهان واحدة من اللي فوق if H is separable إذا كانت
+
+277
+00:19:48,000 --> 00:19:51,880
+H separable then every orthonormal sitting H
+
+278
+00:19:51,880 --> 00:19:56,700
+إشمالها يعني كلهين countable بمثلين اللي هي ال
+
+279
+00:19:56,700 --> 00:20:01,350
+totalالـ Total Orthonormal بما فين هنا إذا صار كل
+
+280
+00:20:01,350 --> 00:20:05,970
+اللي هي الـ Total Orthonormal ستة حسب النظرية هذه
+
+281
+00:20:05,970 --> 00:20:09,530
+في حالة السيبرانجل كلهن أشملن countable number
+
+282
+00:20:09,530 --> 00:20:13,090
+يعني ال cardinality اللي بيساوي ألف note يعني ال
+
+283
+00:20:13,090 --> 00:20:15,510
+dimension اللي بدنا نسميه بيصير أشمل ألف percent
+
+284
+00:20:15,510 --> 00:20:19,940
+اللي فوق هنا ماشي في حالة السيبرانجلإذا H تحتوي
+
+285
+00:20:19,940 --> 00:20:24,520
+على سيكوان أورثو نورمال يكون تماماً لـ H، فهو
+
+286
+00:20:24,520 --> 00:20:25,600
+أيضاً Separable
+
+287
+00:20:30,890 --> 00:20:35,530
+هذا بيعطينا إنه هذا الـ Total Orthonormal هي سر
+
+288
+00:20:35,530 --> 00:20:38,630
+إنه يكون separable ولا مش separable إذا كان إحنا
+
+289
+00:20:38,630 --> 00:20:42,390
+اللي جينا أتش بتحتوي على واحدة من الـOrthonormal
+
+290
+00:20:42,390 --> 00:20:45,570
+Sequences وتكون Total، يعني الـCardinality اللي
+
+291
+00:20:45,570 --> 00:20:50,250
+هالف Note وهي Total، هيطلع الأتش separable، ماشي
+
+292
+00:20:50,250 --> 00:20:52,930
+الحال، إذا اللي هو في حالة الـseparable يعني
+
+293
+00:20:52,930 --> 00:20:56,810
+الأمور تمام تمام ومافيش إشكالية، وحتكون اللي هي
+
+294
+00:20:57,510 --> 00:21:01,610
+اللي هي الـ cardinality بتساوي اللي هو ألف نوت
+
+295
+00:21:01,610 --> 00:21:08,570
+فنجي برهن الأولى نتأتش بـ separable الان انتوا
+
+296
+00:21:08,570 --> 00:21:10,810
+بيقولوا البرهن البرهن اللذيذ وفيه فكرة يعني
+
+297
+00:21:24,720 --> 00:21:28,580
+الان انزل بس عشان نقولكم ايش اللي بدنا نثبته شوية
+
+298
+00:21:28,580 --> 00:21:32,760
+بقى الان اذا كانت بدنا نثبت نفرض انه H separable و
+
+299
+00:21:32,760 --> 00:21:37,220
+منها نصل انه ناخد اي orthonormal set in H و نثبت
+
+300
+00:21:37,220 --> 00:21:41,480
+انها accountable يعني بتاخد الان M اي orthonormal
+
+301
+00:21:41,480 --> 00:21:49,520
+set in H و اثبتلكم انه و لما يكون H separable
+
+302
+00:21:49,520 --> 00:21:55,250
+اثبتلكم من هذا مع بعض انه Mاللي هو إيه شمالها
+
+303
+00:21:55,250 --> 00:22:02,590
+countable تنشوف كده شوفوا اللي بدي أسوي بدي أخد
+
+304
+00:22:02,590 --> 00:22:07,390
+أخد H بـ separable space شو معناه separable؟ ركزوا
+
+305
+00:22:07,390 --> 00:22:12,810
+في اللي بحكي إنه اللاجي اللاجي اللي هو countable
+
+306
+00:22:12,810 --> 00:22:17,450
+dense من مين؟ من اللي هي الـH أنا بدي أخدوا لكم
+
+307
+00:22:17,450 --> 00:22:28,560
+الآن I Bdense set in mean in H ايه dense set in H؟
+
+308
+00:22:28,560 --> 00:22:34,360
+وبدى الآن افرضلكم ان Hم نفسها اشمالها م
+
+309
+00:22:34,360 --> 00:22:44,270
+uncountable واصل لك ان هذا هيقدىإن هذولا ولا واحدة
+
+310
+00:22:44,270 --> 00:22:47,230
+منهم هتكون countable يعني كلهم uncountable
+
+311
+00:22:47,230 --> 00:22:51,830
+للمؤهلات إنهم يدوء يكونوا يقوموا بدور إنه هنا
+
+312
+00:22:51,830 --> 00:22:55,130
+dense subset in H كلهم يكونوا uncountable وهذا
+
+313
+00:22:55,130 --> 00:22:59,210
+معناته بطل H separable إذن هي كما يكون التناقض إذن
+
+314
+00:22:59,210 --> 00:23:03,250
+هي هي السرتيجية الحل نيجي الآن نقول لت H بيه
+
+315
+00:23:03,250 --> 00:23:08,690
+separableand suppose that او let B be any dense
+
+316
+00:23:08,690 --> 00:23:14,550
+set in H وsuppose that M any orthonormal H set
+
+317
+00:23:14,550 --> 00:23:19,350
+ماشي الحال بعد شوية بثبتلكم انه لو كانت M الهي is
+
+318
+00:23:19,350 --> 00:23:23,430
+uncountable هيكون H اللي هو contradiction ومنه على
+
+319
+00:23:23,430 --> 00:23:26,670
+طول ال sentence uncountable since M is orthonormal
+
+320
+00:23:26,670 --> 00:23:31,610
+set شوفوا هذه الخاصية الحلوة فيهاأم orthonormal
+
+321
+00:23:31,610 --> 00:23:36,170
+إذا لأي x و y في الام و المسافة بين x لا تسوى y
+
+322
+00:23:36,170 --> 00:23:41,490
+احسبولي احسبولي المسافة او ال x لا تسوى y احسبولي
+
+323
+00:23:41,490 --> 00:23:45,730
+المسافة بين x minus y تربيع ايش بتساوي نحسبها
+
+324
+00:23:45,730 --> 00:23:48,610
+عبارة عن linear product بين x ناقص y و x ناقص y
+
+325
+00:23:48,610 --> 00:23:52,170
+وهذا عبارة عن اللي كلهم بيروحوا معاها ده بيظل x و
+
+326
+00:23:52,170 --> 00:23:55,710
+x و 100 و y و y لإن x و y و y و x كلهم إياش أسفار
+
+327
+00:23:55,710 --> 00:24:00,380
+لإنه orthonormalهذه نورمها واحد وهذه نورمها واحد
+
+328
+00:24:00,380 --> 00:24:02,860
+لأن هذه نورم تربيع واحد لها وهذه تربيع واحد لها
+
+329
+00:24:02,860 --> 00:24:06,380
+إذا إيش هيطلع عند المسافة بين أي نقطتين إذا في ال
+
+330
+00:24:06,380 --> 00:24:12,100
+M في داخل ال M المسافة بين كل نقطتين إيش بساوي هذا
+
+331
+00:24:12,100 --> 00:24:15,600
+بس يعني تجرب اللي هدا بساوي اللي هو مين عبارة عن
+
+332
+00:24:15,600 --> 00:24:18,700
+جدر التنين صح المسافة بين التنتين هدولة بين
+
+333
+00:24:18,700 --> 00:24:24,490
+النقطتين جدر التنينإذا بقدر .. بقدر أعمل حوالين
+
+334
+00:24:24,490 --> 00:24:28,590
+هذه neighborhood هذه ال X و هذه ال Y وهذا بعمل
+
+335
+00:24:28,590 --> 00:24:31,430
+حوالين neighborhood بحيث أنه يكون ال neighborhood
+
+336
+00:24:31,430 --> 00:24:36,810
+دين التقطح مش بساوي فيه ماشي بقدر .. خده مثلا ..
+
+337
+00:24:36,810 --> 00:24:39,970
+خده اللي هو ال .. ال .. ال .. ال .. ال radius تبع
+
+338
+00:24:39,970 --> 00:24:42,830
+هذا اللي هو عبارة عن جدر التنين على تلاتة عشان
+
+339
+00:24:42,830 --> 00:24:46,630
+أضمن كمان يبعدن عن بعض و هذا جدر التنين عالمين على
+
+340
+00:24:46,630 --> 00:24:53,430
+تلاتةالأنصار الآن كل نقطتين في داخل الـ M أنا بقدر
+
+341
+00:24:53,430 --> 00:24:57,750
+أبعدهن عن بعض بحيث أن هذا برضه النقطة اللي بعد هو
+
+342
+00:24:57,750 --> 00:25:00,850
+ده اللي بعد هو اللي بعد كلهين disjoint ماشي الحال
+
+343
+00:25:00,850 --> 00:25:04,810
+طيب هنا الخطورة أصلا شوفوا الآن هو ال superiority
+
+344
+00:25:04,810 --> 00:25:09,130
+شو معناته انه انه هذي اللي بتكون dense بتجيب ال
+
+345
+00:25:09,130 --> 00:25:12,250
+dense بتجيب كل space يعني ال double does لازم ايش
+
+346
+00:25:12,250 --> 00:25:16,770
+تكون item تاني تكون فيه تقاطع بين احتياط
+
+347
+00:25:20,340 --> 00:25:24,420
+Hence spherical neighbourhoods NX of X and NY of Y
+
+348
+00:25:24,420 --> 00:25:28,420
+of radii جدر التنين على تلاتة are disjoint Y قلت Y
+
+349
+00:25:28,420 --> 00:25:33,880
+لأن B is dense in H لكن بيه dense in H احنا بنقول
+
+350
+00:25:33,880 --> 00:25:38,780
+مادام بيه dense in H اذا أي X في ال M بقدر الاقي
+
+351
+00:25:38,780 --> 00:25:43,020
+neighbourhoodن X اللي هو بيكون .. بيكون أي
+
+352
+00:25:43,020 --> 00:25:46,900
+neighborhood ن X تقاطع ال B إيش ما له لا يساوي فاي
+
+353
+00:25:46,900 --> 00:25:50,500
+لإن اللي هي مالها B dense ماشي الآن، dense يعني
+
+354
+00:25:50,500 --> 00:25:54,420
+مهما زغرت ال neighborhood بدك تبعد عن B بتقدرش لإن
+
+355
+00:25:54,420 --> 00:25:57,400
+B هي ال .. ال .. ال .. الكلوة دي اللي لها بيساوي
+
+356
+00:25:57,400 --> 00:26:02,600
+كل space إذن لكل then for N X element of M ن X
+
+357
+00:26:02,600 --> 00:26:07,320
+تقاطع ال B لا يساوي إيش فايإذا كل واحدة من هذولة
+
+358
+00:26:07,320 --> 00:26:10,740
+من هذولة الان اكس و الان واي و الان زد و الان كل
+
+359
+00:26:10,740 --> 00:26:16,360
+هنا دولة كل واحدة بكون ان اكس تقاطع البي لايساو في
+
+360
+00:26:16,360 --> 00:26:20,500
+يعني بمعنى أخر في element هنا مصبوط ال element
+
+361
+00:26:20,500 --> 00:26:25,440
+الأول a في الان اكسالتاني في الـ NY فيه element
+
+362
+00:26:25,440 --> 00:26:29,420
+ومش هيكون الـ A ليش مش هيكون الـ A؟ لأن MX مع الـ
+
+363
+00:26:29,420 --> 00:26:33,520
+NY أشمعنى الـ Phi إذا هذه برضه فيها مين B وهذه
+
+364
+00:26:33,520 --> 00:26:38,200
+فيها C وهذه فيها D وهذه كذا لو كانت .. لو كانت الـ
+
+365
+00:26:38,200 --> 00:26:43,380
+N uncountable معناته أنه صار عندي uncountable
+
+366
+00:26:43,380 --> 00:26:48,260
+points هدولة موجودات كل من في مين في الـ Bإذا صارت
+
+367
+00:26:48,260 --> 00:26:51,200
+بيه إشمالها uncountable وهذا contradiction لأنه
+
+368
+00:26:51,200 --> 00:26:55,600
+كانت بيه arbitral dense set إذا اللي قلته اللي
+
+369
+00:26:55,600 --> 00:27:00,280
+قلته اللي هناك قلتهAnd since B is densely notched
+
+370
+00:27:00,280 --> 00:27:04,420
+in for any X element in M, NX تقاطع الـ B ليسوى
+
+371
+00:27:04,420 --> 00:27:09,160
+Phi Hence there is A element in NX تقاطع الـ B و B
+
+372
+00:27:09,160 --> 00:27:14,400
+في NAY تقاطع الـ B و الـ B لا تسوى A لأن الـ NX
+
+373
+00:27:14,400 --> 00:27:17,460
+نفسها و الـ NY تقاطعهم بسوى Phi في الشأنص المشتركة
+
+374
+00:27:17,460 --> 00:27:21,860
+بينهملأن لو فرضنا إن M is uncountable، then we
+
+375
+00:27:21,860 --> 00:27:26,940
+have uncountably many pairwise disjoint spherical
+
+376
+00:27:26,940 --> 00:27:31,900
+neighborhoods، فإن هدول النقسات So that B would
+
+377
+00:27:31,900 --> 00:27:35,060
+contains uncountable number of points، يعني B
+
+378
+00:27:35,060 --> 00:27:38,060
+would be uncountable since B was arbitrary dense
+
+379
+00:27:38,060 --> 00:27:41,800
+set، this makes that H would not contain a
+
+380
+00:27:41,800 --> 00:27:45,920
+countable dense setwhich contradicts the fact that
+
+381
+00:27:45,920 --> 00:27:49,200
+which is separable therefore انا لازم تكون ايه اش
+
+382
+00:27:49,200 --> 00:27:54,800
+مالها اللي هي countable واضح؟ ماشي الحال نيجي نشوف
+
+383
+00:27:54,800 --> 00:28:00,520
+اللي بعدها بيكون طوله روحكم برضه شوية نيجي لين؟
+
+384
+00:28:00,520 --> 00:28:05,120
+ارجعلنا للنص عشان نذكركم بإيش اللي بدنا نثبتهالان
+
+385
+00:28:05,120 --> 00:28:08,920
+النظرية بتقول إذا كانت H بتحتوي على orthonormal
+
+386
+00:28:08,920 --> 00:28:12,840
+sequence اه orthonormal sequence which is total
+
+387
+00:28:12,840 --> 00:28:17,320
+يعني بتحتوي على total orthonormal sequence لازم
+
+388
+00:28:17,320 --> 00:28:19,420
+الـHش تكون separable
+
+389
+00:28:21,650 --> 00:28:24,870
+Total orthonormal sequence معناته countable الست
+
+390
+00:28:24,870 --> 00:28:29,010
+هي ماشي لأن orthonormal sequence بنقصد فيها اللي
+
+391
+00:28:29,010 --> 00:28:33,070
+هو a1, a2, a3 أو x1, x2, x3 لما لا نهاية يعني
+
+392
+00:28:33,070 --> 00:28:37,790
+بمعنى آخر اللي هو countable set طيب اطلع للبرهاد
+
+393
+00:28:37,790 --> 00:28:43,240
+لنشوف بدنا نثبت أن H is separableطيب بدنا نجيلنا
+
+394
+00:28:43,240 --> 00:28:47,340
+بمعنى واخر بدنا نعملنا construction هو بده يعملنا
+
+395
+00:28:47,340 --> 00:28:54,100
+construction بده يعملنا construction لاللي هي set
+
+396
+00:28:54,100 --> 00:28:58,420
+تكون dense in H من ال orthonormal sequence اللي
+
+397
+00:28:58,420 --> 00:29:04,100
+عندها let em be a total orthonormal sequence in
+
+398
+00:29:04,100 --> 00:29:08,470
+mean in H قالي لها هي بين إيديناعند خد A إيش
+
+399
+00:29:08,470 --> 00:29:13,370
+بتساوي؟ بساوي عبارة عن كل ال formations Gamma K N
+
+400
+00:29:13,370 --> 00:29:19,250
+E K K من واحد لعندها ال E K هذولة اللي من هذه ماشي
+
+401
+00:29:19,250 --> 00:29:25,750
+الحال الآن ال ال coefficients هذولة بتدخلهم طبعا
+
+402
+00:29:25,750 --> 00:29:28,430
+أنا بحكي بس يشتغل في real أو complex خلينا ال
+
+403
+00:29:28,430 --> 00:29:30,810
+complex in general وفي حالة ال real بتسافروا ال
+
+404
+00:29:30,810 --> 00:29:34,850
+imaginary partالان Gamma K N هذا ال coefficients
+
+405
+00:29:34,850 --> 00:29:38,970
+اللي Gamma K N بتساوي اللي هو عبارة عن A K N زي I
+
+406
+00:29:38,970 --> 00:29:42,990
+B K N ماشي الحال هذولة اللي هو ال real
+
+407
+00:29:42,990 --> 00:29:45,650
+coefficients و ال imaginary coefficients بتاخدهم
+
+408
+00:29:45,650 --> 00:29:51,290
+من مين؟ من ال Q عشان أضمن انه تطلع اللي هو الصمم
+
+409
+00:29:51,290 --> 00:29:54,970
+هذه ال 6 is countableلأنه بيصير عندي هذا اللي هو
+
+410
+00:29:54,970 --> 00:29:58,770
+وكأنه اللي هي هدولة جايات هدولة نفسي جايات من Q
+
+411
+00:29:58,770 --> 00:30:01,590
+cross Q ماشي الحالة او ايزا ما اللي هو ال
+
+412
+00:30:01,590 --> 00:30:04,310
+cardinality اللي هنا هيكون اللي هو عبارة عن الف
+
+413
+00:30:04,310 --> 00:30:07,270
+note countable لأن countable cross countable is
+
+414
+00:30:07,270 --> 00:30:10,930
+countableوالـ finite union الـ finite اللي هو
+
+415
+00:30:10,930 --> 00:30:15,910
+summation هذا وكأني باخد ال union ل finite number
+
+416
+00:30:15,910 --> 00:30:20,770
+ال finite ال union ل countable sets برضه هيطلع إيش
+
+417
+00:30:20,770 --> 00:30:25,370
+ماله countable إذا بكل الأحوال A is countable طيب
+
+418
+00:30:25,370 --> 00:30:30,810
+كيف شكلوا ال summation هذا يعني مثلا لو ناخدناها
+
+419
+00:30:30,810 --> 00:30:34,030
+واحد بيصير الصمي اللي هو عبارة عن العنصر هذا Gamma
+
+420
+00:30:34,030 --> 00:30:39,960
+K واحد EKممكن أنصر تاني يقولك أنا بدي أبقيها من
+
+421
+00:30:39,960 --> 00:30:43,360
+واحد لعند مين لعند عشرة اللي هو ال submission a,k
+
+422
+00:30:43,360 --> 00:30:48,760
+,n,e,k عده من واحد لعشرة لعشرين للا تلاتي لكل ال
+
+423
+00:30:48,760 --> 00:30:50,880
+finite اللي في الدنيا جات ما بدك اللي هي الأن
+
+424
+00:30:50,880 --> 00:30:54,560
+تاخدها واحد اتنين تلاتة إذا شكل العناصر هذا أنا
+
+425
+00:30:54,560 --> 00:30:58,020
+عارف كيف شكله اللي هي ال coefficients هدولة من مين
+
+426
+00:30:58,020 --> 00:31:01,920
+من ال complex numbers لكن ال coefficients تبعات
+
+427
+00:31:01,920 --> 00:31:04,740
+اللي هي ال real part و ال imaginary part عبارة عن
+
+428
+00:31:04,740 --> 00:31:09,080
+أعداد نسبية rational numbersطيب عشان نضمن اللي هو
+
+429
+00:31:09,080 --> 00:31:13,360
+تكون countable الان BKM بتساوي سفر لما ال H تكون
+
+430
+00:31:13,360 --> 00:31:16,940
+أيش ما لها real Hilbert space هنا خلينا نشتغل عن
+
+431
+00:31:16,940 --> 00:31:20,760
+ال general و بيكون ده كحالة خاصة منه زي ما قولت A
+
+432
+00:31:20,760 --> 00:31:24,900
+is countable هو قولناها هو ايش الان we show that
+
+433
+00:31:24,900 --> 00:31:28,380
+هذه المؤهلة اننا اثبتناها انها dense in H اذا
+
+434
+00:31:28,380 --> 00:31:30,980
+اثبتناها dense in H بيكون خلصناها بتكون H أيش ما
+
+435
+00:31:30,980 --> 00:31:35,900
+لها inseparable اطلع تشوف كإعلانكيف بدي اثبت انه
+
+436
+00:31:35,900 --> 00:31:40,240
+dense؟ بدي اخد الـ NX and fixed element in mean in
+
+437
+00:31:40,240 --> 00:31:45,380
+H ماشي الحال هو ألاجيه لك ان NX تقاطع اللي هو الـ
+
+438
+00:31:45,380 --> 00:31:49,020
+set هذه لا يساوي 5 بقول خلصها بس ماتناهيش انها
+
+439
+00:31:49,020 --> 00:31:52,320
+dense عشان اثبت انها dense انه لو أخدنا أي element
+
+440
+00:31:52,320 --> 00:31:55,700
+هنا بقدر ألاجي اللي هو بيكون عندى أي neighborhood
+
+441
+00:31:55,700 --> 00:31:57,920
+حوالينها ذاك و بطلع هذاك اللي بتشوفه ان شاء الله
+
+442
+00:31:57,920 --> 00:32:03,320
+let X be and fixed element in mean in Hالآن since
+
+443
+00:32:03,320 --> 00:32:07,660
+EM is a total or from a total set in H إذا
+
+444
+00:32:07,660 --> 00:32:11,640
+الإسبانيك لو جعل ال EM إيش حيساوي؟ من التعريف طيب
+
+445
+00:32:11,640 --> 00:32:15,720
+إذا for every إبسلون أكبر من سفر مهما كانت إبسلون
+
+446
+00:32:15,720 --> 00:32:19,020
+صغيرة هذه اللي بتبتعبر عن ال arbitrary
+
+447
+00:32:19,020 --> 00:32:24,340
+neighborhoodالان there is w element ل span em such
+
+448
+00:32:24,340 --> 00:32:28,700
+that المسافة بين x نقص w أصغر من أي أسغر من أي
+
+449
+00:32:28,700 --> 00:32:31,980
+epsilon في الدنيا أنا بتسميه y على 2 للحسابات ماشي
+
+450
+00:32:31,980 --> 00:32:37,340
+الحال إذا الأن لإن span لل em dense in H إذا لأي x
+
+451
+00:32:37,340 --> 00:32:41,260
+في ال H بقدر ألاقي اللي هو element في اللي جوا هذا
+
+452
+00:32:41,260 --> 00:32:46,240
+بحيث المسافة بين x و w أصغر من أي epsilon في
+
+453
+00:32:46,240 --> 00:32:50,710
+الدنياماشي الحال أو تعبير اللي هو ان نكس و Y على
+
+454
+00:32:50,710 --> 00:32:54,750
+اتنين اللي هو تقاطع اللي هو ال H اللي نسباننا
+
+455
+00:32:54,750 --> 00:32:59,110
+اليوم ليه ال W هذه ماشي ان شاء الله نجمعين معايا
+
+456
+00:32:59,110 --> 00:33:01,230
+طيب الان
+
+457
+00:33:03,350 --> 00:33:11,450
+Hence وين موجودة؟ و موجودة في الـ YN و ما هي وين
+
+458
+00:33:11,450 --> 00:33:14,350
+موجودة في الإسماعيل للـ EM؟ مادام هي في الإسماعيل
+
+459
+00:33:14,350 --> 00:33:17,710
+للـ EM يعني و عبارة عن اللي هو الـ Finite Linear
+
+460
+00:33:17,710 --> 00:33:21,120
+combination من مين؟ من عناصر من الـ EMنفترض إنه
+
+461
+00:33:21,120 --> 00:33:25,060
+finite combination من E1 وE2 وE3 وE4 لعندي يعني مش
+
+462
+00:33:25,060 --> 00:33:28,560
+عاجبكم EI واحد EI اتنين لعندي EIN على الأساس ما
+
+463
+00:33:28,560 --> 00:33:31,560
+تقولوش أول أول تلاتة من هدول أو أول خمسة من هدول
+
+464
+00:33:31,560 --> 00:33:35,560
+مش مشكلة فاهمين إنهم تكون finite اللي هو summation
+
+465
+00:33:35,560 --> 00:33:39,680
+أو finite combination من مين من عناصر اللي هي
+
+466
+00:33:39,680 --> 00:33:44,960
+موجودة في مين في الإيام طيبأسميتها هذه الـ span
+
+467
+00:33:44,960 --> 00:33:48,580
+للـ E1 و E2 اللي عندي لأن إيش سميتها وي أنت ماشي
+
+468
+00:33:48,580 --> 00:33:52,980
+الحال إذا صارت الـ W هذه اللي لجيتها للمسافة بينها
+
+469
+00:33:52,980 --> 00:33:56,560
+وبين ال X اللي بتحكي عليها أصغر من X أسلوب على 2
+
+470
+00:33:56,560 --> 00:34:00,870
+سميتها W في ال span اللي عندي for someoneby لمّة
+
+471
+00:34:00,870 --> 00:34:04,670
+قبل بشوية تلاتة و تلاتة اتنين there is y element
+
+472
+00:34:04,670 --> 00:34:07,050
+اللي هي أخدناها قبل هيك there is y element in yn
+
+473
+00:34:07,050 --> 00:34:11,510
+such that x minus y element عمودي عالميين على ال
+
+474
+00:34:11,510 --> 00:34:15,050
+yn ايش هتستنى عشان ماتطلعوش عنها ايش اللمّة هذه
+
+475
+00:34:15,050 --> 00:34:19,890
+احنا المرة اللي فاتت لما نأجينا خدنا x في ال space
+
+476
+00:34:20,550 --> 00:34:25,050
+X في الـ Space جينا و رسمتلكم عدة رسمات إذا
+
+477
+00:34:25,050 --> 00:34:29,870
+بتتذكروا اللي هو هاي الرسم هادي و قولنا إن هذا الـ
+
+478
+00:34:29,870 --> 00:34:33,430
+Space H أو هذا الـ Space H و هاي الـ X هنا و هاي
+
+479
+00:34:33,430 --> 00:34:38,370
+الـ X هنا ماشي الحال قولنا أنه عرفنا إن الـ Delta
+
+480
+00:34:38,370 --> 00:34:44,530
+هي عبارة عن المسافة بين النقطة X و بين الـ Space
+
+481
+00:34:44,530 --> 00:34:49,420
+الـ M هذه سميناها M هذه بين الـ X و مين و Mفي
+
+482
+00:34:49,420 --> 00:34:54,280
+نظرية قلنا إذا كانت M subspace بنضمن اللي نجيلكم
+
+483
+00:34:54,280 --> 00:34:58,760
+واحدة وحيدة ان there exist unique Y such that
+
+484
+00:34:58,760 --> 00:35:04,680
+normal X minus Y هو اللي بيمثل مين ال Deltaوفي
+
+485
+00:35:04,680 --> 00:35:10,280
+النظرية اللي بعدها اللي هي 3 3 2 قلنا إنه لو كانت
+
+486
+00:35:10,280 --> 00:35:15,460
+هذه complete هيكون عندي ال Y الوحيدة هذه اللي هي
+
+487
+00:35:15,460 --> 00:35:19,240
+هتنزل هذه العمود هذي بيصير X هي عندي ال X وهي ال Y
+
+488
+00:35:19,240 --> 00:35:24,060
+اللي وجناها هذه المسافة هتنزل عمودي على مين؟ على
+
+489
+00:35:24,060 --> 00:35:29,520
+هذا، هيكون ال X minus Y Orthogonal على مين؟ على
+
+490
+00:35:29,520 --> 00:35:34,430
+العين، ماشي الحال، إذن الآن بهذه النظريةبهذه
+
+491
+00:35:34,430 --> 00:35:37,870
+النظرية بقدر هذا هذا هذا ال subspace اللي عندي
+
+492
+00:35:37,870 --> 00:35:41,750
+اللي عليه بده اطبق فبصير عندي الآن بقدر الاقي y في
+
+493
+00:35:41,750 --> 00:35:45,750
+داخله وكأنه هذا ال subspace يا جماعة اه هذا ال
+
+494
+00:35:45,750 --> 00:35:50,590
+subspace بقدر الاقي في داخله y بحيث انه norm x
+
+495
+00:35:50,590 --> 00:35:54,530
+minus y هو اللي يمثل delta ويكون x minus y نفسه
+
+496
+00:35:54,530 --> 00:36:00,830
+عمود عالمين على ال M طيب اذاالان there exists y
+
+497
+00:36:00,830 --> 00:36:04,990
+element in y-end such that x minus y عمودي على ال
+
+498
+00:36:04,990 --> 00:36:08,450
+y-end ما هو احنا في الطبيعي بنقول اقرب واحد على
+
+499
+00:36:08,450 --> 00:36:12,610
+الست اللي هو القمود عليه اه اه طيب الان صار عندي
+
+500
+00:36:12,610 --> 00:36:15,650
+ايه هدف الهندسة الطبيعية اللي في ال space اللي
+
+501
+00:36:15,650 --> 00:36:18,110
+منيح اللي .. اللي .. اللي .. اللي منيحه و مش فيه
+
+502
+00:36:18,110 --> 00:36:23,300
+مشاكل اللي هو بيقول complete subspaceThere is y
+
+503
+00:36:23,300 --> 00:36:26,040
+element in yn such that x minus y عمودي عالمين على
+
+504
+00:36:26,040 --> 00:36:30,380
+yn و ال norm ل ال x minus y هو ال infimum هو ال
+
+505
+00:36:30,380 --> 00:36:34,020
+delta مدام هو ال delta إذا حيكون أصغر أو يساوي ال
+
+506
+00:36:34,020 --> 00:36:37,760
+norm ل ال x ناقص أي element في الدنيا تاني في ال
+
+507
+00:36:37,760 --> 00:36:39,660
+.. في ال .. في ال .. في ال .. في ال .. في ال M
+
+508
+00:36:39,660 --> 00:36:44,020
+اللي عندى اللي بشغل عليها أو ال H من ضمن اليومين
+
+509
+00:36:44,020 --> 00:36:49,260
+ال W لجناهاإذا صار عند نورنا الـ X-Y أصغر من مين؟
+
+510
+00:36:49,260 --> 00:36:53,560
+من Y على 2 لأن X-W من فوق يشملها أصغر من Y على 2
+
+511
+00:36:54,350 --> 00:37:01,170
+الان by a و b in theorem 3-4 y can be written as
+
+512
+00:37:01,170 --> 00:37:06,150
+اللي هي أخدناها قبل هيك انه y اللي عندها دي بنقدر
+
+513
+00:37:06,150 --> 00:37:08,810
+نكتبها على صورة summation ال for real coefficient
+
+514
+00:37:08,810 --> 00:37:12,090
+بتاعتها summation x و ek , ek كامل عند واحد لمين
+
+515
+00:37:12,090 --> 00:37:17,030
+لعند n اللي هي موجودة في مين y في الاسم علي طيب
+
+516
+00:37:17,780 --> 00:37:22,400
+الان اذا احسبولي اطلع لفوق احسبلي الان normal X
+
+517
+00:37:22,400 --> 00:37:27,000
+نقص ال summation هذا اللي هو ال Y حسبنا اصغر من
+
+518
+00:37:27,000 --> 00:37:31,300
+مين من نفسنا على اتنين الان ال Q نفسها الان هل جيه
+
+519
+00:37:31,300 --> 00:37:33,980
+تبدأ تيجي اللي هو استخدام اللي هو التركيب الأصلي
+
+520
+00:37:33,980 --> 00:37:39,700
+لل A since Q is dense in R then for any X و E K
+
+521
+00:37:39,700 --> 00:37:43,900
+هذا اللي هو عبارة عن complex numberهذا في ال .. في
+
+522
+00:37:43,900 --> 00:37:48,120
+ال complex number ماشي الحال أي x .. ال .. ال ..
+
+523
+00:37:48,120 --> 00:37:50,060
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+524
+00:37:50,060 --> 00:37:50,220
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+525
+00:37:50,220 --> 00:37:50,300
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+526
+00:37:50,300 --> 00:37:50,740
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+527
+00:37:50,740 --> 00:37:51,420
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+528
+00:37:51,420 --> 00:37:51,840
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+529
+00:37:51,840 --> 00:37:52,420
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+530
+00:37:52,420 --> 00:37:52,960
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+531
+00:37:52,960 --> 00:37:54,600
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+532
+00:37:54,600 --> 00:37:54,660
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+533
+00:37:54,660 --> 00:37:54,920
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+534
+00:37:54,920 --> 00:37:57,140
+..ال ..ال ..ال ..ال ..ال ..ال ..ال ..ال
+
+535
+00:38:02,140 --> 00:38:06,680
+ننتقل من R كيو دينس في R إذا كيو كروس كيو دينس في
+
+536
+00:38:06,680 --> 00:38:09,620
+مين في C اللي هو اللي حكينا عنه لأنه كامتر
+
+537
+00:38:09,620 --> 00:38:13,400
+بالتقرير سنس كيو سنس في R هي المفتاح then for any
+
+538
+00:38:13,400 --> 00:38:18,700
+X و EK there is Gamma KN AKN زاد IBKN such that
+
+539
+00:38:18,700 --> 00:38:24,000
+AKN و BKN element لكيو such that اللي هو المسافة
+
+540
+00:38:24,000 --> 00:38:28,050
+بين اللي هو ال summation لل X و EKلحالة هذه
+
+541
+00:38:28,050 --> 00:38:31,570
+المسافة بين الـ X و الـ E K و العدد اللي هنا أصغر
+
+542
+00:38:31,570 --> 00:38:36,030
+ما يكون لأن مجموحا هذا برضه ما هو Complex هيطلع أو
+
+543
+00:38:36,030 --> 00:38:39,170
+هيطلع اللي هو .. خلّيني .. نقدر نطبق عليه اللي
+
+544
+00:38:39,170 --> 00:38:42,950
+بنطبقه على هذا لأن أنا بتدث .. بتدث بتتثار ال ..
+
+545
+00:38:42,950 --> 00:38:47,250
+ال summation لل X و ال E K over ال K اللي بحكي
+
+546
+00:38:47,250 --> 00:38:52,980
+عنها من 1 لـ N في الآخر هذا الآن ال summationفي
+
+547
+00:38:52,980 --> 00:38:57,440
+الآخر اللي هو بقدر اتعامل معاه بدل ما هي ال X E K
+
+548
+00:38:57,440 --> 00:39:04,320
+لحالها عندى بما انه Q dense in Rوطبيعي اللي هو أنا
+
+549
+00:39:04,320 --> 00:39:07,080
+أخدت ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+550
+00:39:07,080 --> 00:39:07,220
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+551
+00:39:07,220 --> 00:39:07,360
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+552
+00:39:07,360 --> 00:39:07,440
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+553
+00:39:07,440 --> 00:39:08,680
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+554
+00:39:08,680 --> 00:39:09,120
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+555
+00:39:09,120 --> 00:39:09,480
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+556
+00:39:09,480 --> 00:39:09,560
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+557
+00:39:09,560 --> 00:39:11,420
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+558
+00:39:11,420 --> 00:39:19,220
+ال .. ال .. ال .. ال ..
+
+559
+00:39:19,220 --> 00:39:19,560
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+560
+00:39:19,560 --> 00:39:22,680
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+561
+00:39:22,680 --> 00:39:25,880
+ال
+
+562
+00:39:27,860 --> 00:39:30,780
+ما دامت اللي هي Q dense إذا بقدر أجلاج ال
+
+563
+00:39:30,780 --> 00:39:37,540
+coefficients من اللي هي ال .. ال Q العصورة AKN
+
+564
+00:39:37,540 --> 00:39:44,360
+زائد IBKN اللي سنتها Gamma KN بحيث أنه المسافة بين
+
+565
+00:39:44,360 --> 00:39:50,360
+هذه و بين اللي هي ال elements اللي عندي Gamma KEK
+
+566
+00:39:50,360 --> 00:39:55,240
+يكون ايش ماله اصغر ما يمكن و ليكن اصغر من مين من
+
+567
+00:39:55,240 --> 00:40:01,300
+ابسلون على اتنين اذا الان من
+
+568
+00:40:01,300 --> 00:40:07,530
+كل اللي فات بقدر الخص ما يليإنه لجهة الـ V اللي هي
+
+569
+00:40:07,530 --> 00:40:11,170
+عبارة عن X و EK في EK الـ summation اللي لها V
+
+570
+00:40:11,170 --> 00:40:16,690
+بيساوي ال summation لـ Gamma KN و EK SF Element NA
+
+571
+00:40:16,690 --> 00:40:23,890
+بحيث أن المسافة بين X و V X و V اللي هو بيساوي X
+
+572
+00:40:23,890 --> 00:40:27,810
+خلوها زي ما هي ناقص اللي هي ال summation هذا أصغر
+
+573
+00:40:27,810 --> 00:40:31,590
+أو يساوي بدأت
+
+574
+00:40:31,590 --> 00:40:36,030
+بـ X arbitraryولاجئت اللي هو element v element a
+
+575
+00:40:36,030 --> 00:40:41,770
+بحيث المسافة بين x minus v يساوي .. انشوف x ناقص
+
+576
+00:40:41,770 --> 00:40:45,750
+هذا العوضت بال triangling quality بدي اضيف term
+
+577
+00:40:45,750 --> 00:40:49,450
+واطح term اصغر او ساوي x ناقص اللي هو المفتاح هذا
+
+578
+00:40:49,450 --> 00:40:58,190
+اللي حصلته هنا x ek و ekزائد اللي هو نفسه هذا ناقص
+
+579
+00:40:58,190 --> 00:41:02,970
+ال V اللي هي ال submission هذا أثبتناها سابقا أصغر
+
+580
+00:41:02,970 --> 00:41:06,030
+من يبسلون على اتنين وهذا أثبتناها سابقا أصغر من
+
+581
+00:41:06,030 --> 00:41:09,070
+يبسلون على اتنين من الجهتين صار عند ال X minus V
+
+582
+00:41:09,070 --> 00:41:13,230
+أصغر من مين من يبسلون أيش اللي عملته أخدت X
+
+583
+00:41:13,230 --> 00:41:18,780
+arbitraryو لجيت اللي هو V في الـA بحيث انه المسافة
+
+584
+00:41:18,780 --> 00:41:23,260
+بين الـX والـV اللي لجيتها أقل ما يمكن يعني بمعنى
+
+585
+00:41:23,260 --> 00:41:29,020
+آخر انه for every اللي هو ball أو every
+
+586
+00:41:29,020 --> 00:41:34,030
+neighborhood بيكس وإبسلونتقاطع اللي إيه إيه إيه
+
+587
+00:41:34,030 --> 00:41:35,490
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+588
+00:41:35,490 --> 00:41:39,370
+إيه
+
+589
+00:41:39,370 --> 00:41:48,170
+إيه
+
+590
+00:41:48,690 --> 00:41:53,350
+الان ال V هذه موجودة هان أثبتت هيها من خلال هذه و
+
+591
+00:41:53,350 --> 00:41:56,570
+في نفس الوجهة ال V و الموجودة في ال A يعني ال ball
+
+592
+00:41:56,570 --> 00:42:01,490
+تقاطع ال A ليس هو Phi و هذا يعني أن ال A صارت
+
+593
+00:42:01,490 --> 00:42:05,170
+dense في mean في ال space الأصل اللي أخدت X فيه
+
+594
+00:42:05,170 --> 00:42:09,670
+arbitrary و معناته صارت اللي هي H is separable يلا
+
+595
+00:42:09,670 --> 00:42:15,000
+اللي بعده اللي بعده يا باباالنظرية الأخيرة في هذا
+
+596
+00:42:15,000 --> 00:42:18,460
+الـ section Theorem two Hilbert spaces H and H
+
+597
+00:42:18,460 --> 00:42:22,700
+tilde both real or both complex are isomorphic if
+
+598
+00:42:22,700 --> 00:42:25,100
+and only if they have the same Hilbert dimension
+
+599
+00:42:25,100 --> 00:42:32,480
+يعني و كأنه بيقولنا من تحت بطن أنه يا جماعة كل ال
+
+600
+00:42:32,480 --> 00:42:35,940
+Hilbert spaces اللي ال dimension إليهم زي بعض
+
+601
+00:42:35,940 --> 00:42:39,260
+هدولة isomorphic يعني واحدة كلها تجدوش و تقولي
+
+602
+00:42:39,260 --> 00:42:45,350
+انها واحدة كلها واحدة ماشي بناء عليهأحنا اللي بدنا
+
+603
+00:42:45,350 --> 00:42:52,170
+نثبته انه ناخد اي two Hilbert spaces قدش قدش تل ده
+
+604
+00:42:52,170 --> 00:42:57,070
+او او اذا أثبتنا انه isomorphic معناته اي شمالها
+
+605
+00:42:57,070 --> 00:43:00,430
+اللي هو الهن the same Hilbert dimension اذا الهن
+
+606
+00:43:00,430 --> 00:43:02,750
+the same Hilbert dimension معناته اي شمالهن
+
+607
+00:43:02,750 --> 00:43:07,800
+isomorphicالان نجي للاتجاه الاول suppose that او
+
+608
+00:43:07,800 --> 00:43:10,660
+isomorphism بين هنا عارفين واش معناه isomorphism
+
+609
+00:43:10,660 --> 00:43:14,260
+بينهم بنحكيها الان الان suppose that H is
+
+610
+00:43:14,260 --> 00:43:17,080
+isomorphic with H تلده مابديش ادخل في التفاصيل
+
+611
+00:43:17,080 --> 00:43:20,360
+تفاصيل الحسابات هتكون لكم suppose that H is
+
+612
+00:43:20,360 --> 00:43:24,110
+isomorphic لمن لH تلدهيعني في isomorphism بين
+
+613
+00:43:24,110 --> 00:43:28,390
+التنتين then there is a bijective linear mapping T
+
+614
+00:43:28,390 --> 00:43:33,350
+من H لH تل ده that satisfies T X و T Y بيساوي X و
+
+615
+00:43:33,350 --> 00:43:37,830
+Y يعني اللي هي preserve the inner product زي ما
+
+616
+00:43:37,830 --> 00:43:40,150
+قلنا شو معناته ال geomorphic preserve inner
+
+617
+00:43:40,150 --> 00:43:43,690
+product preserve اللي هو العمليات اللي هو preserve
+
+618
+00:43:43,690 --> 00:43:46,550
+cardinality اللي هي one to one او انتوا هي التلات
+
+619
+00:43:46,550 --> 00:43:54,920
+شغلاتالأن صار عندى اطلع لفوق اللى فوق الان ال ال
+
+620
+00:43:54,920 --> 00:43:58,540
+orthonormal hence orthonormal elements in H have
+
+621
+00:43:58,540 --> 00:44:02,120
+orthonormal images under mean under T أكيد لإنه
+
+622
+00:44:02,120 --> 00:44:05,380
+اللى بيحصل ال ال inner product بين X و X بيساوي X
+
+623
+00:44:05,380 --> 00:44:08,500
+و Y بيساوي T X و T Y لو كان ال inner product بين
+
+624
+00:44:08,500 --> 00:44:11,200
+هدولة سفر هكون بين سفر لو كان واحد بيكون واحد اذا
+
+625
+00:44:11,200 --> 00:44:15,040
+أكيد اللى بيكون اللى هو ال orthonormal هان image
+
+626
+00:44:15,040 --> 00:44:19,870
+ها هيكون إيه شماله orthonormal طيبالآن however T
+
+627
+00:44:19,870 --> 00:44:23,850
+is bijective إذا T تنقل every total orthonormal
+
+628
+00:44:23,850 --> 00:44:28,650
+set in إيش onto a total orthonormal set in مين in
+
+629
+00:44:28,650 --> 00:44:34,090
+H تلده ماشي و تفصيله لكم لإنه بيصير ال span هنا ال
+
+630
+00:44:34,090 --> 00:44:40,610
+span لل M الأولى ال closure بيساوي ال H الان T لل
+
+631
+00:44:40,610 --> 00:44:43,750
+span لل M ال closure للثاني هتصير إيش ما لها ال H
+
+632
+00:44:43,750 --> 00:44:48,460
+تلدهطيب، therefore H and H tilde have the same إيش
+
+633
+00:44:48,460 --> 00:44:52,100
+مالين هل بار دايمينشين لإنه صارت اللي هي نفس
+
+634
+00:44:52,100 --> 00:44:56,920
+العدد، طيب، الان conversely suppose that، في تفصيل
+
+635
+00:44:56,920 --> 00:45:00,080
+الكلام، بس تفصيله مش صعب، suppose that, conversely
+
+636
+00:45:00,080 --> 00:45:02,700
+suppose that H and H tilde have the same hell bar
+
+637
+00:45:02,700 --> 00:45:06,280
+dimension، برضه بتلاقي isomorphism بينهم اللي هو
+
+638
+00:45:06,280 --> 00:45:08,620
+one to one و one to one و كده و كده، تفاصيله برضه
+
+639
+00:45:08,620 --> 00:45:15,770
+اللي هو صارت معهودة يعني،الان في حالة H تسوى 0 و H
+
+640
+00:45:15,770 --> 00:45:19,290
+تلدة تسوى 0 هي تريفيال لأنه مادام تنتين الهن في
+
+641
+00:45:19,290 --> 00:45:21,830
+نفس القرص اللي لديه واحد سفر تان هيتلاعياش سفر
+
+642
+00:45:21,830 --> 00:45:24,810
+معناته ال function بينهن سهل انك ترتاب ال function
+
+643
+00:45:24,810 --> 00:45:28,690
+بينهن تكون one to one و one to كل شيء الان اذا let
+
+644
+00:45:28,690 --> 00:45:33,110
+H لا تسوى مين لا تسوى سفر automatic ال H تلدة
+
+645
+00:45:33,110 --> 00:45:36,050
+هتكون اي شمالها برضه مش سفر لأن احنا قلنا ان
+
+646
+00:45:36,050 --> 00:45:40,630
+الـCMDL برضه مينشينand any total orthonormal set M
+
+647
+00:45:40,630 --> 00:45:44,350
+in H و M tilde in H اله in the same cardinality هه
+
+648
+00:45:44,350 --> 00:45:47,070
+ايش معناته انه in the same dimension ان ال total
+
+649
+00:45:47,070 --> 00:45:50,410
+orthonormal set هنا ال cardinality لها هي نفس ال
+
+650
+00:45:50,410 --> 00:45:56,970
+cardinality في من؟ في التانية معاياطيب الان so we
+
+651
+00:45:56,970 --> 00:46:00,250
+can index them by the same index set يعني احنا
+
+652
+00:46:00,250 --> 00:46:03,330
+بنقدر نرمزلهم بنفس ال index set لو هذولة كان
+
+653
+00:46:03,330 --> 00:46:05,890
+countable هذولة countable لو هذولة uncountable
+
+654
+00:46:05,890 --> 00:46:09,090
+uncountable لو عددهم ألف note ألف note لو عددهم
+
+655
+00:46:09,090 --> 00:46:13,050
+اللي هو زي عدد ال power of R عددهم زي عدد ال power
+
+656
+00:46:13,050 --> 00:46:15,610
+of R لو عددهم زي ال R بيكون عددهم زي ال R عارفين
+
+657
+00:46:15,610 --> 00:46:19,310
+ايش عدد ال R؟ cardinal of ال R هو C اللي هو ال
+
+658
+00:46:19,310 --> 00:46:23,750
+power of R بيصير 2 to the C و هكذا عارفين ما هذا
+
+659
+00:46:23,750 --> 00:46:28,400
+الكلام؟إذا نسينا تذكروا it so we can index them by
+
+660
+00:46:28,400 --> 00:46:32,860
+the same index set اللي هي K and write M بتساوي EK
+
+661
+00:46:32,860 --> 00:46:38,960
+and M تلده بتساوي EK شمالها تلده لإن هم نفس ال ..
+
+662
+00:46:38,960 --> 00:46:42,200
+ال .. ال .. البرده دايما شده now define بقولك اللي
+
+663
+00:46:42,200 --> 00:46:45,660
+هنعرف اللي هو T من H للH تلده بناء على ال teamتين
+
+664
+00:46:45,660 --> 00:46:51,270
+هذوله بدنا نعرفTX X من وين جاية من H بتساوي اللي
+
+665
+00:46:51,270 --> 00:46:56,190
+هو الـ X إيش أصلا هي summation X و EK في EK ماشي
+
+666
+00:46:56,190 --> 00:46:59,890
+هذا جلطنات زي ما أقولنا عبّر عنها على طول زي هي
+
+667
+00:46:59,890 --> 00:47:05,290
+لأن TX بده عبّر عن X و EK في مين في EK إيش مالها
+
+668
+00:47:05,290 --> 00:47:09,190
+تلدة تبعت اللي هي ال M تلدة this is well defined
+
+669
+00:47:09,190 --> 00:47:13,350
+because لكل X element in H we have ال X بتساوي ال
+
+670
+00:47:13,350 --> 00:47:17,370
+summation هذا زي ما قلناالان عندي by Bezel's
+
+671
+00:47:17,370 --> 00:47:20,970
+Inquality ال summation هذا هيكون يشمل و converge
+
+672
+00:47:20,970 --> 00:47:24,270
+ماشي الحال اذا اكيد اللي هداك له قيمة then by
+
+673
+00:47:24,270 --> 00:47:27,810
+theorem تلتة خمسة اتنين ال X و ال EK و EK تلتة
+
+674
+00:47:27,810 --> 00:47:31,990
+over K مدام هداك converge هيكون converge so that
+
+675
+00:47:31,990 --> 00:47:35,530
+ال TX و الموجودة في ال H تلتة يعني well defined
+
+676
+00:47:35,530 --> 00:47:41,550
+اللي الها قيمة الانلت X بتساوي كده و Y بتساوي كده
+
+677
+00:47:41,550 --> 00:47:44,870
+بيدثبتوا انه Linear وهذه شغل الحسابات اللي هي
+
+678
+00:47:44,870 --> 00:47:51,730
+الحسابات سهلة أخدت X اللي هي بشكل هذا و Y بشكل هذا
+
+679
+00:47:51,730 --> 00:47:56,990
+عارفين هذا الكلام سنة بي any element سيناتش والألف
+
+680
+00:47:56,990 --> 00:48:00,580
+عن ال scalar وحسبلي T Alpha X زائد Yحسب اللي ..
+
+681
+00:48:00,580 --> 00:48:02,900
+اللي .. اللي حكينا عنه قبل شوية بيصير الـ
+
+682
+00:48:02,900 --> 00:48:07,040
+summation اللي هو Alpha X زائد Y E K مع مين؟ مع E
+
+683
+00:48:07,040 --> 00:48:12,200
+K تلدة هيت القانون Y ساوي Alpha الآن بطالة الأن دي
+
+684
+00:48:12,200 --> 00:48:17,370
+اللي جوا هذه اللي هي بيصير X وE K وE K تلدةبقى الـ
+
+685
+00:48:17,370 --> 00:48:22,350
+inner product بفصلهم عادي و ال YK و ال A أشماله و
+
+686
+00:48:22,350 --> 00:48:26,370
+EK تلده هذه إيه اللي هي عبارة عن TX و هذه أشمالها
+
+687
+00:48:26,370 --> 00:48:30,230
+TY فبصينا عند Alpha TX زي TY hence T is linear
+
+688
+00:48:30,230 --> 00:48:36,250
+اطلع على السوق الآن since EK تلده
+
+689
+00:48:36,250 --> 00:48:41,990
+is orthonormal then اللي هو احسب ليه ال TX و TX
+
+690
+00:48:42,830 --> 00:48:46,090
+بنسخد منها Orthonormal الـ TX والـ TX الـ TX إيش
+
+691
+00:48:46,090 --> 00:48:50,390
+أعرفناها summation X و EK و EK تلدة كله هتلاقو
+
+692
+00:48:50,390 --> 00:48:54,710
+شغلات سهلة و بتنحسن و ال X و EK و EK تلدة over K
+
+693
+00:48:54,710 --> 00:48:58,030
+طلعوهم برا ال summation زي ما بنعمل دايما اللي
+
+694
+00:48:58,030 --> 00:49:00,990
+بعيد اللي هو بتلعب conjugate و الجريب بتلعب عادي
+
+695
+00:49:00,990 --> 00:49:05,110
+ماشي اللي عملناها عشرين مرة هذه بيساوي X و EK و X
+
+696
+00:49:05,110 --> 00:49:10,640
+و EM تلدة و EK و EK تلدةكل هيتسفر هيبقى البث مين
+
+697
+00:49:10,640 --> 00:49:13,880
+اللي هو summation واحدة عند K بيساوي M وهيكون اللي
+
+698
+00:49:13,880 --> 00:49:16,580
+هو هذا بيساوي واحد والتنتين هذا هو ال conjugate
+
+699
+00:49:16,580 --> 00:49:20,000
+تبعه اللي هو بيطلع هذا المضولة السربيع وهذا ايش
+
+700
+00:49:20,000 --> 00:49:25,440
+بيساوي normal X سربيع اتوح منها لسه اذا صار عندى
+
+701
+00:49:25,440 --> 00:49:29,700
+الان اللي ايش اللي سويته انا اللي اثبته انا بدي
+
+702
+00:49:29,700 --> 00:49:34,570
+اثبت ايش بدي اثبت انه preserve inner productإيش
+
+703
+00:49:34,570 --> 00:49:40,650
+يعني .. يعني X TX و TY بساوة X و Y أنا إيش اللي
+
+704
+00:49:40,650 --> 00:49:44,350
+أثبتته قبل .. الآن اللي أثبتته في الحسابات اللي
+
+705
+00:49:44,350 --> 00:49:53,450
+قبل بشوية أثبتت أنه اللي هو ال X و ال Xبساوة Tx
+
+706
+00:49:53,450 --> 00:49:59,830
+وTx بدأ نتقل من هذه لل general عشان نقول preserve
+
+707
+00:49:59,830 --> 00:50:04,790
+inner product طيب عشان تكون اللي هو خلصنا الجزء
+
+708
+00:50:04,790 --> 00:50:08,050
+اللي .. اللي .. اللي خلنا نقول الأهم الان for any
+
+709
+00:50:08,050 --> 00:50:12,030
+x و h element .. x و y element in H بدأ نشتغل على
+
+710
+00:50:12,030 --> 00:50:16,190
+الريال و ال .. و ال complex بنفس الأسلوب كان اللي
+
+711
+00:50:16,190 --> 00:50:21,050
+هي .. اللي هي حالتين إذا بتذكروا لما أثبتناهم
+
+712
+00:50:21,450 --> 00:50:27,210
+الأولى كانت تي إكس وتي واي بتساوي ربع في تي إكس
+
+713
+00:50:27,210 --> 00:50:30,290
+ناقص تي واي لكل تربيع ناقص تي إكس وتي واي لكل إش
+
+714
+00:50:30,290 --> 00:50:36,850
+ماله تربيع ماشي الحال الان وي ساوي ربع في تي إكس
+
+715
+00:50:36,850 --> 00:50:40,010
+زي تي واي هي عبارة عن تي إكس زي إدوى لكل إش ماله
+
+716
+00:50:40,010 --> 00:50:45,050
+تربيع ماشي والتانية تي ويكس واي لكل إش ماله تربيع
+
+717
+00:50:45,050 --> 00:50:50,540
+أنا اللي قبل بشوية أثبتها في حالة اللي هي هذهأه
+
+718
+00:50:50,540 --> 00:50:54,000
+بساوي اللي هو x زي دوي تربيع اللي اتبعته مش اتبعت
+
+719
+00:50:54,000 --> 00:50:57,980
+ان انا x وx بتساوي Tx وTx ايه ان كانت x, x minus
+
+720
+00:50:57,980 --> 00:51:02,580
+y, x زي دوي اللي كانت بيصير عندي الآن هذه كلها
+
+721
+00:51:02,580 --> 00:51:06,360
+حولتها ل x زي دوي تربيع و الت .. هذه اسف و هذه
+
+722
+00:51:06,360 --> 00:51:11,080
+حولتها ل x minus y لكل تربيع لأن احسبوا هذه مع هذه
+
+723
+00:51:11,080 --> 00:51:14,760
+اللي هي اش بتساوي بتساوي ال inner product بين x و
+
+724
+00:51:14,760 --> 00:51:18,670
+y similarly for the complex case بتعملوها انتوانفس
+
+725
+00:51:18,670 --> 00:51:23,510
+الحسبة في .. في .. في برضه equality زيها بالظبط
+
+726
+00:51:23,510 --> 00:51:27,890
+طيب hence T preserves the main, the inner product
+
+727
+00:51:27,890 --> 00:51:32,790
+لأنه أثبتنا أن T X Y ياشو بتساوي X أو Y طيب
+
+728
+00:51:32,790 --> 00:51:35,770
+similarly for the complex hence T preserves the
+
+729
+00:51:35,770 --> 00:51:39,630
+inner product which implies T is ما لها one to one
+
+730
+00:51:39,630 --> 00:51:42,860
+بدنا نثبت أخر حاجة اللي هي إيش ما لها انتواماشي،
+
+731
+00:51:42,860 --> 00:51:46,320
+أنتوا كيف بناخد؟ بناخد أي X تلدة الموجودة في الـH
+
+732
+00:51:46,320 --> 00:51:52,160
+تلدة وبدنا نجيلها أصل، ماشي؟ شوفوا، خدوا أي X تلدة
+
+733
+00:51:52,160 --> 00:51:55,380
+بتساوي summation Alpha K E K تلدة over K element
+
+734
+00:51:55,380 --> 00:51:59,420
+in mean الـH تلدة، هذه الصورة أناصرها طيب، by
+
+735
+00:51:59,420 --> 00:52:02,280
+Besselin quality ال summation للـAlpha K تربيع
+
+736
+00:52:02,280 --> 00:52:08,810
+over K convertsالأن الـ summation للـ α K E K is
+
+737
+00:52:08,810 --> 00:52:12,910
+finite sum of a series which converts to X element
+
+738
+00:52:12,910 --> 00:52:16,130
+in H by theorem تلاتة خمس اتنين مادام ال summation
+
+739
+00:52:16,130 --> 00:52:21,810
+هذه اشملها معايا؟ طيب
+
+740
+00:52:21,810 --> 00:52:28,180
+الآن صحيح عند ال summation هذا is finiteاللي هو
+
+741
+00:52:28,180 --> 00:52:32,480
+قيمته finite بغض النظر اللي هو عبارة عن finite sum
+
+742
+00:52:32,480 --> 00:52:37,280
+من الواحد اللي عند أن أو series convertsاللي هو
+
+743
+00:52:37,280 --> 00:52:41,520
+twitch من theorem طلعت خمس اتنين and الفا كيه هدول
+
+744
+00:52:41,520 --> 00:52:44,880
+الفا كيه عبارة عن فرير coefficients بتطلع اللي هي
+
+745
+00:52:44,880 --> 00:52:49,360
+ال X و ال E K الآن نفس النظرية فبتصير الآن ال X
+
+746
+00:52:49,360 --> 00:52:53,900
+تلد هذه هتساوي ال Alpha K هي عبارة عن X و E K اي K
+
+747
+00:52:53,900 --> 00:52:58,880
+تلدة اللي هي في الواقع ايش هتكون ال TX اذا لجيت
+
+748
+00:52:58,880 --> 00:53:04,910
+انا الآن بدأت ب X تلد arbitrary و لجيت Xموجودة في
+
+749
+00:53:04,910 --> 00:53:09,150
+الـ H بحيث أن TX بتساوي X تلدى معناته صارت T is
+
+750
+00:53:09,150 --> 00:53:13,330
+onto و أثبتت إنها Linear و أثبتت بـ Reserve the
+
+751
+00:53:13,330 --> 00:53:17,270
+norm و أثبتت onto one to one صارت اللي هي T is an
+
+752
+00:53:17,270 --> 00:53:20,910
+isomorphism بين H and H تلدى و إلى لقاء آخر السلام
+
+753
+00:53:20,910 --> 00:53:21,670
+عليكم و رحمة الله
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/CRLpGXH9NAM_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/CRLpGXH9NAM_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..70a1f924888598a376cb1e5682792f155b549b11
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/CRLpGXH9NAM_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2552, "start": 5.06, "end": 25.52, "text": "بسم الله الرحمن الرحيم الحمد لله رب العالمين والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى آله وصحبه أجمعين هذه المحاضرة رقم 22 مساب تحليل اقتراني او تحليل دالي طلاب طالبات الجامعة الإسلامية مجلسية الرياضيات اليوم وصلنا لعند او اليوم هنحكي في هذه المحاضرة على تلاتة ستة", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21542, 2304, 3215, 24976, 3224, 12602, 3555, 18863, 45340, 9957, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 8608, 25708, 9673, 2288, 3794, 1211, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 19753, 43761, 4032, 9381, 5016, 3555, 3224, 5551, 7435, 2304, 3615, 9957, 29538, 9673, 5016, 46958, 25720, 12602, 4587, 2304, 5853, 47524, 16758, 6055, 5016, 20292, 1211, 1975, 38149, 2288, 7649, 1829, 1975, 2407, 6055, 5016, 20292, 1211, 11778, 6027, 1829, 23032, 15040, 3555, 23032, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 3714, 7435, 1211, 3794, 10632, 2423, 16572, 46958, 1829, 9307, 45595, 20498, 4032, 36520, 8315, 5296, 3615, 41260, 1975, 2407, 45595, 20498, 8032, 1863, 5016, 4117, 1829, 8978, 29538, 9673, 5016, 46958, 25720, 15844, 6055, 1211, 9307, 3660, 8608, 2655, 3660], "avg_logprob": -0.1286830327340535, "compression_ratio": 2.1196581196581197, "no_speech_prob": 2.9742717742919922e-05, "words": [{"start": 5.06, "end": 5.44, "word": "بسم", "probability": 0.87060546875}, {"start": 5.44, "end": 5.62, "word": " الله", "probability": 0.9619140625}, {"start": 5.62, "end": 5.96, "word": " الرحمن", "probability": 0.9479166666666666}, {"start": 5.96, "end": 6.4, "word": " الرحيم", "probability": 0.9954427083333334}, {"start": 6.4, "end": 6.8, "word": " الحمد", "probability": 0.8976236979166666}, {"start": 6.8, "end": 7.08, "word": " لله", "probability": 0.93359375}, {"start": 7.08, "end": 7.3, "word": " رب", "probability": 0.9638671875}, {"start": 7.3, "end": 7.82, "word": " العالمين", "probability": 0.994140625}, {"start": 7.82, "end": 8.26, "word": " والصلاة", "probability": 0.86767578125}, {"start": 8.26, "end": 8.66, "word": " والسلام", "probability": 0.9627278645833334}, {"start": 8.66, "end": 8.88, "word": " على", "probability": 0.70361328125}, {"start": 8.88, "end": 9.22, "word": " سيد", "probability": 0.96826171875}, {"start": 9.22, "end": 9.7, "word": " المرسلين", "probability": 0.981640625}, {"start": 9.7, "end": 10.08, "word": " سيدنا", "probability": 0.9697265625}, {"start": 10.08, "end": 10.48, "word": " محمد", "probability": 0.9895833333333334}, {"start": 10.48, "end": 10.74, "word": " وعلى", "probability": 0.9319661458333334}, {"start": 10.74, "end": 10.98, "word": " آله", "probability": 0.888671875}, {"start": 10.98, "end": 11.46, "word": " وصحبه", "probability": 0.95576171875}, {"start": 11.46, "end": 12.04, "word": " أجمعين", "probability": 0.82255859375}, {"start": 12.04, "end": 13.0, "word": " هذه", "probability": 0.93994140625}, {"start": 13.0, "end": 13.64, "word": " المحاضرة", "probability": 0.87451171875}, {"start": 13.64, "end": 13.92, "word": " رقم", "probability": 0.9332682291666666}, {"start": 13.92, "end": 14.72, "word": " 22", "probability": 0.77880859375}, {"start": 14.72, "end": 15.7, "word": " مساب", "probability": 0.827392578125}, {"start": 15.7, "end": 16.16, "word": " تحليل", "probability": 0.979248046875}, {"start": 16.16, "end": 16.78, "word": " اقتراني", "probability": 0.87001953125}, {"start": 16.78, "end": 16.86, "word": " او", "probability": 0.742431640625}, {"start": 16.86, "end": 17.28, "word": " تحليل", "probability": 0.98779296875}, {"start": 17.28, "end": 17.66, "word": " دالي", "probability": 0.9801432291666666}, {"start": 17.66, "end": 18.08, "word": " طلاب", "probability": 0.9397786458333334}, {"start": 18.08, "end": 18.6, "word": " طالبات", "probability": 0.9571533203125}, {"start": 18.6, "end": 18.96, "word": " الجامعة", "probability": 0.9864908854166666}, {"start": 18.96, "end": 19.44, "word": " الإسلامية", "probability": 0.865234375}, {"start": 19.44, "end": 19.98, "word": " مجلسية", "probability": 0.80185546875}, {"start": 19.98, "end": 20.7, "word": " الرياضيات", "probability": 0.79990234375}, {"start": 20.7, "end": 21.56, "word": " اليوم", "probability": 0.94384765625}, {"start": 21.56, "end": 21.98, "word": " وصلنا", "probability": 0.9505208333333334}, {"start": 21.98, "end": 22.32, "word": " لعند", "probability": 0.60107421875}, {"start": 22.32, "end": 22.44, "word": " او", "probability": 0.7105712890625}, {"start": 22.44, "end": 22.62, "word": " اليوم", "probability": 0.982421875}, {"start": 22.62, "end": 23.12, "word": " هنحكي", "probability": 0.86005859375}, {"start": 23.12, "end": 23.22, "word": " في", "probability": 0.95654296875}, {"start": 23.22, "end": 23.8, "word": " هذه", "probability": 0.11712646484375}, {"start": 23.8, "end": 24.32, "word": " المحاضرة", "probability": 0.9974365234375}, {"start": 24.32, "end": 24.58, "word": " على", "probability": 0.90966796875}, {"start": 24.58, "end": 25.08, "word": " تلاتة", "probability": 0.8834228515625}, {"start": 25.08, "end": 25.52, "word": " ستة", "probability": 0.908203125}], "temperature": 1.0}, {"id": 2, "seek": 4933, "start": 25.77, "end": 49.33, "text": "اللي هي تحت عنوان Total Orthonormal Sets and Sequences احنا حكينا عن الـ Orthonormal Sets و Orthonormal Sequences الآن الفكرة في الـ Total Orthonormal Sets and Sequences احنا بدنا نبحث عن set انها من خلالها نجيب ال space كله", "tokens": [6027, 20292, 39896, 6055, 33753, 18871, 2407, 7649, 23170, 1610, 11943, 24440, 318, 1385, 293, 46859, 2667, 1975, 5016, 8315, 11331, 4117, 1829, 8315, 18871, 2423, 39184, 1610, 11943, 24440, 318, 1385, 4032, 1610, 11943, 24440, 46859, 2667, 6024, 48506, 27188, 4117, 25720, 8978, 2423, 39184, 23170, 1610, 11943, 24440, 318, 1385, 293, 46859, 2667, 1975, 5016, 8315, 47525, 8315, 8717, 49628, 12984, 18871, 992, 16472, 11296, 9154, 16490, 1211, 6027, 11296, 8717, 7435, 1829, 3555, 2423, 1901, 28242, 3224], 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0.987060546875}, {"start": 31.89, "end": 32.07, "word": " عن", "probability": 0.990234375}, {"start": 32.07, "end": 32.23, "word": " الـ", "probability": 0.6871337890625}, {"start": 32.23, "end": 32.83, "word": " Orthonormal", "probability": 0.7750651041666666}, {"start": 32.83, "end": 33.31, "word": " Sets", "probability": 0.909423828125}, {"start": 33.31, "end": 33.55, "word": " و", "probability": 0.95849609375}, {"start": 33.55, "end": 34.13, "word": " Orthonormal", "probability": 0.8873697916666666}, {"start": 34.13, "end": 34.87, "word": " Sequences", "probability": 0.987060546875}, {"start": 34.87, "end": 35.99, "word": " الآن", "probability": 0.56890869140625}, {"start": 35.99, "end": 36.67, "word": " الفكرة", "probability": 0.9860026041666666}, {"start": 36.67, "end": 36.85, "word": " في", "probability": 0.814453125}, {"start": 36.85, "end": 37.03, "word": " الـ", "probability": 0.7333984375}, {"start": 37.03, "end": 37.27, "word": " Total", "probability": 0.86376953125}, 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"word": " نجيب", "probability": 0.9610595703125}, {"start": 48.53, "end": 48.65, "word": " ال", "probability": 0.97802734375}, {"start": 48.65, "end": 48.91, "word": " space", "probability": 0.64794921875}, {"start": 48.91, "end": 49.33, "word": " كله", "probability": 0.98583984375}], "temperature": 1.0}, {"id": 3, "seek": 6954, "start": 49.88, "end": 69.54, "text": "كل space يعني ما كأنه مشابه لعمل اللي هي roughly هذا الكلام مشابه لعمل ال bases في حالة اللي هو في ال finite dimensional case في حالة ال finite dimensional case اللي بتجيب ال space اللي هو اللي انتوا عارفين ال bases انه على طول اللي هو linearly independent independent", "tokens": [28820, 1901, 37495, 22653, 19446, 9122, 33456, 3224, 37893, 16758, 3224, 5296, 25957, 1211, 13672, 1829, 39896, 9810, 23758, 2423, 28820, 10943, 37893, 16758, 3224, 5296, 25957, 1211, 2423, 17949, 8978, 11331, 6027, 3660, 13672, 1829, 31439, 8978, 2423, 19362, 18795, 1389, 8978, 11331, 6027, 3660, 2423, 19362, 18795, 1389, 13672, 1829, 39894, 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اللي من ال theorem اللي قبل بشوية، تلاتة، ستة اتنين، B، هيكون عندي أكيد في اللي هو الـ M أرثجون المش Zero", "tokens": [28814, 15730, 2423, 39184, 376, 4386, 13672, 1829, 1975, 5016, 8315, 12174, 1211, 8315, 45164, 25961, 2655, 376, 3217, 376, 3217, 13672, 1829, 31439, 20449, 8315, 47395, 13672, 1829, 4386, 13672, 1829, 31439, 39894, 30544, 376, 5551, 2288, 12984, 7435, 11536, 16247, 8592, 2304, 6027, 12399, 11296, 17182, 3714, 33599, 1829, 12399, 3714, 3215, 10943, 2655, 376, 4386, 4032, 29538, 479, 293, 479, 12399, 5551, 8592, 2655, 17082, 1211, 8315, 12174, 3215, 11703, 1829, 11296, 6055, 7649, 1829, 11933, 15730, 25961, 2655, 376, 307, 406, 3217, 12399, 13672, 1829, 9154, 2423, 20904, 13672, 1829, 12174, 36150, 4724, 8592, 2407, 10632, 12399, 6055, 1211, 9307, 3660, 12399, 8608, 2655, 3660, 1975, 2655, 1863, 9957, 12399, 363, 12399, 39896, 30544, 18871, 16254, 5551, 4117, 25708, 8978, 13672, 1829, 31439, 2423, 39184, 376, 5551, 2288, 12984, 7435, 11536, 9673, 8592, 17182], 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0.990234375}, {"start": 766.64, "end": 766.84, "word": " قبل", "probability": 0.631103515625}, {"start": 766.84, "end": 767.34, "word": " بشوية،", "probability": 0.778369140625}, {"start": 767.34, "end": 767.54, "word": " تلاتة،", "probability": 0.7419921875}, {"start": 767.54, "end": 767.74, "word": " ستة", "probability": 0.8427734375}, {"start": 767.74, "end": 768.06, "word": " اتنين،", "probability": 0.756640625}, {"start": 768.06, "end": 768.86, "word": " B،", "probability": 0.5386962890625}, {"start": 768.86, "end": 769.64, "word": " هيكون", "probability": 0.839111328125}, {"start": 769.64, "end": 770.1, "word": " عندي", "probability": 0.787841796875}, {"start": 770.1, "end": 770.78, "word": " أكيد", "probability": 0.9527994791666666}, {"start": 770.78, "end": 771.1, "word": " في", "probability": 0.9833984375}, {"start": 771.1, "end": 772.28, "word": " اللي", "probability": 0.766357421875}, {"start": 772.28, "end": 772.52, "word": " هو", "probability": 0.99072265625}, {"start": 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عندي ال contraposition تحققت إنه لو كانت هذه مش total هتأدي هذا وهذا معناه أن هذا يؤدي هذا therefore if ال summation بيساوي كذا for all اللي هي X المتناش then M اسمها is total in H و conversely", "tokens": [9566, 1829, 3555, 11933, 15730, 16678, 2423, 28811, 5296, 1783, 4032, 46078, 6055, 2288, 21292, 3615, 670, 591, 28242, 3224, 8717, 36178, 3224, 39896, 3794, 995, 45865, 8608, 5172, 2288, 4032, 37893, 39896, 3794, 995, 45865, 9154, 2026, 1783, 6055, 2288, 21292, 3615, 3224, 36145, 1783, 8717, 36178, 3224, 37893, 4018, 11933, 15730, 20328, 9640, 18871, 16254, 2423, 660, 4007, 5830, 6055, 5016, 4587, 38149, 36145, 3224, 45164, 25961, 2655, 29538, 37893, 3217, 8032, 2655, 10721, 16254, 23758, 37037, 15730, 20449, 8315, 3224, 14739, 23758, 7251, 33604, 16254, 23758, 4412, 498, 2423, 28811, 4724, 1829, 3794, 995, 45865, 9122, 15730, 337, 439, 13672, 1829, 39896, 1783, 9673, 2655, 1863, 33599, 550, 376, 24525, 2304, 11296, 307, 3217, 294, 389, 4032, 2615, 736], "avg_logprob": 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0.9775390625}, {"start": 821.04, "end": 821.8, "word": " therefore", "probability": 0.7216796875}, {"start": 821.8, "end": 822.56, "word": " if", "probability": 0.87939453125}, {"start": 822.56, "end": 822.76, "word": " ال", "probability": 0.454833984375}, {"start": 822.76, "end": 823.08, "word": " summation", "probability": 0.91943359375}, {"start": 823.08, "end": 823.6, "word": " بيساوي", "probability": 0.8603515625}, {"start": 823.6, "end": 823.96, "word": " كذا", "probability": 0.7127685546875}, {"start": 823.96, "end": 824.66, "word": " for", "probability": 0.9609375}, {"start": 824.66, "end": 825.12, "word": " all", "probability": 0.95361328125}, {"start": 825.12, "end": 825.38, "word": " اللي", "probability": 0.59033203125}, {"start": 825.38, "end": 825.6, "word": " هي", "probability": 0.87451171875}, {"start": 825.6, "end": 825.88, "word": " X", "probability": 0.9228515625}, {"start": 825.88, "end": 826.34, "word": " المتناش", "probability": 0.58795166015625}, {"start": 826.34, 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متربية بساوي ال summation اللي عندها طيب صلى الله عليه الصلاة والسلام", "tokens": [6027, 7649, 47525, 10721, 1975, 5172, 2655, 43042, 16472, 3224, 376, 307, 3217, 4032, 33546, 1211, 5296, 19528, 3794, 995, 14407, 3660, 11778, 1829, 13672, 1829, 2423, 4724, 9640, 3794, 33911, 6027, 3714, 6027, 11296, 44650, 5016, 4587, 28671, 20193, 5016, 19913, 14407, 19446, 39896, 13672, 1829, 2423, 7649, 7297, 300, 376, 307, 3217, 294, 389, 4032, 9778, 3215, 1783, 312, 604, 4478, 294, 376, 294, 389, 8978, 23211, 44381, 6806, 6225, 8592, 7649, 1975, 12984, 3555, 2655, 5296, 24793, 16472, 3224, 8717, 13063, 44650, 25513, 10632, 4724, 3794, 995, 45865, 2423, 28811, 13672, 1829, 43242, 11296, 23032, 1829, 3555, 20328, 23942, 21984, 47356, 31767, 15040, 3660, 16070, 3794, 37440], "avg_logprob": -0.34206082423528034, "compression_ratio": 1.627906976744186, "no_speech_prob": 0.0, "words": [{"start": 833.12, "end": 833.68, "word": "الان", "probability": 0.6646728515625}, {"start": 833.68, "end": 834.46, 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"word": " لكن", "probability": 0.85107421875}, {"start": 852.12, "end": 852.6, "word": " fixed", "probability": 0.8271484375}, {"start": 852.6, "end": 853.18, "word": " عشان", "probability": 0.9728190104166666}, {"start": 853.18, "end": 853.52, "word": " اثبت", "probability": 0.8829345703125}, {"start": 853.52, "end": 853.76, "word": " لكم", "probability": 0.769287109375}, {"start": 853.76, "end": 854.06, "word": " انه", "probability": 0.798828125}, {"start": 854.06, "end": 854.38, "word": " نور", "probability": 0.97314453125}, {"start": 854.38, "end": 855.02, "word": " متربية", "probability": 0.72900390625}, {"start": 855.02, "end": 855.52, "word": " بساوي", "probability": 0.87255859375}, {"start": 855.52, "end": 855.7, "word": " ال", "probability": 0.44677734375}, {"start": 855.7, "end": 856.06, "word": " summation", "probability": 0.54833984375}, {"start": 856.06, "end": 856.3, "word": " اللي", "probability": 0.943359375}, {"start": 856.3, "end": 856.7, "word": " عندها", "probability": 0.822021484375}, {"start": 856.7, "end": 857.78, "word": " طيب", "probability": 0.873046875}, {"start": 857.78, "end": 858.08, "word": " صلى", "probability": 0.905517578125}, {"start": 858.08, "end": 858.18, "word": " الله", "probability": 0.65478515625}, {"start": 858.18, "end": 858.5, "word": " عليه", "probability": 0.50732421875}, {"start": 858.5, "end": 858.96, "word": " الصلاة", "probability": 0.9710286458333334}, {"start": 858.96, "end": 859.42, "word": " والسلام", "probability": 0.9640299479166666}], "temperature": 1.0}, {"id": 39, "seek": 87640, "start": 860.94, "end": 876.4, "text": "الان الـ Range of all its non-zero Fourier coefficients in a sequence X و E1 و X و E2 و الى اخرها و بقدر اعمل هيك حتى لو كانت uncountable ليش؟ لان قبل شوية قلتلكم اللي هي الـ non-zero منها", "tokens": [6027, 7649, 2423, 39184, 33778, 295, 439, 1080, 2107, 12, 32226, 36810, 31994, 294, 257, 8310, 1783, 4032, 462, 16, 4032, 1783, 4032, 462, 17, 4032, 2423, 7578, 1975, 34740, 11296, 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"word": "-zero", "probability": 0.6826171875}, {"start": 864.6, "end": 864.86, "word": " Fourier", "probability": 0.433837890625}, {"start": 864.86, "end": 865.54, "word": " coefficients", "probability": 0.92578125}, {"start": 865.54, "end": 865.78, "word": " in", "probability": 0.81103515625}, {"start": 865.78, "end": 865.94, "word": " a", "probability": 0.875}, {"start": 865.94, "end": 866.4, "word": " sequence", "probability": 0.96484375}, {"start": 866.4, "end": 866.68, "word": " X", "probability": 0.6796875}, {"start": 866.68, "end": 866.86, "word": " و", "probability": 0.27734375}, {"start": 866.86, "end": 867.22, "word": " E1", "probability": 0.5546875}, {"start": 867.22, "end": 867.36, "word": " و", "probability": 0.9072265625}, {"start": 867.36, "end": 867.5, "word": " X", "probability": 0.92138671875}, {"start": 867.5, "end": 867.62, "word": " و", "probability": 0.98779296875}, {"start": 867.62, "end": 868.12, "word": " E2", "probability": 0.97021484375}, {"start": 868.12, 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"word": " لان", "probability": 0.6923828125}, {"start": 872.86, "end": 873.1, "word": " قبل", "probability": 0.958740234375}, {"start": 873.1, "end": 873.4, "word": " شوية", "probability": 0.88037109375}, {"start": 873.4, "end": 873.94, "word": " قلتلكم", "probability": 0.877734375}, {"start": 873.94, "end": 874.24, "word": " اللي", "probability": 0.81103515625}, {"start": 874.24, "end": 874.34, "word": " هي", "probability": 0.90234375}, {"start": 874.34, "end": 875.18, "word": " الـ", "probability": 0.5362548828125}, {"start": 875.18, "end": 875.38, "word": " non", "probability": 0.51416015625}, {"start": 875.38, "end": 875.86, "word": "-zero", "probability": 0.85888671875}, {"start": 875.86, "end": 876.4, "word": " منها", "probability": 0.9873046875}], "temperature": 1.0}, {"id": 40, "seek": 89236, "start": 877.06, "end": 892.36, "text": "اللي هي حاجة تكون countable هم اللي بيعملوا هنا arrangement إذا الأن هدول اللي اختارتهم من هنا اللي هم مش سفر فبصير عندي X و E واحد و X و E اتنين 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{"start": 887.52, "end": 887.68, "word": " X", "probability": 0.92822265625}, {"start": 887.68, "end": 887.8, "word": " و", "probability": 0.9384765625}, {"start": 887.8, "end": 887.92, "word": " E", "probability": 0.88427734375}, {"start": 887.92, "end": 888.16, "word": " اتنين", "probability": 0.8792724609375}, {"start": 888.16, "end": 888.42, "word": " إلى", "probability": 0.62158203125}, {"start": 888.42, "end": 888.78, "word": " مالة", "probability": 0.6353352864583334}, {"start": 888.78, "end": 889.32, "word": " نهاية", "probability": 0.8583984375}, {"start": 889.32, "end": 890.12, "word": " اللي", "probability": 0.9365234375}, {"start": 890.12, "end": 890.22, "word": " هي", "probability": 0.58837890625}, {"start": 890.22, "end": 891.12, "word": " أعملت", "probability": 0.77484130859375}, {"start": 891.12, "end": 891.26, "word": " ..", "probability": 0.167724609375}, {"start": 891.26, "end": 891.92, "word": " أحطيتهم", "probability": 0.7671875}, {"start": 891.92, "end": 892.04, "word": " في", "probability": 0.9580078125}, {"start": 892.04, "end": 892.36, "word": " sequence", "probability": 0.916015625}], "temperature": 1.0}, {"id": 41, "seek": 90561, "start": 893.57, "end": 905.61, "text": "وإذا كان في نايت خلاص من كتب ال X و X و Y أحد و X و Y اتنين و X و Y انتصار اذا ر مكتوب في حركة محددة إذا كان هناك عدد منهم فقط في نايت", "tokens": [2407, 28814, 15730, 25961, 8978, 8717, 995, 36081, 16490, 1211, 33546, 9154, 9122, 2655, 3555, 2423, 1783, 4032, 1783, 4032, 398, 5551, 24401, 4032, 1783, 4032, 398, 1975, 2655, 1863, 9957, 4032, 1783, 4032, 398, 16472, 2655, 9381, 9640, 1975, 15730, 12602, 3714, 4117, 2655, 37746, 8978, 11331, 31747, 3660, 3714, 24401, 41891, 11933, 15730, 25961, 34105, 4117, 6225, 3215, 3215, 9154, 16095, 6156, 47432, 8978, 8717, 995, 36081], "avg_logprob": -0.6281249897820609, "compression_ratio": 1.6842105263157894, "no_speech_prob": 0.0, "words": [{"start": 893.5699999999999, "end": 894.03, "word": "وإذا", "probability": 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{"start": 900.91, "end": 901.25, "word": " مكتوب", "probability": 0.680419921875}, {"start": 901.25, "end": 901.59, "word": " في", "probability": 0.48779296875}, {"start": 901.59, "end": 901.81, "word": " حركة", "probability": 0.478515625}, {"start": 901.81, "end": 902.29, "word": " محددة", "probability": 0.5379231770833334}, {"start": 902.29, "end": 903.47, "word": " إذا", "probability": 0.607177734375}, {"start": 903.47, "end": 904.29, "word": " كان", "probability": 0.74658203125}, {"start": 904.29, "end": 904.41, "word": " هناك", "probability": 0.726318359375}, {"start": 904.41, "end": 904.71, "word": " عدد", "probability": 0.5049641927083334}, {"start": 904.71, "end": 904.71, "word": " منهم", "probability": 0.4532470703125}, {"start": 904.71, "end": 904.71, "word": " فقط", "probability": 0.607666015625}, {"start": 904.71, "end": 904.85, "word": " في", "probability": 0.5732421875}, {"start": 904.85, "end": 905.61, "word": " نايت", "probability": 0.9371744791666666}], "temperature": 1.0}, {"id": 42, "seek": 93713, "start": 909.69, "end": 937.13, "text": "واضح طيب الان define y by الان هاي الألداء اللي بتوصلني للي بديها الان خليني أن أعرف y بواسطة y بالسواء و ال summation x و ek ek كامن عند واحد إلى مين إلى مال نهاية طيب شو سميلي هذه واحدة لأن بعد شوية أرجعلها أنا بعرف أن أم اشمالها is orthonormal set مدام orthonormal set", "tokens": [2407, 46958, 5016, 23032, 1829, 3555, 2423, 7649, 6964, 288, 538, 2423, 7649, 8032, 47302, 16247, 1211, 3215, 16606, 13672, 1829, 39894, 2407, 36520, 22653, 5296, 20292, 4724, 16254, 11296, 2423, 7649, 16490, 1211, 9957, 1829, 14739, 5551, 3615, 28480, 288, 4724, 14407, 3794, 9566, 3660, 288, 20666, 3794, 2407, 16606, 4032, 2423, 28811, 2031, 4032, 13359, 13359, 9122, 10943, 1863, 43242, 36764, 24401, 30731, 3714, 9957, 30731, 3714, 6027, 8717, 11296, 10632, 23032, 1829, 3555, 13412, 2407, 8608, 2304, 1829, 20292, 29538, 36764, 24401, 3660, 5296, 33456, 39182, 13412, 2407, 10632, 5551, 47341, 3615, 1211, 11296, 41850, 45030, 28480, 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"probability": 0.71533203125}, {"start": 924.37, "end": 924.81, "word": " مال", "probability": 0.759521484375}, {"start": 924.81, "end": 925.35, "word": " نهاية", "probability": 0.7332356770833334}, {"start": 925.35, "end": 926.27, "word": " طيب", "probability": 0.9619140625}, {"start": 926.27, "end": 926.57, "word": " شو", "probability": 0.594482421875}, {"start": 926.57, "end": 926.99, "word": " سميلي", "probability": 0.50958251953125}, {"start": 926.99, "end": 927.19, "word": " هذه", "probability": 0.75048828125}, {"start": 927.19, "end": 927.47, "word": " واحدة", "probability": 0.9368489583333334}, {"start": 927.47, "end": 927.59, "word": " لأن", "probability": 0.567626953125}, {"start": 927.59, "end": 928.03, "word": " بعد", "probability": 0.442626953125}, {"start": 928.03, "end": 928.55, "word": " شوية", "probability": 0.9134114583333334}, {"start": 928.55, "end": 929.37, "word": " أرجعلها", "probability": 0.782177734375}, {"start": 929.37, "end": 930.09, "word": " أنا", "probability": 0.53271484375}, {"start": 930.09, "end": 930.47, "word": " بعرف", "probability": 0.97216796875}, {"start": 930.47, "end": 930.63, "word": " أن", "probability": 0.57666015625}, {"start": 930.63, "end": 931.07, "word": " أم", "probability": 0.5919189453125}, {"start": 931.07, "end": 933.05, "word": " اشمالها", "probability": 0.7953125}, {"start": 933.05, "end": 933.43, "word": " is", "probability": 0.57666015625}, {"start": 933.43, "end": 934.35, "word": " orthonormal", "probability": 0.8650716145833334}, {"start": 934.35, "end": 934.87, "word": " set", "probability": 0.9638671875}, {"start": 934.87, "end": 935.89, "word": " مدام", "probability": 0.79736328125}, {"start": 935.89, "end": 936.69, "word": " orthonormal", "probability": 0.9171549479166666}, {"start": 936.69, "end": 937.13, "word": " set", "probability": 0.97412109375}], "temperature": 1.0}, {"id": 43, "seek": 96408, "start": 937.84, "end": 964.08, "text": "then for every ej occurring in one اللي هي الاج اللي في واحد اللي هي واحد لما أخدنا ال summation هذا over k فيه جزئين جزء منه اللي هو عملتله arranging اللي هو xe واحد إلى آخرهم وهدولة اللي هي non-zero elements والجزء الثاني منهم خلّينا نسميه v و ال v هذا ايش مالوسفار ماشي الحال طيب او", "tokens": [19096, 337, 633, 10012, 18386, 294, 472, 13672, 1829, 39896, 2423, 26108, 13672, 1829, 8978, 36764, 24401, 13672, 1829, 39896, 36764, 24401, 5296, 15042, 5551, 9778, 3215, 8315, 2423, 28811, 23758, 670, 350, 8978, 3224, 10874, 11622, 19986, 9957, 10874, 11622, 38207, 9154, 3224, 13672, 1829, 31439, 6225, 42213, 2655, 43761, 5539, 9741, 13672, 1829, 31439, 2031, 68, 36764, 24401, 30731, 19753, 34740, 16095, 37037, 3215, 12610, 3660, 13672, 1829, 39896, 2107, 12, 32226, 4959, 16070, 7435, 11622, 38207, 6024, 104, 7649, 1829, 9154, 16095, 16490, 1211, 11703, 9957, 995, 8717, 38251, 1829, 3224, 371, 4032, 2423, 371, 23758, 1975, 1829, 8592, 3714, 6027, 41779, 5172, 9640, 3714, 33599, 1829, 21542, 6027, 23032, 1829, 3555, 1975, 2407], "avg_logprob": 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الآن عملنا arrangement since M is orthonormal then for every EJ occurring in one اللي عملنا لها arrangement we have X minus Y و EJ ال X ال arbitrator ال botfix اللي خدناها في الأول هي عليها الشغل طيب بتساوي X و EJ ناقص Y مين و EJ", "tokens": [3555, 2655, 1829, 7435, 1829, 6024, 48506, 6225, 42213, 8315, 17620, 1670, 376, 307, 420, 11943, 24440, 550, 337, 633, 462, 41, 18386, 294, 472, 13672, 1829, 6225, 42213, 8315, 5296, 11296, 17620, 321, 362, 1783, 3175, 398, 4032, 462, 41, 2423, 1783, 2423, 19071, 1639, 2423, 10592, 69, 970, 13672, 1829, 16490, 3215, 8315, 11296, 8978, 16247, 12610, 39896, 25894, 11296, 25124, 17082, 1211, 23032, 1829, 3555, 39894, 3794, 995, 45865, 1783, 4032, 462, 41, 8717, 995, 4587, 9381, 398, 3714, 9957, 4032, 462, 41], "avg_logprob": -0.33961926383533697, "compression_ratio": 1.4651162790697674, "no_speech_prob": 2.5033950805664062e-06, "words": [{"start": 964.89, "end": 965.31, "word": "بتيجي", "probability": 0.693408203125}, {"start": 965.31, "end": 965.55, 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هذه ناقص ال summation X و EK في EK و EJ الان عندنا كل هين هيتسفر مع ده EJ ايش مع EJ لإن هو orthonormal إذا صار عند هذا X EJ و هذا X EJ إذا إيش هيساوي؟ هيساوي سفر إذا أثبت لكم الآن X minus Y و EJ بساوي سفر لكل واحدة من العائلة الأولى هذه نيجي الآن ناخد", "tokens": [2407, 7251, 3794, 995, 45865, 1783, 4032, 462, 41, 30767, 1829, 19446, 39896, 8717, 995, 4587, 9381, 29538, 8717, 995, 4587, 9381, 2423, 28811, 1783, 4032, 46078, 8978, 46078, 4032, 462, 41, 2423, 7649, 43242, 8315, 28242, 8032, 9957, 8032, 36081, 3794, 5172, 2288, 20449, 11778, 3224, 462, 41, 1975, 1829, 8592, 20449, 462, 41, 5296, 28814, 1863, 31439, 420, 11943, 24440, 11933, 15730, 20328, 9640, 43242, 23758, 1783, 462, 41, 4032, 23758, 1783, 462, 41, 11933, 15730, 11933, 1829, 8592, 39896, 3794, 995, 45865, 22807, 39896, 3794, 995, 45865, 8608, 5172, 2288, 11933, 15730, 5551, 12984, 3555, 2655, 5296, 24793, 6024, 48506, 1783, 3175, 398, 4032, 462, 41, 4724, 3794, 995, 45865, 8608, 5172, 2288, 5296, 28820, 36764, 24401, 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0.91015625}, {"start": 1337.99, "end": 1338.87, "word": " I", "probability": 0.3759765625}, {"start": 1338.87, "end": 1339.39, "word": " B", "probability": 0.322265625}], "temperature": 1.0}, {"id": 59, "seek": 136140, "start": 1340.48, "end": 1361.4, "text": "dense set in mean in H ايه dense set in H؟ وبدى الآن افرضلكم ان Hم نفسها اشمالها م uncountable واصل لك ان هذا هيقدى", "tokens": [67, 1288, 992, 294, 914, 294, 389, 1975, 1829, 3224, 18011, 992, 294, 389, 22807, 4032, 44510, 7578, 6024, 48506, 1975, 5172, 43042, 23275, 2304, 16472, 389, 2304, 8717, 36178, 11296, 1975, 8592, 2304, 6027, 11296, 3714, 6219, 792, 712, 4032, 33546, 1211, 5296, 4117, 16472, 23758, 39896, 28543, 7578], "avg_logprob": -0.44546568510579126, "compression_ratio": 1.2868217054263567, "no_speech_prob": 1.0371208190917969e-05, "words": [{"start": 1340.48, "end": 1341.3, "word": "dense", "probability": 0.43798828125}, {"start": 1341.3, "end": 1342.96, "word": " set", "probability": 0.337158203125}, {"start": 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واحدة منهم هتكون countable يعني كلهم uncountable للمؤهلات إنهم يدوء يكونوا يقوموا بدور إنه هنا dense subset in H كلهم يكونوا uncountable وهذا معناته بطل H separable إذن هي كما يكون التناقض إذن هي هي السرتيجية الحل نيجي الآن نقول لت H بيه separable", "tokens": [28814, 1863, 8032, 8848, 12610, 995, 49429, 36764, 24401, 3660, 9154, 16095, 8032, 2655, 30544, 1207, 712, 37495, 22653, 28242, 16095, 517, 26050, 712, 5296, 19528, 33604, 3224, 1211, 9307, 36145, 16095, 7251, 3215, 2407, 38207, 7251, 30544, 14407, 7251, 4587, 20498, 14407, 47525, 13063, 36145, 3224, 34105, 18011, 25993, 294, 389, 28242, 16095, 7251, 30544, 14407, 517, 26050, 712, 37037, 15730, 20449, 8315, 47395, 4724, 9566, 1211, 389, 3128, 712, 11933, 8848, 1863, 39896, 9122, 15042, 7251, 30544, 16712, 8315, 4587, 11242, 11933, 8848, 1863, 39896, 39896, 21136, 2288, 31371, 7435, 10632, 21542, 1211, 8717, 1829, 7435, 1829, 6024, 48506, 8717, 39648, 5296, 2655, 389, 4724, 1829, 3224, 3128, 712], "avg_logprob": 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spherical neighborhoods، فإن هدول النقسات So that B would contains uncountable number of points، يعني B would be uncountable since B was arbitrary dense set، this makes that H would not contain a countable dense set", "tokens": [1211, 33456, 45164, 6156, 43042, 8315, 36145, 376, 307, 6219, 792, 712, 12399, 550, 321, 362, 6219, 792, 1188, 867, 6119, 3711, 717, 48613, 37300, 20052, 12399, 6156, 28814, 1863, 8032, 3215, 12610, 28239, 4587, 3794, 9307, 407, 300, 363, 576, 8306, 6219, 792, 712, 1230, 295, 2793, 12399, 37495, 22653, 363, 576, 312, 6219, 792, 712, 1670, 363, 390, 23211, 18011, 992, 12399, 341, 1669, 300, 389, 576, 406, 5304, 257, 1207, 712, 18011, 992], "avg_logprob": -0.30478897497251434, "compression_ratio": 1.484304932735426, "no_speech_prob": 0.0, "words": [{"start": 1638.24, "end": 1638.6, "word": "لأن", "probability": 0.822265625}, {"start": 1638.6, "end": 1638.82, "word": " لو", "probability": 0.93896484375}, {"start": 1638.82, "end": 1639.36, "word": " فرضنا", 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"temperature": 1.0}, {"id": 73, "seek": 168342, "start": 1663.06, "end": 1683.42, "text": "which contradicts the fact that which is separable therefore انا لازم تكون ايه اش مالها اللي هي countable واضح؟ ماشي الحال نيجي نشوف اللي بعدها بيكون طوله روحكم برضه شوية نيجي لين؟ ارجعلنا للنص عشان نذكركم بإيش اللي بدنا نثبته", "tokens": [13690, 28900, 82, 264, 1186, 300, 597, 307, 3128, 712, 4412, 1975, 8315, 5296, 31377, 2304, 6055, 30544, 1975, 1829, 3224, 1975, 8592, 3714, 6027, 11296, 13672, 1829, 39896, 1207, 712, 4032, 46958, 5016, 22807, 3714, 33599, 1829, 21542, 6027, 8717, 1829, 7435, 1829, 8717, 8592, 38688, 13672, 1829, 39182, 11296, 4724, 1829, 30544, 23032, 12610, 3224, 12602, 2407, 5016, 24793, 4724, 43042, 3224, 13412, 2407, 10632, 8717, 1829, 7435, 1829, 5296, 9957, 22807, 1975, 47341, 30241, 8315, 24976, 1863, 9381, 6225, 8592, 7649, 8717, 8848, 37983, 24793, 4724, 28814, 1829, 8592, 13672, 1829, 47525, 8315, 8717, 12984, 3555, 47395], "avg_logprob": -0.28016708865024076, "compression_ratio": 1.5784753363228698, "no_speech_prob": 3.141164779663086e-05, "words": [{"start": 1663.06, "end": 1663.72, "word": "which", "probability": 0.1307373046875}, {"start": 1663.72, "end": 1664.96, "word": " contradicts", "probability": 0.66748046875}, {"start": 1664.96, "end": 1665.06, "word": " the", "probability": 0.84326171875}, {"start": 1665.06, "end": 1665.32, "word": " fact", "probability": 0.92822265625}, {"start": 1665.32, "end": 1665.92, "word": " that", "probability": 0.92236328125}, {"start": 1665.92, "end": 1666.54, "word": " which", "probability": 0.0853271484375}, {"start": 1666.54, "end": 1666.74, "word": " is", "probability": 0.88818359375}, {"start": 1666.74, "end": 1667.28, "word": " separable", "probability": 0.92578125}, {"start": 1667.28, "end": 1667.88, "word": " therefore", "probability": 0.18994140625}, {"start": 1667.88, "end": 1668.36, "word": " انا", "probability": 0.621337890625}, {"start": 1668.36, "end": 1668.7, "word": " لازم", "probability": 0.8390299479166666}, {"start": 1668.7, "end": 1668.96, "word": " تكون", "probability": 0.7320556640625}, {"start": 1668.96, "end": 1669.12, "word": " ايه", "probability": 0.6852213541666666}, {"start": 1669.12, "end": 1669.2, "word": " اش", "probability": 0.656982421875}, {"start": 1669.2, "end": 1669.62, "word": " مالها", "probability": 0.8057454427083334}, {"start": 1669.62, "end": 1670.28, "word": " اللي", "probability": 0.814697265625}, {"start": 1670.28, "end": 1670.42, "word": " هي", "probability": 0.8291015625}, {"start": 1670.42, "end": 1670.98, "word": " countable", "probability": 0.908935546875}, {"start": 1670.98, "end": 1673.14, "word": " واضح؟", "probability": 0.75250244140625}, {"start": 1673.14, "end": 1673.62, "word": " ماشي", "probability": 0.8580729166666666}, {"start": 1673.62, "end": 1673.9, "word": " الحال", "probability": 0.91064453125}, {"start": 1673.9, "end": 1674.58, "word": " نيجي", "probability": 0.889404296875}, {"start": 1674.58, "end": 1674.8, "word": " نشوف", "probability": 0.9923502604166666}, {"start": 1674.8, "end": 1674.92, "word": " اللي", "probability": 0.965087890625}, {"start": 1674.92, "end": 1675.4, "word": " بعدها", "probability": 0.934814453125}, {"start": 1675.4, "end": 1675.82, "word": " بيكون", "probability": 0.6340738932291666}, {"start": 1675.82, "end": 1676.18, "word": " طوله", "probability": 0.48681640625}, {"start": 1676.18, "end": 1676.52, "word": " روحكم", "probability": 0.86572265625}, {"start": 1676.52, "end": 1676.78, "word": " برضه", "probability": 0.9208984375}, {"start": 1676.78, "end": 1677.18, "word": " شوية", "probability": 0.8846028645833334}, {"start": 1677.18, "end": 1679.32, "word": " نيجي", "probability": 0.88525390625}, {"start": 1679.32, "end": 1680.52, "word": " لين؟", "probability": 0.64306640625}, {"start": 1680.52, "end": 1681.1, "word": " ارجعلنا", "probability": 0.73992919921875}, {"start": 1681.1, "end": 1681.5, "word": " للنص", "probability": 0.91552734375}, {"start": 1681.5, "end": 1681.76, "word": " عشان", "probability": 0.95751953125}, {"start": 1681.76, "end": 1682.32, "word": " نذكركم", "probability": 0.9686279296875}, {"start": 1682.32, "end": 1682.58, "word": " بإيش", "probability": 0.7998046875}, {"start": 1682.58, "end": 1682.7, "word": " اللي", "probability": 0.9853515625}, {"start": 1682.7, "end": 1682.92, "word": " بدنا", "probability": 0.88671875}, {"start": 1682.92, "end": 1683.42, "word": " نثبته", "probability": 0.89990234375}], "temperature": 1.0}, {"id": 74, "seek": 169942, "start": 1684.44, "end": 1699.42, "text": "الان النظرية بتقول إذا كانت H بتحتوي على orthonormal sequence اه orthonormal sequence which is total يعني بتحتوي على total orthonormal sequence لازم الـHش تكون separable", "tokens": [6027, 7649, 28239, 19913, 2288, 10632, 39894, 39648, 11933, 15730, 25961, 2655, 389, 39894, 33753, 45865, 15844, 420, 11943, 24440, 8310, 1975, 3224, 420, 11943, 24440, 8310, 597, 307, 3217, 37495, 22653, 39894, 33753, 45865, 15844, 3217, 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separable", "probability": 0.843505859375}], "temperature": 1.0}, {"id": 76, "seek": 174666, "start": 1722.14, "end": 1746.66, "text": "طيب بدنا نجيلنا بمعنى واخر بدنا نعملنا construction هو بده يعملنا construction بده يعملنا construction لاللي هي set تكون dense in H من ال orthonormal sequence اللي عندها let em be a total orthonormal sequence in mean in H قالي لها هي بين إيدينا", "tokens": [9566, 1829, 3555, 47525, 8315, 8717, 7435, 26895, 8315, 4724, 2304, 3615, 1863, 7578, 4032, 47283, 2288, 47525, 8315, 8717, 25957, 1211, 8315, 6435, 31439, 47525, 3224, 7251, 25957, 1211, 8315, 6435, 47525, 3224, 7251, 25957, 1211, 8315, 6435, 5296, 6027, 20292, 39896, 992, 6055, 30544, 18011, 294, 389, 9154, 2423, 420, 11943, 24440, 8310, 13672, 1829, 43242, 11296, 718, 846, 312, 257, 3217, 420, 11943, 24440, 8310, 294, 914, 294, 389, 50239, 1829, 5296, 11296, 39896, 49374, 11933, 1829, 16254, 8315], "avg_logprob": -0.3254894492137863, "compression_ratio": 1.7883597883597884, "no_speech_prob": 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1744.1, "word": " in", "probability": 0.95263671875}, {"start": 1744.1, "end": 1744.44, "word": " mean", "probability": 0.264404296875}, {"start": 1744.44, "end": 1744.96, "word": " in", "probability": 0.85498046875}, {"start": 1744.96, "end": 1745.26, "word": " H", "probability": 0.9033203125}, {"start": 1745.26, "end": 1745.84, "word": " قالي", "probability": 0.3328857421875}, {"start": 1745.84, "end": 1745.96, "word": " لها", "probability": 0.637939453125}, {"start": 1745.96, "end": 1746.08, "word": " هي", "probability": 0.88037109375}, {"start": 1746.08, "end": 1746.28, "word": " بين", "probability": 0.9013671875}, {"start": 1746.28, "end": 1746.66, "word": " إيدينا", "probability": 0.6522216796875}], "temperature": 1.0}, {"id": 77, "seek": 177151, "start": 1747.25, "end": 1771.51, "text": "عند خد A إيش بتساوي؟ بساوي عبارة عن كل ال formations Gamma K N E K K من واحد لعندها ال E K هذولة اللي من هذه ماشي الحال الآن ال ال coefficients هذولة بتدخلهم طبعا أنا بحكي بس يشتغل في real أو complex خلينا ال complex in general وفي حالة ال real بتسافروا ال imaginary part", "tokens": [3615, 41260, 16490, 3215, 316, 11933, 1829, 8592, 39894, 3794, 995, 45865, 22807, 4724, 3794, 995, 45865, 6225, 3555, 9640, 3660, 18871, 28242, 2423, 39652, 24723, 1696, 591, 426, 462, 591, 591, 9154, 36764, 24401, 5296, 3615, 41260, 11296, 2423, 462, 591, 8032, 8848, 12610, 3660, 13672, 1829, 9154, 29538, 3714, 33599, 1829, 21542, 6027, 6024, 48506, 2423, 2423, 31994, 8032, 8848, 12610, 3660, 39894, 3215, 9778, 1211, 16095, 23032, 3555, 3615, 995, 41850, 4724, 5016, 4117, 1829, 4724, 3794, 7251, 8592, 2655, 17082, 1211, 8978, 957, 34051, 3997, 16490, 1211, 9957, 995, 2423, 3997, 294, 2674, 4032, 41185, 11331, 6027, 3660, 2423, 957, 39894, 3794, 31845, 2288, 14407, 2423, 26164, 644], "avg_logprob": -0.2837389338332995, "compression_ratio": 1.6023622047244095, "no_speech_prob": 7.748603820800781e-07, "words": [{"start": 1747.25, "end": 1747.61, "word": "عند", "probability": 0.783447265625}, {"start": 1747.61, "end": 1748.01, "word": " خد", "probability": 0.58447265625}, {"start": 1748.01, "end": 1748.23, "word": " A", "probability": 0.295654296875}, {"start": 1748.23, "end": 1748.47, "word": " إيش", "probability": 0.7670084635416666}, {"start": 1748.47, "end": 1749.99, "word": " بتساوي؟", "probability": 0.8830078125}, {"start": 1749.99, "end": 1750.43, "word": " بساوي", "probability": 0.84423828125}, {"start": 1750.43, "end": 1750.83, "word": " عبارة", "probability": 0.99365234375}, {"start": 1750.83, "end": 1750.99, "word": " عن", "probability": 0.99755859375}, {"start": 1750.99, "end": 1751.25, "word": " كل", "probability": 0.984375}, {"start": 1751.25, "end": 1751.39, "word": " ال", "probability": 0.90380859375}, {"start": 1751.39, "end": 1752.01, "word": " formations", "probability": 0.09564208984375}, {"start": 1752.01, "end": 1752.95, "word": " Gamma", "probability": 0.663818359375}, {"start": 1752.95, "end": 1753.11, "word": " K", "probability": 0.396728515625}, {"start": 1753.11, "end": 1753.37, "word": " N", "probability": 0.56201171875}, {"start": 1753.37, "end": 1753.89, "word": " E", "probability": 0.40771484375}, {"start": 1753.89, "end": 1754.19, "word": " K", "probability": 0.908203125}, {"start": 1754.19, "end": 1754.61, "word": " K", "probability": 0.240966796875}, {"start": 1754.61, "end": 1754.73, "word": " من", "probability": 0.92529296875}, {"start": 1754.73, "end": 1755.03, "word": " واحد", "probability": 0.95068359375}, {"start": 1755.03, "end": 1755.47, "word": " لعندها", "probability": 0.730224609375}, {"start": 1755.47, "end": 1756.33, "word": " ال", "probability": 0.59765625}, {"start": 1756.33, "end": 1756.61, "word": " E", "probability": 0.734375}, {"start": 1756.61, "end": 1756.87, "word": " K", "probability": 0.85009765625}, {"start": 1756.87, "end": 1757.71, "word": " هذولة", "probability": 0.746337890625}, {"start": 1757.71, "end": 1758.01, "word": " اللي", "probability": 0.949462890625}, {"start": 1758.01, "end": 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1831.95, "end": 1832.07, "word": " هو", "probability": 0.92041015625}, {"start": 1832.07, "end": 1832.35, "word": " عبارة", "probability": 0.969970703125}, {"start": 1832.35, "end": 1832.53, "word": " عن", "probability": 0.99853515625}, {"start": 1832.53, "end": 1832.97, "word": " العنصر", "probability": 0.9210205078125}, {"start": 1832.97, "end": 1833.33, "word": " هذا", "probability": 0.80859375}, {"start": 1833.33, "end": 1834.03, "word": " Gamma", "probability": 0.642333984375}, {"start": 1834.03, "end": 1834.33, "word": " K", "probability": 0.759765625}, {"start": 1834.33, "end": 1835.21, "word": " واحد", "probability": 0.6300048828125}, {"start": 1835.21, "end": 1835.69, "word": " EK", "probability": 0.405517578125}], "temperature": 1.0}, {"id": 81, "seek": 186666, "start": 1837.32, "end": 1866.66, "text": "ممكن أنصر تاني يقولك أنا بدي أبقيها من واحد لعند مين لعند عشرة اللي هو ال submission a,k,n,e,k عده من واحد لعشرة لعشرين للا تلاتي لكل ال finite اللي في الدنيا جات ما بدك اللي هي الأن تاخدها واحد اتنين تلاتة إذا شكل العناصر هذا أنا عارف كيف شكله اللي هي ال coefficients هدولة من مين من ال complex numbers لكن ال coefficients تبعات اللي هي ال real part و ال imaginary part عبارة عن أعداد نسبية rational numbers", "tokens": [2304, 43020, 14739, 9381, 2288, 6055, 7649, 1829, 7251, 39648, 4117, 41850, 4724, 16254, 5551, 3555, 38436, 11296, 9154, 36764, 24401, 5296, 3615, 41260, 3714, 9957, 5296, 3615, 41260, 6225, 8592, 25720, 13672, 1829, 31439, 2423, 23689, 257, 11, 74, 11, 77, 11, 68, 11, 74, 6225, 3215, 3224, 9154, 36764, 24401, 5296, 3615, 8592, 25720, 5296, 3615, 46309, 9957, 5296, 15040, 6055, 1211, 9307, 1829, 5296, 28820, 2423, 19362, 13672, 1829, 8978, 32748, 22653, 995, 10874, 9307, 19446, 47525, 4117, 13672, 1829, 39896, 16247, 1863, 6055, 47283, 3215, 11296, 36764, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 11933, 15730, 13412, 28820, 18863, 1863, 33546, 2288, 23758, 41850, 6225, 9640, 5172, 9122, 33911, 13412, 28820, 3224, 13672, 1829, 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" finite", "probability": 0.86328125}, {"start": 1849.04, "end": 1849.34, "word": " اللي", "probability": 0.986328125}, {"start": 1849.34, "end": 1849.46, "word": " في", "probability": 0.89306640625}, {"start": 1849.46, "end": 1849.78, "word": " الدنيا", "probability": 0.9925130208333334}, {"start": 1849.78, "end": 1849.98, "word": " جات", "probability": 0.69384765625}, {"start": 1849.98, "end": 1850.06, "word": " ما", "probability": 0.75341796875}, {"start": 1850.06, "end": 1850.36, "word": " بدك", "probability": 0.88720703125}, {"start": 1850.36, "end": 1850.5, "word": " اللي", "probability": 0.9775390625}, {"start": 1850.5, "end": 1850.6, "word": " هي", "probability": 0.912109375}, {"start": 1850.6, "end": 1850.88, "word": " الأن", "probability": 0.61962890625}, {"start": 1850.88, "end": 1851.6, "word": " تاخدها", "probability": 0.9532470703125}, {"start": 1851.6, "end": 1851.94, "word": " واحد", "probability": 0.9921875}, {"start": 1851.94, "end": 1852.3, "word": " اتنين", "probability": 0.9381103515625}, {"start": 1852.3, "end": 1852.74, "word": " تلاتة", "probability": 0.9493408203125}, {"start": 1852.74, "end": 1853.28, "word": " إذا", "probability": 0.6458740234375}, {"start": 1853.28, "end": 1853.74, "word": " شكل", "probability": 0.950439453125}, {"start": 1853.74, "end": 1854.28, "word": " العناصر", "probability": 0.9747314453125}, {"start": 1854.28, "end": 1854.46, "word": " هذا", "probability": 0.9296875}, {"start": 1854.46, "end": 1854.56, "word": " أنا", "probability": 0.484375}, {"start": 1854.56, "end": 1854.78, "word": " عارف", "probability": 0.9215494791666666}, {"start": 1854.78, "end": 1854.96, "word": " كيف", "probability": 0.938232421875}, {"start": 1854.96, "end": 1855.84, "word": " شكله", "probability": 0.9884440104166666}, {"start": 1855.84, "end": 1856.1, "word": " اللي", "probability": 0.955078125}, {"start": 1856.1, "end": 1856.24, "word": " هي", "probability": 0.89306640625}, {"start": 1856.24, "end": 1856.38, "word": " ال", "probability": 0.9501953125}, {"start": 1856.38, "end": 1856.88, "word": " coefficients", "probability": 0.8349609375}, {"start": 1856.88, "end": 1857.5, "word": " هدولة", "probability": 0.7779541015625}, {"start": 1857.5, "end": 1857.68, "word": " من", "probability": 0.927734375}, {"start": 1857.68, "end": 1858.02, "word": " مين", "probability": 0.743896484375}, {"start": 1858.02, "end": 1858.28, "word": " من", "probability": 0.91943359375}, {"start": 1858.28, "end": 1858.44, "word": " ال", "probability": 0.970703125}, {"start": 1858.44, "end": 1858.8, "word": " complex", "probability": 0.873046875}, {"start": 1858.8, "end": 1859.26, "word": " numbers", "probability": 0.81591796875}, {"start": 1859.26, "end": 1859.94, "word": " لكن", "probability": 0.93017578125}, {"start": 1859.94, "end": 1860.7, "word": " ال", "probability": 0.98291015625}, {"start": 1860.7, "end": 1861.26, "word": " coefficients", "probability": 0.93994140625}, {"start": 1861.26, "end": 1861.92, "word": " تبعات", "probability": 0.824462890625}, {"start": 1861.92, "end": 1862.06, "word": " اللي", "probability": 0.958740234375}, {"start": 1862.06, "end": 1862.26, "word": " هي", "probability": 0.9345703125}, {"start": 1862.26, "end": 1862.62, "word": " ال", "probability": 0.91650390625}, {"start": 1862.62, "end": 1862.86, "word": " real", "probability": 0.41845703125}, {"start": 1862.86, "end": 1863.12, "word": " part", "probability": 0.90673828125}, {"start": 1863.12, "end": 1863.24, "word": " و", "probability": 0.60205078125}, {"start": 1863.24, "end": 1863.3, "word": " ال", "probability": 0.81689453125}, {"start": 1863.3, "end": 1863.54, "word": " imaginary", "probability": 0.79150390625}, {"start": 1863.54, "end": 1864.0, "word": " part", "probability": 0.953125}, {"start": 1864.0, "end": 1864.48, "word": " عبارة", "probability": 0.98291015625}, {"start": 1864.48, "end": 1864.74, "word": " عن", "probability": 0.9931640625}, {"start": 1864.74, "end": 1865.3, "word": " أعداد", "probability": 0.93212890625}, {"start": 1865.3, "end": 1865.76, "word": " نسبية", "probability": 0.9326171875}, {"start": 1865.76, "end": 1866.06, "word": " rational", "probability": 0.68701171875}, {"start": 1866.06, "end": 1866.66, "word": " numbers", "probability": 0.787109375}], "temperature": 1.0}, {"id": 82, "seek": 189372, "start": 1867.22, "end": 1893.72, "text": "طيب عشان نضمن اللي هو تكون countable الان BKM بتساوي سفر لما ال H تكون أيش ما لها real Hilbert space هنا خلينا نشتغل عن ال general و بيكون ده كحالة خاصة منه زي ما قولت A is countable هو قولناها هو ايش الان we show that هذه المؤهلة اننا اثبتناها انها dense in H اذا اثبتناها dense in H بيكون خلصناها بتكون H أيش ما لها inseparable اطلع تشوف كإعلان", "tokens": [9566, 1829, 3555, 6225, 8592, 7649, 8717, 11242, 27842, 13672, 1829, 31439, 6055, 30544, 1207, 712, 2423, 7649, 363, 42, 44, 39894, 3794, 995, 45865, 8608, 5172, 2288, 5296, 15042, 2423, 389, 6055, 30544, 36632, 8592, 19446, 5296, 11296, 957, 19914, 4290, 1901, 34105, 16490, 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"word": " نضمن", "probability": 0.9837239583333334}, {"start": 1868.52, "end": 1868.8, "word": " اللي", "probability": 0.79296875}, {"start": 1868.8, "end": 1869.08, "word": " هو", "probability": 0.984375}, {"start": 1869.08, "end": 1869.46, "word": " تكون", "probability": 0.775634765625}, {"start": 1869.46, "end": 1869.98, "word": " countable", "probability": 0.932373046875}, {"start": 1869.98, "end": 1870.6, "word": " الان", "probability": 0.6534423828125}, {"start": 1870.6, "end": 1871.74, "word": " BKM", "probability": 0.6358235677083334}, {"start": 1871.74, "end": 1872.26, "word": " بتساوي", "probability": 0.72650146484375}, {"start": 1872.26, "end": 1872.58, "word": " سفر", "probability": 0.771484375}, {"start": 1872.58, "end": 1872.84, "word": " لما", "probability": 0.90966796875}, {"start": 1872.84, "end": 1872.94, "word": " ال", "probability": 0.88037109375}, {"start": 1872.94, "end": 1873.1, "word": " H", "probability": 0.45703125}, {"start": 1873.1, "end": 1873.36, "word": " تكون", "probability": 0.974853515625}, {"start": 1873.36, "end": 1873.58, "word": " أيش", "probability": 0.3707275390625}, {"start": 1873.58, "end": 1873.68, "word": " ما", "probability": 0.84130859375}, {"start": 1873.68, "end": 1873.94, "word": " لها", "probability": 0.719970703125}, {"start": 1873.94, "end": 1874.7, "word": " real", "probability": 0.638671875}, {"start": 1874.7, "end": 1875.36, "word": " Hilbert", "probability": 0.83935546875}, {"start": 1875.36, "end": 1875.86, "word": " space", "probability": 0.796875}, {"start": 1875.86, "end": 1876.16, "word": " هنا", "probability": 0.1513671875}, {"start": 1876.16, "end": 1876.48, "word": " خلينا", "probability": 0.591552734375}, {"start": 1876.48, "end": 1876.8, "word": " نشتغل", "probability": 0.9947265625}, {"start": 1876.8, "end": 1876.94, "word": " عن", "probability": 0.7470703125}, {"start": 1876.94, "end": 1877.08, "word": " ال", "probability": 0.94091796875}, {"start": 1877.08, "end": 1877.38, "word": " general", "probability": 0.86865234375}, {"start": 1877.38, "end": 1877.64, "word": " و", "probability": 0.701171875}, {"start": 1877.64, "end": 1877.88, "word": " بيكون", "probability": 0.6691080729166666}, {"start": 1877.88, "end": 1878.1, "word": " ده", "probability": 0.772705078125}, {"start": 1878.1, "end": 1878.94, "word": " كحالة", "probability": 0.83648681640625}, {"start": 1878.94, "end": 1879.24, "word": " خاصة", "probability": 0.96630859375}, {"start": 1879.24, "end": 1879.54, "word": " منه", "probability": 0.978271484375}, {"start": 1879.54, "end": 1880.26, "word": " زي", "probability": 0.958984375}, {"start": 1880.26, "end": 1880.32, "word": " ما", "probability": 0.98388671875}, {"start": 1880.32, "end": 1880.62, "word": " قولت", "probability": 0.9099934895833334}, {"start": 1880.62, "end": 1880.76, "word": " A", "probability": 0.488525390625}, {"start": 1880.76, "end": 1880.96, "word": " is", "probability": 0.95263671875}, {"start": 1880.96, "end": 1881.42, "word": " countable", "probability": 0.97607421875}, {"start": 1881.42, "end": 1882.02, "word": " هو", "probability": 0.52001953125}, {"start": 1882.02, "end": 1882.6, "word": " قولناها", "probability": 0.9112548828125}, {"start": 1882.6, "end": 1882.82, "word": " هو", "probability": 0.53955078125}, {"start": 1882.82, "end": 1883.14, "word": " ايش", "probability": 0.7414143880208334}, {"start": 1883.14, "end": 1883.82, "word": " الان", "probability": 0.7041015625}, {"start": 1883.82, "end": 1884.1, "word": " we", "probability": 0.74267578125}, {"start": 1884.1, "end": 1884.48, "word": " show", "probability": 0.96044921875}, {"start": 1884.48, "end": 1884.9, "word": " that", "probability": 0.9482421875}, {"start": 1884.9, "end": 1885.32, "word": " هذه", "probability": 0.796875}, {"start": 1885.32, "end": 1886.06, "word": " المؤهلة", "probability": 0.9906005859375}, {"start": 1886.06, "end": 1886.84, "word": " اننا", "probability": 0.5302734375}, {"start": 1886.84, "end": 1887.38, "word": " اثبتناها", "probability": 0.86083984375}, {"start": 1887.38, "end": 1887.66, "word": " انها", "probability": 0.89794921875}, {"start": 1887.66, "end": 1887.88, "word": " dense", "probability": 0.6767578125}, {"start": 1887.88, "end": 1888.08, "word": " in", "probability": 0.54345703125}, {"start": 1888.08, "end": 1888.2, "word": " H", "probability": 0.9736328125}, {"start": 1888.2, "end": 1888.38, "word": " اذا", "probability": 0.7056884765625}, {"start": 1888.38, "end": 1888.88, "word": " اثبتناها", "probability": 0.953369140625}, {"start": 1888.88, "end": 1889.08, "word": " dense", "probability": 0.83544921875}, {"start": 1889.08, "end": 1889.24, "word": " in", "probability": 0.74560546875}, {"start": 1889.24, "end": 1889.38, "word": " H", "probability": 0.95458984375}, {"start": 1889.38, "end": 1889.62, "word": " بيكون", "probability": 0.768310546875}, {"start": 1889.62, "end": 1890.12, "word": " خلصناها", "probability": 0.86240234375}, {"start": 1890.12, "end": 1890.4, "word": " بتكون", "probability": 0.787353515625}, {"start": 1890.4, "end": 1890.66, "word": " H", "probability": 0.88427734375}, {"start": 1890.66, "end": 1890.86, "word": " أيش", "probability": 0.943359375}, {"start": 1890.86, "end": 1890.98, "word": " ما", "probability": 0.9443359375}, {"start": 1890.98, "end": 1891.3, "word": " لها", "probability": 0.944580078125}, {"start": 1891.3, "end": 1892.22, "word": " inseparable", "probability": 0.77490234375}, {"start": 1892.22, "end": 1892.7, "word": " اطلع", "probability": 0.929443359375}, {"start": 1892.7, "end": 1893.06, "word": " تشوف", "probability": 0.97314453125}, {"start": 1893.06, "end": 1893.72, "word": " كإعلان", "probability": 0.61346435546875}], "temperature": 1.0}, {"id": 83, "seek": 192114, "start": 1894.84, "end": 1921.14, "text": "كيف بدي اثبت انه dense؟ بدي اخد الـ NX and fixed element in mean in H ماشي الحال هو ألاجيه لك ان NX تقاطع اللي هو الـ set هذه لا يساوي 5 بقول خلصها بس ماتناهيش انها dense عشان اثبت انها dense انه لو أخدنا أي element هنا بقدر ألاجي اللي هو بيكون عندى أي neighborhood حوالينها ذاك و بطلع هذاك اللي بتشوفه ان شاء الله let X be and fixed element in mean in H", "tokens": [4117, 33911, 4724, 16254, 1975, 12984, 3555, 2655, 16472, 3224, 18011, 22807, 4724, 16254, 1975, 9778, 3215, 2423, 39184, 426, 55, 293, 6806, 4478, 294, 914, 294, 389, 3714, 33599, 1829, 21542, 6027, 31439, 5551, 15040, 7435, 1829, 3224, 5296, 4117, 16472, 426, 55, 6055, 4587, 41193, 3615, 13672, 1829, 31439, 2423, 39184, 992, 29538, 20193, 7251, 3794, 995, 45865, 1025, 4724, 39648, 16490, 1211, 9381, 11296, 4724, 3794, 3714, 9307, 8315, 3224, 1829, 8592, 16472, 11296, 18011, 6225, 8592, 7649, 1975, 12984, 3555, 2655, 16472, 11296, 18011, 16472, 3224, 45164, 5551, 9778, 3215, 8315, 36632, 4478, 34105, 4724, 28543, 2288, 5551, 15040, 7435, 1829, 13672, 1829, 31439, 4724, 1829, 30544, 43242, 7578, 36632, 7630, 11331, 2407, 6027, 9957, 11296, 29910, 995, 4117, 4032, 4724, 9566, 1211, 3615, 8032, 8848, 995, 4117, 13672, 1829, 39894, 8592, 38688, 3224, 16472, 13412, 16606, 21984, 718, 1783, 312, 293, 6806, 4478, 294, 914, 294, 389], "avg_logprob": -0.35723040618148505, "compression_ratio": 1.8265306122448979, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1894.84, "end": 1895.16, "word": "كيف", "probability": 0.796142578125}, {"start": 1895.16, "end": 1895.32, "word": " بدي", "probability": 0.23529052734375}, {"start": 1895.32, "end": 1895.64, "word": " اثبت", "probability": 0.8536376953125}, {"start": 1895.64, "end": 1895.9, "word": " انه", "probability": 0.847900390625}, {"start": 1895.9, "end": 1896.54, "word": " dense؟", "probability": 0.650390625}, {"start": 1896.54, "end": 1896.76, "word": " بدي", "probability": 0.72509765625}, {"start": 1896.76, "end": 1897.04, "word": " اخد", "probability": 0.8380533854166666}, {"start": 1897.04, "end": 1897.26, "word": " الـ", "probability": 0.545166015625}, {"start": 1897.26, "end": 1897.76, "word": " NX", "probability": 0.540771484375}, {"start": 1897.76, "end": 1898.04, "word": " and", "probability": 0.0980224609375}, {"start": 1898.04, "end": 1898.36, "word": " fixed", "probability": 0.1572265625}, {"start": 1898.36, "end": 1898.86, "word": " element", "probability": 0.88916015625}, {"start": 1898.86, "end": 1899.18, "word": " in", "probability": 0.7421875}, {"start": 1899.18, "end": 1899.7, "word": " mean", "probability": 0.393310546875}, {"start": 1899.7, "end": 1900.24, "word": " in", "probability": 0.4755859375}, {"start": 1900.24, "end": 1900.58, "word": " H", "probability": 0.8115234375}, {"start": 1900.58, "end": 1901.1, "word": " ماشي", "probability": 0.767822265625}, {"start": 1901.1, "end": 1901.46, "word": " الحال", "probability": 0.9609375}, {"start": 1901.46, "end": 1902.46, "word": " هو", "probability": 0.7275390625}, {"start": 1902.46, "end": 1902.94, "word": " ألاجيه", "probability": 0.643359375}, {"start": 1902.94, "end": 1903.08, "word": " لك", "probability": 0.4732666015625}, {"start": 1903.08, "end": 1903.18, "word": " ان", "probability": 0.736328125}, {"start": 1903.18, "end": 1903.82, "word": " NX", "probability": 0.6531982421875}, {"start": 1903.82, "end": 1904.52, "word": " تقاطع", "probability": 0.9107666015625}, {"start": 1904.52, "end": 1904.7, "word": " اللي", "probability": 0.7020263671875}, {"start": 1904.7, "end": 1905.0, "word": " هو", "probability": 0.83349609375}, {"start": 1905.0, "end": 1905.38, "word": " الـ", "probability": 0.5906982421875}, {"start": 1905.38, "end": 1905.84, "word": " set", "probability": 0.491943359375}, {"start": 1905.84, "end": 1906.28, "word": " هذه", "probability": 0.68359375}, {"start": 1906.28, "end": 1906.62, "word": " لا", "probability": 0.466552734375}, {"start": 1906.62, "end": 1906.98, "word": " يساوي", "probability": 0.794677734375}, {"start": 1906.98, "end": 1907.26, "word": " 5", "probability": 0.439208984375}, {"start": 1907.26, "end": 1907.64, "word": " بقول", "probability": 0.38763427734375}, {"start": 1907.64, "end": 1908.14, "word": " خلصها", "probability": 0.9154052734375}, {"start": 1908.14, "end": 1908.36, "word": " بس", "probability": 0.69189453125}, {"start": 1908.36, "end": 1908.82, "word": " ماتناهيش", "probability": 0.546630859375}, {"start": 1908.82, "end": 1909.02, "word": " انها", "probability": 0.8212890625}, {"start": 1909.02, "end": 1909.32, "word": " dense", "probability": 0.96533203125}, {"start": 1909.32, "end": 1910.12, "word": " عشان", "probability": 0.9749348958333334}, {"start": 1910.12, "end": 1910.4, "word": " اثبت", "probability": 0.9324951171875}, {"start": 1910.4, "end": 1910.62, "word": " انها", "probability": 0.6031494140625}, {"start": 1910.62, "end": 1910.94, "word": " dense", "probability": 0.79150390625}, {"start": 1910.94, "end": 1911.24, "word": " انه", "probability": 0.5196533203125}, {"start": 1911.24, "end": 1911.32, "word": " لو", "probability": 0.94970703125}, {"start": 1911.32, "end": 1911.68, "word": " أخدنا", "probability": 0.869140625}, {"start": 1911.68, "end": 1911.88, "word": " أي", "probability": 0.60595703125}, {"start": 1911.88, "end": 1912.32, "word": " element", "probability": 0.9736328125}, {"start": 1912.32, "end": 1912.72, "word": " هنا", "probability": 0.9677734375}, {"start": 1912.72, "end": 1913.68, "word": " بقدر", "probability": 0.9816080729166666}, {"start": 1913.68, "end": 1914.16, "word": " ألاجي", "probability": 0.9029541015625}, {"start": 1914.16, "end": 1914.3, "word": " اللي", "probability": 0.885009765625}, {"start": 1914.3, "end": 1914.5, "word": " هو", "probability": 0.9462890625}, {"start": 1914.5, "end": 1914.88, "word": " بيكون", "probability": 0.66064453125}, {"start": 1914.88, "end": 1915.2, "word": " عندى", "probability": 0.650634765625}, {"start": 1915.2, "end": 1915.36, "word": " أي", "probability": 0.67431640625}, {"start": 1915.36, "end": 1915.7, "word": " neighborhood", "probability": 0.59228515625}, {"start": 1915.7, "end": 1916.34, "word": " حوالينها", "probability": 0.89404296875}, {"start": 1916.34, "end": 1916.5, "word": " ذاك", "probability": 0.638671875}, {"start": 1916.5, "end": 1916.58, "word": " و", "probability": 0.294189453125}, {"start": 1916.58, "end": 1916.82, "word": " بطلع", "probability": 0.783172607421875}, {"start": 1916.82, "end": 1917.08, "word": " هذاك", "probability": 0.73590087890625}, {"start": 1917.08, "end": 1917.16, "word": " اللي", "probability": 0.908935546875}, {"start": 1917.16, "end": 1917.62, "word": " بتشوفه", "probability": 0.9259033203125}, {"start": 1917.62, "end": 1917.68, "word": " ان", "probability": 0.74072265625}, {"start": 1917.68, "end": 1917.82, "word": " شاء", "probability": 0.895751953125}, {"start": 1917.82, "end": 1917.92, "word": " الله", "probability": 0.94775390625}, {"start": 1917.92, "end": 1918.52, "word": " let", "probability": 0.62939453125}, {"start": 1918.52, "end": 1918.78, "word": " X", "probability": 0.765625}, {"start": 1918.78, "end": 1918.94, "word": " be", "probability": 0.75244140625}, {"start": 1918.94, "end": 1919.14, "word": " and", "probability": 0.8017578125}, {"start": 1919.14, "end": 1919.44, "word": " fixed", "probability": 0.90771484375}, {"start": 1919.44, "end": 1919.8, "word": " element", "probability": 0.9599609375}, {"start": 1919.8, "end": 1920.16, "word": " in", "probability": 0.9599609375}, {"start": 1920.16, "end": 1920.5, "word": " mean", "probability": 0.96630859375}, {"start": 1920.5, "end": 1920.9, "word": " in", "probability": 0.93798828125}, {"start": 1920.9, "end": 1921.14, "word": " H", "probability": 0.97705078125}], "temperature": 1.0}, {"id": 84, "seek": 193990, "start": 1921.82, "end": 1939.9, "text": "الآن since EM is a total or from a total set in H إذا الإسبانيك لو جعل ال EM إيش حيساوي؟ من التعريف طيب إذا for every إبسلون أكبر من سفر مهما كانت إبسلون صغيرة هذه اللي بتبتعبر عن ال arbitrary neighborhood", "tokens": [6027, 148, 48506, 1670, 16237, 307, 257, 3217, 420, 490, 257, 3217, 992, 294, 389, 11933, 15730, 33688, 35457, 7649, 1829, 4117, 45164, 10874, 30241, 2423, 16237, 11933, 1829, 8592, 11331, 1829, 3794, 995, 45865, 22807, 9154, 16712, 3615, 16572, 5172, 23032, 1829, 3555, 11933, 15730, 337, 633, 11933, 3555, 3794, 1211, 11536, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 3714, 3224, 15042, 25961, 2655, 11933, 3555, 3794, 1211, 11536, 20328, 17082, 48923, 29538, 13672, 1829, 39894, 3555, 2655, 3615, 26890, 18871, 2423, 23211, 7630], "avg_logprob": -0.2997819680807202, "compression_ratio": 1.4386792452830188, "no_speech_prob": 1.430511474609375e-06, "words": [{"start": 1921.82, "end": 1922.26, "word": "الآن", "probability": 0.6474609375}, {"start": 1922.26, "end": 1923.32, "word": " since", "probability": 0.609375}, {"start": 1923.32, "end": 1923.86, "word": " EM", "probability": 0.34375}, {"start": 1923.86, "end": 1924.32, "word": " is", "probability": 0.93408203125}, {"start": 1924.32, "end": 1924.52, "word": " a", "probability": 0.9453125}, {"start": 1924.52, "end": 1924.88, "word": " total", "probability": 0.85595703125}, {"start": 1924.88, "end": 1925.4, "word": " or", "probability": 0.401123046875}, {"start": 1925.4, "end": 1925.7, "word": " from", "probability": 0.2425537109375}, {"start": 1925.7, "end": 1925.86, "word": " a", "probability": 0.85986328125}, {"start": 1925.86, "end": 1926.16, "word": " total", "probability": 0.876953125}, {"start": 1926.16, "end": 1926.48, "word": " set", "probability": 0.32861328125}, {"start": 1926.48, "end": 1926.7, "word": " in", "probability": 0.80322265625}, {"start": 1926.7, "end": 1927.02, "word": " H", "probability": 0.94580078125}, {"start": 1927.02, "end": 1927.66, "word": " إذا", "probability": 0.6414794921875}, {"start": 1927.66, "end": 1928.34, "word": " الإسبانيك", "probability": 0.727294921875}, {"start": 1928.34, "end": 1928.5, "word": " لو", "probability": 0.1861572265625}, {"start": 1928.5, "end": 1928.74, "word": " جعل", "probability": 0.735107421875}, {"start": 1928.74, "end": 1928.9, "word": " ال", "probability": 0.354248046875}, {"start": 1928.9, "end": 1929.1, "word": " EM", "probability": 0.77978515625}, {"start": 1929.1, "end": 1929.36, "word": " إيش", "probability": 0.8248697916666666}, {"start": 1929.36, "end": 1930.08, "word": " حيساوي؟", "probability": 0.6772867838541666}, {"start": 1930.08, "end": 1930.44, "word": " من", "probability": 0.93408203125}, {"start": 1930.44, "end": 1930.96, "word": " التعريف", "probability": 0.9857177734375}, {"start": 1930.96, "end": 1931.64, "word": " طيب", "probability": 0.9034830729166666}, {"start": 1931.64, "end": 1932.22, "word": " إذا", "probability": 0.798828125}, {"start": 1932.22, "end": 1932.52, "word": " for", "probability": 0.935546875}, {"start": 1932.52, "end": 1933.0, "word": " every", "probability": 0.8203125}, {"start": 1933.0, "end": 1933.48, "word": " إبسلون", "probability": 0.733837890625}, {"start": 1933.48, "end": 1933.84, "word": " أكبر", "probability": 0.9763997395833334}, {"start": 1933.84, "end": 1934.02, "word": " من", "probability": 0.9931640625}, {"start": 1934.02, "end": 1934.34, "word": " سفر", "probability": 0.7625325520833334}, {"start": 1934.34, "end": 1934.78, "word": " مهما", "probability": 0.9036458333333334}, {"start": 1934.78, "end": 1935.24, "word": " كانت", "probability": 0.991943359375}, {"start": 1935.24, "end": 1935.72, "word": " إبسلون", "probability": 0.975390625}, {"start": 1935.72, "end": 1936.24, "word": " صغيرة", "probability": 0.99462890625}, {"start": 1936.24, "end": 1937.04, "word": " هذه", "probability": 0.397705078125}, {"start": 1937.04, "end": 1937.18, "word": " اللي", "probability": 0.91357421875}, {"start": 1937.18, "end": 1937.86, "word": " بتبتعبر", "probability": 0.709619140625}, {"start": 1937.86, "end": 1938.06, "word": " عن", "probability": 0.99072265625}, {"start": 1938.06, "end": 1938.2, "word": " ال", "probability": 0.9541015625}, {"start": 1938.2, "end": 1939.02, "word": " arbitrary", "probability": 0.71240234375}, {"start": 1939.02, "end": 1939.9, "word": " neighborhood", "probability": 0.59912109375}], "temperature": 1.0}, {"id": 85, "seek": 196668, "start": 1940.72, "end": 1966.68, "text": "الان there is w element ل span em such that المسافة بين x نقص w أصغر من أي أسغر من أي epsilon في الدنيا أنا بتسميه y على 2 للحسابات ماشي الحال إذا الأن لإن span لل em dense in H إذا لأي x في ال H بقدر ألاقي اللي هو element في اللي جوا هذا بحيث المسافة بين x و w أصغر من أي epsilon في الدنيا", "tokens": [6027, 7649, 456, 307, 261, 4478, 5296, 16174, 846, 1270, 300, 9673, 3794, 31845, 3660, 49374, 2031, 8717, 4587, 9381, 261, 5551, 9381, 17082, 2288, 9154, 36632, 5551, 3794, 17082, 2288, 9154, 36632, 17889, 8978, 32748, 22653, 995, 41850, 39894, 38251, 1829, 3224, 288, 15844, 568, 24976, 5016, 3794, 16758, 9307, 3714, 33599, 1829, 21542, 6027, 11933, 15730, 16247, 1863, 5296, 28814, 1863, 16174, 24976, 846, 18011, 294, 389, 11933, 15730, 5296, 10721, 1829, 2031, 8978, 2423, 389, 4724, 28543, 2288, 5551, 15040, 38436, 13672, 1829, 31439, 4478, 8978, 13672, 1829, 10874, 14407, 23758, 4724, 5016, 1829, 12984, 9673, 3794, 31845, 3660, 49374, 2031, 4032, 261, 5551, 9381, 17082, 2288, 9154, 36632, 17889, 8978, 32748, 22653, 995], "avg_logprob": -0.2764830417552237, "compression_ratio": 1.8375, "no_speech_prob": 8.940696716308594e-07, "words": [{"start": 1940.72, "end": 1941.16, "word": "الان", "probability": 0.6524658203125}, {"start": 1941.16, "end": 1941.86, "word": " there", "probability": 0.38232421875}, {"start": 1941.86, "end": 1942.14, "word": " is", "probability": 0.923828125}, {"start": 1942.14, "end": 1942.68, "word": " w", "probability": 0.6796875}, {"start": 1942.68, "end": 1943.2, "word": " element", "probability": 0.8701171875}, {"start": 1943.2, "end": 1943.4, "word": " ل", "probability": 0.53466796875}, {"start": 1943.4, "end": 1943.68, "word": " span", "probability": 0.57666015625}, {"start": 1943.68, "end": 1943.94, "word": " em", "probability": 0.3671875}, {"start": 1943.94, "end": 1944.34, "word": " such", "probability": 0.85546875}, {"start": 1944.34, "end": 1944.64, "word": " that", "probability": 0.890625}, {"start": 1944.64, "end": 1946.26, "word": " المسافة", "probability": 0.883056640625}, {"start": 1946.26, "end": 1946.42, "word": " بين", "probability": 0.9150390625}, {"start": 1946.42, "end": 1946.58, "word": " x", "probability": 0.736328125}, {"start": 1946.58, "end": 1946.82, "word": " نقص", "probability": 0.6594645182291666}, {"start": 1946.82, "end": 1947.12, "word": " w", "probability": 0.599609375}, {"start": 1947.12, "end": 1947.46, "word": " أصغر", "probability": 0.9622802734375}, {"start": 1947.46, "end": 1947.62, "word": " من", "probability": 0.97119140625}, {"start": 1947.62, "end": 1947.86, "word": " أي", "probability": 0.39208984375}, {"start": 1947.86, "end": 1948.48, "word": " أسغر", "probability": 0.492431640625}, {"start": 1948.48, "end": 1948.58, "word": " من", "probability": 0.97509765625}, {"start": 1948.58, "end": 1948.7, "word": " أي", "probability": 0.5712890625}, {"start": 1948.7, "end": 1948.92, "word": " 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تقاطع اللي هو ال H اللي نسباننا اليوم ليه ال W هذه ماشي ان شاء الله نجمعين معايا طيب الان", "tokens": [2304, 33599, 1829, 21542, 6027, 34051, 37279, 3555, 13546, 13672, 1829, 31439, 16472, 8717, 4117, 3794, 4032, 398, 15844, 1975, 2655, 1863, 9957, 13672, 1829, 31439, 6055, 4587, 41193, 3615, 13672, 1829, 31439, 2423, 389, 13672, 1829, 8717, 35457, 7649, 8315, 45595, 20498, 5296, 1829, 3224, 2423, 343, 29538, 3714, 33599, 1829, 16472, 13412, 16606, 21984, 8717, 7435, 2304, 3615, 9957, 20449, 995, 25528, 23032, 1829, 3555, 2423, 7649], "avg_logprob": -0.40334821726594655, "compression_ratio": 1.7777777777777777, "no_speech_prob": 2.9385089874267578e-05, "words": [{"start": 1966.93, "end": 1967.21, "word": "ماشي", "probability": 0.76513671875}, {"start": 1967.21, "end": 1967.47, "word": " الحال", "probability": 0.915771484375}, {"start": 1967.47, "end": 1967.99, "word": " أو", "probability": 0.450927734375}, {"start": 1967.99, "end": 1968.53, "word": " تعبير", "probability": 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Finite", "probability": 0.54986572265625}, {"start": 1997.43, "end": 1997.71, "word": " Linear", "probability": 0.36083984375}, {"start": 1997.71, "end": 1998.17, "word": " combination", "probability": 0.239501953125}, {"start": 1998.17, "end": 1998.47, "word": " من", "probability": 0.98779296875}, {"start": 1998.47, "end": 1998.79, "word": " مين؟", "probability": 0.6897786458333334}, {"start": 1998.79, "end": 1998.91, "word": " من", "probability": 0.94921875}, {"start": 1998.91, "end": 1999.37, "word": " عناصر", "probability": 0.99072265625}, {"start": 1999.37, "end": 1999.49, "word": " من", "probability": 0.52734375}, {"start": 1999.49, "end": 1999.67, "word": " الـ", "probability": 0.8837890625}, {"start": 1999.67, "end": 1999.85, "word": " EM", "probability": 0.9150390625}], "temperature": 1.0}, {"id": 88, "seek": 202230, "start": 2000.46, "end": 2022.3, "text": "نفترض إنه finite combination من E1 وE2 وE3 وE4 لعندي يعني مش عاجبكم EI واحد EI اتنين لعندي EIN على الأساس ما تقولوش أول أول تلاتة من هدول أو أول خمسة من هدول مش مشكلة فاهمين إنهم تكون finite اللي هو summation أو finite combination من مين من عناصر اللي هي موجودة في مين في الإيام طيب", "tokens": [1863, 5172, 2655, 43042, 36145, 3224, 19362, 6562, 9154, 462, 16, 4032, 36, 17, 4032, 36, 18, 4032, 36, 19, 5296, 3615, 1863, 16254, 37495, 22653, 37893, 6225, 26108, 3555, 24793, 462, 40, 36764, 24401, 462, 40, 1975, 2655, 1863, 9957, 5296, 3615, 1863, 16254, 462, 1464, 15844, 16247, 3794, 32277, 19446, 6055, 39648, 2407, 8592, 5551, 12610, 5551, 12610, 6055, 1211, 9307, 3660, 9154, 8032, 3215, 12610, 34051, 5551, 12610, 16490, 2304, 3794, 3660, 9154, 8032, 3215, 12610, 37893, 37893, 28820, 3660, 6156, 995, 16095, 9957, 36145, 16095, 6055, 30544, 19362, 13672, 1829, 31439, 28811, 34051, 19362, 6562, 9154, 3714, 9957, 9154, 18871, 33546, 2288, 13672, 1829, 39896, 3714, 29245, 23328, 3660, 8978, 3714, 9957, 8978, 33688, 1829, 10943, 23032, 1829, 3555], "avg_logprob": -0.22530242620456603, "compression_ratio": 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"end": 2582.31, "word": " اي", "probability": 0.872802734375}, {"start": 2582.31, "end": 2582.75, "word": " شمالهن", "probability": 0.9388671875}, {"start": 2582.75, "end": 2583.53, "word": " isomorphic", "probability": 0.9046223958333334}], "temperature": 1.0}, {"id": 115, "seek": 260223, "start": 2584.88, "end": 2602.24, "text": "الان نجي للاتجاه الاول suppose that او isomorphism بين هنا عارفين واش معناه isomorphism بينهم بنحكيها الان الان suppose that H is isomorphic with H تلده مابديش ادخل في التفاصيل تفاصيل الحسابات هتكون لكم suppose that H is isomorphic لمن لH تلده", "tokens": [6027, 7649, 8717, 7435, 1829, 24976, 9307, 7435, 40294, 42963, 12610, 7297, 300, 1975, 2407, 307, 32702, 1434, 49374, 34105, 6225, 9640, 5172, 9957, 4032, 33599, 20449, 8315, 3224, 307, 32702, 1434, 49374, 16095, 44945, 5016, 4117, 1829, 11296, 2423, 7649, 2423, 7649, 7297, 300, 389, 307, 307, 32702, 299, 365, 389, 6055, 1211, 3215, 3224, 3714, 16758, 16254, 8592, 1975, 3215, 9778, 1211, 8978, 16712, 5172, 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اللي عملناها عشرين مرة هذه بيساوي X و EK و X و EM تلدة و EK و EK تلدة", "tokens": [3555, 1863, 3794, 9778, 3215, 9154, 11296, 1610, 11943, 24440, 2423, 39184, 314, 55, 16070, 39184, 314, 55, 2423, 39184, 314, 55, 11933, 1829, 8592, 5551, 3615, 28480, 8315, 11296, 28811, 1783, 4032, 46078, 4032, 46078, 6055, 1211, 3215, 3660, 28242, 3224, 8032, 2655, 15040, 4587, 2407, 13412, 17082, 1211, 9307, 8608, 3224, 37977, 4032, 39894, 1863, 5016, 3794, 1863, 4032, 2423, 1783, 4032, 46078, 4032, 46078, 6055, 1211, 3215, 3660, 670, 591, 23032, 1211, 3615, 2407, 16095, 4724, 23557, 2423, 28811, 30767, 1829, 19446, 44945, 25957, 1211, 11778, 47302, 15042, 13672, 1829, 45030, 25708, 13672, 1829, 31439, 39894, 1211, 3615, 3555, 45064, 4032, 25724, 16572, 3555, 39894, 1211, 3615, 3555, 6225, 995, 16254, 3714, 33599, 1829, 13672, 1829, 6225, 42213, 8315, 11296, 6225, 46309, 9957, 3714, 25720, 29538, 4724, 1829, 3794, 995, 45865, 1783, 4032, 46078, 4032, 1783, 4032, 16237, 6055, 1211, 3215, 3660, 4032, 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0.6746419270833334}, {"start": 3161.52, "end": 3161.94, "word": " الفا", "probability": 0.840087890625}, {"start": 3161.94, "end": 3162.44, "word": " كيه", "probability": 0.9254557291666666}, {"start": 3162.44, "end": 3162.88, "word": " عبارة", "probability": 0.929443359375}, {"start": 3162.88, "end": 3163.0, "word": " عن", "probability": 0.99560546875}, {"start": 3163.0, "end": 3163.3, "word": " فرير", "probability": 0.42413330078125}, {"start": 3163.3, "end": 3163.7, "word": " coefficients", "probability": 0.39404296875}, {"start": 3163.7, "end": 3164.34, "word": " بتطلع", "probability": 0.96240234375}, {"start": 3164.34, "end": 3164.78, "word": " اللي", "probability": 0.959228515625}, {"start": 3164.78, "end": 3164.88, "word": " هي", "probability": 0.7978515625}, {"start": 3164.88, "end": 3165.02, "word": " ال", "probability": 0.85791015625}, {"start": 3165.02, "end": 3165.18, "word": " X", "probability": 0.66162109375}, {"start": 3165.18, "end": 3165.34, "word": " و", 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0.291015625}, {"start": 3170.16, "end": 3171.16, "word": " هتساوي", "probability": 0.9353515625}, {"start": 3171.16, "end": 3171.38, "word": " ال", "probability": 0.83203125}, {"start": 3171.38, "end": 3171.64, "word": " Alpha", "probability": 0.336181640625}, {"start": 3171.64, "end": 3171.84, "word": " K", "probability": 0.87451171875}, {"start": 3171.84, "end": 3172.04, "word": " هي", "probability": 0.9365234375}, {"start": 3172.04, "end": 3172.32, "word": " عبارة", "probability": 0.9951171875}, {"start": 3172.32, "end": 3172.48, "word": " عن", "probability": 0.990234375}, {"start": 3172.48, "end": 3172.68, "word": " X", "probability": 0.962890625}, {"start": 3172.68, "end": 3172.84, "word": " و", "probability": 0.5810546875}, {"start": 3172.84, "end": 3173.0, "word": " E", "probability": 0.296142578125}, {"start": 3173.0, "end": 3173.46, "word": " K", "probability": 0.7373046875}, {"start": 3173.46, "end": 3173.78, "word": " اي", "probability": 0.555908203125}, {"start": 3173.78, "end": 3173.9, "word": " K", "probability": 0.60986328125}, {"start": 3173.9, "end": 3174.56, "word": " تلدة", "probability": 0.821533203125}, {"start": 3174.56, "end": 3175.2, "word": " اللي", "probability": 0.9853515625}, {"start": 3175.2, "end": 3175.36, "word": " هي", "probability": 0.77392578125}, {"start": 3175.36, "end": 3175.48, "word": " في", "probability": 0.9013671875}, {"start": 3175.48, "end": 3175.82, "word": " الواقع", "probability": 0.9847412109375}, {"start": 3175.82, "end": 3176.0, "word": " ايش", "probability": 0.6905110677083334}, {"start": 3176.0, "end": 3176.58, "word": " هتكون", "probability": 0.9777018229166666}, {"start": 3176.58, "end": 3177.24, "word": " ال", "probability": 0.87451171875}, {"start": 3177.24, "end": 3177.74, "word": " TX", "probability": 0.737060546875}, {"start": 3177.74, "end": 3178.42, "word": " اذا", "probability": 0.812744140625}, {"start": 3178.42, "end": 3178.88, "word": " لجيت", "probability": 0.9324544270833334}, {"start": 3178.88, "end": 3179.14, "word": " انا", "probability": 0.914306640625}, {"start": 3179.14, "end": 3179.66, "word": " الآن", "probability": 0.70751953125}, {"start": 3179.66, "end": 3180.7, "word": " بدأت", "probability": 0.8572591145833334}, {"start": 3180.7, "end": 3180.82, "word": " ب", "probability": 0.841796875}, {"start": 3180.82, "end": 3181.02, "word": " X", "probability": 0.8662109375}, {"start": 3181.02, "end": 3181.32, "word": " تلد", "probability": 0.91748046875}, {"start": 3181.32, "end": 3181.88, "word": " arbitrary", "probability": 0.7763671875}, {"start": 3181.88, "end": 3182.4, "word": " و", "probability": 0.68017578125}, {"start": 3182.4, "end": 3182.76, "word": " لجيت", "probability": 0.9436848958333334}, {"start": 3182.76, "end": 3183.24, "word": " X", "probability": 0.990234375}], "temperature": 1.0}, {"id": 140, "seek": 320167, "start": 3184.01, "end": 3201.67, "text": "موجودة في الـ H بحيث أن TX بتساوي X تلدى معناته صارت T is onto و أثبتت إنها Linear و أثبتت بـ Reserve the norm و أثبتت onto one to one صارت اللي هي T is an isomorphism بين H and H تلدى و إلى لقاء آخر السلام عليكم و رحمة الله", "tokens": [2304, 29245, 23328, 3660, 8978, 2423, 39184, 389, 4724, 5016, 1829, 12984, 14739, 314, 55, 39894, 3794, 995, 45865, 1783, 6055, 1211, 3215, 7578, 20449, 8315, 47395, 20328, 9640, 2655, 314, 307, 3911, 4032, 5551, 12984, 3555, 2655, 2655, 36145, 11296, 14670, 289, 4032, 5551, 12984, 3555, 2655, 2655, 4724, 39184, 26049, 264, 2026, 4032, 5551, 12984, 3555, 2655, 2655, 3911, 472, 281, 472, 20328, 9640, 2655, 13672, 1829, 39896, 314, 307, 364, 307, 32702, 1434, 49374, 389, 293, 389, 6055, 1211, 3215, 7578, 4032, 30731, 5296, 4587, 16606, 19753, 34740, 21136, 37440, 25894, 24793, 4032, 12602, 35571, 3660, 21984], "avg_logprob": -0.239480190938062, "compression_ratio": 1.5, "no_speech_prob": 0.0004506111145019531, "words": [{"start": 3184.01, "end": 3184.55, "word": "موجودة", "probability": 0.9185791015625}, {"start": 3184.55, "end": 3184.91, "word": " في", "probability": 0.9638671875}, {"start": 3184.91, "end": 3185.15, "word": " الـ", "probability": 0.860107421875}, {"start": 3185.15, "end": 3185.43, "word": " H", "probability": 0.5712890625}, {"start": 3185.43, "end": 3186.27, "word": " بحيث", "probability": 0.884765625}, {"start": 3186.27, "end": 3186.41, "word": " أن", "probability": 0.365478515625}, {"start": 3186.41, "end": 3186.91, "word": " TX", "probability": 0.607666015625}, {"start": 3186.91, "end": 3187.29, "word": " بتساوي", "probability": 0.6347084045410156}, {"start": 3187.29, "end": 3187.51, "word": " X", "probability": 0.8955078125}, {"start": 3187.51, "end": 3187.93, "word": " تلدى", "probability": 0.60345458984375}, {"start": 3187.93, "end": 3188.53, "word": " معناته", "probability": 0.79248046875}, {"start": 3188.53, "end": 3188.87, "word": " صارت", "probability": 0.8250325520833334}, {"start": 3188.87, "end": 3188.99, "word": " T", "probability": 0.798828125}, {"start": 3188.99, "end": 3189.15, "word": " is", "probability": 0.91748046875}, {"start": 3189.15, "end": 3189.43, "word": " onto", "probability": 0.471923828125}, {"start": 3189.43, "end": 3190.33, "word": " و", "probability": 0.70703125}, {"start": 3190.33, "end": 3191.31, "word": " أثبتت", "probability": 0.919921875}, {"start": 3191.31, "end": 3191.51, "word": " إنها", "probability": 0.6873779296875}, {"start": 3191.51, "end": 3192.01, "word": " Linear", "probability": 0.82470703125}, {"start": 3192.01, "end": 3192.29, "word": " و", "probability": 0.8564453125}, {"start": 3192.29, "end": 3192.69, "word": " أثبتت", "probability": 0.984375}, {"start": 3192.69, "end": 3192.87, "word": " بـ", "probability": 0.381591796875}, {"start": 3192.87, "end": 3193.11, "word": " Reserve", "probability": 0.48095703125}, {"start": 3193.11, "end": 3193.33, "word": " the", "probability": 0.685546875}, {"start": 3193.33, "end": 3193.67, "word": " norm", "probability": 0.79541015625}, {"start": 3193.67, "end": 3193.93, "word": " و", "probability": 0.88134765625}, {"start": 3193.93, "end": 3194.33, "word": " أثبتت", "probability": 0.99111328125}, {"start": 3194.33, "end": 3194.73, "word": " onto", "probability": 0.246337890625}, {"start": 3194.73, "end": 3195.71, "word": " one", "probability": 0.6826171875}, {"start": 3195.71, "end": 3195.85, "word": " to", "probability": 0.8564453125}, {"start": 3195.85, "end": 3196.07, "word": " one", "probability": 0.9541015625}, {"start": 3196.07, "end": 3196.47, "word": " صارت", "probability": 0.9669596354166666}, {"start": 3196.47, "end": 3196.59, "word": " اللي", "probability": 0.8544921875}, {"start": 3196.59, "end": 3196.71, "word": " هي", "probability": 0.65478515625}, {"start": 3196.71, "end": 3196.93, "word": " T", "probability": 0.88037109375}, {"start": 3196.93, "end": 3197.13, "word": " is", "probability": 0.94873046875}, {"start": 3197.13, "end": 3197.27, "word": " an", "probability": 0.83056640625}, {"start": 3197.27, "end": 3197.93, "word": " isomorphism", "probability": 0.9327799479166666}, {"start": 3197.93, "end": 3198.17, "word": " بين", "probability": 0.91162109375}, {"start": 3198.17, "end": 3198.41, "word": " H", "probability": 0.92236328125}, {"start": 3198.41, "end": 3198.61, "word": " and", "probability": 0.73388671875}, {"start": 3198.61, "end": 3198.81, "word": " H", "probability": 0.875}, {"start": 3198.81, "end": 3199.33, "word": " تلدى", "probability": 0.9580078125}, {"start": 3199.33, "end": 3199.71, "word": " و", "probability": 0.82275390625}, {"start": 3199.71, "end": 3199.89, "word": " إلى", "probability": 0.65966796875}, {"start": 3199.89, "end": 3200.27, "word": " لقاء", "probability": 0.9376627604166666}, {"start": 3200.27, "end": 3200.57, "word": " آخر", "probability": 0.8017578125}, {"start": 3200.57, "end": 3200.91, "word": " السلام", "probability": 0.783447265625}, {"start": 3200.91, "end": 3201.17, "word": " عليكم", "probability": 0.897216796875}, {"start": 3201.17, "end": 3201.31, "word": " و", "probability": 0.9853515625}, {"start": 3201.31, "end": 3201.45, "word": " رحمة", "probability": 0.7029622395833334}, {"start": 3201.45, "end": 3201.67, "word": " الله", "probability": 0.9609375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3202.14775, "duration_after_vad": 3152.66562499999}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/ClvCjQJddZs_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/ClvCjQJddZs_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..076b595748558780e41a42e08f3a6de081dc951b
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/ClvCjQJddZs_postprocess.srt
@@ -0,0 +1,840 @@
+1
+00:00:05,350 --> 00:00:07,910
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,910 --> 00:00:10,770
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,770 --> 00:00:15,390
+أهله وصحابه الأجمعين هذه هي المحاضرة رقم 26 مساق
+
+4
+00:00:15,390 --> 00:00:20,290
+تحليل اقتراني او تحليل دالي طلاب طالبات الجامعة
+
+5
+00:00:20,290 --> 00:00:23,710
+الإسلامية مجلسين رياضيات هنبدأ اليوم ان شاء الله
+
+6
+00:00:23,710 --> 00:00:28,370
+في اللي هو chapter 4 بعد ما خلصنا chapter 3 اللي
+
+7
+00:00:28,370 --> 00:00:31,810
+هو chapter 4 خليني أقول فمرة المادة اللي هو
+
+8
+00:00:31,810 --> 00:00:35,850
+Fundamental Theoremsof أو for normed and banach
+
+9
+00:00:35,850 --> 00:00:39,490
+spaces اللي هي النظريات الأربعة أو الثلاثة
+
+10
+00:00:39,490 --> 00:00:43,530
+الرئيسية في المساق أو في ال functionalists بصورة
+
+11
+00:00:43,530 --> 00:00:50,650
+عامة بما يتعلق بال normed أو الbanach spacesعشان
+
+12
+00:00:50,650 --> 00:00:55,870
+نصب لهذه النظريات الأساسية هنحكي أول اشي عن حاجة
+
+13
+00:00:55,870 --> 00:00:58,970
+اسمها zone slimma هذا المفروض يعني هذا section
+
+14
+00:00:58,970 --> 00:01:02,930
+سريع يعني خلينا نقول هو background لشغل احنا
+
+15
+00:01:02,930 --> 00:01:06,130
+بنشتغله في ال set theory لكن بعض الناس ممكن يكون
+
+16
+00:01:06,130 --> 00:01:11,070
+ممردش عليهم فعشان هيك نشرحه على السريع نيجي ل zone
+
+17
+00:01:11,070 --> 00:01:16,310
+slimma عشان نعرف ايش هي zone slimma بالزمن اللي هو
+
+18
+00:01:16,310 --> 00:01:18,670
+اعرف اللي هو بعض التعريفات
+
+19
+00:01:21,080 --> 00:01:23,800
+اللي هو إيش معناه partially ordered set a
+
+20
+00:01:23,800 --> 00:01:26,680
+partially ordered set is a set أمن مجرد set أمن
+
+21
+00:01:27,950 --> 00:01:31,970
+عليها partial order relation الان احنا ال .. في
+
+22
+00:01:31,970 --> 00:01:37,210
+عندى 6M وفي عندى عليها اللى هى relation اللى هى
+
+23
+00:01:37,210 --> 00:01:40,990
+تيمنا بالأصغر أو يساوي اللى فى الأعداد اللى هى M
+
+24
+00:01:40,990 --> 00:01:44,150
+اللى هى 6 و هد partial order relation ايش ال
+
+25
+00:01:44,150 --> 00:01:47,710
+partial order relation تحقق تلت شروط الشرط الأول
+
+26
+00:01:47,710 --> 00:01:52,490
+انها تكون اللى هو A أصغر يساوي A for all A limited
+
+27
+00:01:52,490 --> 00:01:56,410
+A اللى هم بنسميها ايش مالها اللى هو reflexive الان
+
+28
+00:01:56,860 --> 00:02:00,500
+ب فأ أصغر أساوة و ب أد ب أصغر أساوة و a بتعطيني a
+
+29
+00:02:00,500 --> 00:02:03,520
+بساوة و b اللي بيسميها antisymmetric السيميترك
+
+30
+00:02:03,520 --> 00:02:07,760
+طبعا احنا اللي هي الخاصية في ال equivalence
+
+31
+00:02:07,760 --> 00:02:11,240
+relation اللي بتختلف عن ال equivalence relation بس
+
+32
+00:02:11,240 --> 00:02:14,930
+اللي هي منين ال antisymmetricالخاصية تالفة FA أصغر
+
+33
+00:02:14,930 --> 00:02:18,310
+أو B and B أصغر أو C بيعطينا A أصغر أو C لخاصية
+
+34
+00:02:18,310 --> 00:02:21,930
+التعد أو Transitive التلت خواصة دول مع بعض بيعمل
+
+35
+00:02:21,930 --> 00:02:25,850
+انهدف بارعنين partial order relation ولو استبدلنا
+
+36
+00:02:25,850 --> 00:02:28,670
+ال antisymmetric بالsymmetric بتصير equivalence
+
+37
+00:02:28,670 --> 00:02:33,770
+relation مش موضوعناالان احنا هذه اللي هي partial
+
+38
+00:02:33,770 --> 00:02:37,830
+order relation اول مثال احنا بنعطيه بنعطيه على ال
+
+39
+00:02:37,830 --> 00:02:40,990
+partial order relation اللي هو كنا نعطيه اللي هي
+
+40
+00:02:40,990 --> 00:02:44,730
+اللي هي لو أخدنا set X واخدنا subset من ال bar set
+
+41
+00:02:44,730 --> 00:02:48,170
+of X واخدنا عليها اللي هي مين اللي هي ال inclusion
+
+42
+00:02:48,170 --> 00:02:51,250
+ال set inclusion هذه بتعمل partial order relation
+
+43
+00:02:51,250 --> 00:02:54,470
+ماشي الحال مش موضوعنا بس هذا في ال .. في ال ..
+
+44
+00:02:54,470 --> 00:02:58,480
+يعني بنعطيه مثال في اللي هي ال set theoryالان نيجي
+
+45
+00:02:58,480 --> 00:03:02,540
+لتعريف نعرف حاجة اسمها upper bound اللي هي an
+
+46
+00:03:02,540 --> 00:03:05,800
+upper bound of a subset W of a partially ordered
+
+47
+00:03:05,800 --> 00:03:09,080
+set M يعني لو كانت عندي partially ordered set هي
+
+48
+00:03:09,080 --> 00:03:11,820
+partially ordered set هي partially ordered set هي
+
+49
+00:03:11,820 --> 00:03:15,700
+اللي هي اللي هي ال set اللي عندى و كانت مش شكل هذا
+
+50
+00:03:15,700 --> 00:03:19,740
+او اي ان كانت هذه W هذه M ال set M لو جينا أخدنا
+
+51
+00:03:19,740 --> 00:03:26,100
+جزء منهااللي هي هذا و و جزء منها من هذه الست هذه
+
+52
+00:03:26,100 --> 00:03:29,540
+عنصر عنصرين تلاتة أربعة هذه البرتشال الأوردو رليش
+
+53
+00:03:29,540 --> 00:03:33,580
+يعني هذا أصغر شهو هذا فهذا أصغر شهو هذاكـ partial
+
+54
+00:03:33,580 --> 00:03:37,600
+order و هذا أصغر شويه هذا و هذا أصغر شويه هذا لو
+
+55
+00:03:37,600 --> 00:03:41,380
+أخدنا ال W جزء من ال M بدنا نعرف حاجة إيش اسمها an
+
+56
+00:03:41,380 --> 00:03:44,840
+upper bound an upper bound of a subset W of a
+
+57
+00:03:44,840 --> 00:03:49,940
+partially ordered set M is U element من M إذا ال
+
+58
+00:03:49,940 --> 00:03:54,380
+upper bound عبارة عن مين؟ عن عنصر وين بيكون في ال
+
+59
+00:03:54,380 --> 00:03:58,080
+M يعني مش شرط يكون بس في ال W ممكن يكون وين برا ت
+
+60
+00:03:58,080 --> 00:04:02,810
+ال W المهم وين من ال Msuch that بيحقق إن X أصغر
+
+61
+00:04:02,810 --> 00:04:07,530
+شويه لكل X و الموجودة في W بيكون أكبر شويه كل
+
+62
+00:04:07,530 --> 00:04:11,810
+عناصر مين الـ W اللي هو such that U أصغر شويه X
+
+63
+00:04:11,810 --> 00:04:14,950
+أصغر شويه for all X element in M هذا اللي بنسميه
+
+64
+00:04:14,950 --> 00:04:19,210
+إيش ماله عبارة عن اللي هو elementاللي هو إيش ماله؟
+
+65
+00:04:19,210 --> 00:04:23,350
+اللي هو Upper Bound يعني الآن لو أجينا أخدنا اللي
+
+66
+00:04:23,350 --> 00:04:27,190
+هو بالشكل هذا و أخدنا بالشكل هذا هذا أكيد إيش
+
+67
+00:04:27,190 --> 00:04:31,110
+ماله؟ عبارة عن Upper Bound لمين؟ اللي هي الـCW
+
+68
+00:04:31,110 --> 00:04:36,130
+لأنه أكبر شو مين كل عناصرها، معايا؟ طيب، الآن بدنا
+
+69
+00:04:36,130 --> 00:04:40,000
+نحلل رفحاجة اسمها Maximal Element of MA maximal
+
+70
+00:04:40,000 --> 00:04:43,260
+element of M is M element of M إذا الماكسيمال من
+
+71
+00:04:43,260 --> 00:04:47,240
+وين هيكون من نفس الست نفسها لو بدي أجيب ال maximum
+
+72
+00:04:47,240 --> 00:04:51,160
+لل W في ال W الماكسيمال لل M الماكسيمال من وين في
+
+73
+00:04:51,160 --> 00:04:56,120
+ال M بحيث ما لو such that if M أصغر أساوي X then M
+
+74
+00:04:56,120 --> 00:05:01,080
+بتساوي X يعني ماحد بيكون أنا maximal إذا ماكانش حد
+
+75
+00:05:01,080 --> 00:05:06,030
+إله علاقة فيه أكبر منيشرطه ان يكون له علاقة فيه
+
+76
+00:05:06,030 --> 00:05:09,710
+اما أصغر ساوي X بيكون ام ايش بيبقى تساوي X يعني كل
+
+77
+00:05:09,710 --> 00:05:13,650
+اللي له علاقة فيه ماحدش يكون أكبر منه يعني هذا لو
+
+78
+00:05:13,650 --> 00:05:17,150
+جينا للست هذه اللي جوا هذا هيكون maximal ماشي
+
+79
+00:05:17,150 --> 00:05:21,270
+الحال و هذا هيكون maximal اه لإنه مافيش واحد له
+
+80
+00:05:21,270 --> 00:05:23,890
+على .. انسى اللي فوق بحكي عن .. عن هذه ال maximal
+
+81
+00:05:23,890 --> 00:05:27,030
+.. ال .. ال .. هذا maximal و هذا maximal لكن ال
+
+82
+00:05:27,030 --> 00:05:30,690
+upper bound بيكون ايش معله أكبر من كل العناصر
+
+83
+00:05:30,690 --> 00:05:36,870
+ماشي؟ طيبالـ N a subset C of M is called a chain
+
+84
+00:05:36,870 --> 00:05:40,210
+بنقول اللي هو C مجموعة جزئية من M بنتسميها chain
+
+85
+00:05:40,210 --> 00:05:44,810
+or a totally ordered set إذا كان لكل A و B في الـ
+
+86
+00:05:44,810 --> 00:05:47,650
+C الـ A أصغر شوهو B أو الـ B أصغر شوهو A الـ A
+
+87
+00:05:47,650 --> 00:05:51,790
+يعني الـ chain هي عناصر لازم يكون كلها نقلها علاقة
+
+88
+00:05:51,790 --> 00:05:55,550
+في بعض هذه مش chain هذه على بعض مش chain لأن هذا
+
+89
+00:05:55,550 --> 00:05:59,500
+العنصر مالهوش علاقة في هذا لكن هذه chainوهذا الـ
+
+90
+00:05:59,500 --> 00:06:02,900
+Chain و هدول اللي حالهم ال Chain و هدول اللي حالهم
+
+91
+00:06:02,900 --> 00:06:06,000
+ال Chain و هدول اللي حالهم ال Chain واضح؟ إذا
+
+92
+00:06:06,000 --> 00:06:09,020
+مافهم إيش معناة ال Chain طيب، الآن نيجي لـ Zones
+
+93
+00:06:09,020 --> 00:06:11,940
+لمّة هو مش موضوعنا بس عشان تفهموا علينا إيش بنقول
+
+94
+00:06:11,940 --> 00:06:14,740
+Zones لمّة، أطلع لـ Zones لمّة عشان Zones لمّة
+
+95
+00:06:14,740 --> 00:06:20,040
+أبدأ استخدامها في برهان النظرية الـ 4114 عندنا
+
+96
+00:06:20,040 --> 00:06:24,740
+إحنا، إذا بتذكروا الـ Will Ordering Principle و
+
+97
+00:06:24,740 --> 00:06:31,420
+الـ Hausdorff Principle و الـ Zones لمّةهذه كلها
+
+98
+00:06:31,420 --> 00:06:37,440
+اكسيوم الاختيار الاربع اللي هي اكسيوم في الواقع
+
+99
+00:06:37,440 --> 00:06:42,780
+واحدة فيها اكسيوم والتانية بتتبرن منها او بتتبرن
+
+100
+00:06:42,780 --> 00:06:45,640
+انها بتكافئهايعني هدول الأربعة الـ House of
+
+101
+00:06:45,640 --> 00:06:51,320
+Principles و الـ Zones Limma و الـ Axiom of Choice
+
+102
+00:06:51,320 --> 00:06:55,660
+و الأربعة
+
+103
+00:06:55,660 --> 00:07:02,260
+هدول كلهم متكافئات لكن لازم نفترض واحدة منها Axiom
+
+104
+00:07:02,700 --> 00:07:07,040
+ومن ثم الباقية بيبرهنوا منها طيب zones لما let m
+
+105
+00:07:07,040 --> 00:07:09,780
+اللي بتديها اللي بتديها اللي بتديها اللي بتديها
+
+106
+00:07:09,780 --> 00:07:10,120
+اللي بتديها اللي بتديها اللي بتديها اللي بتديها
+
+107
+00:07:10,120 --> 00:07:10,420
+اللي بتديها اللي بتديها اللي بتديها اللي بتديها
+
+108
+00:07:10,420 --> 00:07:11,080
+اللي بتديها اللي بتديها اللي بتديها اللي بتديها
+
+109
+00:07:11,080 --> 00:07:11,460
+اللي بتديها اللي بتديها اللي بتديها اللي بتديها
+
+110
+00:07:11,460 --> 00:07:11,800
+اللي بتديها اللي بتديها اللي بتديها اللي بتديها
+
+111
+00:07:11,800 --> 00:07:13,360
+اللي بتديها اللي بتديها اللي بتديها اللي بتديها
+
+112
+00:07:13,360 --> 00:07:32,660
+اللي بتديها اللي بتديها اللي بتديها اللي
+
+113
+00:07:32,660 --> 00:07:37,650
+بتعيه اللي أنا بقوللي لو كانت M اللي عبارة عن
+
+114
+00:07:37,650 --> 00:07:41,650
+order partial order set طبعا من M to T وكانت
+
+115
+00:07:41,650 --> 00:07:45,510
+بخاصية انه كل chain منها subset من M لها upper
+
+116
+00:07:45,510 --> 00:07:50,630
+bound لازم تكون M إيه شمالها at least one maximal
+
+117
+00:07:50,630 --> 00:07:54,070
+element هذه ال zones اللي بدي استخدمها في قرهان
+
+118
+00:07:54,070 --> 00:08:01,220
+نظريتي اللي هيالـ existence اللي وعدناكم فيه للـ
+
+119
+00:08:01,220 --> 00:08:08,040
+total orthonormal set الان الإعلان هو كالتالي in
+
+120
+00:08:08,040 --> 00:08:15,460
+every Hilbert space H لا تساوي سفر there exists a
+
+121
+00:08:15,460 --> 00:08:22,080
+total orthonormal set بغض النظر عن ال Hilbert
+
+122
+00:08:22,080 --> 00:08:28,100
+space اللي هو finite، dimensionalأو اللي هو
+
+123
+00:08:28,100 --> 00:08:32,840
+separable أو non-separable في اللي هو واحدة تلعب
+
+124
+00:08:32,840 --> 00:08:37,560
+دور اللي هو roughly .. roughly دور ال bases في
+
+125
+00:08:37,560 --> 00:08:39,920
+المين ال finite dimensional اللي هي إيش اسمها
+
+126
+00:08:39,920 --> 00:08:45,320
+total orthonormal 6 وهذه دائما إيه شمالها موجودة
+
+127
+00:08:45,320 --> 00:08:49,980
+هذه بدنا نثبتها اعتمادا عالميا على الأكسيوم اللي
+
+128
+00:08:49,980 --> 00:08:54,950
+هي zone slimشوفوا كيف بدنا نبرهن البرهان البرهان
+
+129
+00:08:54,950 --> 00:09:02,080
+سهل وبسيط مش يعني مش صعببنشوف كيف الان let M be
+
+130
+00:09:02,080 --> 00:09:05,860
+the set of all orthonormal subsets of H إجينا الآن
+
+131
+00:09:05,860 --> 00:09:10,420
+بدنا نجيب عائلة ال orthonormal subsets و نسميها
+
+132
+00:09:10,420 --> 00:09:17,100
+إيش M كل ال orthonormal subsets of H نسميها M طب
+
+133
+00:09:17,100 --> 00:09:21,400
+هل هال موجودة؟ يعني في عناصر فيها اللي هي هذه
+
+134
+00:09:21,400 --> 00:09:27,250
+العائلةهل العائلة هذه فيها عناصر؟ اه فيها عناصر ما
+
+135
+00:09:27,250 --> 00:09:31,430
+احنا فرضنا ان الـH أشماله لا يساوي سفر مدام الـH
+
+136
+00:09:31,430 --> 00:09:36,090
+لا يساوي سفر إذا بقدر ألاقي من Zero element سميه
+
+137
+00:09:36,090 --> 00:09:39,530
+من X إذا there is X element ان الـH شاشه ده X ماله
+
+138
+00:09:39,530 --> 00:09:44,140
+لا تساوي سفرإذا خدوا ال X على ال normal X هذي
+
+139
+00:09:44,140 --> 00:09:48,640
+orthonormal set لإنه ال norm اللي هو ايش بيساوي
+
+140
+00:09:48,640 --> 00:09:52,960
+normها بيساوي واحد ماشي الحالة إذا هذي بتمثل
+
+141
+00:09:52,960 --> 00:09:57,880
+orthonormal subset من مين من H إذا أكيد ال M إيش
+
+142
+00:09:57,880 --> 00:10:02,260
+مالها لاتساوي Phi إذا هي أول حاجة M لاتساوي Phi
+
+143
+00:10:03,280 --> 00:10:07,600
+الان لو جينا اخدنا هذه عائلة من المجموعات ال
+
+144
+00:10:07,600 --> 00:10:11,120
+subset مع العائلة من المجموعات بتعمل partial order
+
+145
+00:10:11,120 --> 00:10:14,440
+relation لأن ال subset مالها ايش مالها اللي هي ال
+
+146
+00:10:14,440 --> 00:10:19,000
+subset نفسها ايه ال subset من ايه؟لأي a subset
+
+147
+00:10:19,000 --> 00:10:25,500
+منهم اتنين لو a subset من b ل a و b في ال m و b
+
+148
+00:10:25,500 --> 00:10:29,340
+subset من a ل b و a في ال m اكيد هيعطينا ال a
+
+149
+00:10:29,340 --> 00:10:33,720
+بتساوي من ال b هذا بنعرفه من خلاص المجموعات اللي
+
+150
+00:10:33,720 --> 00:10:38,640
+قال الخصية الثالثة لو a subset من bو B subset من C
+
+151
+00:10:38,640 --> 00:10:43,680
+و A و B و C في الـ M هيعطينا الـ A subset من C إذا
+
+152
+00:10:43,680 --> 00:10:48,280
+أكيد هذه إيش بتعمل ليه partial order relation إذا
+
+153
+00:10:48,280 --> 00:10:53,380
+صارت عندها دي the collection of all ortho normal
+
+154
+00:10:53,380 --> 00:10:59,220
+subsets of H with the set inclusion is a partially
+
+155
+00:10:59,220 --> 00:11:03,200
+order relation جاعت بحقق في خواص ال zones لما أو
+
+156
+00:11:03,200 --> 00:11:04,280
+معتادة من ال zones لما
+
+157
+00:11:07,620 --> 00:11:12,440
+طيب .. let الـ N .. اطلع لفوق .. اطلع .. let C ..
+
+158
+00:11:12,440 --> 00:11:15,220
+حلوة ال .. ال inclusion هذا انه على طول ال chain
+
+159
+00:11:15,220 --> 00:11:18,360
+اللي .. اللي هو ال .. ال .. ال .. ال .. ال upper
+
+160
+00:11:18,360 --> 00:11:22,740
+bound بتجيبه على طول .. let C ال N subset من M ب N
+
+161
+00:11:22,740 --> 00:11:27,420
+chain خد أي chain في ال M .. ماشي الحال .. ال N ..
+
+162
+00:11:27,420 --> 00:11:32,290
+then خد ال X بتساويالـ Union للـ A حيث A element
+
+163
+00:11:32,290 --> 00:11:37,430
+in C يعني جمع هالـ .. هالـ Chains وخدوله للاتحاد
+
+164
+00:11:37,430 --> 00:11:42,270
+ماشي؟ لو الـ C الأولى فيها A1 وA2 وA3 وC تانى فيها
+
+165
+00:11:42,270 --> 00:11:46,250
+A5 وA6 خد اتحاد بين كلهين اللي في الـ Chains
+
+166
+00:11:46,250 --> 00:11:52,010
+وسميهمين Xصار هذا أكيد Upper Bound of C ليش Upper
+
+167
+00:11:52,010 --> 00:11:57,650
+Bound of C؟ Upper Bound لمن؟ لـ Chain ليش؟ لأن ال
+
+168
+00:11:57,650 --> 00:12:02,430
+union لهم بحتوي كل واحد فيهم إذا صار Upper Bound
+
+169
+00:12:02,430 --> 00:12:05,470
+طيب إذا صار عندي الآن
+
+170
+00:12:07,940 --> 00:12:13,080
+each chain under the set inclusion لهاد الـ M لهاد
+
+171
+00:12:13,080 --> 00:12:15,700
+الـ M لهاد الـ M لهاد الـ M لهاد الـ M لهاد الـ M
+
+172
+00:12:15,700 --> 00:12:16,720
+لهاد الـ M لهاد الـ M لهاد الـ M لهاد الـ M لهاد
+
+173
+00:12:16,720 --> 00:12:17,500
+الـ M لهاد الـ M لهاد الـ M لهاد الـ M لهاد الـ M
+
+174
+00:12:17,500 --> 00:12:17,700
+لهاد الـ M لهاد الـ M لهاد الـ M لهاد الـ M لهاد
+
+175
+00:12:17,700 --> 00:12:19,440
+الـ M لهاد الـ M لهاد الـ M لهاد الـ M لهاد الـ M
+
+176
+00:12:19,440 --> 00:12:21,340
+الـ M لهاd the M لهاd the M لهاd the M لهاd the M
+
+177
+00:12:21,340 --> 00:12:34,600
+لهاd the M لهاd the M لهاd the M لهاd the M لهاd
+
+178
+00:12:34,630 --> 00:12:39,750
+الـ total orthonormal set لأن هذا موجود و وين
+
+179
+00:12:39,750 --> 00:12:43,230
+موجود في الـ M إذا الـ orthonormal أنا بقولك هيكون
+
+180
+00:12:43,230 --> 00:12:48,490
+total ال F هيكون إيه شماله؟ total ماشي إذا نضل
+
+181
+00:12:48,490 --> 00:12:52,690
+عليه أثبت لكم إنه total طيب الآن suppose that F is
+
+182
+00:12:52,690 --> 00:12:58,190
+not total in H لكن في theorem 3.6.2 إذا بتتذكروا
+
+183
+00:12:58,190 --> 00:13:05,280
+لما قلنا M أو خلينا نقول F is totalهيعطيني على طول
+
+184
+00:13:05,280 --> 00:13:10,280
+ال F Orthogonal ايش بيساوي بيساوي Zeroالـ F
+
+185
+00:13:10,280 --> 00:13:14,260
+أرثجونال أيش بيساوي؟ بيساوي 0 هدف 362 إذا من
+
+186
+00:13:14,260 --> 00:13:19,080
+theorem 362 لو جينا قولنا نفترض أن F is not total
+
+187
+00:13:19,080 --> 00:13:23,880
+إذا من theorem 362 هيكون الـ F أرثجونال إشماله لا
+
+188
+00:13:23,880 --> 00:13:29,300
+يساوي 0 إشماله لا يساوي 0 يعني في عنصر في مش سفر
+
+189
+00:13:29,300 --> 00:13:33,320
+يعني there exists z element in F أرثجونال و الـ z
+
+190
+00:13:33,320 --> 00:13:39,740
+إشماله بساوي 0 لا يساوي 0الان ساعرفلي F1 بتساوي F
+
+191
+00:13:39,740 --> 00:13:45,060
+اتحاد العنصر هذا بس على normal ماشي صار هذا اللي
+
+192
+00:13:45,060 --> 00:13:49,140
+هو إيش معله normal واحد إذا صارت F اتحاد العنصر
+
+193
+00:13:49,140 --> 00:13:52,720
+هذا والعنصر هذا ال Z مع كل واحد اللي هو product
+
+194
+00:13:52,720 --> 00:13:56,840
+صفر يعني Orthogonal على كل مين معاهن إذا صارت كل
+
+195
+00:13:56,840 --> 00:14:01,630
+ال F1 عبارة عن orthonormal setبصبوط الان هذه F
+
+196
+00:14:01,630 --> 00:14:05,410
+orthonormal ماشي اللي هو ال product من أي عنصرين
+
+197
+00:14:05,410 --> 00:14:09,250
+فيها سفروهذا الـ Z عمودي على الـ F إذا الـ inner
+
+198
+00:14:09,250 --> 00:14:12,490
+product بينه بين أي عنصر هنا برضه مش بساوي سفر إذا
+
+199
+00:14:12,490 --> 00:14:16,530
+صار F إتحاد و هذا مش موجود هان دلوا بالكم صار F
+
+200
+00:14:16,530 --> 00:14:23,370
+إتحاد هذا عبارة عن Orthonormal set ماشي الحال و
+
+201
+00:14:23,370 --> 00:14:27,450
+أكبر من مين؟ بتحتوى على مين على الـ F إذا بطل الـ
+
+202
+00:14:27,450 --> 00:14:30,880
+F maximal element which is a contradictionالان
+
+203
+00:14:30,880 --> 00:14:34,440
+which is orthonormal and F is a proper subset of
+
+204
+00:14:34,440 --> 00:14:39,160
+F1 which is a contradiction of the maximality of F
+
+205
+00:14:39,160 --> 00:14:43,720
+therefore الفرضية اللي فرضناها ان F is not total
+
+206
+00:14:43,720 --> 00:14:47,520
+مش صحيحة therefore the orthonormal set اللي هي ال
+
+207
+00:14:47,520 --> 00:14:51,120
+F اللي كانت اللي هي maximum لازم تكون ايش ما لها
+
+208
+00:14:51,120 --> 00:14:55,960
+total in H وبهيك ان احنا اثبتنا ان any Hilbert
+
+209
+00:14:55,960 --> 00:15:01,690
+space H لا تساوي سفر hasالـ Total Orthonormal Set
+
+210
+00:15:01,690 --> 00:15:03,610
+وإلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Dna28R7jBBs_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Dna28R7jBBs_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..71242690ca32ed89df9805ede6746ab79f47c82a
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Dna28R7jBBs_raw.srt
@@ -0,0 +1,3424 @@
+1
+00:00:05,620 --> 00:00:08,620
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,620 --> 00:00:11,440
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:11,440 --> 00:00:15,240
+آله وصحبه أجمعين هذه هي المحاضرة السادسة مساق
+
+4
+00:00:15,240 --> 00:00:19,140
+تحليل اقتراني أو تحليل دالي طلاب طالبات الجامعة
+
+5
+00:00:19,140 --> 00:00:27,110
+الإسلامية قسم رياضيات مجستير رياضيةحكينا احنا عند
+
+6
+00:00:27,110 --> 00:00:31,530
+واحد اربعة وصلنا ونهينا واحد اربعة وقلنا خلينا
+
+7
+00:00:31,530 --> 00:00:33,930
+اللي هو المرة الجاية اللي نحكي عن واحد خمسة اللي
+
+8
+00:00:33,930 --> 00:00:39,390
+هو examples أمثلة على completeness proofsعلى
+
+9
+00:00:39,390 --> 00:00:43,870
+براهين اللي هي ناخد هناخد أمثلة ل spaces تكون
+
+10
+00:00:43,870 --> 00:00:48,030
+complete و spaces تكون ايش منها non complete طبعا
+
+11
+00:00:48,030 --> 00:00:53,330
+هذا الموضوع من الموضوعات الهامة في اللي هو المادة
+
+12
+00:00:53,330 --> 00:00:59,470
+فخلينا نركز منيح على اللي هو اللي بنحكيه اليوم أول
+
+13
+00:00:59,470 --> 00:01:04,870
+مثالطبعا احنا عرفنا على اللي هو الـ space Rn و الـ
+
+14
+00:01:04,870 --> 00:01:09,730
+Cn و قلنا الـ Rn ايش عناصره الـ Rn هو عبارة عن
+
+15
+00:01:09,730 --> 00:01:14,490
+عناصر XI واحد و XI اتنين لعند XI and untables كل
+
+16
+00:01:14,490 --> 00:01:18,770
+واحد منهم موجود وين XI element in R for every I
+
+17
+00:01:18,770 --> 00:01:22,130
+للي عندنا هذه اللي هي عناصر مين اللي هي الـ Rn
+
+18
+00:01:22,130 --> 00:01:26,090
+طبعا تعميم للـ R لر تربيع و لر تكعيب اللي هو Rn in
+
+19
+00:01:26,090 --> 00:01:28,410
+general اللي الـ N بتاخد واحد اتنين تلاتة اربعة
+
+20
+00:01:28,410 --> 00:01:33,330
+اللي بدناهاالان بدنا نعرف عليه اللي هو metric هذا
+
+21
+00:01:33,330 --> 00:01:36,130
+اللي هو الـ Euclidean metric عرفنا عليه هذا
+
+22
+00:01:36,130 --> 00:01:39,850
+متذكرين اللي هو و الـCN برضه نفس الاشي بيصير
+
+23
+00:01:39,850 --> 00:01:44,130
+doubles من الـC نسميه اللي هو Euclidean space RN
+
+24
+00:01:44,130 --> 00:01:47,510
+and Unitary space اللي هو الـCN التانية أشمالين
+
+25
+00:01:47,510 --> 00:01:51,530
+are complete spaces هنبرهن على الـ RN والتانية
+
+26
+00:01:51,530 --> 00:01:56,480
+بالظبط زي اللي هو نفس البرهانالان ايش استراتيجية
+
+27
+00:01:56,480 --> 00:02:00,400
+البرهان اللي هناخدها عشان اثبت انه complete بدي
+
+28
+00:02:00,400 --> 00:02:04,600
+اخد اي كوشي sequence و اثبت ال .. اي كوشي sequence
+
+29
+00:02:04,600 --> 00:02:07,380
+في الارقن و اثبت ال .. و اثبت الهيناي شمالها
+
+30
+00:02:07,380 --> 00:02:11,940
+converge في وين في الارقن مش الحال فالان بدي اخد
+
+31
+00:02:11,940 --> 00:02:19,240
+اي sequence xmتكون كوشي ون موجودة في الـ RN مدام X
+
+32
+00:02:19,240 --> 00:02:23,340
+يعني بمعنى آخر X1 و X2 و X3 و X4 و X5 إلى ما
+
+33
+00:02:23,340 --> 00:02:27,580
+لنهاية عبارة عن عناصر من وين ماخدها أنا من الـ RN
+
+34
+00:02:27,580 --> 00:02:31,580
+والـ XN هذه أشمالها كوشي sequence خلّينا نتطلع على
+
+35
+00:02:31,580 --> 00:02:38,530
+عناصرها X1 مثلا هي عبارة عن Xi 11ماشي هذه الواحد
+
+36
+00:02:38,530 --> 00:02:42,370
+اللي هي مين ل .. اللي هو الـ Inter اللي هان إكساي
+
+37
+00:02:42,370 --> 00:02:47,910
+اتنين واحد إكساي تلاتة واحد مجرد رموز المقول هنا
+
+38
+00:02:47,910 --> 00:02:50,990
+دول real numbers اللي عنده أصل لآخر واحد لانه كيف
+
+39
+00:02:50,990 --> 00:02:54,490
+شكل العناصر اللي في الـ RN عبارة عن إن عنده أصل
+
+40
+00:02:54,490 --> 00:02:59,370
+لآخر واحد إكساي N هذه إيش؟ واحد هي اللي هو العنصر
+
+41
+00:02:59,370 --> 00:03:03,590
+الأول في ال sequence X1 X2 بنفس الاسلوب بساوي
+
+42
+00:03:03,590 --> 00:03:16,100
+إكساي اتنينXI1 XI2 XI3 XI4 XI5 XI6 XI7 XI8 XI9
+
+43
+00:03:16,100 --> 00:03:16,820
+XI10 XI11 XI12 XI12 XI13 XI14 XI15 XI16 XI16 XI17
+
+44
+00:03:16,820 --> 00:03:18,280
+XI18 XI19 XI20 XI20 XI21 XI21 XI21 XI21 XI21 XI21
+
+45
+00:03:18,280 --> 00:03:19,000
+XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21
+
+46
+00:03:19,000 --> 00:03:20,260
+XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21
+
+47
+00:03:20,260 --> 00:03:20,740
+XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21
+
+48
+00:03:20,740 --> 00:03:21,120
+XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21
+
+49
+00:03:21,120 --> 00:03:27,820
+XI21 XI21 XI21 XI21
+
+50
+00:03:27,820 --> 00:03:31,840
+XI21
+
+51
+00:03:31,840 --> 00:03:37,790
+XIكساي اتنين ام لعند مقاصة اللي عندك كساي ام ايش
+
+52
+00:03:37,790 --> 00:03:42,130
+ام اذا هذه هي ال sequence اللي عندي اللي ماخدها
+
+53
+00:03:42,130 --> 00:03:48,230
+كوشي sequence في وين انا في الار ان غرضي ان اوصلكم
+
+54
+00:03:48,230 --> 00:03:56,400
+ان في اكسو موجودة في الارعن بحيث ان Xm بتروح لل X
+
+55
+00:03:56,400 --> 00:04:06,100
+under the مترك اللي عندنا في الارعن خلّيني
+
+56
+00:04:06,100 --> 00:04:09,420
+انحقق اللي بدناها
+
+57
+00:04:19,570 --> 00:04:26,360
+بما أن Xm كوشي عرفين شو معناه كوشيبما أن XM كوشي
+
+58
+00:04:26,360 --> 00:04:31,840
+سيكوانس إذا لكل Y أكبر من 0 بقدر ألاقي K بحيث ال
+
+59
+00:04:31,840 --> 00:04:39,040
+مسافة بين XM و XR أشمالها أصغر من Y لكل M و R
+
+60
+00:04:39,040 --> 00:04:44,340
+أشمالها أكبر من K هذا تعريف مين الكوشي سيكوانس طيب
+
+61
+00:04:44,340 --> 00:04:51,250
+المسافة بين XM و XR احنا عارفين إيش هيوالـ XR إيش
+
+62
+00:04:51,250 --> 00:05:00,870
+هي؟ بتساوي XI 1R XI 2R لعند ما أصل XI أنهينR هذه
+
+63
+00:05:00,870 --> 00:05:04,590
+اللي هي المسافة بين عنصرين موجودات في الـ R عن إيش
+
+64
+00:05:04,590 --> 00:05:11,570
+هي عبارة عن اللي هو XI هذا ناقص هذا تربية مظلوط
+
+65
+00:05:11,570 --> 00:05:15,510
+زائد هذا ناقص التربية و الأخير لما أصل لهم كلهم
+
+66
+00:05:15,510 --> 00:05:19,770
+بجمحهم و كل وش بياخدوه أص نص هذا ال متر اجتلعنا
+
+67
+00:05:19,770 --> 00:05:26,770
+الآن بما أنه ال X مكوشي إذا المسافة اللي هي هذه
+
+68
+00:05:26,770 --> 00:05:33,360
+أصغر من مين من Yلاحظوا التالي، الآن أنا بدي أحول
+
+69
+00:05:33,360 --> 00:05:38,140
+استراتيجية حلّي بدي أحول الحديث إلى من اللي هي
+
+70
+00:05:38,140 --> 00:05:43,020
+قوشي sequences في الـRN إلى قوشي sequences في الـR
+
+71
+00:05:43,020 --> 00:05:47,220
+وانا بعرف سابقا أن الـR يشمالها is complete ركزوا
+
+72
+00:05:47,220 --> 00:05:50,600
+كيف بدي أعملها، الان بما أن المجموح هذا كله أصغر
+
+73
+00:05:50,600 --> 00:05:55,740
+من Epsilon إذا أكيد اللي هو كل واحدة منهم، كل
+
+74
+00:05:55,740 --> 00:05:59,810
+واحدة من هذه تربية أصغر من الصممش انت راحهاهذه
+
+75
+00:05:59,810 --> 00:06:04,310
+مجموحة كلها وهذه واحدة منها لكل I I واحد اتنين
+
+76
+00:06:04,310 --> 00:06:08,370
+تلاتة انهي يعني لكل واحدة من هذول وكأن انا بتاخد
+
+77
+00:06:08,370 --> 00:06:13,700
+ال sequence هذه مع بعضوالـ sequence هذه مع بعض و
+
+78
+00:06:13,700 --> 00:06:17,580
+الـ sequence التانية مع بعض الاخره و كل واحدة منهم
+
+79
+00:06:17,580 --> 00:06:22,620
+هي xi i m نقص xi r ار كل تربيع ا بتساوي واحد او
+
+80
+00:06:22,620 --> 00:06:27,140
+اتنين او تلاتة او ان كله صح انهم اصغر او صحوا
+
+81
+00:06:27,140 --> 00:06:32,800
+المجموع اللي هو اصغر منين من y تربيع من هذهبصير كل
+
+82
+00:06:32,800 --> 00:06:36,880
+واحدة أصغر من نين من ويبسولون إذا صار هذه اللي عند
+
+83
+00:06:36,880 --> 00:06:41,000
+ال absolute value لها أصغر من ويبسولون هذه لكل
+
+84
+00:06:41,000 --> 00:06:49,480
+sequence اللي هي xi i واقة xi i واحد xi i اتنين xi
+
+85
+00:06:49,480 --> 00:06:55,240
+i m الاخره هذه ال sequence الآن إيش أثبتت أنا إلها
+
+86
+00:06:55,240 --> 00:07:04,000
+إن xi i m ناقص xi i rعندي أصغر من مين من أبسلون
+
+87
+00:07:04,000 --> 00:07:09,160
+لكن هذه sequence of numbers إذا صارت كوشي sequence
+
+88
+00:07:09,160 --> 00:07:13,320
+in real numbers إذا أكيد اي شمالها converge إذا
+
+89
+00:07:13,320 --> 00:07:18,180
+hence for any fixed I I من واحد لعين دلان the
+
+90
+00:07:18,180 --> 00:07:22,920
+sequence xi I واحد xi I اتنين إلى ما لنهاية هيها
+
+91
+00:07:22,920 --> 00:07:26,460
+xi I واحد xi I اتنين xi I تلتة إلى ما لنهاية
+
+92
+00:07:27,690 --> 00:07:31,990
+converges لما صارت ايش ما لها كوشي sequence of
+
+93
+00:07:31,990 --> 00:07:34,730
+real numbers then it converges خلّيني أقول
+
+94
+00:07:34,730 --> 00:07:41,190
+converges ده مين لـXi I إذا صار عندي الآن كل
+
+95
+00:07:41,190 --> 00:07:45,950
+البرهين لها نفس الروح فركزوا كويس عشان نرتاح في
+
+96
+00:07:45,950 --> 00:07:51,700
+اللي بعدهاصارت عندي الآن الـ sequence XII M
+
+97
+00:07:51,700 --> 00:07:54,960
+converged domain قلنا يعني خلّيت هذا الـ sequence
+
+98
+00:07:54,960 --> 00:07:58,920
+شايفين هذا XII قلنا هذا as M goes to infinity ..
+
+99
+00:07:58,920 --> 00:08:01,880
+as I goes to infinity .. as M goes to infinity هذه
+
+100
+00:08:01,880 --> 00:08:06,440
+بدت تروح لمين؟ للـ XII سميت XII يعني وكأني أخدت
+
+101
+00:08:06,440 --> 00:08:10,280
+هذه الـ sequenceأثبت انها كوشي و راحت لك صي واحد
+
+102
+00:08:10,280 --> 00:08:14,820
+هذه كوشي و راحت لك صي اتنين هذه كوشي و راحت لك صي
+
+103
+00:08:14,820 --> 00:08:18,980
+ايه الأخيرة كوشي و راحت لك صي اتنين اذا صار عند
+
+104
+00:08:18,980 --> 00:08:24,180
+الانX بيتساوي XY واحد XI اتنين XI N كل هى نوع
+
+105
+00:08:24,180 --> 00:08:30,780
+موجودات في الار أن الان بتثبتلكم أثبتتلكم ان ال X
+
+106
+00:08:30,780 --> 00:08:36,620
+بتساوي XI واحد و XI اتنين لعند XI N و موجودة في
+
+107
+00:08:36,620 --> 00:08:41,280
+الار أن وكل واحدة من هدولة converge لواحدة من ال
+
+108
+00:08:41,280 --> 00:08:48,180
+interest هدى بتثبتلكم ان XM convergence لهدى ال X
+
+109
+00:08:48,660 --> 00:08:53,820
+يعني إيش؟ يعني المسافة بين Xm و X تكون أصغر من
+
+110
+00:08:53,820 --> 00:08:59,140
+الإمسلون تحت الشروط اللي حكيتناها طيب الآن by one
+
+111
+00:08:59,140 --> 00:09:04,320
+اللي حكينا عنها في الأول هي شايفين هذه by one الآن
+
+112
+00:09:04,320 --> 00:09:10,480
+as N as M أو R اللي بتديها وديها لنا لنهاية بتروح
+
+113
+00:09:10,480 --> 00:09:14,360
+حسب اللي حكيته as R goes to infinity ل Xir وين
+
+114
+00:09:14,360 --> 00:09:19,910
+هتروح؟ ل Xirهي يا جماعة اللي أثبتته قبل بشوية اللي
+
+115
+00:09:19,910 --> 00:09:23,730
+هو هذه بتروح ل XI واحد هذه ل XI اتنين XII in
+
+116
+00:09:23,730 --> 00:09:27,990
+general بتروح لمين ل XII اذا as M goes to infinity
+
+117
+00:09:27,990 --> 00:09:34,210
+بيسير عندي من واحد هي من واحد الان as M أو R goes
+
+118
+00:09:34,210 --> 00:09:37,570
+to infinity we have المسافة بين X M و Xهي عبارة عن
+
+119
+00:09:37,570 --> 00:09:41,810
+XII M XII تربيع أصغر يساوي مين إبسلون هذا صحيح لكل
+
+120
+00:09:41,810 --> 00:09:46,550
+مين لكل M أكبر من K وهذا في حد ذاته ايش يعني بيعني
+
+121
+00:09:46,550 --> 00:09:51,530
+ان XM is converged ل X واتلتت انها في الارأن فصارت
+
+122
+00:09:51,530 --> 00:09:54,590
+اللي هي الارأن اشمالها is complete
+
+123
+00:09:57,610 --> 00:10:03,290
+هي عندنا واحد اللي أخدته وديت R إلى مالة نهاية هذه
+
+124
+00:10:03,290 --> 00:10:09,450
+as R goes to infinity راحت XI IR إلى XI I فصار
+
+125
+00:10:09,450 --> 00:10:13,350
+اللي هو المقدار اللي تحت XI I كل تربية أصلي نص
+
+126
+00:10:13,350 --> 00:10:19,170
+أصلي من Y وهذه المسافة زي ما قلنا بين X و Xالان لو
+
+127
+00:10:19,170 --> 00:10:24,250
+بدنا نفسه بالـCN كل الكلام اللي حد هنا بنفسه بس
+
+128
+00:10:24,250 --> 00:10:27,870
+بنقول بدل الإكسايات هدول ما فنهانا في الارواح بدين
+
+129
+00:10:27,870 --> 00:10:32,530
+نكون في الـC وبس بيكون هو نفس البرهر
+
+130
+00:10:37,110 --> 00:10:41,390
+فاهم صلوا عنا باللي ما ركزش معايا هنا هنعيد تقريبا
+
+131
+00:10:41,390 --> 00:10:46,110
+كلام مشابه في إثبات الـ completeness لمن؟ لـ L
+
+132
+00:10:46,110 --> 00:10:48,310
+infinity و L completeness اللي بعد ما هي اختلافات
+
+133
+00:10:48,310 --> 00:10:52,050
+بسيطة تناسب ال space اللي موجود عندنا الان
+
+134
+00:10:52,050 --> 00:10:55,290
+completeness of L infinity L infinity عارفين انتوا
+
+135
+00:10:55,290 --> 00:10:59,190
+هو the space of bounded sequences اللي هي the
+
+136
+00:10:59,190 --> 00:11:02,290
+space L infinity is complete كله under the metric
+
+137
+00:11:02,290 --> 00:11:09,490
+اللي احنا خدناه الآن عنديعماصر برضه نفس ال
+
+138
+00:11:09,490 --> 00:11:13,710
+استراتيجية ايش بتاخد بتاخد XM أي كوش سيكوينس في ال
+
+139
+00:11:13,710 --> 00:11:18,010
+L Infinity ولاجه X في ال L Infinity بحيث ان XM
+
+140
+00:11:18,010 --> 00:11:22,350
+Converges لها بقول خلصت اثبتت انه Complete معناته
+
+141
+00:11:22,350 --> 00:11:31,230
+انه بدايته انه بتاخد اي XMكوشي سيكوانس لت اكس ام
+
+142
+00:11:31,230 --> 00:11:33,890
+بياني كوشي سيكوانس ينقل لإنفينيتي هتلاقيه
+
+143
+00:11:33,890 --> 00:11:38,870
+استراتيجية البرهام في الأمثلة الثلاثة الأولى زي
+
+144
+00:11:38,870 --> 00:11:42,010
+بعض وان اكس ام بتساوي اكسهاي واحد ام اكسهاي اتنين
+
+145
+00:11:42,010 --> 00:11:45,400
+ام إلى ما لنهايةلأن شكل العنصر في الـ L-Infinity
+
+146
+00:11:45,400 --> 00:11:54,520
+Sequence لما نقول X1 بساوي XI 1 1 XI 2 1 XI 3 1 ده
+
+147
+00:11:54,520 --> 00:11:58,060
+جافش لعند الـ Un بتضلها إشنانها لأنها دي مش
+
+148
+00:11:58,060 --> 00:12:00,520
+Untables اللي هي عناصرها الـ L-Infinity عناصرها
+
+149
+00:12:00,520 --> 00:12:06,290
+عبارة عن Sequencesو X2 نفس الاشي بيساوي XI واحد
+
+150
+00:12:06,290 --> 00:12:11,790
+اتنين XI اتنين اتنين إلى مال نهاية و نفس الاشي XM
+
+151
+00:12:11,790 --> 00:12:17,590
+in general بيساوي XI واحد M XI اتنين M إلى مال
+
+152
+00:12:17,590 --> 00:12:22,530
+نهاية و عندك XR برضه نفس الاشي و بيضلوا إلى مال
+
+153
+00:12:22,530 --> 00:12:28,110
+نهاية XI واحد R XI اتنين R إلى مال نهايةواضح إذا
+
+154
+00:12:28,110 --> 00:12:31,310
+هذه اللي هي الـ Cauchy Sequence اللي بدي أخدها بدي
+
+155
+00:12:31,310 --> 00:12:34,130
+أقول let Xm be any Cauchy Sequence in N infinity
+
+156
+00:12:34,130 --> 00:12:37,930
+where Xm بتساوي كدهذنب من تعريف الـ Cauchy
+
+157
+00:12:37,930 --> 00:12:41,470
+sequence إيش بيكون for every Y أكبر من 0 there
+
+158
+00:12:41,470 --> 00:12:44,930
+exists K element in N such that المسافة بين X و M
+
+159
+00:12:44,930 --> 00:12:49,330
+و XR أصغر من Y لكل N و M إيه شمالها أكبر من K هذا
+
+160
+00:12:49,330 --> 00:12:53,510
+التعريف العام للـ Cauchy sequence طيب المسافة في
+
+161
+00:12:53,510 --> 00:12:56,950
+هذا ال space اللي هي ال infinity بين XM و XR اللي
+
+162
+00:12:56,950 --> 00:13:01,210
+هو عبارة عن ال supremum للأبعاد XI واحد مقص XI
+
+163
+00:13:01,210 --> 00:13:04,470
+واحد اللهان XI اتنين اللهان مقص XI اتنين اللهان
+
+164
+00:13:04,700 --> 00:13:10,200
+الآخره كله بيصير عندي الـ Supremum لإكساي IM ناقص
+
+165
+00:13:10,200 --> 00:13:15,200
+إكساي IN over I يعني إكساي واحد M، إكساي واحد N
+
+166
+00:13:15,200 --> 00:13:19,980
+التانية إكساي اتنين M، إكساي تلاء اتنين N الـ
+
+167
+00:13:19,980 --> 00:13:24,140
+Supremum اللي هو عبارة عن المسافة بينين؟ بين XM و
+
+168
+00:13:24,140 --> 00:13:30,780
+XN وهذا أخدناه سابقالأن مدام الـ Supremum أصغر من
+
+169
+00:13:30,780 --> 00:13:34,640
+إبسلون إذاً كل واحدة منهم أصغر من إبسلون إذاً أكيد
+
+170
+00:13:34,640 --> 00:13:38,840
+صار عندي كل واحدة من هدولة لأي Fixed I وين موجودة
+
+171
+00:13:38,840 --> 00:13:43,140
+هنا الـ I هذه اللي هي أشمالها ليها واحد اللي هنا
+
+172
+00:13:43,140 --> 00:13:46,420
+واتنين اللي هنا وكأن زي ما أعملت قبل بشوية باخد
+
+173
+00:13:46,420 --> 00:13:49,640
+Sequences Sequences هذه الـ Sequence صارت عبارة عن
+
+174
+00:13:49,640 --> 00:13:57,670
+إيش؟ اللي هي تحققإن KSI IM نقص KSI IN أصغر من مين؟
+
+175
+00:13:57,670 --> 00:14:02,150
+من إبسلون يعني صارت هي نفس أشمالها كوشي sequence
+
+176
+00:14:03,530 --> 00:14:07,010
+هذه الـ sequence صارت إيش مالها؟ كوشي sequence of
+
+177
+00:14:07,010 --> 00:14:10,310
+إيش؟ of real numbers لأن هذولا ال interest إيش
+
+178
+00:14:10,310 --> 00:14:14,970
+مالهم؟ عبارة عن مين؟ عن أعداد حقيقية أو complex
+
+179
+00:14:14,970 --> 00:14:19,410
+سواء في C أو في R إحنا بنعرف C وR إيش مالهم
+
+180
+00:14:19,410 --> 00:14:23,650
+complete إذا مدانيك إذا أكيد بتروح لمين؟ لـ limit
+
+181
+00:14:23,650 --> 00:14:27,390
+سموها XI واحد وهذه ل limit سموها مين؟ XI اتنين
+
+182
+00:14:27,390 --> 00:14:34,970
+وهذه ل limit سموها XI مين؟ I فصار عند الـ Mثم لكل
+
+183
+00:14:34,970 --> 00:14:40,870
+M أكبر من K و لأي I مخصصة من هؤلاء هذا المقدار
+
+184
+00:14:40,870 --> 00:14:47,530
+أصغر من Y وهذا يعني لأي I مخصصة سيكون سيكوينس XI I
+
+185
+00:14:47,530 --> 00:14:51,230
+واحد XI I اتنين إلى ما لا نهاية is a Cauchy
+
+186
+00:14:51,230 --> 00:14:57,050
+sequence of numbers سواء حقيقية أو كمبليكسية في كل
+
+187
+00:14:57,050 --> 00:15:02,520
+حالةبعد ذلك تتعامل بالخطوط التي تتعامل بالخطوط
+
+188
+00:15:02,520 --> 00:15:03,040
+التي تتعامل بالخطوط التي تتعامل بالخطوط التي
+
+189
+00:15:03,040 --> 00:15:04,660
+تتعامل بالخطوط التي تتعامل بالخطوط التي تتعامل
+
+190
+00:15:04,660 --> 00:15:08,480
+بالخطوط التي تتعامل بالخطوط التي تتعامل بالخطوط
+
+191
+00:15:08,480 --> 00:15:09,980
+اللي تتعامل بالخطوط اللي تتعامل بالخطوط اللي
+
+192
+00:15:09,980 --> 00:15:09,980
+تتعامل بالخطوط اللي تتعامل بالخطوط اللي تتعامل
+
+193
+00:15:09,980 --> 00:15:09,980
+بالخطوط اللي تتعامل بالخطوط اللي تتعامل بالخطوط
+
+194
+00:15:09,980 --> 00:15:12,180
+اللي تتعامل بالخطوط اللي تتعامل بالخطوط اللي
+
+195
+00:15:12,180 --> 00:15:21,120
+تتعامل بالخطوط
+
+196
+00:15:21,120 --> 00:15:25,150
+اللياللي انا متوقع ان الـ sequence ايه تروح لها
+
+197
+00:15:25,150 --> 00:15:29,870
+انا غرض ان اناجي xn بتروح ل some x و الـ x هذه
+
+198
+00:15:29,870 --> 00:15:33,670
+تكون في الـ L infinity الـ L من الـ x ركبتها انا
+
+199
+00:15:33,670 --> 00:15:37,050
+بس بدي اتأكد انها في الـ L infinity ايش الـ x عندى
+
+200
+00:15:37,050 --> 00:15:40,390
+الـ x بالساوية صاري واحد صاري اتنين إلى معناه
+
+201
+00:15:40,390 --> 00:15:43,290
+نهايةأول حاجة أريد أن أثبت لكم أن هادف الـL
+
+202
+00:15:43,290 --> 00:15:46,490
+infinity هو واحد بالاستعانة باللي حكيته قبل شوية
+
+203
+00:15:46,490 --> 00:15:51,110
+اتنين أثبت لكم إن الـX فعلا بدأ تروح لمين؟ للـX و
+
+204
+00:15:51,110 --> 00:15:55,070
+هذا الكلام مشابه بالظبط للي حكيته قبل شوية عشان هي
+
+205
+00:15:55,070 --> 00:15:59,270
+كالأول أسرعت مهمش لأن using these infinity limits
+
+206
+00:16:00,100 --> 00:16:03,040
+اللي هي XI واحد و XI اتنين و XI تلاتة اللي رقبتهم
+
+207
+00:16:03,040 --> 00:16:07,620
+We define XI واحد و XI اتنين إلى مالانهية We show
+
+208
+00:16:07,620 --> 00:16:11,840
+that X وين موجودة في الـL infinity و هنثبت أن XM
+
+209
+00:16:11,840 --> 00:16:15,340
+بتروح لمين؟ للـ X as M goes to infinity لأن
+
+210
+00:16:15,340 --> 00:16:20,320
+الاتنين اللي جابل بشوية as M goes to infinitywe
+
+211
+00:16:20,320 --> 00:16:25,380
+see that اتنين هيها as n goes so infinity ومن مين
+
+212
+00:16:25,380 --> 00:16:30,760
+بدى يودى الان بدى يودى الان تروح إلى ما لنهاية لما
+
+213
+00:16:30,760 --> 00:16:34,960
+الان تروح لما لنهاية بيصير عنده او خلينا نودى ان
+
+214
+00:16:34,960 --> 00:16:39,880
+هي ان تروح لما نهاية اي واحد منهم بنفع ناشط ودنيل
+
+215
+00:16:39,880 --> 00:16:43,040
+الان ان بتروح لما نهاية على افتراض ان ان اكبر من
+
+216
+00:16:43,040 --> 00:16:47,730
+مين من ان فبنودى الان إلى ما لنهايةيابنات و شباب
+
+217
+00:16:47,730 --> 00:16:52,950
+المثبتتك صي M نقص صي N أصغر من إبسلون هذا لكل ال N
+
+218
+00:16:52,950 --> 00:16:58,150
+و ال M أكبر من K لو فرضت أنا ال N أكبر من M مش
+
+219
+00:16:58,150 --> 00:17:01,930
+هتجيبكم بثبتوا لهم أكبر من M لو فرضنا أن ال N أكبر
+
+220
+00:17:01,930 --> 00:17:06,390
+من M هذه as N plus infinity هيصير اللي هو هذا
+
+221
+00:17:06,390 --> 00:17:11,140
+limitه أنا أثبتتهانه بيساوي مين؟ XII فبصير هذا
+
+222
+00:17:11,140 --> 00:17:16,340
+المقدار XII M ناقص XII أصغر من مين؟ من إبسلون فصار
+
+223
+00:17:16,340 --> 00:17:21,600
+XII M أصغر أو يساوي إيش؟ إبسلون وهذا صار عندى لكل
+
+224
+00:17:21,600 --> 00:17:26,100
+M أكبر من K XII M ناقص XII أصغر من إبسلون وهذا
+
+225
+00:17:26,100 --> 00:17:32,600
+يعني إيش؟ هذا يعني انه صار عندى كل واحدة منهمهتصير
+
+226
+00:17:32,600 --> 00:17:38,680
+بعد شوية اللي هي X نفسها في الـ L Infinity والـ X
+
+227
+00:17:38,680 --> 00:17:44,170
+هم بتروح للـ X، انشوف هذا الكلام، انكملأحفظونها دي
+
+228
+00:17:44,170 --> 00:17:48,370
+لإني بديها حتى سأتي الزمن بعد شوية Xm قلنا هيها
+
+229
+00:17:48,370 --> 00:17:52,590
+ماشي الحال واتفجين وين لها في L infinity مدان في L
+
+230
+00:17:52,590 --> 00:17:56,010
+infinity is a bounded sequence يعني بمعنى أخر اللي
+
+231
+00:17:56,010 --> 00:18:02,150
+هي Xim لها أصغر من some number اذا then there is
+
+232
+00:18:02,150 --> 00:18:07,050
+km such that Xim أصغر من some number سمناه km على
+
+233
+00:18:07,050 --> 00:18:10,610
+اساس أنه للواحد
+
+234
+00:18:11,220 --> 00:18:15,120
+الـ K الواحد للإتنين الـ K إتنين للتلاتة الـ K
+
+235
+00:18:15,120 --> 00:18:20,220
+تلاتة أيها كذا ال X I M أصغر أو شويه منين K M for
+
+236
+00:18:20,220 --> 00:18:25,540
+all منين or all or all I وين رايحنا؟ رايح أثبت لكم
+
+237
+00:18:25,540 --> 00:18:31,220
+إن ال X هذي is bounded رايح
+
+238
+00:18:31,220 --> 00:18:34,560
+أثبت لكم إن ال X is bounded إيش يعني؟ ده أثبت لكم
+
+239
+00:18:34,560 --> 00:18:40,810
+إن ال X I I هذي أصغر أو شويه some numberهذه اللي
+
+240
+00:18:40,810 --> 00:18:46,190
+بدأت أدوى، معناه بيصار في الأقل infinity لأن
+
+241
+00:18:46,190 --> 00:18:50,470
+XI I triangle inequality أصغر شوي XI I ناقص XI M
+
+242
+00:18:50,470 --> 00:18:56,130
+دخلت اللي بيحت خدمني، زاد XI IM هذي من اللي فوق
+
+243
+00:18:56,130 --> 00:19:01,760
+اللي أثبتناها أصغر من Epsilonوهذه اللي هو الـ L
+
+244
+00:19:01,760 --> 00:19:05,200
+infinity أصغر من KM هذا صار رقم صار عندي هذا
+
+245
+00:19:05,200 --> 00:19:08,560
+المقدار أصغر أو ساوية XI إذا صارت الـ sequence
+
+246
+00:19:08,560 --> 00:19:12,560
+bounded إذا صارت U الموجودة الـ X صارت موجودة في
+
+247
+00:19:12,560 --> 00:19:17,920
+الـ L infinityالأن من ثلاثة هذه اللي فوق مدام كل
+
+248
+00:19:17,920 --> 00:19:21,760
+واحدة منهم هذولة لأي I أصغر أو ساوي يابسيلون إذا
+
+249
+00:19:21,760 --> 00:19:24,920
+السبريمام منهم برضه كون أصغر أو ساوي يابسيلون إذا
+
+250
+00:19:24,920 --> 00:19:28,620
+صار السبريمام لهدي over I أصغر أو ساوي يابسيلون
+
+251
+00:19:29,380 --> 00:19:34,140
+وهذا الكلام صحيح لكل مين لكل M أكبر من K وهذه في
+
+252
+00:19:34,140 --> 00:19:38,440
+الواقع هي عبارة عن مسافة بين XM و Min و XM خاصة X
+
+253
+00:19:38,440 --> 00:19:41,120
+في الأقل Infinity و XM في الأقل Infinity زي
+
+254
+00:19:41,120 --> 00:19:44,220
+المشروع أن أخد اللي هي المسافة بينهم حسب الأقل
+
+255
+00:19:44,220 --> 00:19:47,870
+Infinityفصار عندها الـ distance أزار أسوأ أو أسوأ
+
+256
+00:19:47,870 --> 00:19:52,410
+أبسلون لكل أكم أكبر من K وهذا يعني أنه limit الـ
+
+257
+00:19:52,410 --> 00:19:56,090
+XM بسوء X معناته بدأنا بـ XM Cauchy sequence
+
+258
+00:19:56,090 --> 00:19:59,410
+وانتهينا بـ XM Converged في الـ X بالقلة
+
+259
+00:19:59,410 --> 00:20:02,610
+الانفينيتي وهذا يعني أن القلة الانفينيتي is إيش؟
+
+260
+00:20:02,610 --> 00:20:06,810
+is a complete space طيب يلّا الان ال complete نسنا
+
+261
+00:20:06,810 --> 00:20:14,650
+من؟ نصي احنا لحد الآن اللي عملناه في المثالينناخد
+
+262
+00:20:14,650 --> 00:20:18,530
+الـ Cauchy Sequence ونصل إلي إشمالها Converse
+
+263
+00:20:18,530 --> 00:20:26,570
+وتقريبا طريقة الأصول متشابهة في الجهتين الآن بدنا
+
+264
+00:20:26,570 --> 00:20:30,770
+نروح لفكرة أخرىبدنا ناخد الـ completeness للـ
+
+265
+00:20:30,770 --> 00:20:34,990
+scene مافيش داعي ناخد أي كوش سيكوينس في ال scene و
+
+266
+00:20:34,990 --> 00:20:38,130
+بعدين أثبتها و أديها وين اللي هي ال convinced في
+
+267
+00:20:38,130 --> 00:20:42,530
+شيء خلّيني أقول أبسط أو أنسب لهذا المثال لإن هو
+
+268
+00:20:42,530 --> 00:20:46,970
+يغلبني في الأول أنا واخدت فيه هذه و بعدين وديتها ل
+
+269
+00:20:46,970 --> 00:20:53,020
+X ده spaceC Consists Of All Convergent Sequences
+
+270
+00:20:53,020 --> 00:20:56,300
+Of Complex Numbers أو ريال مش مشكلة With The
+
+271
+00:20:56,300 --> 00:20:59,280
+Metric Induced From The Space الانفينيتي is
+
+272
+00:20:59,280 --> 00:21:05,140
+complete ايش اللي بقوله بقول احنا بنعرف ان any
+
+273
+00:21:05,140 --> 00:21:11,610
+convergent sequence is boundedإذاً الـ space of
+
+274
+00:21:11,610 --> 00:21:16,610
+all convergent sequences is a subspace أو is a
+
+275
+00:21:16,610 --> 00:21:19,050
+subset .. خلّيني أقول subspace لسه ما حكيناش عن ال
+
+276
+00:21:19,050 --> 00:21:22,910
+vector space is a subset من مين؟ من ال infinity ال
+
+277
+00:21:22,910 --> 00:21:26,030
+infinity كل ال bounded sequences ال C هي ال
+
+278
+00:21:26,030 --> 00:21:29,250
+convergent sequences وكل convergence اللي هي
+
+279
+00:21:29,250 --> 00:21:33,830
+bounded إذاً C جزء من مين؟ من ال infinity وكأنه
+
+280
+00:21:33,830 --> 00:21:38,550
+الآنأذكركم في اللي حكيناها المرة الماضية وكيف بدي
+
+281
+00:21:38,550 --> 00:21:44,890
+أستخدمه عندي أنا ال ال infinity ال ال infinity علي
+
+282
+00:21:44,890 --> 00:21:49,520
+مترك اللي هو ال D تبع ال supremumالان بدي اخد الـ
+
+283
+00:21:49,520 --> 00:21:55,560
+C واخد نفس الـ D صار جزء منه صار .. صار sub metric
+
+284
+00:21:55,560 --> 00:21:59,700
+space منه اه sub metric space منه من الـ D لأن كل
+
+285
+00:21:59,700 --> 00:22:02,460
+أنصر هنا موجود هنا و ال metric اللي هنا هو نفس
+
+286
+00:22:02,460 --> 00:22:06,340
+اللي هنا بدي اثبتلكم انه الآن هذا برضه ايش
+
+287
+00:22:06,340 --> 00:22:11,300
+complete ماشي الحالة طبعا هذا أثبتنا complete طيب
+
+288
+00:22:11,300 --> 00:22:14,780
+احنا المرة الفاتة قلنا ان ال .. نعم
+
+289
+00:22:17,650 --> 00:22:23,730
+اخدنا من المرة الماضية قلنا إنه لو كان في عندي
+
+290
+00:22:23,730 --> 00:22:27,630
+space closed subspace من complete space إيش هيكون
+
+291
+00:22:27,630 --> 00:22:31,970
+is complete إذا يكفي عشان أثبت إنه هذا إنه
+
+292
+00:22:31,970 --> 00:22:36,230
+complete إن أثبته إنه closed space طب كيف بدأ أثبت
+
+293
+00:22:36,230 --> 00:22:41,270
+إنه closed space؟ بدي أخد X في الـC closure و أثبت
+
+294
+00:22:41,270 --> 00:22:45,940
+لك إن X موجودة في الـCيعني صار الـC closure بيساوي
+
+295
+00:22:45,940 --> 00:22:49,820
+الـC، معناته صار الـC is إيش؟ closed، إذا هي
+
+296
+00:22:49,820 --> 00:22:54,280
+استراتيجية البرهان اللي بدي أعملها، واضح؟ طيب، إذا
+
+297
+00:22:54,280 --> 00:22:57,900
+الآن بدي أقولكم عشان أثبتوا الـcompleteness of C،
+
+298
+00:22:57,900 --> 00:23:01,380
+let X بيساوي إكساي I، اللي هي هذه الـsequence،
+
+299
+00:23:01,380 --> 00:23:03,660
+إكساي 1، إكساي 2، إكساي 3، إكساي 4، إلى مهلا
+
+300
+00:23:03,660 --> 00:23:09,120
+نهاية، element in C closureو أثبت لكم أن هذه ستكون
+
+301
+00:23:09,120 --> 00:23:13,720
+في الـ C طيب، ما معنى الـ X في الـ C-closure؟ ان
+
+302
+00:23:13,720 --> 00:23:18,760
+هناك C .. خدناها المرة الماضية ان X element in C
+
+303
+00:23:18,760 --> 00:23:25,800
+-closure هذا معناته ان هناك سيكوينس XMNC in C such
+
+304
+00:23:25,800 --> 00:23:30,620
+that الـ XN بتروح لمين للـ C هذا معناه ان الـ X
+
+305
+00:23:30,620 --> 00:23:35,720
+أشوان موجودة في اللي هو الـ C closure اللي ناسي
+
+306
+00:23:35,720 --> 00:23:36,300
+يتذكر
+
+307
+00:23:39,080 --> 00:23:44,680
+إنه X in between C closure إيش معناته إنه بنلاقي
+
+308
+00:23:44,680 --> 00:23:49,200
+sequence XM أو XN اللي بدكم إياها في الـC بحيث إن
+
+309
+00:23:49,200 --> 00:23:55,800
+XM بتروح لمين لأسفة لمين للـX فبتكون اللي هي X
+
+310
+00:23:55,800 --> 00:24:02,700
+واللي موجودة في الـC closure طيب الآن أخدت ال ..
+
+311
+00:24:02,700 --> 00:24:07,230
+ال .. ال .. لو أثبتت هذاإن هاد الـ X في الـ C
+
+312
+00:24:07,230 --> 00:24:10,950
+closure وصلت في الـ C بكون خلصت اتفجنا؟ يلّا
+
+313
+00:24:10,950 --> 00:24:16,930
+خلّينا نروح نشوف الآن أخدت X في الـ C closure إذا
+
+314
+00:24:16,930 --> 00:24:20,110
+حسب تعريف X في الـ C closure you get sequence XM
+
+315
+00:24:20,110 --> 00:24:24,910
+in C بحيث أن XM بتروح لمين؟ لل X where؟ إيش هي الـ
+
+316
+00:24:24,910 --> 00:24:28,670
+XM؟ زي ما عملنا قبل شوية X واحد يعني X واحد واحد
+
+317
+00:24:28,670 --> 00:24:32,190
+واحد X اتنين واحد الاخري XM in general X واحد أم X
+
+318
+00:24:32,190 --> 00:24:35,190
+اتنين أم إلى مدى نهايةهذه الـ sequence of elements
+
+319
+00:24:35,190 --> 00:24:40,930
+هو الموجودة في الـ C نفسها ماشي الحال؟ طيب، مدان
+
+320
+00:24:40,930 --> 00:24:43,930
+في الـ C، إذا كل واحدة converges لأن مدينة الـ C
+
+321
+00:24:43,930 --> 00:24:46,850
+عبارة عن الـ space أو الـ set of all convergent
+
+322
+00:24:46,850 --> 00:24:50,690
+sequences إذا hence for every ي أكبر من سفر there
+
+323
+00:24:50,690 --> 00:24:53,670
+exists k elements and such that تعريف أيش؟ إنها
+
+324
+00:24:53,670 --> 00:24:59,890
+الـ sequence converges إيش هو للتعريف أن الـ
+
+325
+00:24:59,890 --> 00:25:04,320
+distance بين Xم أو Xاللي هو أصغر من ي على تلاتة
+
+326
+00:25:04,320 --> 00:25:08,540
+أصغر من أي قيمة من ضمنها ي على تلاتة اللي هتخدمني
+
+327
+00:25:08,540 --> 00:25:11,580
+في الحسابات زي ما بنقول دايما for all M أكبر من
+
+328
+00:25:11,580 --> 00:25:17,460
+مين مين or سوى K هذا معنى إنه XM مالها converge ال
+
+329
+00:25:17,460 --> 00:25:23,770
+mean لل X اللي فوقما هو الـ metric اللي موجود هنا
+
+330
+00:25:23,770 --> 00:25:28,330
+ال metric ان ال distance بين xm و x بتساوي ال
+
+331
+00:25:28,330 --> 00:25:33,370
+supremum من xi m نقص xi i over mu over I هاي اللي
+
+332
+00:25:33,370 --> 00:25:39,600
+هي ال sequenceاللي هي ال XM وهي ال X اللي عندي
+
+333
+00:25:39,600 --> 00:25:43,840
+اللي سمنها XI واحد XI اتنين XI تلاتة اللي هي هذه
+
+334
+00:25:43,840 --> 00:25:48,200
+فالفرق بينهم واخدوا ال supermom له فقبل ال
+
+335
+00:25:48,200 --> 00:25:51,100
+interest اللي عاجبها البعض اللي هو بساوي اللي هو
+
+336
+00:25:51,100 --> 00:25:56,960
+دي XM و X أصغر من Y ع التلاتة إذا الآن هذه من XM
+
+337
+00:25:56,960 --> 00:26:04,340
+بتروح لل Xمن جهة الأخرى ما احنا عامال بنقول الان
+
+338
+00:26:04,340 --> 00:26:10,040
+عندى الـ XI .. XII موجودة في الـ C Clotar طيب
+
+339
+00:26:10,040 --> 00:26:12,880
+انتجوا لها .. لها المعلومة خذوا المعلومة الأولى
+
+340
+00:26:14,420 --> 00:26:19,640
+عندي الأن for all m أكبر أو ساوء k and any fixed i
+
+341
+00:26:19,640 --> 00:26:24,840
+هيكون عندي x i i m ناقص x i i أصغر من مين من
+
+342
+00:26:24,840 --> 00:26:27,840
+epsilon ع تلاتة وعملت هذا قبل بشوية مدام السوبرمان
+
+343
+00:26:27,840 --> 00:26:31,760
+نفسه أصغر من epsilon ع تلاتة إذا كل ال interest
+
+344
+00:26:31,760 --> 00:26:36,380
+اللي جوا برضه اصغر من epsilon ع تلاتة طيب الان بدي
+
+345
+00:26:36,380 --> 00:26:39,560
+أخد أحكي عن إشي محدد عشان بدي أحطه بين إيديا و
+
+346
+00:26:39,560 --> 00:26:44,580
+أشتغل عليهعشان هي أخدت .. طبعا هذا صحيح لمن؟ لكل M
+
+347
+00:26:44,580 --> 00:26:49,980
+أكبر سوى إيش؟ K لكل M أكبر سوى K بدي أخد اللي هو
+
+348
+00:26:49,980 --> 00:26:54,500
+الـ K عند M أيش بتساوي K؟ بتبقى ده أشمالها صحيحة
+
+349
+00:26:54,500 --> 00:27:00,000
+إذا XI I K نقص XI I أصغر من مين؟ من إبسن ع تلاتة
+
+350
+00:27:00,000 --> 00:27:04,980
+إذا أخدت مين أنا ال M بتساوي K عشان بتعمل حساباتي
+
+351
+00:27:04,980 --> 00:27:11,470
+على إشي بين إيدي ملموس يعني عن واحدة محددة طيبالان
+
+352
+00:27:11,470 --> 00:27:15,890
+كما قلنا قبل بشوية كل مننا دولة ال sequence من نوع
+
+353
+00:27:15,890 --> 00:27:20,610
+جاية من ال C يعني X واحد من ال C يعني convergence
+
+354
+00:27:20,610 --> 00:27:24,530
+sequence of real numbers او of complex X اتنين في
+
+355
+00:27:24,530 --> 00:27:28,830
+ال C X ثلاثة في ال C X M in general في ال C X K في
+
+356
+00:27:28,830 --> 00:27:32,170
+ال C إذا ال sequence هذه كل العناصرها موجودة في ال
+
+357
+00:27:32,170 --> 00:27:37,870
+C مدام XK في ال C إذا نفس ال XK converge ال XK مين
+
+358
+00:27:37,870 --> 00:27:46,180
+هيعبارة عن x1k, x2k, x3k, x4k, x5k إلى مالا نهاية
+
+359
+00:27:46,180 --> 00:27:52,100
+هذا الـ sequence أجمع لـ converge الان its terms
+
+360
+00:27:52,100 --> 00:27:55,440
+xik form a convergent sequence such that الـ
+
+361
+00:27:55,440 --> 00:28:00,340
+sequence is Cauchy أكيد عن مين بحكي يا جماعة؟ بحكي
+
+362
+00:28:00,340 --> 00:28:07,360
+عن الـ sequence x1k, x2k, x3k
+
+363
+00:28:13,050 --> 00:28:19,370
+من الـ real numbers مظبوط الـ N اللي هي مزام في
+
+364
+00:28:19,370 --> 00:28:23,350
+الـ C في الـ C حسب تعريف الـ C وهو converse إذا
+
+365
+00:28:23,350 --> 00:28:25,370
+ركيب كوشي من تعريف الكوشي
+
+366
+00:28:38,700 --> 00:28:42,880
+طيب، الآن بدي ألمها المعلومات كلها اللي عندي و
+
+367
+00:28:42,880 --> 00:28:49,260
+أحصل على اللي بدياه الآن، إيش أنا بديه؟ بدي أثبت
+
+368
+00:28:49,260 --> 00:28:56,080
+لكم إن XII هذه، اللي هي X هذه، و إن موجودة في
+
+369
+00:28:56,080 --> 00:28:59,180
+الـC، يعني أثبت لكم إنها Converges، رايح بهذا
+
+370
+00:28:59,180 --> 00:29:04,380
+الاتجاه، بكون خلصته شوفوا الآن، حسبولي الآن، لكل I
+
+371
+00:29:04,380 --> 00:29:08,760
+و J أكبر من مين؟ من أنت، إذا هذا بنطبق عليهبكون
+
+372
+00:29:08,760 --> 00:29:14,020
+بيساوي أصغر ويساوي XII-XIIK اللي حسبتها قبل و شوية
+
+373
+00:29:14,020 --> 00:29:20,780
+زاد XIIK XIJK زاد XIJK-XIAJ عملت ال training
+
+374
+00:29:20,780 --> 00:29:26,160
+quality ع مرتين مرة دخلت XIIK و مرة دخلت XIJK
+
+375
+00:29:26,160 --> 00:29:33,000
+بالسلب والإيجاب اللي هو أصغرالأولى xi i ناقص xi ik
+
+376
+00:29:33,000 --> 00:29:38,200
+اللي هو هي أصغر من مين إبسلن ع تلاتة و xi ik ناقص
+
+377
+00:29:38,200 --> 00:29:42,700
+xi jk هي أصغر من مين برضه إبسلن ع تلاتة و xi jk
+
+378
+00:29:42,700 --> 00:29:48,680
+ناقص xi j نفسها برضه أصغر من مين من إبسلن ع تلاتة
+
+379
+00:29:48,680 --> 00:29:55,880
+برضه اللي هو عملناها قبل هيك ماشي الحال هذه
+
+380
+00:29:55,880 --> 00:30:00,970
+ما هي صحيحة لكل I مظبوطهذه صحيحة لكل I اللي هي هذه
+
+381
+00:30:00,970 --> 00:30:05,830
+لكل صحيحة لكل I إذا سواء I أو J صحيحة لها هي ال I
+
+382
+00:30:05,830 --> 00:30:09,390
+هنا وهي ال J هنا فاهمين؟ فبصير هذا أصغر من هذا
+
+383
+00:30:09,390 --> 00:30:11,090
+أصغر من هذا اصغر من هذا اصغر من هذا اصغر من هذا
+
+384
+00:30:11,090 --> 00:30:11,710
+اصغر من هذا اصغر من هذا اصغر من هذا اصغر من هذا
+
+385
+00:30:11,710 --> 00:30:11,810
+اصغر من هذا اصغر من هذا اصغر من هذا اصغر من هذا
+
+386
+00:30:11,810 --> 00:30:11,910
+اصغر من هذا اصغر من هذا اصغر من هذا اصغر من هذا
+
+387
+00:30:11,910 --> 00:30:12,070
+اصغر من هذا اصغر من هذا اصغر من هذا اصغر من هذا
+
+388
+00:30:12,070 --> 00:30:13,030
+اصغر من هذا اصغر من هذا اصغر من هذا اصغر من هذا
+
+389
+00:30:13,030 --> 00:30:19,310
+اصغر من هذا اصغر
+
+390
+00:30:19,310 --> 00:30:25,290
+من هذا اصغرof numbers و ال number سواء real او
+
+391
+00:30:25,290 --> 00:30:30,010
+complex هتكون complete مادام complete اذا صارت
+
+392
+00:30:30,010 --> 00:30:33,990
+اللي هي ال sequence هذا يشملها convergence مادام
+
+393
+00:30:33,990 --> 00:30:39,870
+convergence اذا صارت عند ال xاللي هي مِساوي XII
+
+394
+00:30:39,870 --> 00:30:45,590
+هذه صارت موجودة في الـC نفسها لإنه صارت converge
+
+395
+00:30:45,590 --> 00:30:48,530
+ومعناته انه صار الـC بتساوي C closure زي ما بدأنا
+
+396
+00:30:48,530 --> 00:30:53,430
+في الأول معناته صارت اللي هو الـC اللي هي عبارة عن
+
+397
+00:30:53,430 --> 00:30:57,110
+complete metric space لإن هي صارت closed subspace
+
+398
+00:30:57,110 --> 00:31:02,230
+of a complete metric space which is complete أي
+
+399
+00:31:02,230 --> 00:31:04,350
+سؤال طيب
+
+400
+00:31:07,100 --> 00:31:11,980
+الان بدنا نيجي ل ال completeness of LB جاعدين احنا
+
+401
+00:31:11,980 --> 00:31:15,580
+بنجرد كل ال spaces اللي هتعيش معنا طول الفصل اللي
+
+402
+00:31:15,580 --> 00:31:20,360
+هو ال RN و ال CN و ال L∞ و ال LB و ال C و بعد شوية
+
+403
+00:31:20,360 --> 00:31:24,700
+ال continuous functions كل
+
+404
+00:31:24,700 --> 00:31:27,780
+هذه هنميز مين ال complete و مين اللي هو مش
+
+405
+00:31:27,780 --> 00:31:32,400
+complete و كل واحدة completeness تبعها حسب تريكها
+
+406
+00:31:38,690 --> 00:31:45,450
+هلاجة spaces إذا غيرنا المترقب بيتبطل complete أو
+
+407
+00:31:45,450 --> 00:31:50,730
+غيرنا المترقب بتصير complete حسب الأصل والتغيير
+
+408
+00:31:50,730 --> 00:31:55,310
+طيب شوفوا صلى الله عليه الصلاة والسلام الان الال
+
+409
+00:31:55,310 --> 00:31:59,050
+بيه برضه من ال spaces الملازمة لنا برضه spaces of
+
+410
+00:31:59,050 --> 00:32:02,740
+sequencesلكن احنا بقول الـ spaces و ال sequences
+
+411
+00:32:02,740 --> 00:32:07,660
+ده شرطه انه انها تكون ال summation لل XI I بي is
+
+412
+00:32:07,660 --> 00:32:10,380
+finite ماشي الحال يعني ال sequence هتكون converse
+
+413
+00:32:10,380 --> 00:32:13,680
+السيريز هتكون converse هاي شرط انها تكون ال X ..
+
+414
+00:32:13,680 --> 00:32:16,140
+اللي .. اللي هي ال sequence .. اللي هي X وا .. X
+
+415
+00:32:16,140 --> 00:32:18,580
+واحد .. XI واحد .. XI اتنين .. XI تلت .. XI اربعة
+
+416
+00:32:18,580 --> 00:32:21,640
+إلى ما لان هي تكون وين في القلبي طيب
+
+417
+00:32:25,310 --> 00:32:33,650
+أي رقم بين واحد وبين مين ماله نهاية بكل مكان الـ B
+
+418
+00:32:33,650 --> 00:32:40,230
+تبعه أشمالها is a complete metric spaceنفس القصة،
+
+419
+00:32:40,230 --> 00:32:44,470
+هأسرع شوية لأن الكلام مكرر Let XM be any Cauchy
+
+420
+00:32:44,470 --> 00:32:48,970
+Sequence الموجودة في الـ LB بالدرجة لـ X حيث أن XM
+
+421
+00:32:48,970 --> 00:32:51,210
+هي الـ Conversion لها والـ X تكون في الـ LB، هي
+
+422
+00:32:51,210 --> 00:32:56,530
+القصة كلها، الآن Where XM، صرنا عارفين، XI و XII M
+
+423
+00:32:56,530 --> 00:33:01,350
+إلى مالا نهاية، الآن من تعريف اللي هو الـ Sequence
+
+424
+00:33:01,350 --> 00:33:06,910
+في الـ LBومن تعريف ان الـ XM كون أكوشي إذا لكل Y
+
+425
+00:33:06,910 --> 00:33:10,870
+أكبر من 0 بيلاجي K بحيث ان لكل N و M أكبر من K
+
+426
+00:33:10,870 --> 00:33:15,310
+بيكون المسافة بين XM و XN أشملها أصغر من Y المسافة
+
+427
+00:33:15,310 --> 00:33:19,710
+في حالة الـ L بي مين هي summation XI IM نقص XI IM
+
+428
+00:33:19,710 --> 00:33:25,090
+اللي هو أص بي وكل أص نص أصغر من مين من Y هذه خلوها
+
+429
+00:33:25,090 --> 00:33:31,930
+اسمها أربعةالان من اللي فوق هذه برضه بنفس الأسلوب
+
+430
+00:33:31,930 --> 00:33:35,650
+مدام ال summation كله أصغر من epsilon إذا أكيد كل
+
+431
+00:33:35,650 --> 00:33:39,130
+واحد من جوا ال summation برضه هيكون أشمله اللي هو
+
+432
+00:33:39,130 --> 00:33:42,650
+أصغر من epsilon هذي بيصير كلها .. شو سيبكوا من هذي
+
+433
+00:33:42,650 --> 00:33:45,390
+.. هذي بدون الواحد على B بيصير هذا ال summation
+
+434
+00:33:45,390 --> 00:33:49,710
+أصغر من أُس B ماتجه؟ إذا كل واحدة منهم أُس B أصغر
+
+435
+00:33:49,710 --> 00:33:53,150
+من هذي أُس B يعني كل واحدة أصغر من مين؟ من epsilon
+
+436
+00:33:53,150 --> 00:33:58,000
+زي ما عملنا في التربيةإذا صار عنده هذا ايش بثبت
+
+437
+00:33:58,000 --> 00:34:02,940
+this shows that for any fixed I هذه أصغر من Y يعني
+
+438
+00:34:02,940 --> 00:34:06,600
+صارت عبارة عن Cauchy sequence نفس الاشي اللي هي ال
+
+439
+00:34:06,600 --> 00:34:09,700
+sequence اللي هنا و ال sequence اللي هنا الطولية
+
+440
+00:34:09,700 --> 00:34:12,640
+هذه اللي عملها في الأول كلهم Cauchy sequences و
+
+441
+00:34:12,640 --> 00:34:15,780
+Cauchy sequences of mean of numbers نفس اللي يعني
+
+442
+00:34:15,780 --> 00:34:19,650
+ان كله حكيتهالان مادام كوشي سيكوانسيز of number
+
+443
+00:34:19,650 --> 00:34:23,150
+سواء real او complex و بعرف ال R والC complete
+
+444
+00:34:23,150 --> 00:34:26,410
+بعيد نفس الكلام اذا اكيد هذه ال sequence الشمالها
+
+445
+00:34:26,410 --> 00:34:30,750
+converge خلّينا نسمي ان هذا ال XI IM اللي هي ال
+
+446
+00:34:30,750 --> 00:34:35,210
+converge هذي converge لمن؟ لل XII فانصرت عندى انا
+
+447
+00:34:35,210 --> 00:34:40,900
+Xبتساوي XI واحد XI اتنين إلى مال انهيار غلط زي قبل
+
+448
+00:34:40,900 --> 00:34:44,440
+شوية اهد ال XM على مين؟ على ال X واثبت لك ال X هو
+
+449
+00:34:44,440 --> 00:34:47,980
+الموجودة في القلبي كله بالاستعانة بالموجود وبنفس
+
+450
+00:34:47,980 --> 00:34:48,580
+الأسلوب
+
+451
+00:34:52,210 --> 00:34:55,950
+الان using these infinitely limits we define ال X
+
+452
+00:34:55,950 --> 00:34:59,290
+اللي قلنا عنها X واحد X اتنين كده و بدنا نثبت
+
+453
+00:34:59,290 --> 00:35:03,230
+أملنا انه نثبت ان ال X و موجودة في القلبي و نثبت
+
+454
+00:35:03,230 --> 00:35:06,750
+ان XM بتروح لل X as M goes to infinity ماشي الحال
+
+455
+00:35:06,750 --> 00:35:11,370
+من أربعة فوق we have that هاي أربعة أربعة أربعة
+
+456
+00:35:11,870 --> 00:35:15,890
+أربعة هذه أربعة شايفينها هي اللي عندى بطلع عندى ال
+
+457
+00:35:15,890 --> 00:35:19,990
+summation لهذا أصغر من ياس و نص بي ماشي الحال الان
+
+458
+00:35:19,990 --> 00:35:24,430
+ود ان تروح لمين إلى مالة نهاية بتسير لما ان تروح
+
+459
+00:35:24,430 --> 00:35:27,710
+لمالة نهاية على افتراض ان ان أكبر من بي بيسير هذي
+
+460
+00:35:27,710 --> 00:35:30,890
+تروح لمالة نهاية لما ان تروح لمناهد تروح لمين
+
+461
+00:35:30,890 --> 00:35:35,570
+للنهاية لل XII فبيصير عندى ال summation ال
+
+462
+00:35:35,570 --> 00:35:41,270
+summation لل XIIماقص XII اللي راحت إله أُس بي أزرع
+
+463
+00:35:41,270 --> 00:35:44,630
+أساومين أُس نص بي طبعا أخدت أنا لعند مين عشان حدش
+
+464
+00:35:44,630 --> 00:35:48,130
+يقول أنت بدأت تدخل limit علامة بدأ أخد اللي هو I
+
+465
+00:35:48,130 --> 00:35:51,330
+من واحد لعند مين لعند L أخدت L arbitrarily مش كله
+
+466
+00:35:51,330 --> 00:35:55,370
+الصممش اللي أخدته أخدته لعند أي L فاهمين عليا؟
+
+467
+00:35:55,370 --> 00:35:58,250
+عساس إنه مايصيرش limit علامة و يصير فيه عندي
+
+468
+00:35:58,250 --> 00:36:03,750
+إيشكاليةفالان as n يعني هدول مجموعات لبعض هذا زائد
+
+469
+00:36:03,750 --> 00:36:06,750
+هذا زائد هذا خمس مرات عشر مرات مجموعات ألا من
+
+470
+00:36:06,750 --> 00:36:09,610
+المرات إلى إذا بقدر أدخل ال limit و أزاى على
+
+471
+00:36:09,610 --> 00:36:13,030
+الجمال احنا عارفين ما زالت موجودة إذا صار عندي ال
+
+472
+00:36:13,030 --> 00:36:17,290
+limit هذه as n goes to infinity راح تقل إكس آي I I
+
+473
+00:36:17,290 --> 00:36:22,110
+من واحد لمين للأل لأن بعد ما خلصت شروع عامة الأمر
+
+474
+00:36:22,110 --> 00:36:26,970
+وصلت لهذا الحد كانت المهيأ arbitraryأذا بقدر أور
+
+475
+00:36:26,970 --> 00:36:30,870
+بL وين ما بدي لأن هذا الكلام صحيح لمن؟ لأي L في
+
+476
+00:36:30,870 --> 00:36:34,350
+الدنيا لأن ال L أخدت fixed لكن arbitrarily إذا صار
+
+477
+00:36:34,350 --> 00:36:37,850
+عندي as L goes to infinity برجع هذا I من واحد إلى
+
+478
+00:36:37,850 --> 00:36:46,190
+المقدار هذا أصغر من Y الأسمن أس Band منه ال
+
+479
+00:36:46,190 --> 00:36:51,570
+summation أزرع سواء من epsilon أي سؤال طيب هذه
+
+480
+00:36:51,570 --> 00:36:57,490
+اليمين خمسة الان x and y موجودة في ال LB إذا ال
+
+481
+00:36:57,490 --> 00:37:02,610
+summation هذا is found out من تعرف ال LB الآن بدي
+
+482
+00:37:02,610 --> 00:37:06,870
+أثبت لكم إن هذه في ال LB بدي أستخدم ال course key
+
+483
+00:37:06,870 --> 00:37:13,650
+inequalityاللي هي بيصير عندي على اللي هي xii وxim
+
+484
+00:37:16,160 --> 00:37:18,740
+هي عند باقي من ال course keen quality ال summation
+
+485
+00:37:18,740 --> 00:37:23,600
+هذا xi i اص بي الكل اص واحد على بي اصغر اي ساوي xi
+
+486
+00:37:23,600 --> 00:37:29,900
+i m ماقص xi j بي اللي اضفتها مين هي xi i m مطرحتها
+
+487
+00:37:29,900 --> 00:37:34,220
+اص بي اص واحد على بي زاد ال summation xi j m اص بي
+
+488
+00:37:34,220 --> 00:37:37,200
+اص واحد على بي هذه اللي هي مينها مين هي ال main
+
+489
+00:37:37,200 --> 00:37:41,040
+course keen quality اللي نسيها يرجحهاالآن صارت هذه
+
+490
+00:37:41,040 --> 00:37:46,120
+عندي أصلاً عندي finite من فوق أثبتناها وهذه finite
+
+491
+00:37:46,120 --> 00:37:49,320
+من فوق أثبتناها إذاً هذا المقدار كله إيش حيصير
+
+492
+00:37:49,320 --> 00:37:53,400
+حيصير finite شوفتوا أنها من فوق finite هذه finite
+
+493
+00:37:53,400 --> 00:37:58,240
+هيها واللي فوق هذه برضه إيش مالها finite إذاً صارت
+
+494
+00:37:58,240 --> 00:38:01,800
+تنتين finite وهذا بعني مدام هذه صارت ال summation
+
+495
+00:38:01,800 --> 00:38:07,100
+finite إذاً x بالساوية اللي هي هذه xi I element in
+
+496
+00:38:07,100 --> 00:38:12,650
+LBالان بمثل الأسلوب مدينة صارت في الال بي إذا
+
+497
+00:38:12,650 --> 00:38:17,830
+بيصير الان عندي من خمسة من خمسة اللي هي ال
+
+498
+00:38:17,830 --> 00:38:23,230
+distance هذه في الواقع إيش بتمثل المسافة بين XM و
+
+499
+00:38:23,230 --> 00:38:28,590
+Xمعايا اه هذه اللي هي الجوا بس حس واحد عربية يعني
+
+500
+00:38:28,590 --> 00:38:34,030
+هذه اشمالها المسافة بين XM و X أصغر يساوي Y لكل
+
+501
+00:38:34,030 --> 00:38:38,510
+أكبر من K إذا صارت عندي XM بتروح لل X وال X في
+
+502
+00:38:38,510 --> 00:38:43,690
+القلبي اللي هي صارت القلبي اشمالها is complete
+
+503
+00:38:43,690 --> 00:38:46,870
+نيجي الآن عندي the space of continuous functions
+
+504
+00:38:46,870 --> 00:38:52,940
+the space of continuous functions بدأ أثبت لكمإن
+
+505
+00:38:52,940 --> 00:38:58,280
+هذا الـ space is complete under the maximum metric
+
+506
+00:38:58,280 --> 00:39:02,260
+اللي هو الـ metric اللي عرفنا عليه هو اللي بيساوي
+
+507
+00:39:02,260 --> 00:39:07,460
+ال maximum لل X of T ناقص اللي هو Y of T, T over
+
+508
+00:39:07,460 --> 00:39:19,560
+ال interval اللي عندنا اللي أما C of A وBis the
+
+509
+00:39:19,560 --> 00:39:25,780
+space of all continuous functions على closed
+
+510
+00:39:25,780 --> 00:39:29,940
+bounded interval a و b مذا تبقلكم أن هذا ال space
+
+511
+00:39:29,940 --> 00:39:33,100
+is complete under our metric اللي هو ال maximum
+
+512
+00:39:33,100 --> 00:39:36,020
+نفس الأسئلة، إيش بتسوي؟ هتلاقيوا نفس الأسئلة
+
+513
+00:39:36,020 --> 00:39:42,210
+بالظبطلت XM be any Cauchy sequence in C or B إذاً
+
+514
+00:39:42,210 --> 00:39:44,250
+for every Y أكبر من سفر there exists K element
+
+515
+00:39:44,250 --> 00:39:47,690
+such that for all M أكبر من K نحن لدينا المسافة
+
+516
+00:39:47,690 --> 00:39:52,070
+بين XM و XM أصغر من إبسلون المسافة بين XM و XM
+
+517
+00:39:52,070 --> 00:39:56,150
+دوال هذولة اللي هي عبارة عن XM of T نقص XM of T
+
+518
+00:39:56,150 --> 00:39:58,970
+الـT الموجودة في الـJ اللي هي الـinterval اللي
+
+519
+00:39:58,970 --> 00:40:02,870
+عليها اللي هي معرفة هذه الدوال ماشي الحال هذه اللي
+
+520
+00:40:02,870 --> 00:40:09,070
+هي المسافة بين أي XMو Xn الـ Xm والـ Xn ويمال هنا
+
+521
+00:40:09,070 --> 00:40:13,010
+يا جماعة الـ Xm والـ Xn موجودات في الـ C A وB يعني
+
+522
+00:40:13,010 --> 00:40:17,210
+عبارة عن continuous functions إذن السبريموم أو ال
+
+523
+00:40:17,210 --> 00:40:20,030
+maximum للـ Xm of T نقص Xn of T ومضمون إنها موجودة
+
+524
+00:40:20,030 --> 00:40:23,250
+لإنها على close bounded interval T element in J
+
+525
+00:40:23,250 --> 00:40:28,130
+أصغر من Y هذا تعريف الكوشي مباشرة إذن بدل ما
+
+526
+00:40:28,130 --> 00:40:31,510
+نتعامل مع الـN اللي قبل بشوية أو الـI أو الـJ
+
+527
+00:40:31,510 --> 00:40:37,660
+بنتعامل مع الـTفبصير عندى لان مدام ال maximum أصغر
+
+528
+00:40:37,660 --> 00:40:41,880
+من epsilon لكل N و M أكبر من K إذا لكل N و M أكبر
+
+529
+00:40:41,880 --> 00:40:45,300
+من K هيكون هذا المقدار اللى جوا أصغر من epsilon
+
+530
+00:40:45,300 --> 00:40:48,940
+لكل مين لكل T المخود عليه كل إياش ال maximum مدام
+
+531
+00:40:48,940 --> 00:40:52,580
+ال maximum أصغر من epsilon إذا قيمة الدولة هذه مع
+
+532
+00:40:52,580 --> 00:40:56,780
+قصدها عند أي نقطة في الinterval أصغر من epsilonهذا
+
+533
+00:40:56,780 --> 00:41:00,960
+نصارى عندى four or انه اما اكبر من كهان ده نفقز D
+
+534
+00:41:00,960 --> 00:41:04,700
+انه متين جوهر ان جهر ان جهر هيكون XM of T not نقص
+
+535
+00:41:04,700 --> 00:41:09,500
+XM of T not اصغر من مين من ابسلون هذا ايش معناته؟
+
+536
+00:41:09,500 --> 00:41:16,200
+معناته ال sequence هذه X1 of T not X2 of T not X3
+
+537
+00:41:16,200 --> 00:41:20,760
+of T not X4 of T not عبارة عن كوشي sequence ومرمية
+
+538
+00:41:20,760 --> 00:41:25,060
+وين خنتها في R لأن هذا عبارة عنcontinuous function
+
+539
+00:41:25,060 --> 00:41:27,880
+قيمتها الو هي real valued function او complex مش
+
+540
+00:41:27,880 --> 00:41:31,880
+مشكلة خلّيني أقول علي الـ real بيكون x1 of t0 real
+
+541
+00:41:31,880 --> 00:41:34,880
+و هذا real و هذا real إذا صارت sequence of real
+
+542
+00:41:34,880 --> 00:41:39,360
+numbers و قوشي إذا converge نفترض إنها converge
+
+543
+00:41:39,360 --> 00:41:44,900
+خلّيني أقول نفترض إن xm of t0 إيش بتروح لل x of t0
+
+544
+00:41:44,900 --> 00:41:49,680
+و هذا الكلام أخدناه ل arbitrary t0 لكل t0 يعني
+
+545
+00:41:49,680 --> 00:41:57,710
+بمعنى آخر صارت الآن xmxm of t بتروح ل x of t و
+
+546
+00:41:57,710 --> 00:42:00,650
+الان انا اخدت ال t و ات اربط لها اذا بتروح كل
+
+547
+00:42:00,650 --> 00:42:04,350
+حدثين وقت بتروح لها ايش xm of t بتروح لقيمة x of t
+
+548
+00:42:04,350 --> 00:42:08,870
+xm of t براين بتروح ل x of t براين ده كل ال t اللي
+
+549
+00:42:08,870 --> 00:42:14,860
+موجود امامي في ال j وكأني انا هذه عملتلي دالةده لو
+
+550
+00:42:14,860 --> 00:42:20,920
+يعني على اللي هي من اللي هو A وB لعند مين لعند R
+
+551
+00:42:20,920 --> 00:42:25,120
+لأن هذا الـT صحيح على كل element هنا إذا أنا عمال
+
+552
+00:42:25,120 --> 00:42:29,980
+بعمل construction للـLimit X اللي هتكون وين موجودة
+
+553
+00:42:29,980 --> 00:42:35,460
+في الـC of A وB زي الأول مشابه للأولهذا يظهر أن
+
+554
+00:42:35,460 --> 00:42:38,140
+هناك سيكوانس كثيرة و كثيرة و كثيرة و كثيرة و كثيرة
+
+555
+00:42:38,140 --> 00:42:38,360
+و كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و
+
+556
+00:42:38,360 --> 00:42:38,840
+كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و
+
+557
+00:42:38,840 --> 00:42:39,860
+كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و
+
+558
+00:42:39,860 --> 00:42:42,060
+كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و
+
+559
+00:42:42,060 --> 00:42:46,400
+كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و
+
+560
+00:42:46,400 --> 00:42:46,900
+كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و
+
+561
+00:42:46,900 --> 00:42:47,320
+كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و
+
+562
+00:42:47,320 --> 00:42:53,220
+كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و كلو ودينا
+
+563
+00:42:53,220 --> 00:42:56,960
+على افتراض انه M أكبر من M لما M تروح لنا لنهاية
+
+564
+00:42:56,960 --> 00:43:00,680
+بيصير عندي هذا المقدار اللي هو ال maximum ال XM of
+
+565
+00:43:00,680 --> 00:43:05,760
+T لما M تروح لنا لنهاية هيروح لمن؟ ل X of T فكدا
+
+566
+00:43:05,760 --> 00:43:11,180
+نثبتنا ل X of T صار عندي XM of T بتروح لنقص X of T
+
+567
+00:43:11,180 --> 00:43:14,700
+ال maximum اللي هين أزروا سوى مين؟ Y من هذه لأن as
+
+568
+00:43:14,700 --> 00:43:19,690
+M goes to infinity XM of T بتروح لل X of Tالآن ما
+
+569
+00:43:19,690 --> 00:43:23,190
+ده ايش معناته؟ هذا هو عبارة عن المسافة بين xm ومين
+
+570
+00:43:23,190 --> 00:43:28,890
+و الـ x صارت اللي هي عندي الـ n اللي وصلناله for
+
+571
+00:43:28,890 --> 00:43:32,370
+every epsilon أكبر من سفر and any t element من كده
+
+572
+00:43:32,370 --> 00:43:37,390
+xm of t نقص x of t أصغر أو يساوي epsilon هانا من
+
+573
+00:43:37,390 --> 00:43:40,690
+هذه، مدنها أصغر وإبسلون كلها that means xm ايش ما
+
+574
+00:43:40,690 --> 00:43:45,650
+لها converges uniformly من x انتبهوا عند ال
+
+575
+00:43:45,650 --> 00:43:52,070
+maximum أصغر أو يساوي epsilonبغض النظر عن اللي هي
+
+576
+00:43:52,070 --> 00:43:57,510
+الـ T ال maximum أصغر من Y إذا أكيد اللي جوا فيهم
+
+577
+00:43:57,510 --> 00:44:01,070
+بغض النظر عن مين هي T يعني مش لكل T بلاجي Y
+
+578
+00:44:01,070 --> 00:44:07,210
+المحددة لأ عند XM of T ناقص X of T أصغر أو ساوي Y
+
+579
+00:44:07,210 --> 00:44:11,970
+من هذه لكل T في الدنيا إذا الـY للنجاة هذه لا
+
+580
+00:44:11,970 --> 00:44:16,430
+تعتمد على الـTإذا معناته ان ال convergence ل XM of
+
+581
+00:44:16,430 --> 00:44:20,370
+T هيروح ل X of T يشماله uniform convergence إذا
+
+582
+00:44:20,370 --> 00:44:23,230
+نسينا ان هو uniform convergence احنا كنا نقول for
+
+583
+00:44:23,230 --> 00:44:27,290
+every epsilon أكبر من سفر and for every T there
+
+584
+00:44:27,290 --> 00:44:31,170
+exists Delta أو there exists K حسب اللي هو اللي
+
+585
+00:44:31,170 --> 00:44:36,710
+بنها الان اللي بيكون متبد على ال T عالمياعلى الـ A
+
+586
+00:44:36,710 --> 00:44:39,990
+أعلادك بيكون continuity عادي لكن ال continuity ال
+
+587
+00:44:39,990 --> 00:44:43,110
+uniform ليه؟ بنقول for every ي أكبر من صفرها على
+
+588
+00:44:43,110 --> 00:44:47,530
+طول there exists ي such that و بتتحقق هذه لكل T
+
+589
+00:44:47,530 --> 00:44:51,170
+يعني لا تعتمد عالميا على ال T فبكون ال convergence
+
+590
+00:44:51,170 --> 00:44:54,890
+إيش اسمه؟ uniform convergence إذا صارت عندي
+
+591
+00:44:54,890 --> 00:44:57,790
+sequence of continuous functions و هذا مهم طبعا
+
+592
+00:44:57,790 --> 00:45:00,950
+أخدته في تحليل واحد تحليل اتنين أسف عندي صار
+
+593
+00:45:00,950 --> 00:45:06,090
+sequence XM of continuous functionsConverts لـ
+
+594
+00:45:06,090 --> 00:45:10,090
+Function X وهذه كلها الـ Continuous والـ
+
+595
+00:45:10,090 --> 00:45:13,590
+Convergence uniformly إذا غصب عنها ستظهر الـ X
+
+596
+00:45:13,590 --> 00:45:18,130
+أشمالها Continuous كمان مرة اللي بقوله اللي
+
+597
+00:45:18,130 --> 00:45:22,150
+استخدمت قبل شوية لو كانت عند XM Sequence of
+
+598
+00:45:22,150 --> 00:45:27,480
+Continuous Functionsوكانت converge uniformly to
+
+599
+00:45:27,480 --> 00:45:33,020
+some x function x هتطلع ال x نفسها برضه continuous
+
+600
+00:45:33,020 --> 00:45:36,760
+function لكن لو كانت ال convergence مش uniformly
+
+601
+00:45:36,760 --> 00:45:40,080
+ليس شرط انها تطلع continuous وهذا الكلام أخدناه في
+
+602
+00:45:40,080 --> 00:45:42,940
+تحليل اتنين وفيه أمثلة تبع ال bachelor's طيب يا
+
+603
+00:45:42,940 --> 00:45:48,020
+جماعةمُنَخَص الحديث اللي حكيته الآن أنا إنه من ال
+
+604
+00:45:48,020 --> 00:45:51,200
+maximum أزرع يساوي إبسلون طلعت ال absolute value
+
+605
+00:45:51,200 --> 00:45:55,400
+هذا أزرع يساوي إبسلون لكل T بغض النظر عن ال T يعني
+
+606
+00:45:55,400 --> 00:46:00,780
+بمعنى أخر XM of T بتروح لل X of T بغض النظر عن ال
+
+607
+00:46:00,780 --> 00:46:04,600
+T بنلاقي إبسلون تصلح لكل ال T اللي موجودة عندنا
+
+608
+00:46:04,600 --> 00:46:09,820
+وهذا يعني XM of T أو XM بتروح لل X uniformly و XM
+
+609
+00:46:09,820 --> 00:46:13,370
+continuous إذا الإكس إيش هتطلع continuousإذا صار
+
+610
+00:46:13,370 --> 00:46:20,010
+عندى الان ال distance هذا عنالى يعني ان ال xm
+
+611
+00:46:20,010 --> 00:46:25,030
+بتروح لل x و الكلام اللى تحت اعطانى x element اللى
+
+612
+00:46:25,030 --> 00:46:29,970
+هو c of a و b إذا صارت ال xm ال sequence converge
+
+613
+00:46:29,970 --> 00:46:35,490
+to some x in c of a و b وهذا يعني ان ال xm اللى هي
+
+614
+00:46:35,490 --> 00:46:39,230
+ال c of a و b is a complete metric space
+
+615
+00:46:42,560 --> 00:46:47,740
+الان في البرهان اللى .. اللى بضغطناه قبل بشوية فى
+
+616
+00:46:47,740 --> 00:46:51,940
+داخله فى الواقع أثبتنا ان ال convergence اللى فى
+
+617
+00:46:51,940 --> 00:46:55,700
+الـC of A بيinvolve convergence ده بعمل بقول يعنى
+
+618
+00:46:55,700 --> 00:46:59,380
+بقوللى الآنTheorem of Uniform Convergence
+
+619
+00:46:59,380 --> 00:47:03,520
+Convergence XM بتروح للـ X in the space C of A و B
+
+620
+00:47:03,520 --> 00:47:07,580
+Under the metric اللي حكينا عنه is a Uniform
+
+621
+00:47:07,580 --> 00:47:12,680
+Convergence That is XM converges uniformly on A و
+
+622
+00:47:12,680 --> 00:47:18,420
+B to mean 2X الأهمية حطناها لحالهاالان مثالات من
+
+623
+00:47:18,420 --> 00:47:21,820
+مجموعات متركز بيس هل كل المجموعات يجب أن تكون
+
+624
+00:47:21,820 --> 00:47:25,860
+مكملة؟ بالتأكيد لا، اذا قمتم بإزالة مجموعة منها
+
+625
+00:47:25,860 --> 00:47:30,320
+فإن نقطة واحدة لا تبقى مكملة لأن بلاغ سيكوينس تذهب
+
+626
+00:47:30,320 --> 00:47:34,120
+إلى النقطة التي نتحدث عنها أو هي ليست موجودة يعني
+
+627
+00:47:34,120 --> 00:47:38,890
+كوشي ليس convergenceطيب صلى الله عليه الصلاة
+
+628
+00:47:38,890 --> 00:47:43,390
+والسلام الان اول مثال عندنا المثال المشهور انه
+
+629
+00:47:43,390 --> 00:47:46,990
+examples of incomplete metric spaces اللي هو space
+
+630
+00:47:46,990 --> 00:47:51,690
+Q اللي هو Q the set of all rational numbers the
+
+631
+00:47:51,690 --> 00:47:55,530
+set of all rational numbers with the usual metric
+
+632
+00:47:56,040 --> 00:48:00,800
+الـ Metrical هو DXY بسوء إيه أبسط قيمة X-Y عندنا
+
+633
+00:48:00,800 --> 00:48:04,680
+احنا ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+634
+00:48:04,680 --> 00:48:04,840
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+635
+00:48:04,840 --> 00:48:04,840
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+636
+00:48:04,840 --> 00:48:04,960
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+637
+00:48:04,960 --> 00:48:05,380
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+638
+00:48:05,380 --> 00:48:05,380
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+639
+00:48:05,380 --> 00:48:05,620
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+640
+00:48:05,620 --> 00:48:06,000
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+641
+00:48:06,000 --> 00:48:06,360
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+642
+00:48:06,360 --> 00:48:07,520
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+643
+00:48:07,520 --> 00:48:07,940
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+644
+00:48:07,940 --> 00:48:08,160
+.. ال .. ال .. ال .. ال .. ال
+
+645
+00:48:14,460 --> 00:48:18,620
+جدر التنين مثلا جدر التنين او اي rational number
+
+646
+00:48:18,620 --> 00:48:24,280
+بقولك لكل n اليمتن ان بقدر الاقي rn اليمتن q بحيث
+
+647
+00:48:24,280 --> 00:48:28,780
+ان rn بين x و بين x زائد 2 واحدة الان لأن between
+
+648
+00:48:28,780 --> 00:48:30,480
+any two real numbers there exists a rational
+
+649
+00:48:30,480 --> 00:48:33,100
+number يعني الان مثلا خدوا جدر التنين على سبيل
+
+650
+00:48:33,100 --> 00:48:38,560
+المثال الان عندي جدر التنين اكيد بقدر الاقي r واحد
+
+651
+00:48:38,560 --> 00:48:43,540
+اصغر منه اصغر من جدر التنين زائداش واحد اكيدهؤلاء
+
+652
+00:48:43,540 --> 00:48:47,900
+ريالين number أكيد في بينها relational number لأن
+
+653
+00:48:47,900 --> 00:48:53,500
+R رتنين أكبر من جدر التنين و أصغر من جدر التنين
+
+654
+00:48:53,500 --> 00:48:54,140
+زائد نص
+
+655
+00:48:59,350 --> 00:49:05,290
+الأن جدر التنين زائد واحد على n in general أكبر من
+
+656
+00:49:05,290 --> 00:49:09,410
+جدر التنين إذا ماقدر ألاقي بينهم مين Rn يعني قدرت
+
+657
+00:49:09,410 --> 00:49:13,350
+ألاقي sequence of rational numbers لو أخدنا ال
+
+658
+00:49:13,350 --> 00:49:15,790
+limit لهذه as n goes to infinity هتظهر هذه جدر
+
+659
+00:49:15,790 --> 00:49:19,510
+التنين و هتصبح as n goes to infinity بيصير جدر
+
+660
+00:49:19,510 --> 00:49:22,730
+التنين بيصير هذه ال limit اللي موجودة وال limit لل
+
+661
+00:49:22,730 --> 00:49:27,470
+Rn إيش بيساوي جدر التنين إذا يعني بمعنى آخر إذا
+
+662
+00:49:27,470 --> 00:49:32,390
+جيت sequenceof rational numbers converts the mean
+
+663
+00:49:32,390 --> 00:49:36,510
+ل irrational number يعني بمعنى أخر لجأت sequence
+
+664
+00:49:36,510 --> 00:49:40,970
+of rational numbers which is Cauchy but not
+
+665
+00:49:40,970 --> 00:49:45,630
+converts ليش not converts يعني هي لما بتروح بتروح
+
+666
+00:49:45,630 --> 00:49:48,670
+under the norm اللي عندنا بتروح لعنصر مش موجود
+
+667
+00:49:48,670 --> 00:49:54,070
+فيها فإذا صارت عندي أشملها a queue is not complete
+
+668
+00:49:54,070 --> 00:50:00,950
+طيب يا جماعة اللي بعدهصلوا على النبي عليه الصلاة
+
+669
+00:50:00,950 --> 00:50:06,030
+والسلام الان space of all polynomials البرونوميالز
+
+670
+00:50:06,030 --> 00:50:09,830
+انتم تذكرين كيف كنا نجيب ال exponential function
+
+671
+00:50:09,830 --> 00:50:12,970
+لما
+
+672
+00:50:12,970 --> 00:50:18,840
+لها exponential سيريز فيها سيريزماشي الحال let x
+
+673
+00:50:18,840 --> 00:50:23,520
+be the set of all polynomials over the real
+
+674
+00:50:23,520 --> 00:50:28,940
+interval d of a,b and define a metric d on x by d
+
+675
+00:50:28,940 --> 00:50:32,100
+of x بساوية من ال maximum ال polynomials اللي
+
+676
+00:50:32,100 --> 00:50:35,200
+موجودة في continuous functions صح ولا لأ فانا أخدت
+
+677
+00:50:35,200 --> 00:50:38,900
+بس هالعائلة من ال continuous functions اللي يمين
+
+678
+00:50:38,900 --> 00:50:43,100
+اللي هي ال polynomials بقولك هذه العائلة هتعمل لي
+
+679
+00:50:43,100 --> 00:50:46,360
+إيش مالهالـ Incomplete metric space is not
+
+680
+00:50:46,360 --> 00:50:49,360
+complete ماهي اللي بدنا ياه بدنا تجيبونا كوشي
+
+681
+00:50:49,360 --> 00:50:56,180
+sequence من ال polynomials تروح وين إلى element مش
+
+682
+00:50:56,180 --> 00:50:59,580
+في ال polynomials under the metric DXY بيسوي
+
+683
+00:50:59,580 --> 00:51:02,940
+ماكسيمال هذا و هذا بيكون معاكم إيه اشماله exercise
+
+684
+00:51:02,940 --> 00:51:10,480
+من المطلبات نجي الآن نحكي عن space آخر ال space
+
+685
+00:51:10,480 --> 00:51:15,070
+هذا إيش أنا بدي أسويعشان أقول الرسمة بس ال space
+
+686
+00:51:15,070 --> 00:51:26,410
+أنا بدي أجي اللي هو أعمل اللي هو أجيبلكم ال space
+
+687
+00:51:26,410 --> 00:51:31,530
+of continuous functions بس بتغير ال metric بتغير
+
+688
+00:51:31,530 --> 00:51:35,630
+ال metric من metric اللي هو ال maximum إلى ال
+
+689
+00:51:35,630 --> 00:51:40,320
+integrationسأقول لكم إن في هذه الحالة بيبطل الـ
+
+690
+00:51:40,320 --> 00:51:44,940
+metric ايش معناه Complete metric space ماشي الحال
+
+691
+00:51:44,940 --> 00:51:50,880
+طيب خلّينا أنه نشوف إيش اللي هي الدالة اللي عندنا
+
+692
+00:51:50,880 --> 00:51:57,210
+الدالة اللي عندناالدوال اللي عندنا انا اسف او ال
+
+693
+00:51:57,210 --> 00:52:00,730
+sequence اللي عندنا sequence of دوال ماهي لان انا
+
+694
+00:52:00,730 --> 00:52:04,470
+بحكي عن مين عن space of continuous functions يعني
+
+695
+00:52:04,470 --> 00:52:09,090
+أنصرها دوال صلوا على النبي عليه الصلاة والسلام ال
+
+696
+00:52:09,090 --> 00:52:11,930
+space of continuous functions let X be the set of
+
+697
+00:52:11,930 --> 00:52:15,170
+all continuous functions real valid functions على
+
+698
+00:52:15,170 --> 00:52:18,950
+مين على الفترة 0 و1 and define a metric D on X by
+
+699
+00:52:20,230 --> 00:52:22,610
+عرفه الـ metric كتر يعني بديش ال maximum ال
+
+700
+00:52:22,610 --> 00:52:25,050
+maximum يعمل ليه complete؟ بدي أعرف دي x و y
+
+701
+00:52:25,050 --> 00:52:26,870
+بسهولة integration من صفر إلى واحد سنين value of x
+
+702
+00:52:26,870 --> 00:52:30,330
+of t minus y of t dt then x و d is not complete
+
+703
+00:52:30,330 --> 00:52:33,790
+metric space طبعا هذا ال D بيعمل metric لأن هذا ال
+
+704
+00:52:33,790 --> 00:52:38,610
+metric مش complete طيب بنشوف كيف let x m بيه أقاشي
+
+705
+00:52:38,610 --> 00:52:43,220
+بيه a sequence of continuous functions of 0 و 1هذه
+
+706
+00:52:43,220 --> 00:52:48,680
+الـ XM بدي أقولكم إن هذه الـ sequence اللي هو كوشي
+
+707
+00:52:48,680 --> 00:52:53,340
+sequence لكن مستحيل .. مستحيل تكون إيه شمالها؟
+
+708
+00:52:53,340 --> 00:52:57,560
+تكون convergence، ماشي؟ هتكون convergence لـ
+
+709
+00:52:57,560 --> 00:53:01,680
+sequence مش continuous في الواقع .. في الواقع
+
+710
+00:53:01,680 --> 00:53:05,780
+السبب هتلاقوه إن ال convergence في هذه الحالة مش
+
+711
+00:53:05,780 --> 00:53:11,970
+uniform convergenceمش uniform فهيودي لدالة مش شرط
+
+712
+00:53:11,970 --> 00:53:14,810
+انها تكون continuous تكون خلاص نعم ماشي
+
+713
+00:53:18,480 --> 00:53:22,160
+عرفونا اللي هي xM of T بتساوي 0 إذا كانت T في
+
+714
+00:53:22,160 --> 00:53:26,320
+الفترة 0.5 و بتساوي M في T نقص نص إذا كانت T
+
+715
+00:53:26,320 --> 00:53:29,760
+element نص و نص زائد واحدة لM بس بدون ال M من
+
+716
+00:53:29,760 --> 00:53:36,360
+اتنين و طالع عشان يكون التعريف مكتمل و بساوي 1 إذا
+
+717
+00:53:36,360 --> 00:53:39,480
+كانت T في الفترة المتبقية و كإن إيجيت أنا فترة ال
+
+718
+00:53:39,480 --> 00:53:43,200
+domain اللي هي 01 فهي فترة ال domain 01 هي 01
+
+719
+00:53:43,200 --> 00:53:47,770
+لعندي 1 دزأتها إلى 3 أجزاءالجزء الأول من سفر لعند
+
+720
+00:53:47,770 --> 00:53:53,530
+نص و قلتله أثبت والتاني اللي هو عبارة عن مين عن
+
+721
+00:53:53,530 --> 00:54:01,250
+اللي هو نص زائد واحد علمفي الفترة هذه فأعرفت دلّا
+
+722
+00:54:01,250 --> 00:54:05,830
+صفر ماشي الحال في الفترة التانية عبارة عن MFT ماكس
+
+723
+00:54:05,830 --> 00:54:10,370
+نصف في الآخر اللي هو عبارة عن خط دلّا خطية خط خط
+
+724
+00:54:10,370 --> 00:54:14,490
+فالخط بيجي خط بالشكل هذا ومن عند واقع ان هذه
+
+725
+00:54:14,490 --> 00:54:19,490
+المنطقة نص واحدة انت بيصير ايش بيساوي واحد ايه اه
+
+726
+00:54:19,490 --> 00:54:23,730
+فهذه الرسمة in general ماشي الحال هذه رسمتها in
+
+727
+00:54:23,730 --> 00:54:30,080
+general الآنأنا بدي أثبتلكم أن هذه كوجي sequence
+
+728
+00:54:30,080 --> 00:54:33,920
+انتبهوا كيف واضح الرسمة واضح اللي بحكيه طيب سلّع
+
+729
+00:54:33,920 --> 00:54:36,800
+النبع عليه الصلاة والسلام لأن لكل إبسلون أكبر من 0
+
+730
+00:54:37,920 --> 00:54:42,640
+بقدر ألاقي natural number كأكبر سوية واحدة أكتر من
+
+731
+00:54:42,640 --> 00:54:44,700
+أكتر من أكتر من أكتر من أكتر من أكتر من أكتر من
+
+732
+00:54:44,700 --> 00:54:44,720
+أكتر من أكتر من أكتر من أكتر من أكتر من أكتر من
+
+733
+00:54:44,720 --> 00:54:48,680
+أكتر من أكتر من أكتر من أكتر من أكتر من أكتر من
+
+734
+00:54:48,680 --> 00:54:56,920
+أكتر من أكتر من أكتر من أكتر من أكتر من أكتر من
+
+735
+00:54:56,920 --> 00:54:57,720
+أكتر من أكتر من أكتر من أكتر من أكتر من أكتر من
+
+736
+00:54:57,720 --> 00:54:57,720
+أكتر من أكتر من أكتر من أكتر من أكتر من أكتر من
+
+737
+00:54:57,720 --> 00:55:00,060
+أكتر من أكتر من أكتر من أكتر من أ
+
+738
+00:55:05,150 --> 00:55:09,190
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر من M
+
+739
+00:55:09,190 --> 00:55:09,430
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر من M
+
+740
+00:55:09,430 --> 00:55:11,830
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر من M
+
+741
+00:55:11,830 --> 00:55:12,930
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر من M
+
+742
+00:55:12,930 --> 00:55:12,930
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر من M
+
+743
+00:55:12,930 --> 00:55:12,930
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر من M
+
+744
+00:55:12,930 --> 00:55:12,930
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر من M
+
+745
+00:55:12,930 --> 00:55:13,050
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر من M
+
+746
+00:55:13,050 --> 00:55:18,340
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر منلو
+
+747
+00:55:18,340 --> 00:55:23,660
+أخدنا الـ 1 على N أصغر من 1 على M فبصير عنده اللي
+
+748
+00:55:23,660 --> 00:55:28,620
+هو عنده اللي هي هذا نص زائد 1 على N بعده بصير نص
+
+749
+00:55:28,620 --> 00:55:33,720
+زائد 1 على M لأن 1 على M أكبر منه صح ولا لأ فبصير
+
+750
+00:55:33,720 --> 00:55:39,340
+دالته هذا الدالة تبعته بتمشي زي هيك وبعدين بتطلع
+
+751
+00:55:39,340 --> 00:55:41,880
+زي هيك عند الـ 1 على M بتجف
+
+752
+00:55:50,110 --> 00:55:55,190
+من وش تعرف الدالة؟ لحظة هذه الأولى لتبعت الواحد
+
+753
+00:55:55,190 --> 00:56:01,250
+على ان اللى هو بتساوي اللى هو سفر لهنا وبعدين
+
+754
+00:56:01,250 --> 00:56:05,650
+بعدها بتظلها بتساوي الخط هذا للفترة من عند نصنا
+
+755
+00:56:05,650 --> 00:56:09,670
+عند نص زائد واحد على ان اه فيها هنا الان اللى
+
+756
+00:56:09,670 --> 00:56:13,490
+بعدها طبعا بتكمن بالواحد اللى بعدها بتسيل من نصنا
+
+757
+00:56:13,490 --> 00:56:18,270
+من نص واحد على ان هناماشي الحال واضح اللي بحكيه؟
+
+758
+00:56:18,270 --> 00:56:25,330
+فالان عشان بدي أحسبلكم XM of T ناقص XN of T الفرق
+
+759
+00:56:25,330 --> 00:56:30,210
+بين مين؟ بين التنين هلجيكم تشوفوا إيش اللي بحكيه
+
+760
+00:56:30,210 --> 00:56:32,090
+طيب شوفوا صلى الله عليه وصلى الله عليه الصلاة
+
+761
+00:56:32,090 --> 00:56:32,350
+والسلام
+
+762
+00:56:42,770 --> 00:56:51,070
+النسافة بين Xm و Xn هي ايش بتساوي ال
+
+763
+00:56:51,070 --> 00:56:57,720
+integrationالانتجريشن من 0 ل 1 هذا كله ايش معله DT
+
+764
+00:56:57,720 --> 00:57:02,800
+صح ولا لأ الفرق بين الدلتين الفرق بين الدلتين يعني
+
+765
+00:57:02,800 --> 00:57:07,380
+المساحة المساحة الفرق بين المساحتين مساحة الدلة
+
+766
+00:57:07,380 --> 00:57:12,360
+الأولى هذه 0 شوفوا منها مساحة الدلة هذه و المساحة
+
+767
+00:57:12,360 --> 00:57:15,580
+اللي هي هذه المنطقة اللي تحت هذه الدلة الأولى
+
+768
+00:57:16,320 --> 00:57:20,160
+الدالة التانية من هان و من هان لما تطرح المساحتين
+
+769
+00:57:20,160 --> 00:57:24,820
+من بعض مين اللي بقى الباس المثلج هذاماشي الحال
+
+770
+00:57:24,820 --> 00:57:30,420
+المثلث هذا قدش طوله من هان لهان هذه عبارة عن واحد
+
+771
+00:57:30,420 --> 00:57:35,540
+نص زاد واحدة لان و نص واحدة لان بيطلع واحدة لان
+
+772
+00:57:35,540 --> 00:57:39,860
+ناقص واحدة لان ال fact بين هذي المنطقة واحدة لان
+
+773
+00:57:39,860 --> 00:57:44,540
+ناقص واحدة لان هذه القاعدة وضربه في الارتفاع ايش
+
+774
+00:57:44,540 --> 00:57:48,240
+بيساوي واحد فبيصير هذا ال integration بساوي نص
+
+775
+00:57:48,240 --> 00:57:53,240
+القاعدة فواحدة لان ناقص واحدة لان هذا قيمة ال
+
+776
+00:57:53,240 --> 00:57:57,230
+rhetoricاللي هو الـ integration إذا بيصير عندى ال
+
+777
+00:57:57,230 --> 00:58:03,370
+distance بين X و M و XM عبارة عن نص في واحدة ل M
+
+778
+00:58:03,370 --> 00:58:07,870
+واقص مين؟ واحدة ل M هذا حسب ال triangle inequality
+
+779
+00:58:07,870 --> 00:58:15,290
+أصغر منه أو ساوى نص في واحدة ل M زائد واحدة ل مين؟
+
+780
+00:58:15,290 --> 00:58:19,230
+على M أكيد أكيد صح ولا لأ؟ طب الواحدة ل M أصغر من
+
+781
+00:58:19,230 --> 00:58:22,210
+واحدة ل K و الواحدة ل M أصغر من واحدة ل K و
+
+782
+00:58:22,210 --> 00:58:29,340
+الواحدة ل K أصغر من Epsilonفهذه أصغر من Y وهذه
+
+783
+00:58:29,340 --> 00:58:34,600
+أصغر من Y إذا أصبح Y وY 2.5 يصبح Y واحدة فبصير هذا
+
+784
+00:58:34,600 --> 00:58:38,420
+شقبه هذا وكتبه هذا يصبح ال distance بين Xm وXn
+
+785
+00:58:38,420 --> 00:58:48,210
+أصغر من Y يعني بمعنى آخر أثبتنا الآنإن المسافة بين
+
+786
+00:58:48,210 --> 00:58:52,630
+X و M و XM أصغر من أي إيزون إذا صارت عندي XM كوشي
+
+787
+00:58:52,630 --> 00:58:57,970
+سيكوانس إذا صارت كل اللي حكيته هنا الان hence XM
+
+788
+00:58:57,970 --> 00:59:03,050
+is a Cauchy sequence عندي الآن بقولكم أي X في
+
+789
+00:59:03,050 --> 00:59:09,570
+الدنيا أي X في الدنيا في ال X مش هتكونفي ال X مش
+
+790
+00:59:09,570 --> 00:59:13,410
+فيش إمكانية إنها تكون عبارة عن continuous function
+
+791
+00:59:13,410 --> 00:59:21,490
+يعني مش هتكون موجودة في ال space اللي عندي لو
+
+792
+00:59:21,490 --> 00:59:26,670
+قدينا قولنا يا جماعة نعمل حسبة عشان نثبت إن هذا ال
+
+793
+00:59:26,670 --> 00:59:30,370
+X اللي في ال X مش مستحيل تكون اللي هي أية شمالها
+
+794
+00:59:30,370 --> 00:59:33,590
+limit ل .. ل .. ل .. ل .. ل .. ل اللي عندنا طيب
+
+795
+00:59:35,210 --> 00:59:41,730
+خُدوا أي X موجودة في الـ X تبعنا وعسبها الحسبة
+
+796
+00:59:41,730 --> 00:59:46,610
+المسافة بين X أم و X بتساوى ال integration من سفر
+
+797
+00:59:46,610 --> 00:59:49,630
+لعند واحد هذه X وين في spaceنا في spaceنا اللي
+
+798
+00:59:49,630 --> 00:59:54,410
+بتقولكم أنه مستحيل أن X أم تروحلها لو بدها تروحلها
+
+799
+00:59:54,410 --> 00:59:57,210
+نقول أنه جبناها تروحلها نقول فيه لأ بضالة العقوبة
+
+800
+00:59:57,480 --> 01:00:00,780
+شوفوا الان المسافة بين Xم و X ايش بتساوي حسب
+
+801
+01:00:00,780 --> 01:00:03,660
+التعريف ال integration من صفر لواحد Xm of T نقص X
+
+802
+01:00:03,660 --> 01:00:09,320
+of T بT ماشي Xm of T معروفة صفر في الأول في الفترة
+
+803
+01:00:09,320 --> 01:00:14,870
+من صفر نمين لنص بربال هذه جاعدة لحالها ماشيزائد ال
+
+804
+01:00:14,870 --> 01:00:18,510
+integration من نص لنص زائد واحد علامة XM of T ناقص
+
+805
+01:00:18,510 --> 01:00:24,370
+مين؟ X of T ماشي الحال XM of T إلها قيمتها اللي هي
+
+806
+01:00:24,370 --> 01:00:30,030
+القيمة هذه الميلة وفي المنطقة الأخيرة من نص زائد
+
+807
+01:00:30,030 --> 01:00:32,830
+واحد علامة عند الواحد بتكون قريتها إيش بتساوي؟
+
+808
+01:00:32,830 --> 01:00:39,590
+واحد ناقص X of T ديتي طيبالان since the integrals
+
+809
+01:00:39,590 --> 01:00:42,990
+on the right are non-negative كل من هدول أشمالهم
+
+810
+01:00:42,990 --> 01:00:48,810
+non-negative مظبوط ولا لأ؟ إذا لما نلها هدولة non
+
+811
+01:00:48,810 --> 01:00:51,830
+-negative مظبوط هدولة non-negative هدولة نفسهم non
+
+812
+01:00:51,830 --> 01:00:54,350
+-negative اللي جوا فبتطلع ليه قيمة ال integration
+
+813
+01:00:54,350 --> 01:00:59,070
+أشماله عبارة عن أكبر أو ساهم سفرإذا لو أنا بدأ
+
+814
+01:00:59,070 --> 01:01:06,230
+أقول أن Xm مستحيل تذهب إلى X في الـ space اللي
+
+815
+01:01:06,230 --> 01:01:11,270
+عندي، لو بدأ أقول، أفترض أن Xm تذهب إلى X، يعني
+
+816
+01:01:11,270 --> 01:01:14,430
+المسافة بين هذه وهذه تذهب إلى سفر As M goes to
+
+817
+01:01:14,430 --> 01:01:19,680
+infinity،ماشي، إذاً بدنا نقول suppose that إن
+
+818
+01:01:19,680 --> 01:01:23,640
+distance بين X أما و X تروح لمين للصفر as M goes
+
+819
+01:01:23,640 --> 01:01:28,220
+to infinity لما أم تروح إلى مالة نهاية طبعاً هذا
+
+820
+01:01:28,220 --> 01:01:30,500
+بيصير ال integration كله أم تروح لمن بيصير من نص
+
+821
+01:01:30,500 --> 01:01:33,760
+لنص بيطلع صفر إذاً هذا هيروح للصفر وهذا يروح لمين
+
+822
+01:01:33,760 --> 01:01:37,960
+للصفرهذا ما هو مش مانتومد على M فبصير ال
+
+823
+01:01:37,960 --> 01:01:41,940
+integration X of T من صفر لنص عشان ساقية صفر وهذا
+
+824
+01:01:41,940 --> 01:01:45,320
+بيصير ال integration اللي بيساوي بروح لصفر as M
+
+825
+01:01:45,320 --> 01:01:49,480
+goes to مين To infinity مظبوط وهذا راح يرميه لما
+
+826
+01:01:49,480 --> 01:01:53,640
+الصفر روح مافيش حيطلع علنا اشي واضح اللي بحكيه طيب
+
+827
+01:01:53,640 --> 01:01:59,370
+اطلع لفوق بيصير عندي ال integrationلـ Integration
+
+828
+01:01:59,370 --> 01:02:06,610
+من 0 لعند نص XM of T DT هي سفر والتاني as M goes
+
+829
+01:02:06,610 --> 01:02:10,370
+to infinity هذي بتروح لنص، مظبوط؟ as M goes to
+
+830
+01:02:10,370 --> 01:02:12,990
+infinity بيصير لو حاجة لها سفر، بيصير من نص لعند
+
+831
+01:02:12,990 --> 01:02:17,610
+واحد أش بساوي سفر، بيصير هذا بساوي سفر وهذا بساوي
+
+832
+01:02:17,610 --> 01:02:21,490
+سفرطيب ما احنا بنقول X of T continuous لان هو
+
+833
+01:02:21,490 --> 01:02:23,810
+موجودة في ال space سبعنا ال space of continuous
+
+834
+01:02:23,810 --> 01:02:29,630
+functions اذا هيطلع عندي الآن مدام هذا المقدار سفر
+
+835
+01:02:29,630 --> 01:02:34,530
+وهذه الدالة متصلة اذا غصب عنها هيطلع ال X of T ال
+
+836
+01:02:34,530 --> 01:02:39,170
+integration على دالة متصلة بساوي سفر معناته الدالة
+
+837
+01:02:39,170 --> 01:02:42,550
+ان هو جوا هي في السفرمن أين جاء الله ذاك؟ و هو
+
+838
+01:02:42,550 --> 01:02:45,370
+أكبر و ساوء صفر ما انخلطتش تقولوا الله صار من تحت
+
+839
+01:02:45,370 --> 01:02:48,970
+و من فوق لأ هي فوق و أكبر و ساوء صفر و طلعت عند ال
+
+840
+01:02:48,970 --> 01:02:51,330
+integration انها بساوء صفر فانا هي قد الصفر و مش
+
+841
+01:02:51,330 --> 01:02:55,210
+غيرها فبصير x of t أشفت ساوء صفر و اللي جوا برضه
+
+842
+01:02:55,210 --> 01:02:59,300
+أيش هيساوي؟ برضه هيساوي صفرلأن نفس الاشي هذا أكبر
+
+843
+01:02:59,300 --> 01:03:03,700
+شو سفر و على فترة و المساحة على فترة و هي على أكبر
+
+844
+01:03:03,700 --> 01:03:07,380
+شو سفر فمستحيل اللي يكون اللي جواي شماله عبارة عن
+
+845
+01:03:07,380 --> 01:03:10,520
+سفر لأنه دالنا متصلة و أكبر شو سفر إذا صار عندي
+
+846
+01:03:10,520 --> 01:03:14,500
+هذا سفر معناه تصار x of t بتسوى واحد صارت عندي x
+
+847
+01:03:14,500 --> 01:03:18,360
+of t بتسوى سفر على فترة من سفر لمين لنص و x of t
+
+848
+01:03:18,360 --> 01:03:21,820
+بتسوى واحد على فترة من نص لعند مين لعند واحد صار
+
+849
+01:03:21,820 --> 01:03:26,730
+في عندي jumpهذه الدالة مش متصلة، بتبقى ماشية سفير
+
+850
+01:03:26,730 --> 01:03:29,810
+وبعدين بتنط لعند مين؟ لعند الواحد، لعند المش بتنط،
+
+851
+01:03:29,810 --> 01:03:35,190
+فبتكون هذه is not continuous، إذا لو فرضنا إن
+
+852
+01:03:35,190 --> 01:03:39,610
+المسافة بين Xm و X بتروح للسفر، يعني لو فرضنا Xm
+
+853
+01:03:39,610 --> 01:03:42,490
+بتروح لل X، ال X مش هتكون continuous function،
+
+854
+01:03:42,490 --> 01:03:48,070
+هتكون براة ال X، وبناء عليه no limit in X
+
+855
+01:03:53,790 --> 01:04:02,290
+وهذا يثبت أن الـ space is not complete وبرك الله
+
+856
+01:04:02,290 --> 01:04:03,790
+فيكم الله يعطيكم العافية
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/EaC1QqfjIDE_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/EaC1QqfjIDE_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..236c7897f7cd58b219da27c3aa117ceddf5c1870
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/EaC1QqfjIDE_postprocess.srt
@@ -0,0 +1,2700 @@
+1
+00:00:05,210 --> 00:00:07,970
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,970 --> 00:00:10,890
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,890 --> 00:00:15,610
+آله وصحبه أجمعين هذه هي المحاضرة رقم 11 مساق تحليل
+
+4
+00:00:15,610 --> 00:00:18,710
+اقتراني او تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:18,710 --> 00:00:23,810
+الإسلامية قسم رياضيات ماجستيريا اليوم ان شاء الله
+
+6
+00:00:23,810 --> 00:00:30,370
+هنكمل اللي هو في المادة هناخد section اتنين وخمسة
+
+7
+00:00:30,370 --> 00:00:33,690
+اللي هو compactness and finite dimension هنحكي عن
+
+8
+00:00:34,570 --> 00:00:39,210
+شو مفهوم الـ compact set و .. و خلّيني أقوله علاقة
+
+9
+00:00:39,210 --> 00:00:42,410
+الـ Finiteness في حالة اللي هو ال .. ال compact في
+
+10
+00:00:42,410 --> 00:00:48,390
+حالة ال Finiteness ك dimension منيح إنه أنا أحكي
+
+11
+00:00:48,390 --> 00:00:54,130
+عن الأمور الكلية في موضوع ال compactness احنا
+
+12
+00:00:54,130 --> 00:00:57,910
+جسمنا الدنيا تبعتنا اللي هو قلنا في عندي
+
+13
+00:00:57,910 --> 00:01:02,000
+topological spaceاللي هو autobiographical space in
+
+14
+00:01:02,000 --> 00:01:05,980
+general في داخله اللي هو autobiographical spaces
+
+15
+00:01:05,980 --> 00:01:10,740
+في داخله اللي هو metric spaces في داخله اللي هو
+
+16
+00:01:10,740 --> 00:01:15,980
+normed spaces في داخله اللي هو Hilbert spacesفيه
+
+17
+00:01:15,980 --> 00:01:19,500
+في داخله الـ spaces تبعاتنا الحلوات هذي R وRR ومش
+
+18
+00:01:19,500 --> 00:01:25,660
+عارف ايش الاخره وC الاخره الآن احنا بندرس ال
+
+19
+00:01:25,660 --> 00:01:28,380
+compactness حتى كنا ندرسها في ال real analysis
+
+20
+00:01:28,380 --> 00:01:33,230
+وممكن ادرسه في ال calculus كمانأو ممكن اللي هو
+
+21
+00:01:33,230 --> 00:01:38,470
+أدرسه اللي هو في normed spaces أو metric spaces و
+
+22
+00:01:38,470 --> 00:01:41,690
+بندرسه في ال topological spaces في ال topological
+
+23
+00:01:41,690 --> 00:01:46,610
+spaces إيش بنعرفه؟ بنقول أن ال .. ال .. ال .. ال
+
+24
+00:01:46,610 --> 00:01:46,930
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+25
+00:01:46,930 --> 00:01:47,050
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+26
+00:01:47,050 --> 00:01:47,130
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+27
+00:01:47,130 --> 00:01:47,270
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+28
+00:01:47,270 --> 00:01:47,510
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+29
+00:01:47,510 --> 00:01:49,070
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+30
+00:01:49,070 --> 00:01:49,110
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+31
+00:01:49,110 --> 00:01:52,710
+ال .. ال .. ال .. ال .. ال .. ال ..
+
+32
+00:01:52,710 --> 00:01:54,670
+ال .. ال
+
+33
+00:01:58,490 --> 00:02:06,110
+لما نحكي في الـ Metric Spaces، سنبدأ بشيء آخر، وهو
+
+34
+00:02:06,110 --> 00:02:10,650
+أن كل .. لأنه صار فيه Sets .. صار فيه Sequences ..
+
+35
+00:02:10,650 --> 00:02:13,290
+كل Sequence .. هذا في الـ Metric Spaces .. كل
+
+36
+00:02:13,290 --> 00:02:16,410
+Sequence لديها Sub-Sequence Convergent .. الـ Set
+
+37
+00:02:16,410 --> 00:02:23,970
+اللي يتحقق هذه، نسميها كمباكد Setفي الـ R وفي الـ
+
+38
+00:02:23,970 --> 00:02:27,370
+RN أو حتى في الـ Finite Dimensional Vector Spaces
+
+39
+00:02:27,370 --> 00:02:31,390
+أو الـ Enormed Spaces بنعرف الـ compact على أساس
+
+40
+00:02:31,390 --> 00:02:33,810
+أنه ال city اللي بتكون closed و bounded على طول
+
+41
+00:02:33,810 --> 00:02:39,790
+أشمالها compact طب هو بنفع أه بنفع هنا ليش؟ لأنه
+
+42
+00:02:39,790 --> 00:02:44,640
+أنافي الـ topological spaces in general every open
+
+43
+00:02:44,640 --> 00:02:48,420
+cover has a finite sub cover لا يكافئ أنه .. اللي
+
+44
+00:02:48,420 --> 00:02:51,560
+هو أنه every sequence has a convergent subsequence
+
+45
+00:02:51,560 --> 00:02:54,840
+عشان هيك بنعرف في ال topological spaces ب every
+
+46
+00:02:54,840 --> 00:02:57,740
+open cover has a finite cover اللي هو تعريف ال
+
+47
+00:02:57,740 --> 00:03:02,520
+compactness الأصليإذا كنت تكتب تعطيهم الكلام اللي
+
+48
+00:03:02,520 --> 00:03:05,920
+حكيته اللي هو every اللي هو set has a convergent
+
+49
+00:03:05,920 --> 00:03:09,860
+.. every sequence has a convergent subsequence لكن
+
+50
+00:03:09,860 --> 00:03:12,740
+العكس مش صحيح هذا في topological spaces in general
+
+51
+00:03:12,740 --> 00:03:17,260
+لأن لما نيجي ندخل في ال metric space لأ بصير صحيح
+
+52
+00:03:17,260 --> 00:03:20,640
+في ال metric space هنلاقي أن every open cover has
+
+53
+00:03:20,640 --> 00:03:25,770
+a finite sub cover يكافئإنه نقول إن every sequence
+
+54
+00:03:25,770 --> 00:03:30,590
+has a convergent subsequence وبناء عليه بنتجرأ للي
+
+55
+00:03:30,590 --> 00:03:33,450
+بديش أعرفله أنا بدي أسهل عليه بديش أنا بديش أتكلم
+
+56
+00:03:33,450 --> 00:03:36,970
+في أمور الطب الجنرال بعد دي أعرفله في ال metric
+
+57
+00:03:36,970 --> 00:03:42,050
+space إن ال comeback يعني every open .. every اللي
+
+58
+00:03:42,050 --> 00:03:46,330
+هي sequence has a convergent subsequenceطب الآن
+
+59
+00:03:46,330 --> 00:03:50,410
+هذا الكلام طب لو أجينا دخلنا طبعا في ال normed
+
+60
+00:03:50,410 --> 00:03:52,590
+spaces و في ال metric spaces التانية اللي بنشتغل
+
+61
+00:03:52,590 --> 00:03:55,630
+فيها بنفس الأسلوب في موضوع ال compactics لكن لما
+
+62
+00:03:55,630 --> 00:04:00,070
+أدخل لل R و Rn و لما أدرسهم في التحليل أو في ال
+
+63
+00:04:00,070 --> 00:04:02,750
+complex على طول بقوله أنا مغمض بس اللي هو ال
+
+64
+00:04:02,750 --> 00:04:06,030
+compacts تتعني إنها closed و bounded ماجبلوش
+
+65
+00:04:06,030 --> 00:04:08,130
+series of sequences ماجبلوش series of sequences
+
+66
+00:04:08,130 --> 00:04:12,230
+ليش لأنه أنا عارف أنه في داخل ال finite
+
+67
+00:04:12,230 --> 00:04:16,420
+dimensional spacesهنلاقي الـ Closed و الـ Bounded
+
+68
+00:04:16,420 --> 00:04:20,180
+تكافئ الـ Compactness يعني تكافئ أن كل سيكوينس هذا
+
+69
+00:04:20,180 --> 00:04:25,480
+Convergent إيش سبسيكوينس يعني في داخل الـR و الـR
+
+70
+00:04:25,480 --> 00:04:28,580
+تربيع و كل الـFinite Dimensional Spaces ما يلي
+
+71
+00:04:28,580 --> 00:04:32,320
+متكافئEvery open cover has a finite sub cover «كل
+
+72
+00:04:32,320 --> 00:04:35,500
+مفتاح مفتاح» «كل مفتاح مفتاح» «كل سيقونس مفتاح
+
+73
+00:04:35,500 --> 00:04:36,720
+مفتاح مفتاح» «كل سيقونس مفتاح مفتاح مفتاح مفتاح»
+
+74
+00:04:36,720 --> 00:04:49,220
+«كل سيقونس
+
+75
+00:04:49,220 --> 00:04:50,780
+مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح
+
+76
+00:04:50,780 --> 00:04:52,160
+مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح
+
+77
+00:04:52,160 --> 00:04:59,320
+مفتاح مفتاح مفتاح م
+
+78
+00:05:01,430 --> 00:05:03,830
+العنوان الـ compactness and finite dimension
+
+79
+00:05:11,270 --> 00:05:13,750
+مافي تعليقات كتير عن الـ compactness بس مش وقته
+
+80
+00:05:13,750 --> 00:05:16,670
+يعني لو في topology احنا بنصح لكن هالجت احنا خلينا
+
+81
+00:05:16,670 --> 00:05:20,990
+حالنا في ال functional definition a metric space X
+
+82
+00:05:20,990 --> 00:05:24,390
+is said to be compact ده بيعرف وين في ال metric
+
+83
+00:05:24,390 --> 00:05:28,010
+space compact if every sequence in X has a
+
+84
+00:05:28,010 --> 00:05:31,810
+convergent subsequence ماشي هذا بيعني فيه compactة
+
+85
+00:05:31,810 --> 00:05:35,910
+الآنلأن a subset M of X is said to be compact if
+
+86
+00:05:35,910 --> 00:05:41,710
+اتعاملنا مع الـ M as a compact subspace من الـ X
+
+87
+00:05:41,710 --> 00:05:45,670
+يعني بمعنى أخر بنتعامل بالـ Metric اللي هو الـ
+
+88
+00:05:45,670 --> 00:05:48,490
+Metric الأصل اللي هنا اللي هو بمعنى is said to be
+
+89
+00:05:48,490 --> 00:05:52,690
+compact if M نفسها is a compact considered as a
+
+90
+00:05:52,690 --> 00:05:55,890
+subspace of X يعني بمعنى أخر that is every
+
+91
+00:05:55,890 --> 00:05:58,710
+sequence in M has a convergent subsequence whose
+
+92
+00:05:58,710 --> 00:06:02,910
+limit belongs to Mفي ضوء الـ Metric المعرف الأصلي
+
+93
+00:06:02,910 --> 00:06:07,690
+في مين؟ في الـ X. طيب، اننا نيجي لأول لمّة، اطلع
+
+94
+00:06:07,690 --> 00:06:12,690
+لللمّة اللي فوق، اللمّة بتقول لي لمّة 2 5 2، a
+
+95
+00:06:12,690 --> 00:06:16,570
+compact subset M of a metric space is closed و
+
+96
+00:06:16,570 --> 00:06:20,430
+bounded، على طول خاصية سهلة دي، إذا كانت compact،
+
+97
+00:06:20,430 --> 00:06:23,950
+على طول بتكون أشمالها closed و bounded، ده نشوف
+
+98
+00:06:23,950 --> 00:06:30,330
+الآن، let X be أي element in M closure،بدي الأن
+
+99
+00:06:30,330 --> 00:06:35,230
+أثبت لك أنه M Closed يعني أخد X في الـ M Closure
+
+100
+00:06:35,230 --> 00:06:37,830
+لأثبت لك أن X دي لازم تكون في مين في الـ M نفسها
+
+101
+00:06:37,830 --> 00:06:41,790
+ماشي الحال طيب مدام X في الـ M Closure then there
+
+102
+00:06:41,790 --> 00:06:45,510
+is a sequence Xn of elements in M such that Xn
+
+103
+00:06:45,510 --> 00:06:49,940
+بتروح لمين لل X هذا مصارت محفوظة يعني مفهوم هذاإذن
+
+104
+00:06:49,940 --> 00:06:55,040
+however M is compact ما زم F is compact إذن every
+
+105
+00:06:55,040 --> 00:06:59,240
+sequence has a convergent subsequence إذن then X
+
+106
+00:06:59,240 --> 00:07:02,660
+element in M لأنه فيه لها subsequence سموها X and
+
+107
+00:07:02,660 --> 00:07:05,260
+K بتروح لل X طب ما هي ال subsequence والsequence
+
+108
+00:07:05,260 --> 00:07:09,600
+الأصلية بروح لنفس ال X معايا؟ إذن غصب عنها هتطلع
+
+109
+00:07:09,600 --> 00:07:13,720
+ال X موجودة في ال M معناته then اللي هي M is
+
+110
+00:07:13,720 --> 00:07:18,670
+enclosed طيببدنا نثبت الأن إيه شمالها is bounded
+
+111
+00:07:18,670 --> 00:07:22,670
+بدنا نفترض العكس suppose that M is not bounded
+
+112
+00:07:22,670 --> 00:07:25,930
+مدام bounded طب إحنا إذا بتتذكر شو معناه bounded
+
+113
+00:07:25,930 --> 00:07:31,450
+أنه ال diameter ال diameter ال diameter ل ماعرفش
+
+114
+00:07:31,450 --> 00:07:35,550
+كيف أقولنا عنه ال diameter ل اللي هو ال M بساوي ال
+
+115
+00:07:35,550 --> 00:07:42,230
+supremumلـDXY لكل الـX وY الموجودة في الـM هذا
+
+116
+00:07:42,230 --> 00:07:44,710
+الـDiameter من الـM بنقول عنها bounded وكان
+
+117
+00:07:44,710 --> 00:07:48,410
+الـDiameter نفسه ماهو؟ is finite يعني الـSupermom
+
+118
+00:07:48,410 --> 00:07:53,530
+ماهو؟ is finite يعني الآن لو أي sequence هنا في
+
+119
+00:07:53,530 --> 00:07:56,790
+الـMلازم المسافة بين الـ sequence هذه وبين أي
+
+120
+00:07:56,790 --> 00:07:59,910
+element هنا يكون إيش مالوفاينات، ماينفعش اللي هو
+
+121
+00:07:59,910 --> 00:08:05,850
+يكبر، يروح لما لا نهاية، لأن لو بدأ أفترض، لو بدأ
+
+122
+00:08:05,850 --> 00:08:10,110
+أفترض الآن أن M is not bounded، suppose that M is
+
+123
+00:08:10,110 --> 00:08:12,750
+not bounded، معناته ال supermom هذا بيروح لمين؟
+
+124
+00:08:12,750 --> 00:08:17,680
+لما لا نهاية،معناته أكيد أكيد أكيد أكيد لازم ألاقي
+
+125
+00:08:17,680 --> 00:08:22,360
+unbounded sequence YN بحيث أن المسافة بين YN و B
+
+126
+00:08:22,360 --> 00:08:26,260
+تكون إيه شمالها أكبر من N لأنه لو مالجيتش معناته
+
+127
+00:08:26,260 --> 00:08:29,000
+أنه حيصير إيش كل المسافات الصغيرة معناته سارة اللي
+
+128
+00:08:29,000 --> 00:08:31,160
+هو إيه إيه إيش ال superman موجود معناته superman
+
+129
+00:08:31,160 --> 00:08:36,040
+finite وانا بقول نفترضإنه Unbounded يعني السبري ما
+
+130
+00:08:36,040 --> 00:08:39,720
+معمله بيروح إلى ما لا نهاية معايا إذا لازم نلاقي
+
+131
+00:08:39,720 --> 00:08:44,000
+subsequence أو unbounded sequence yn بحيث المسافة
+
+132
+00:08:44,000 --> 00:08:49,160
+بين yn و b أكبر من اللي هو الان where b is any
+
+133
+00:08:49,160 --> 00:08:54,100
+fixed element زي ما قلنا هنس yn إشمالها has not a
+
+134
+00:08:54,100 --> 00:08:57,240
+bounded subsequenceما دام ال .. ال .. ال distance
+
+135
+00:08:57,240 --> 00:09:00,600
+بين ال YN و ال B أكبر من N معناته لو أخدت أي
+
+136
+00:09:00,600 --> 00:09:04,780
+subsequence تانية يعني منها .. أسف مش تانية لو
+
+137
+00:09:04,780 --> 00:09:08,280
+أخدت أي subsequence منها YNK هكون ال distance بين
+
+138
+00:09:08,280 --> 00:09:13,040
+YNK و B أكبر من ال NK هذه و هكذا فبتصير فش ولا
+
+139
+00:09:13,040 --> 00:09:17,840
+subsequence bounded لأن كل .. كل .. كل .. كل ال ..
+
+140
+00:09:17,840 --> 00:09:21,880
+كل البعد بين YN و ال B دايما إيه شماله أكبر من N
+
+141
+00:09:21,880 --> 00:09:27,650
+إذاWhy N has not bounded subsequence؟ بدأ مالهاش
+
+142
+00:09:27,650 --> 00:09:31,190
+bounded subsequence إذا أكيد مش converge إذا مافيش
+
+143
+00:09:31,190 --> 00:09:34,770
+ولا subsequence converge وهذا ينقض مين أن M is
+
+144
+00:09:34,770 --> 00:09:40,650
+compact إذا الـ N لازم تكون عنده اللي هي الفرضية
+
+145
+00:09:40,650 --> 00:09:45,090
+مش مظبوطة لازم تكون M is bounded therefore M is
+
+146
+00:09:45,090 --> 00:09:52,580
+boundedالآن زي ما وعدتكم اطلع لفوق اطلع لفوق اطلع
+
+147
+00:09:52,580 --> 00:09:55,320
+لفوق اخدنا نورجينا هنا الان the converse of لما
+
+148
+00:09:55,320 --> 00:09:59,460
+اللي فوق need not be true in general زي ما وعدناكم
+
+149
+00:09:59,460 --> 00:10:03,760
+احنا في ال .. في ال .. في ال .. في ال .. في ال
+
+150
+00:10:03,760 --> 00:10:07,100
+normed space او ال metric space in general ال
+
+151
+00:10:07,100 --> 00:10:10,880
+closed و ال bounded ليس شرطا انه يكافئ ان every
+
+152
+00:10:10,880 --> 00:10:13,940
+sequence is a convergent subsequence اذا الان بدي
+
+153
+00:10:13,940 --> 00:10:19,330
+اجيبلكاللي هو مثلًا اقول لي اللي هو في عنده
+
+154
+00:10:19,330 --> 00:10:25,170
+sequence اللي هو تكون bounded و closed او في عنده
+
+155
+00:10:25,170 --> 00:10:29,230
+ال .. اللي هو set bounded و closed لكن مافيش فيها
+
+156
+00:10:29,990 --> 00:10:34,450
+اللي هو الـ sequence اللي عنده فيه sequence مش
+
+157
+00:10:34,450 --> 00:10:37,650
+هلاقي إليها ولا convergence subsequence يعني مش
+
+158
+00:10:37,650 --> 00:10:43,090
+compact بمعنى أخر الآن بدأ أجيب مثال على a closed
+
+159
+00:10:43,090 --> 00:10:48,180
+bounded set which is not compactباختصار ماشي هذا
+
+160
+00:10:48,180 --> 00:10:52,940
+اكيد من وين بده يجيبه من اللي هو اكيد يعني حسب
+
+161
+00:10:52,940 --> 00:10:55,360
+كلام الأولاني مش هجيبه من ال final dimensional
+
+162
+00:10:55,360 --> 00:10:58,880
+space هجيبه من infinite dimensional space لأنه في
+
+163
+00:10:58,880 --> 00:11:01,080
+ال final dimensional زي ما قعدناكوا هيطلع نقش
+
+164
+00:11:01,080 --> 00:11:05,800
+مهلين زي بعضطيب a proof consider the sequence en
+
+165
+00:11:05,800 --> 00:11:10,020
+in main ال L2 ال L2 the space of all sequences هذا
+
+166
+00:11:10,020 --> 00:11:13,700
+infinite dimensional space where en لأنه جيبنا ال
+
+167
+00:11:13,700 --> 00:11:16,260
+shoulder bases اللي عارفينه E1 E2 E3 المرة الماضية
+
+168
+00:11:16,260 --> 00:11:17,840
+E1 E2 E3 ..
+
+169
+00:11:20,970 --> 00:11:24,530
+Where en بيساوي ل chronicle delta and j اللي هي
+
+170
+00:11:24,530 --> 00:11:29,090
+عارفينها اي واحد واحد و الباقي أسفار اتنين واحد
+
+171
+00:11:29,090 --> 00:11:32,710
+سفر و الباقي أسفار اتلاتة سفر سفر واحد و الباقي
+
+172
+00:11:32,710 --> 00:11:37,720
+أسفار و هكذا الان this sequence is boundedليش
+
+173
+00:11:37,720 --> 00:11:41,620
+bounded؟ لأنه norm كل واحدة اللي هو عبارة عن واحد
+
+174
+00:11:41,620 --> 00:11:45,100
+لإن الـen عبارة عن سفر، سفر، سفر، وفي ال-nth term
+
+175
+00:11:45,100 --> 00:11:48,540
+واحد، والباقي سفر، سفر، نورمها بصممش ينقلهم كلها
+
+176
+00:11:48,540 --> 00:11:51,400
+نصفها ويبقوا الميه الواحد، إذا الـnorm هم إيه إيش
+
+177
+00:11:51,400 --> 00:11:57,120
+واحد، إذا اخترت أن أنا اللي هي عناصر الـL2 هذولة،
+
+178
+00:11:57,120 --> 00:12:00,820
+أراء ليها دي، اخترتهم أنه في بينهم بعض، يعني مش
+
+179
+00:12:00,820 --> 00:12:03,360
+اللي ملزج أدم هو الـcompact هو أرس، في حاجة اسم
+
+180
+00:12:03,360 --> 00:12:09,420
+أرس، فانا اخترت بالعمدن زي هيك، to show thatM is
+
+181
+00:12:09,420 --> 00:12:13,940
+closed we show that M has no accumulation point
+
+182
+00:12:13,940 --> 00:12:21,680
+إذا الأن إيش بده يعملنا ال M اختارها اللي هي عبارة
+
+183
+00:12:21,680 --> 00:12:28,270
+عن مين اللي هو ال sequence EN ماشيأريد أن أثبت أن
+
+184
+00:12:28,270 --> 00:12:34,930
+الـ M هذه مغلقة وبعضية بعضية أثبتناها لأن نورم
+
+185
+00:12:34,930 --> 00:12:38,850
+عنصرها مش بساوي بساوية حد يان كل عنصر نورمه اللي
+
+186
+00:12:38,850 --> 00:12:43,530
+هو finite الـ M يجب أن أثبت أنها مغلقة عارفين كيف
+
+187
+00:12:43,530 --> 00:12:48,080
+تثبت أنها مغلقة؟أريد أن أثبت أنها M Closed بحيث
+
+188
+00:12:48,080 --> 00:12:52,520
+أثبت لك أنه ليس فيها أي مقاومة يعني ليس فيها
+
+189
+00:12:52,520 --> 00:12:56,080
+مقاومة مقاومة الـ M بمعنى آخر بيصير الـ closure هو
+
+190
+00:12:56,080 --> 00:13:01,720
+الـ M لأن M الـ Prime بتسوء Phi واحنا بنعرف أن M
+
+191
+00:13:01,720 --> 00:13:08,500
+closure بتسوء M إتحاد M Prime لو هذه Phi معناته M
+
+192
+00:13:08,500 --> 00:13:11,960
+closure بتسوء M معناته Closedإذن هأثبت لكم إن هناك
+
+193
+00:13:11,960 --> 00:13:16,260
+لا مقاومة إذا أثبتت إن هناك لا مقاومة إذا أخدت الـ
+
+194
+00:13:16,260 --> 00:13:22,120
+M هي إعبارة عن E1 E2 E3 إلى مدى نهاية وهذه جزء من
+
+195
+00:13:22,120 --> 00:13:27,820
+مين؟ من الأقل 2 بدي أبحث فيه أمرين بدي أثبت لكم إن
+
+196
+00:13:27,820 --> 00:13:31,660
+أول إشي ولا واحدة من هدولة ممكن تكون مقاومة السبب
+
+197
+00:13:31,660 --> 00:13:35,400
+بسيط أن البعد بينها جدر التنين لما تاخدوا البعد
+
+198
+00:13:35,400 --> 00:13:39,170
+بين التنين حتى جوا جدر التنين بعد شويةيعني عشان
+
+199
+00:13:39,170 --> 00:13:44,790
+تكون accumulation point دنيا كلها ملزقة فيها ان
+
+200
+00:13:44,790 --> 00:13:47,950
+شاء الله فاهمين عليها الان ال .. ال .. ال .. ال ..
+
+201
+00:13:47,950 --> 00:13:48,810
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+202
+00:13:48,810 --> 00:13:48,830
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+203
+00:13:48,830 --> 00:13:48,950
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+204
+00:13:48,950 --> 00:13:48,990
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+205
+00:13:48,990 --> 00:13:49,190
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+206
+00:13:49,190 --> 00:13:49,610
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+207
+00:13:49,610 --> 00:13:49,630
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+208
+00:13:49,630 --> 00:13:51,730
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+209
+00:13:51,730 --> 00:13:52,290
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+210
+00:13:52,290 --> 00:13:59,250
+ال .. ال .. ال .. ال .. ال ..
+
+211
+00:13:59,250 --> 00:14:00,290
+ال .. ال ..
+
+212
+00:14:07,930 --> 00:14:13,450
+و اولا نظرح ان اي مقام في M يكون مقام اكمال ممكن
+
+213
+00:14:13,450 --> 00:14:23,350
+ان يكون اي مقام مقام مقام مقام مقام مقام مقام مقام
+
+214
+00:14:23,350 --> 00:14:30,470
+مقام مقام مقام مقاميعني بين الـ N عناصر الـ M مين
+
+215
+00:14:30,470 --> 00:14:34,870
+هي؟ E1 E2 E3 الاخرى بيدثبتلكم إن المسافة بين E N
+
+216
+00:14:34,870 --> 00:14:38,550
+وأي عنصر تاني اللي هو بثوجة للاتنين خدوا المسافة
+
+217
+00:14:38,550 --> 00:14:43,330
+بين E N وE M حيث E M أي عنصر موجود في الـ M بيختلف
+
+218
+00:14:43,330 --> 00:14:48,300
+عن الـ E Nهي ساوي النورم هذا ايه اشمله 000 هذا في
+
+219
+00:14:48,300 --> 00:14:52,640
+الانث تير وهذا في الانتر مثلا او العكس ماشي فبكون
+
+220
+00:14:52,640 --> 00:14:57,680
+حاصل ترحيل هيه ماشي الحال او ممكن واحد يكون ناقص
+
+221
+00:14:57,680 --> 00:15:01,360
+واحد مش هتفرج كتير نورم هنا بساوي summation لل
+
+222
+00:15:01,360 --> 00:15:05,560
+absolute value هنا قص نص لان أنا بحكي عن ال two
+
+223
+00:15:06,270 --> 00:15:09,710
+فاهمين عليها إذا هذا بيساوي مين بيطلع عند جذر
+
+224
+00:15:09,710 --> 00:15:13,850
+التنين إذا صار عند المسافة بين EN و EN بيساوي جذر
+
+225
+00:15:13,850 --> 00:15:19,610
+التنين إذا .. إذا لجيت أنا لو جيت لل ball EN واحد
+
+226
+00:15:19,610 --> 00:15:23,170
+و نص القطر واحد مش عادي بكم EN و نص شيله من ال EN
+
+227
+00:15:23,170 --> 00:15:26,930
+طاقاته لأ مش هيساوي fine إذا مش limit point عشان
+
+228
+00:15:26,930 --> 00:15:32,170
+limit point أيش بيكون أنه لأي neighborhoodBEN أي
+
+229
+00:15:32,170 --> 00:15:37,110
+اللي هو ball EN بأي نص خطر شيله منها العنصر هذا
+
+230
+00:15:37,110 --> 00:15:40,790
+تقطحها مع ال M لازم إيش لله؟ لا يساوي five لجتلكم
+
+231
+00:15:40,790 --> 00:15:46,550
+اللي هو نص خطر واحد و نص و ربع كل بعمل إنه BEN هو
+
+232
+00:15:46,550 --> 00:15:50,490
+واحد أو نص أو ربع شيله منه EN تقطع له مش بيساوي
+
+233
+00:15:50,490 --> 00:15:55,150
+five سببه إن المسافات بين العناصر جدر التنين إذن
+
+234
+00:15:55,150 --> 00:15:58,860
+المسافات بين العناصر اللي هنالو بدي اكون في عنصر
+
+235
+00:15:58,860 --> 00:16:05,300
+من M اشمله لازم تاخد هذا اتنين او تلاتة او اربعة
+
+236
+00:16:05,300 --> 00:16:10,560
+او خمسة فاهمين؟ طيب صار عندي الان hence any point
+
+237
+00:16:10,560 --> 00:16:15,080
+in M can't be an accumulation pointsecond اللي ضال
+
+238
+00:16:15,080 --> 00:16:18,360
+we show that any point in M complement يعني براة
+
+239
+00:16:18,360 --> 00:16:21,160
+الـ M في الـ L2 بس مش في الـ M complement can't be
+
+240
+00:16:21,160 --> 00:16:26,000
+an accumulation point ماشي في سؤال اللي هو 13
+
+241
+00:16:26,000 --> 00:16:29,520
+Problem 6 كان بيقولنا إذا كانت النقطة accumulation
+
+242
+00:16:29,520 --> 00:16:35,740
+point بدي يكون أي neighborhood حوالين النقطة تقاطع
+
+243
+00:16:35,740 --> 00:16:39,250
+مع الـ M هيكون infinite number of dotsمش هيكون
+
+244
+00:16:39,250 --> 00:16:41,970
+نقطة في infinite number of points هذا اللي هو سؤال
+
+245
+00:16:41,970 --> 00:16:45,930
+ستة في problem 138 مش صعب عموما طيب شوفوا صلى الله
+
+246
+00:16:45,930 --> 00:16:49,470
+على النبي عز وجل انا بدي استعينيه الان بدي اخد اي
+
+247
+00:16:49,470 --> 00:16:52,790
+نقطة في ال M complement و اثبتلكم انه لا يمكن انها
+
+248
+00:16:52,790 --> 00:16:56,770
+تكون accumulation point او limit point لل M شوف
+
+249
+00:16:56,770 --> 00:17:00,490
+كيف let X be any fixed point in M complement خدوا
+
+250
+00:17:00,490 --> 00:17:05,350
+الان ال ball ال نص خطرها اللي هو نص و مركزها ال X
+
+251
+00:17:05,350 --> 00:17:11,340
+هذهشيلوا منها الـ X تقاطع الـ M مستحيل تحتوي على
+
+252
+00:17:11,340 --> 00:17:14,280
+الأكثر على الأكثر حيكون نقطة واحدة من الـ M على
+
+253
+00:17:14,280 --> 00:17:17,980
+الأكثر نقطة واحدة أيش من الـ M ليش؟ لأن لو كان في
+
+254
+00:17:17,980 --> 00:17:22,220
+نقطتين من الـ M ومصفره .. وهي كانت جواة بهذا ال
+
+255
+00:17:22,220 --> 00:17:25,220
+ball كيف بيبقى تكون جواة ال ball والمسافة بين كل
+
+256
+00:17:25,220 --> 00:17:27,700
+نقطتين في ال .. في ال .. في ال M إيش ماله؟ جدر
+
+257
+00:17:27,700 --> 00:17:29,920
+التنين معايا؟
+
+258
+00:17:31,370 --> 00:17:34,030
+المسافات بين النقاط اللي جوا موجودة هنا إيش هيكون
+
+259
+00:17:34,030 --> 00:17:38,590
+نص؟ لو بدوا يكون تنتين من الأم هنا طب هم المسافات
+
+260
+00:17:38,590 --> 00:17:41,210
+اللي بين التنتين اللي في الأم مش أثبتنا أنها نجدر
+
+261
+00:17:41,210 --> 00:17:44,270
+التنين يعني مش هيكون التنتين جوا يعني إيه ده
+
+262
+00:17:44,270 --> 00:17:47,390
+بيلاجينا .. بيلاجينا واحدة جريبة من هذه اللي هو
+
+263
+00:17:47,390 --> 00:17:50,450
+ابن أُص لكن لو بنجول فيه كمان واحدة بيصير بينها و
+
+264
+00:17:50,450 --> 00:17:54,750
+بين كمان أختها أجال من النص و هذا مش سهل إذن هنا
+
+265
+00:17:54,750 --> 00:18:01,430
+has at most one element why قلته؟ماشي و هذا مستحيل
+
+266
+00:18:01,430 --> 00:18:05,810
+لأن X is not an accumulation point لأنه في ال
+
+267
+00:18:05,810 --> 00:18:08,310
+problem واحدة ستة اللي هي واحدة تلاتة بنقول إنه لو
+
+268
+00:18:08,310 --> 00:18:10,970
+كانت accumulation point لازم يكون في عند infinite
+
+269
+00:18:10,970 --> 00:18:12,990
+number of points مشتركة
+
+270
+00:18:15,030 --> 00:18:18,330
+أي point في الـ mk can't be an accumulation point
+
+271
+00:18:18,330 --> 00:18:21,850
+therefore m has no accumulation point hence m
+
+272
+00:18:21,850 --> 00:18:24,650
+بيسوي m closure زي ما أقولها ومن ثم m is closed
+
+273
+00:18:24,650 --> 00:18:29,070
+إذا صار عندي m closed و open إذا صار عندي اللي هي
+
+274
+00:18:29,070 --> 00:18:34,050
+إيش مالها اللي هي متحققة لأن بدنا نقول إنها إيش
+
+275
+00:18:34,050 --> 00:18:39,670
+مالها خليني بدنا نقول إيش إنها مش compact ماشي
+
+276
+00:18:39,670 --> 00:18:44,710
+moreover m has no convergence subsequenceليش؟
+
+277
+00:18:44,710 --> 00:18:48,490
+Because M has no accumulation point لو بدها تكون
+
+278
+00:18:48,490 --> 00:18:53,530
+في عندي subsequence في الـ M Xn subsequence في الـ
+
+279
+00:18:53,530 --> 00:18:58,550
+M و Xn has a convergence subsequence to some X في
+
+280
+00:18:58,550 --> 00:19:03,730
+الـ M بيصير اللي هو أنه عندي تكدس من ال .. من ..
+
+281
+00:19:03,730 --> 00:19:07,330
+من .. من .. من المقاط اللي موجودة في الـ M المسافة
+
+282
+00:19:07,330 --> 00:19:09,710
+بينها و بينها بقى أصغر من الـ Y في الدنيا طبعاً
+
+283
+00:19:09,710 --> 00:19:14,160
+جدر التنين المسافة بينهم بعاد عن بعضفاهمين اللي
+
+284
+00:19:14,160 --> 00:19:20,080
+بحكيه؟ أي سؤال؟ اذا ال M is not compact M is not
+
+285
+00:19:20,080 --> 00:19:23,500
+compact ليش؟ لأنه لو أخدنا أي sequence في ال M
+
+286
+00:19:23,500 --> 00:19:26,020
+يستحيل يستحيل يستحيل يستحيل يستحيل يستحيل يستحيل
+
+287
+00:19:26,020 --> 00:19:26,320
+يستحيل يستحيل يستحيل يستحيل يستحيل يستحل يستحل
+
+288
+00:19:26,320 --> 00:19:26,380
+يستحل يستحل يستحل يستحل يستحل يستحل يستحل يستحل
+
+289
+00:19:26,380 --> 00:19:26,500
+يستحل يستحل يستحل يستحل يستحل يستحل يستحل يستحل
+
+290
+00:19:26,500 --> 00:19:26,620
+يستحل
+
+291
+00:19:37,700 --> 00:19:40,780
+Xn بتروح للـ X عشان تكون converged إلى الـ X بيكون
+
+292
+00:19:40,780 --> 00:19:44,600
+أي ball حوالين الـ X بحتوي عدد لا نهائي من النخاق
+
+293
+00:19:44,600 --> 00:19:47,660
+مع عدد finite number مش هيك معناه ال limit limit
+
+294
+00:19:47,660 --> 00:19:52,400
+Xn بتروح بتساوي X معناه تقرر every Y أكبر من 0
+
+295
+00:19:52,400 --> 00:19:57,360
+there exist K element in N such that ال ball لل X
+
+296
+00:19:57,360 --> 00:20:03,700
+هذه و ال Y اللي هو تحتوي
+
+297
+00:20:03,700 --> 00:20:10,500
+أو XnXn element الـ ball for every n أكبر شوء إيش
+
+298
+00:20:10,500 --> 00:20:16,040
+فيه وهذا مستحيل لأنه إذا كانت جوا هنا بيصير البقط
+
+299
+00:20:16,040 --> 00:20:19,840
+بين عناصر الـ M إيه شمالهم اللي هو أقل من إبسلون
+
+300
+00:20:19,840 --> 00:20:22,800
+طب إبسلون هذا كل إبسلون طب أنا جدر التنين عن جدر
+
+301
+00:20:22,800 --> 00:20:26,100
+التنين و بس أقل من جدر التنين ببطلر فيه إيش إيه
+
+302
+00:20:27,060 --> 00:20:31,500
+الأن الـ
+
+303
+00:20:31,500 --> 00:20:34,200
+M ليس كمبكت
+
+304
+00:20:37,090 --> 00:20:40,350
+المثال تبعنا جيبناه على infinite dimensional space
+
+305
+00:20:40,350 --> 00:20:44,410
+زي ما وعدناكم بدنا نقول للإعلان التالي in a finite
+
+306
+00:20:44,410 --> 00:20:49,010
+dimensional normed space X any subset M of X is
+
+307
+00:20:49,010 --> 00:20:51,670
+compact if and only if M is closed and A is
+
+308
+00:20:51,670 --> 00:20:54,630
+bounded إذا في ال finite dimensional space الدنيا
+
+309
+00:20:54,630 --> 00:20:58,970
+حلوة و تمامة تمام والclosed و ال compact يكافئ
+
+310
+00:20:58,970 --> 00:21:03,920
+closed و bounded شوفوا كيفبعد مجموعة 2.5.2 مقاومة
+
+311
+00:21:03,920 --> 00:21:07,200
+تشير إلى مقاومة مقاومة ومقاومة هذا موجود في كل
+
+312
+00:21:07,200 --> 00:21:10,780
+الاسباسيات حتى في الاسباسيات التبوليجية الـ M يجب
+
+313
+00:21:10,780 --> 00:21:14,360
+أن نثبت الـ Converse مقاومة مقاومة مقاومة تشير إلى
+
+314
+00:21:14,360 --> 00:21:18,300
+مقاومة مقاومة ومقاومة يجب أن أثبتكم أن M يجب أن
+
+315
+00:21:18,300 --> 00:21:22,070
+تكون مقاومة في هذه الحالةأكيد مدام بحكي عن finite
+
+316
+00:21:22,070 --> 00:21:24,990
+dimension انا هستخدم اللي هو الـ finite dimension
+
+317
+00:21:24,990 --> 00:21:27,730
+له هو أكيد فيدي يكون صح في .. مش صح في ال infinite
+
+318
+00:21:27,730 --> 00:21:31,990
+و أنا صح أكيد هستخدم خاصية انه بما انه dimension
+
+319
+00:21:31,990 --> 00:21:35,750
+ال X finite بساوي N و ال E واحد و ال E اتنين bases
+
+320
+00:21:35,750 --> 00:21:40,530
+له أخد ايه ال bases له؟ اذا عندي consider any
+
+321
+00:21:40,530 --> 00:21:44,410
+sequence XM بده لجيلها إيش ما لها subsequence
+
+322
+00:21:44,410 --> 00:21:47,650
+converged في ال .. في ال M عاية؟ مش هي معناته
+
+323
+00:21:47,650 --> 00:21:51,890
+compactness؟الان انا اخدنا اي sequence xm في ال M
+
+324
+00:21:51,890 --> 00:21:57,250
+الان ال xm موجودة في ال M وال M جزء من ال X وال X
+
+325
+00:21:57,250 --> 00:22:00,450
+finite dimensional اذا اكيد بقدر اكتب عناصر ال XM
+
+326
+00:22:00,450 --> 00:22:03,250
+على صورة Linear Comparison من ال E1 وE2 لإدريان
+
+327
+00:22:04,770 --> 00:22:09,570
+هيكون عندي xm ممكن كتبتها على صورة scalar في E1
+
+328
+00:22:09,570 --> 00:22:15,550
+scalar في E2 لعندي scalar في مين في E1 X1 E1 XI 1
+
+329
+00:22:15,550 --> 00:22:21,090
+E1 XI 2 E1 XI N 1 in general XM بيساوي XI 1 M E1
+
+330
+00:22:21,090 --> 00:22:30,110
+XI 2 M E2 لعندي XI N M E N since M is bounded إذا
+
+331
+00:22:30,110 --> 00:22:34,950
+ال sequence اللي جوه boundedمظبوط؟ إذا since M is
+
+332
+00:22:34,950 --> 00:22:39,750
+bounded so XM is bounded إيش معناه bounded؟
+
+333
+00:22:39,750 --> 00:22:42,970
+معناتها there exists K بحيث انه norm لـ XM أصغر أو
+
+334
+00:22:42,970 --> 00:22:49,230
+شويه مين K for all مين M من لمّة اتنين اربعة واحد
+
+335
+00:22:49,230 --> 00:22:52,090
+المليح هذا اللي استخدمنا .. اللي أثبتناها في الأول
+
+336
+00:22:52,090 --> 00:22:56,010
+there exists C أكبر من صفر such that K أكبر أو
+
+337
+00:22:56,010 --> 00:23:02,790
+شويه اللي هو ال norm هذا اللي هوهيها من هنا ال K
+
+338
+00:23:02,790 --> 00:23:06,970
+أكبر سواء norm XM وال XM هيها هيها ال XM اللي هي
+
+339
+00:23:06,970 --> 00:23:10,910
+هذه أه بس كتر ده في ال summation إذا ال normal X
+
+340
+00:23:10,910 --> 00:23:16,950
+ال K أكبر سواء norm XM اللي هو هذا و هذا من اللمّة
+
+341
+00:23:16,950 --> 00:23:21,730
+اللي قبل بشوية باللاجة C بحيث أنه هي أكبر سواء C
+
+342
+00:23:21,730 --> 00:23:28,640
+في mean في ال summation طيب اللي هنطلع لفوقHence,
+
+343
+00:23:28,820 --> 00:23:35,780
+for any fixed I من 1 إلى N in the sequence Xim is
+
+344
+00:23:35,780 --> 00:23:41,440
+a bounded sequence of numbers أكيد الـ Xim bounded
+
+345
+00:23:41,440 --> 00:23:45,250
+sequence ليه؟ لأنه صار الـ summation هذاأكبر أو
+
+346
+00:23:45,250 --> 00:23:50,210
+أصغر أو ساوي هذا على C كل واحدة من اندولا Cy M
+
+347
+00:23:50,210 --> 00:23:53,670
+هتكون أصغر أو تساوي K على C يعني صارت ال sequence
+
+348
+00:23:53,670 --> 00:23:56,530
+هذي bounded sequence اذا صارت عندي bounded
+
+349
+00:23:56,530 --> 00:24:00,710
+sequence of مين؟ of numbers باشر و دوين على ال R
+
+350
+00:24:00,710 --> 00:24:05,430
+أو على ال C اللي ضامن انه انه في مدام اللي هو
+
+351
+00:24:05,430 --> 00:24:09,010
+sequence of numbers و بولزانو بتقول every sequence
+
+352
+00:24:09,010 --> 00:24:12,210
+bounded sequence هذا convergence subsequenceإذا
+
+353
+00:24:12,210 --> 00:24:17,030
+لازم it has a convergent subsequence say that it
+
+354
+00:24:17,030 --> 00:24:20,530
+converges to mean to Xi I إذا ال subsequence من
+
+355
+00:24:20,530 --> 00:24:25,770
+هذه converges to mean لXi I بالظبط بديش أقول عيد
+
+356
+00:24:25,770 --> 00:24:28,530
+اللي قلناه قبل و شوية then as in the proof of لبمة
+
+357
+00:24:28,530 --> 00:24:34,180
+2 4 5 we show that XM A شمالها hasبنركّب منهن
+
+358
+00:24:34,180 --> 00:24:36,440
+هدولة مش هدولة جيناها الـ bounded بنركّب منهن
+
+359
+00:24:36,440 --> 00:24:42,800
+subsequence ZM اللي هنا الـ scalars سبعتها من الـ
+
+360
+00:24:42,800 --> 00:24:45,940
+XM اللي قبل شوية قلتها اللي كنا بسميينها هنا YM و
+
+361
+00:24:45,940 --> 00:24:50,860
+YM1 و YM2 و الاخرى which converts to mean to اللي
+
+362
+00:24:50,860 --> 00:24:55,560
+هو الـ Z اليمين الـ Z اللي هي XI 1 في E1 اللي
+
+363
+00:24:55,560 --> 00:25:01,200
+عملتين قبل شوية لأنه صارت limit XI IM هي XI Iماشي
+
+364
+00:25:01,200 --> 00:25:07,440
+فال XM اللي قبل بشوية limit هيصير XII EI ال Z
+
+365
+00:25:07,440 --> 00:25:11,120
+بساوي اللي هو Z M converged to Z however M is
+
+366
+00:25:11,120 --> 00:25:16,980
+closed إذا هذي هتكون الموجودة في M therefore M is
+
+367
+00:25:16,980 --> 00:25:23,520
+compact وهو المطلوب نيجي الآن نظرية محترمة ومهمة
+
+368
+00:25:23,520 --> 00:25:29,290
+برضه من النظريات اللياللي .. يعني اللي هسا عملتها
+
+369
+00:25:29,290 --> 00:25:34,470
+عندنا واسعة اطلع لفوق اخليها على رأس اللي هناك
+
+370
+00:25:34,470 --> 00:25:39,650
+ريزيز لمّة اه ريزيز لمّة ايش بتقول ريزيز لمّة
+
+371
+00:25:39,650 --> 00:25:46,670
+خليني اوضحها بالرسم نيح عشان
+
+372
+00:25:46,670 --> 00:25:51,410
+نصها انا بالنسبة لي مهم برضه برهان مش صعب سهل ان
+
+373
+00:25:51,410 --> 00:25:51,670
+شاء الله
+
+374
+00:26:06,170 --> 00:26:10,270
+عندى الان let y and z be subspaces of a normed
+
+375
+00:26:10,270 --> 00:26:15,130
+space x هى فى عندى normed space مين؟ x برا هذا
+
+376
+00:26:15,130 --> 00:26:19,070
+normed space الأصلي x اللى تبعنا اللى هو اللى كلنا
+
+377
+00:26:19,070 --> 00:26:24,870
+subspaces منهو Y و Z subspaces من X و Y closed and
+
+378
+00:26:24,870 --> 00:26:30,810
+proper subset من من من Z يعني هي Y جوا Y و proper
+
+379
+00:26:30,810 --> 00:26:35,790
+subset منين من Z يعني في element هنا مش موجود وين
+
+380
+00:26:35,790 --> 00:26:41,270
+مش موجود في Y و Y و Z نفسهم subspaces من من من X
+
+381
+00:26:41,270 --> 00:26:50,380
+الآن بقولي إذا لأي θ لأي θElement in Zero و واحد
+
+382
+00:26:50,380 --> 00:26:56,220
+بقدر ألاقي Element in Min in Z there exist Z
+
+383
+00:26:56,220 --> 00:27:03,620
+Element in Z ومش هيك كمان و Normal بساوي واحد و
+
+384
+00:27:03,620 --> 00:27:10,120
+بعضه و بعض ال .. يعني بعض ال Z هذا عن ال Y بعض ال
+
+385
+00:27:10,120 --> 00:27:18,460
+Z عن ال Y أكبر أو تساوي Min فترةعنا .. تنسوش هذا
+
+386
+00:27:18,460 --> 00:27:23,780
+أن Y بروبر سبسيط .. بروبر سبسيط من مين؟ من Z مزامه
+
+387
+00:27:23,780 --> 00:27:27,100
+بروبر سبسيط يعني الكلام منطقي أنه بلاقي لكل Z في
+
+388
+00:27:27,100 --> 00:27:31,960
+ال Y في ال Z لكل .. آسف لكل θ التي تزيد واحد بقدر
+
+389
+00:27:31,960 --> 00:27:35,920
+لاقي Z في ال Y بحيث أن المسافة بين ال Z و ال Y
+
+390
+00:27:35,920 --> 00:27:41,450
+أكبر أو يساوي ال θ تبعتكلكل Y وين موجودة في الـ Y
+
+391
+00:27:41,450 --> 00:27:45,450
+Capital يعني بمعنى أخر و كإني بقول Roughly أن لكل
+
+392
+00:27:45,450 --> 00:27:49,170
+θة من Zero لواحد نص ربع طولت حتى لو زغرتها حتى لو
+
+393
+00:27:49,170 --> 00:27:54,250
+كبرتها اللي هو بيكون بقدر ألاقي Z في Z نورمها
+
+394
+00:27:54,250 --> 00:27:58,270
+بيساوي واحد بحيث أن ال norm لل Z minus Y يكون إيه
+
+395
+00:27:58,270 --> 00:28:03,450
+اشمله أكبر أو يساوي θة يعني بعضها عن ال Y أكبر أو
+
+396
+00:28:03,450 --> 00:28:09,900
+يساوي θة و الثتة نفسها أكبر من مين؟ من سفرأه يعني
+
+397
+00:28:09,900 --> 00:28:13,580
+في مسافة لإن هو بروبرت يعني لو مشوا بروبرت بيصيب
+
+398
+00:28:13,580 --> 00:28:16,600
+الموضوع لأ بختلف طيب نشوف إيش البرهان
+
+399
+00:28:21,360 --> 00:28:24,900
+let v be any element in z minus y يعني أخدت
+
+400
+00:28:24,900 --> 00:28:29,840
+element من وين من هنا بين اللي هو ال z في ال z و
+
+401
+00:28:29,840 --> 00:28:33,000
+مش من وين مش في ال y وهذا اللي بدي يوصلني للي
+
+402
+00:28:33,000 --> 00:28:37,260
+بديها الان let v be any element in z minus y and
+
+403
+00:28:37,260 --> 00:28:40,920
+let a بيساوي ال infimum للنورم لل v minus y y
+
+404
+00:28:40,920 --> 00:28:45,300
+element in y يعني بتاخد ال a أشمالها هي عبارة عن
+
+405
+00:28:45,300 --> 00:28:51,990
+المسافة مسافة بين ال v اللي أخدته من هنابين ال ..
+
+406
+00:28:51,990 --> 00:28:57,930
+و بين مين ال Y ال infimum لل norms ال V minus Y و
+
+407
+00:28:57,930 --> 00:29:02,770
+Y limit on Y هو اللي بتسميه ايش بتسميه ال A الان
+
+408
+00:29:02,770 --> 00:29:07,750
+بقوللي since Y is closed then A ايش مالها A أكبر
+
+409
+00:29:07,750 --> 00:29:09,170
+من مين من سفر
+
+410
+00:29:12,520 --> 00:29:17,360
+بما انه Y closed إذا الـ A هد إيش ما لها أكبر من
+
+411
+00:29:17,360 --> 00:29:24,440
+سفر إيش علاقتها؟ عنده ماعطيك الـ A الـ A سوى الـ
+
+412
+00:29:24,440 --> 00:29:31,180
+infimum لـ unknown V minus Y حيث Y element in Y
+
+413
+00:29:32,280 --> 00:29:37,000
+يعني باخد الأبعاد بعض ال V عن ال Y و باخد ال
+
+414
+00:29:37,000 --> 00:29:39,860
+infimum لكل ال ال white اللي في ال Y و باخد ال
+
+415
+00:29:39,860 --> 00:29:43,000
+infimum اللي هم ده سميمين ال A هذا بقول ال A
+
+416
+00:29:43,000 --> 00:29:49,960
+أشماله أكيد أشماله أكبر من سفر و جلت سبب عشان Y
+
+417
+00:29:49,960 --> 00:29:58,800
+closed Y is closed الان الان لو ال infimum هذا بده
+
+418
+00:29:58,800 --> 00:30:05,080
+يساوي سفرالانفمان بيسوي سفر معناته صار عندي من
+
+419
+00:30:05,080 --> 00:30:11,020
+تعريف الانفمان بقدر ألاقي sequence من ال Y YN اللي
+
+420
+00:30:11,020 --> 00:30:16,700
+هو بحيث ان normal V minus ال YN يقول إلى مين ال A
+
+421
+00:30:16,700 --> 00:30:22,140
+هذه اللي أصبحت إيش تسمينها سفرمعناته صار عندى ..
+
+422
+00:30:22,140 --> 00:30:25,860
+هد شو معناته؟ هد معناته انه صار الـ yn converged
+
+423
+00:30:25,860 --> 00:30:33,460
+من للـV يعني لجيت sequence yn من اللي هي الـY
+
+424
+00:30:33,460 --> 00:30:38,900
+converged من للـV طب my Y closed، إذا الـV وين
+
+425
+00:30:38,900 --> 00:30:43,400
+هتكون؟ في الـY Contradictionلأن الـ V من أين أخدها
+
+426
+00:30:43,400 --> 00:30:48,880
+أنا؟ من Z minus Y إذا أكيد ما دامت الـ Y closed و
+
+427
+00:30:48,880 --> 00:30:52,220
+الـ A هي الـ infimum هتكون الـ A أشمالها أكبر من
+
+428
+00:30:52,220 --> 00:31:00,000
+سفر و الـ Y هي اللي وضحتها اطلع لفوق now .. now ..
+
+429
+00:31:00,000 --> 00:31:03,100
+take any θ element in 0 و 1 بتحصر على اللي بديها
+
+430
+00:31:03,100 --> 00:31:07,720
+then by definition of infimum there exists y
+
+431
+00:31:07,720 --> 00:31:11,880
+naught element in Y such thatالـ V minus Y note
+
+432
+00:31:11,880 --> 00:31:14,960
+اللي هو أكبر يساوي A لإنه الـ A infimum لهم كلهم
+
+433
+00:31:14,960 --> 00:31:19,580
+اللي هو greatest lower bound lower bound في
+
+434
+00:31:19,580 --> 00:31:24,640
+النهاية إذاً الـ A أصغر يساويها دي طيب الآن ال θ
+
+435
+00:31:24,640 --> 00:31:29,160
+بين ال 0 و ال 1 مظبوط ولا لأ مزام ال θ بين ال 0 و
+
+436
+00:31:29,160 --> 00:31:33,720
+ال 1 إذاً ال A على θ أيش مالها هتصير أيش مالها
+
+437
+00:31:33,720 --> 00:31:39,240
+أصغرمن الـ A، مظبوط ولا لا؟ آسف أكبر من الـ A،
+
+438
+00:31:39,240 --> 00:31:43,080
+مظبوط؟ يعني مدان صارت أكبر من A، إذا بطلت lower
+
+439
+00:31:43,080 --> 00:31:46,860
+bound لأن الـ A إيش مالها؟ the greatest lower
+
+440
+00:31:46,860 --> 00:31:51,500
+bound أي إيش أكبر منها، ببطل lower bound مدان بطلت
+
+441
+00:31:51,500 --> 00:31:55,180
+هذه lower bound لأنها أكبر من الـ A إذا أكيد،
+
+442
+00:31:55,180 --> 00:31:59,560
+أكيد، أكيد، بلاكي عنصر في ال 6 هنا و اليكن Y note
+
+443
+00:31:59,560 --> 00:32:04,220
+بكون هذاأيه شماله؟ هو اللي أفسد عليها انها تكون
+
+444
+00:32:04,220 --> 00:32:11,940
+lower bound يعني هيكون أصغر أو يسويها واضح؟
+
+445
+00:32:11,940 --> 00:32:18,380
+انه الآن a على θأكبر من الـ A والـ A greatest
+
+446
+00:32:18,380 --> 00:32:23,420
+lower bound يعني الـ A على ثيتا بتبطل lower bound
+
+447
+00:32:23,420 --> 00:32:28,320
+مدام بطلت lower bound لهذه المجموعة إذا أكيد في
+
+448
+00:32:28,320 --> 00:32:32,700
+عنصر في المجموعة خلّها تبطل يعني بمعنى آخر تخلّها
+
+449
+00:32:32,700 --> 00:32:35,160
+تبطل lower bound تخلّها تبطل إنها أصغر من الكل
+
+450
+00:32:35,160 --> 00:32:39,400
+خلّه إن V minus Y not يكون أصغر أو يساوي من A على
+
+451
+00:32:39,400 --> 00:32:43,890
+ثيتا اللي بطل lower bound نتعرف على طولطيب خلوه
+
+452
+00:32:43,890 --> 00:32:47,830
+هادي إذا هادي اللي هي صحيحة مائة بالمائة و لجينا
+
+453
+00:32:47,830 --> 00:32:52,970
+why note بحقق هاديالان انا غلط مين؟ انا انا انا
+
+454
+00:32:52,970 --> 00:33:00,450
+انا انا انا
+
+455
+00:33:00,450 --> 00:33:01,010
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+456
+00:33:01,010 --> 00:33:01,090
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+457
+00:33:01,090 --> 00:33:01,730
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+458
+00:33:01,730 --> 00:33:02,330
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+459
+00:33:02,330 --> 00:33:02,490
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+460
+00:33:02,490 --> 00:33:03,450
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+461
+00:33:03,450 --> 00:33:03,990
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+462
+00:33:03,990 --> 00:33:15,710
+انا انا انا انا
+
+463
+00:33:15,710 --> 00:33:21,130
+انااللي هي مقلوبة دي C في V minus Y not أخدني ال V
+
+464
+00:33:21,130 --> 00:33:26,270
+minus Y not على نورمها يعني Z بتساوي V minus Y not
+
+465
+00:33:26,270 --> 00:33:31,930
+على نورمها ونورمها مش سفر أه لإن هد مش سفر و هد
+
+466
+00:33:31,930 --> 00:33:37,370
+أكبر يسوي هد ان هد اسمه مهدنا قبل إنه قلنا لإيه مش
+
+467
+00:33:37,370 --> 00:33:41,110
+سفر إذا صار هد مش سفر لإنه أكبر منها أسويها إذا
+
+468
+00:33:41,110 --> 00:33:44,750
+صار عندي الآن فيه إمكانية أقسم على نورمها خد الآن
+
+469
+00:33:44,750 --> 00:33:49,620
+Z بتساوي هذا المقدرالان ال C طبعا هي واحد على نورم
+
+470
+00:33:49,620 --> 00:33:54,500
+هذا الان انا بقولك ال Z نورم ال Z ايش هيساوي واحد
+
+471
+00:33:54,500 --> 00:33:59,500
+و هيحقق اللي بديها نورم ال Z بيساوي واحد واضح لان
+
+472
+00:33:59,500 --> 00:34:05,160
+let Y be any fixed element in Y وحسب للان نورم ال
+
+473
+00:34:05,160 --> 00:34:11,160
+Z minus Y ايش بيساوي بساوي Zطلعلي اللي هي عوضليها
+
+474
+00:34:11,160 --> 00:34:14,280
+زي ده إيش بالساوية C فيها ده اللي هو C في V minus
+
+475
+00:34:14,280 --> 00:34:20,780
+Y not ناقص من ال Y طلعلي لو سمحت C برا و بيصير هد
+
+476
+00:34:20,780 --> 00:34:25,260
+V minus Y not و هد بيصير إيش مالها Y على C اللي هو
+
+477
+00:34:25,260 --> 00:34:30,920
+C inverse في مين في Y Y ساوي C في ال norm لل V
+
+478
+00:34:30,920 --> 00:34:35,180
+minus Y واحد إيش ال Y واحد؟ Y واحد أخدت السالب برا
+
+479
+00:34:35,180 --> 00:34:40,240
+صارت هد Y not زاد C inverse في Yأه إذا ال Y واحد
+
+480
+00:34:40,240 --> 00:34:46,280
+هي هذه الآن هذه why not من ال Y و ال Y من ال Y إذا
+
+481
+00:34:46,280 --> 00:34:49,400
+المجموح من ال Y واحد هتكون برضه من وين من ال Y
+
+482
+00:34:49,400 --> 00:34:56,000
+which belongs to Y إذا ملخص الحديث إنه صار V minus
+
+483
+00:34:56,000 --> 00:35:04,060
+Y واحد عندي اللي هو في C بساوي اللي هو المقدار هذا
+
+484
+00:35:06,150 --> 00:35:13,050
+الان عندى V-Y1 هيكون اكبر او يساوي مين او يساوي
+
+485
+00:35:13,050 --> 00:35:25,810
+ايه V-Y1 V-Y1 اكبر او يساوي ايه طيب
+
+486
+00:35:25,810 --> 00:35:27,390
+حلينا عشان نوضح لكم
+
+487
+00:35:38,040 --> 00:35:41,100
+طيب يا جماعة لأ نزلي عشان نشوف ال .. ال .. ال ..
+
+488
+00:35:41,100 --> 00:35:47,120
+عندي أثبتنا أنه عند Normal Z minus Y Z minus Y
+
+489
+00:35:47,120 --> 00:35:53,260
+اللي هو بساوي C في Normal V minus Y واحدالان عندي
+
+490
+00:35:53,260 --> 00:35:56,720
+ال y واحد بيسوي نوت زي c inverse one which belongs
+
+491
+00:35:56,720 --> 00:36:01,740
+to me into y اذا صارت مدام y واحد في ال y اذا اكيد
+
+492
+00:36:01,740 --> 00:36:05,680
+اكيد اكيد ال v minus y واحد اكبر يسوى من ايه لان
+
+493
+00:36:05,680 --> 00:36:11,080
+الامين هي الامسفة من الهن كلهن واضح طيب الان بدنا
+
+494
+00:36:11,080 --> 00:36:16,060
+نستخدم one to get to get الانأنا بدي أستخدم هذه
+
+495
+00:36:16,060 --> 00:36:20,600
+احسبلي يعني حسابات بدي أحسبلك ايه يعني Z-Y بالساوي
+
+496
+00:36:20,600 --> 00:36:25,420
+هيها Z-Y بالساوي C في المقدار هذا C في المقدار هذا
+
+497
+00:36:25,420 --> 00:36:29,380
+والمقدار هذا قولنا عنه اشماله أكبر يساوي ايه اذا
+
+498
+00:36:29,380 --> 00:36:32,220
+اكبر يساوي مين C في A
+
+499
+00:36:35,900 --> 00:36:38,920
+الان عندى ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+500
+00:36:38,920 --> 00:36:39,180
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+501
+00:36:39,180 --> 00:36:39,240
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+502
+00:36:39,240 --> 00:36:39,320
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+503
+00:36:39,320 --> 00:36:40,780
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+504
+00:36:40,780 --> 00:36:41,520
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+505
+00:36:41,520 --> 00:36:43,180
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+506
+00:36:43,180 --> 00:36:43,900
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+507
+00:36:43,900 --> 00:36:49,220
+ال .. ال .. ال .. ال ..
+
+508
+00:36:49,220 --> 00:36:52,440
+ال .. ال .. ال ..
+
+509
+00:36:52,440 --> 00:36:55,700
+ال .. ال .. ال ..
+
+510
+00:36:57,590 --> 00:37:01,430
+الان هذه ليها مقلوبها C بيصير C أكبر أو ثواء ثتا
+
+511
+00:37:01,430 --> 00:37:01,770
+على A
+
+512
+00:37:06,030 --> 00:37:10,510
+أضربه في a بيصير c أكبر من θ على a في a ال a بتروح
+
+513
+00:37:10,510 --> 00:37:13,590
+مع ال a ويبقى المين يعني ال c z minus y أكبر من
+
+514
+00:37:13,590 --> 00:37:18,390
+مين θ أخدت الآن اللي هو أي θ في ال zero و ال واحد
+
+515
+00:37:18,390 --> 00:37:23,950
+أيه من هنا أخدت ال theta أي element من zero و واحد
+
+516
+00:37:23,950 --> 00:37:30,210
+لجيت ال z هيها نورمها بيساوي واحد و البعد بين z و
+
+517
+00:37:30,210 --> 00:37:34,550
+minus y أكبر و يساوي θ وهو المطلوب طيب
+
+518
+00:37:37,750 --> 00:37:47,810
+ملاحظة الان في عندي اطلع لفوق in
+
+519
+00:37:47,810 --> 00:37:53,210
+a finite dimensional space the closed unit ball is
+
+520
+00:37:53,210 --> 00:37:57,900
+compactفي الـ finite dimensional space الـ closed
+
+521
+00:37:57,900 --> 00:38:01,160
+ball is compact أكيد لأن الـ closed ball a closed
+
+522
+00:38:01,160 --> 00:38:06,040
+set abounded و finite dimensional إذا إيش مالها؟
+
+523
+00:38:06,040 --> 00:38:09,880
+compact لكن هذه الخاصية لن تتحقق في ال infinite
+
+524
+00:38:09,880 --> 00:38:13,960
+dimensional space في ال finite dimensional space
+
+525
+00:38:13,960 --> 00:38:18,730
+أي closed unit ball is compactلكن الموضوع بختلف في
+
+526
+00:38:18,730 --> 00:38:23,350
+ال infinite شوف الآن theorem if unknown space X
+
+527
+00:38:23,350 --> 00:38:27,890
+has the property that the closed unit ball M is
+
+528
+00:38:27,890 --> 00:38:32,650
+compact then X is finite dimensionalلاحظ؟ كلام
+
+529
+00:38:32,650 --> 00:38:36,370
+خطير الان إذا كان في ال norm of the space X عندك
+
+530
+00:38:36,370 --> 00:38:40,530
+بتحقق الخاصية في ال .. في ال .. جيت .. أخدتلك norm
+
+531
+00:38:40,530 --> 00:38:44,630
+of the space اسمه X لجيت فيه خاصية انه اي نوع ..
+
+532
+00:38:44,630 --> 00:38:48,010
+اي unit ball .. closed unit ball هذه لجيتها
+
+533
+00:38:48,010 --> 00:38:51,530
+compact على طول و انت مغمض قول عنه ايش هذا finite
+
+534
+00:38:51,530 --> 00:38:55,410
+dimensional space ايش معناته؟ يعني لو كان infinite
+
+535
+00:38:55,410 --> 00:38:58,290
+dimensional مش هتكون اللي هي ال closed unit ball
+
+536
+00:38:58,290 --> 00:39:06,270
+ايش مالها compact طيبSuppose that M is compact but
+
+537
+00:39:06,270 --> 00:39:11,490
+dimension X بساوة Infinity و بدنا نصل إيه؟ لـ
+
+538
+00:39:11,490 --> 00:39:15,470
+Contradiction يعني مستحيل أنه يجتمع أن M is
+
+539
+00:39:15,470 --> 00:39:18,910
+compact و dimension X ملومة لنهاية إذا كانت الـ M
+
+540
+00:39:18,910 --> 00:39:22,010
+close و M compact لازم تكون final dimensional و لو
+
+541
+00:39:22,010 --> 00:39:24,350
+كانت dimension X بساوة Infinity، الـ M مش compact
+
+542
+00:39:24,350 --> 00:39:29,480
+واضح؟ طيبتختار انا X واحد .. شوف كيف الان بده يركب
+
+543
+00:39:29,480 --> 00:39:33,280
+لك تختار انا X واحد الامن X with norm X واحد ايش
+
+544
+00:39:33,280 --> 00:39:39,080
+بساوي واحد بقدر الان هو دائما في الاختصار الانفنت
+
+545
+00:39:39,080 --> 00:39:43,900
+لان في عناصر .. عنصره اسمه Xجسمه على نرمه بطلع
+
+546
+00:39:43,900 --> 00:39:48,620
+نرمه يشماله واحد و بطلع الدوة اذا اذا اختار انا X
+
+547
+00:39:48,620 --> 00:39:52,000
+واحد انا من X with norm ال X واحد بيساوي واحد this
+
+548
+00:39:52,000 --> 00:39:55,620
+X واحد generate a one dimensional space X واحد of
+
+549
+00:39:55,620 --> 00:40:02,680
+X يعني الآن بدي اخد X بيساوي من X واحد هذا ال X
+
+550
+00:40:02,680 --> 00:40:08,600
+واحد هذا اللي هو اللي هو في طبعا الاسباني له
+
+551
+00:40:08,600 --> 00:40:13,380
+الاسباني له كل يعني ال scholars فيههذا ال .. ال ..
+
+552
+00:40:13,380 --> 00:40:16,780
+ال .. ال space اللي هو دايما مش اللي هو مش بساوي
+
+553
+00:40:16,780 --> 00:40:23,140
+بساوي واحد ب .. ب .. ب .. خليني أقول ببساطة أخدت
+
+554
+00:40:23,140 --> 00:40:26,000
+مدام دايما مش ال X بساوي infinity إذا في عناصر مش
+
+555
+00:40:26,000 --> 00:40:31,300
+سفر أخدت واحد من هنا X واحد و .. و .. و .. و من ال
+
+556
+00:40:31,300 --> 00:40:35,180
+X و Normal بساوي واحد الآن كيف Normal بساوي واحد
+
+557
+00:40:35,180 --> 00:40:38,190
+خد أي واحد و جسمه Normal و بطلع واحدوخد اللي هو
+
+558
+00:40:38,190 --> 00:40:41,390
+إيه النتج بيطلع لها x1 element in x وضمه مو بساوي
+
+559
+00:40:41,390 --> 00:40:44,830
+واحد this x1 generates a one dimensional subspace
+
+560
+00:40:44,830 --> 00:40:49,970
+سميه مين؟ x1 of x which is closed وبروبر subspace
+
+561
+00:40:49,970 --> 00:40:53,250
+من مين؟ أكيد لأنه ذاك ال dimension هو infinity
+
+562
+00:40:53,250 --> 00:40:56,790
+وهذا ال dimension له اللي ال x1 إيش ماله؟ بساوي
+
+563
+00:40:56,790 --> 00:41:01,020
+واحد since ال dimension لكسه مش بساوي infinityلأن
+
+564
+00:41:01,020 --> 00:41:04,120
+by raises لمّا .. اطلع لفوق .. by raises لمّا مدام
+
+565
+00:41:04,120 --> 00:41:07,760
+هذا proper subspace close to proper subspace إذن
+
+566
+00:41:07,760 --> 00:41:11,760
+ال raises لمّا تتحقق by raises لمّا there is x2
+
+567
+00:41:11,760 --> 00:41:15,480
+element in x و ال norm لـ x2 بيساوي 1 و المسافة
+
+568
+00:41:15,480 --> 00:41:19,760
+بين x2 نقص x1 أكبر يساوي مين أي θيتا بيداخد مين
+
+569
+00:41:19,760 --> 00:41:25,440
+أنا النص بعد .. بعد ازمكم طيبالان و ال X1 و X2
+
+570
+00:41:25,440 --> 00:41:30,260
+نفسي ايش مالهم بقدر اعمل منهم ايش ماله normed
+
+571
+00:41:30,260 --> 00:41:35,740
+space X2 اه و هيكون subspace من مين؟ من ال X و ال
+
+572
+00:41:35,740 --> 00:41:39,160
+dimension له ايش؟ بساوة 2 يعني هيصير بروبر
+
+573
+00:41:39,160 --> 00:41:44,240
+subspace من مين؟ من X يعني هيكون X2 عبارة عن لسبان
+
+574
+00:41:44,240 --> 00:41:49,400
+لل X1 و X2 ال X1 الأولى و ال X2 اللى جيتها من خلال
+
+575
+00:41:49,400 --> 00:41:55,110
+ال raises لمّا طيبالان by raises لما برضه there
+
+576
+00:41:55,110 --> 00:41:59,570
+exist x3 من x لانه proper subspace with normal x3
+
+577
+00:41:59,570 --> 00:42:05,390
+بسوء واحد and for all x element in x2اللي هو norm
+
+578
+00:42:05,390 --> 00:42:09,910
+الـ X3 عن الـ X أكبر أو ساومين برضه الـ θة اللي
+
+579
+00:42:09,910 --> 00:42:13,810
+بتاخدهاش بالساوية نص يعني طبقت ال raises لمّة كمان
+
+580
+00:42:13,810 --> 00:42:18,710
+مرة بس عالميا على الـ X2 لجيت X3 بحيث بعد الـ X3
+
+581
+00:42:18,710 --> 00:42:23,210
+عن كل عناصرها أكبر أو ساومين نص من ضمنها لإن
+
+582
+00:42:23,210 --> 00:42:29,790
+إسبانها X2 إسبان للـ X1 و X2إذا x3-x1 أكبر شوهو نص
+
+583
+00:42:29,790 --> 00:42:35,210
+و x3-x2 أكبر شوهو إياش نص إذا صار عندي x3-x1 أكبر
+
+584
+00:42:35,210 --> 00:42:39,750
+شوهو نص و x3-x2 أكبر شوهو إياش نص أنا proceeding
+
+585
+00:42:39,750 --> 00:42:43,950
+by induction we obtain a sequence xn of elements
+
+586
+00:42:43,950 --> 00:42:49,430
+xn في ال Mمن الـ M كلهم اللي هي مين الـ M هي الـ
+
+587
+00:42:49,430 --> 00:42:53,950
+span للـ X1 X2 الاخرى such that norm ال XM نقص ال
+
+588
+00:42:53,950 --> 00:42:58,110
+XN أي شماله أكبر أو يسوى نصف البعد بينهم أي شماله
+
+589
+00:42:58,110 --> 00:43:01,990
+أكبر أو يسوى نصف، إذن هذه البعد هناك for all M
+
+590
+00:43:01,990 --> 00:43:06,990
+لاتوا سوى N، hence XN يستحيل يكون لها convergence
+
+591
+00:43:06,990 --> 00:43:12,050
+subsequenceلأن الأبعاد بين كل العناصر ثابتة اللي
+
+592
+00:43:12,050 --> 00:43:16,210
+هي أكبر أو يساوي إيش نص يعني بعيدة عن بعض مستحيل
+
+593
+00:43:16,210 --> 00:43:19,870
+بعد شوية تقولولي والله أجيت العنصرين اللي المسافة
+
+594
+00:43:19,870 --> 00:43:23,550
+بينهم أصغر من نص أو أصغر من ي في الدنيا لأ لأ مدان
+
+595
+00:43:23,550 --> 00:43:27,170
+مافيش إذا X and can't have a convergence
+
+596
+00:43:27,170 --> 00:43:31,360
+subsequence this contradictsThe compactness of M
+
+597
+00:43:31,360 --> 00:43:34,560
+لإنه لجهة Sequence مافيش إلا إشمالها Convergent
+
+598
+00:43:34,560 --> 00:43:38,000
+subsequence Therefore the dimension of X لازم يكون
+
+599
+00:43:38,000 --> 00:43:47,080
+إشماله is finite اللي بعده Theorem let X and Y be
+
+600
+00:43:47,080 --> 00:43:52,000
+metric spaces and خد T من X لعند Y بيكون a
+
+601
+00:43:52,000 --> 00:43:57,550
+continuous mappingالان T T عبارة عن continuous
+
+602
+00:43:57,550 --> 00:44:02,410
+mapping من X لعين مين لعين واحد continuous mapping
+
+603
+00:44:02,410 --> 00:44:08,190
+الآن then the image of a compact subset of T of M
+
+604
+00:44:08,190 --> 00:44:13,030
+under T is compact يعني ال image للكمبكت 6 اشمالها
+
+605
+00:44:13,030 --> 00:44:21,390
+is compact اه الآن شوفعشان أثبت لك في الـ .. بحكي
+
+606
+00:44:21,390 --> 00:44:26,130
+وين أنا في .. اللي هو من metric space X to metric
+
+607
+00:44:26,130 --> 00:44:31,750
+space Y و الـ T is continuous إذا كانت الـ M
+
+608
+00:44:31,750 --> 00:44:34,730
+compact، ده تكون إيش مالها compact؟ يعني ترسل الـ
+
+609
+00:44:34,730 --> 00:44:40,930
+compact إلى compactالآن نشوف كيف let yn yn بيقن
+
+610
+00:44:40,930 --> 00:44:46,290
+الـ sequence in mean in T of M T of M صورة الآن
+
+611
+00:44:46,290 --> 00:44:50,330
+بدّي أجيلك subsequence من هذه conversion في T of M
+
+612
+00:44:50,990 --> 00:44:56,470
+بما إنه اللي هو الـ Yn sequence في الـ T of M إذن
+
+613
+00:44:56,470 --> 00:45:01,290
+هي عبارة عن صور لعناصر وين في الـ M إذا then for
+
+614
+00:45:01,290 --> 00:45:05,910
+any n there exists Xn element in N such that Yn
+
+615
+00:45:05,910 --> 00:45:11,770
+بيساوي بيين TXn الـ Y1 صورة وانصر هنا اسمه TX1 الـ
+
+616
+00:45:11,770 --> 00:45:15,390
+Y2 صورة وانصر هنا اسمه TX2 وين كدا الـ Yn بيساوي
+
+617
+00:45:15,390 --> 00:45:20,090
+TXn صارت الآن الـ Xn عبارة عن sequence وين موجودة
+
+618
+00:45:20,090 --> 00:45:26,050
+في الـ Mلكن M is compact والـ XM موجودة اللي هو في
+
+619
+00:45:26,050 --> 00:45:31,260
+الـ M إذا لازم تحتوي على subsequence منهااللي هي
+
+620
+00:45:31,260 --> 00:45:38,560
+which converges in M إذا صارت ال XNK sub sequence
+
+621
+00:45:38,560 --> 00:45:44,240
+بتروح لمين لل X في وين؟ في ال M وبما أنه T is
+
+622
+00:45:44,240 --> 00:45:49,900
+continuous إذا نقوم تقمتك TXNK اللي هو بتروح لمين؟
+
+623
+00:45:49,900 --> 00:45:55,340
+لل TX وين هتكون ال TX؟ في ال T وفي M إذا صار في
+
+624
+00:45:55,340 --> 00:46:01,340
+عندي sub sequence هذه TXNK من مين؟ من ال YNلأن الـ
+
+625
+00:46:01,340 --> 00:46:06,960
+Yn إيش هي؟ الـ Yn هي عبارة عن الـ TXN لجيت
+
+626
+00:46:06,960 --> 00:46:11,340
+subsequence من هذولة اللي هي subsequence من الـ N
+
+627
+00:46:11,340 --> 00:46:15,440
+راحت للـ TX و الموجودة في الـ T of M صار الآن any
+
+628
+00:46:15,440 --> 00:46:18,520
+sequence Yn في الـ T of M اللي هي subsequence
+
+629
+00:46:18,520 --> 00:46:21,740
+converge برضه في المين في الـ T of M إذا صارت الـ
+
+630
+00:46:21,740 --> 00:46:26,320
+T of M is compact اللي بعدها الكورولر اللي بعدها
+
+631
+00:46:26,320 --> 00:46:32,350
+اطلع لفوقمعنى continuous mapping T of a compact
+
+632
+00:46:32,350 --> 00:46:36,530
+subset M of a metric space X onto R assumes a
+
+633
+00:46:36,530 --> 00:46:40,330
+maximum and a minimum at some point of M هذا إعلان
+
+634
+00:46:40,330 --> 00:46:43,090
+كنا نعلنه للطلاب في الـ Calculus إنه إذا كانت الـ
+
+635
+00:46:43,090 --> 00:46:46,350
+function continuous على closed bounded interval
+
+636
+00:46:46,350 --> 00:46:49,070
+then it attains its maximum and its minimum
+
+637
+00:46:49,070 --> 00:46:54,450
+هلجيتها in general لو كانت T من vectors من .. من
+
+638
+00:46:54,450 --> 00:47:02,540
+.. من metric space لعند R أههترسل اللي هي أو كانت
+
+639
+00:47:02,540 --> 00:47:06,280
+اللي هي a mapping T of a compact subset M of a
+
+640
+00:47:06,280 --> 00:47:09,720
+metric space يعني ايه ده 800 من compact subset
+
+641
+00:47:09,720 --> 00:47:15,640
+يعني T is a continuous on a closed bounded اللي هي
+
+642
+00:47:15,640 --> 00:47:20,460
+6A compact set اسمها في الـ Metric Space The
+
+643
+00:47:20,460 --> 00:47:25,120
+continuous of a continuous function on a compact
+
+644
+00:47:25,120 --> 00:47:29,240
+set must attain its maximum and minimum هم يعني
+
+645
+00:47:29,240 --> 00:47:32,460
+هيكون الآن فيه maximum و فيه minimum و هي موجود في
+
+646
+00:47:32,460 --> 00:47:38,570
+الار موضوع سهل اطلع لفوق اطلعأخر إشي هدى By
+
+647
+00:47:38,570 --> 00:47:42,830
+theorem 2.56 اللي قبل شوية هتطلع الـ T M subset من
+
+648
+00:47:42,830 --> 00:47:47,230
+R و Combact ماشي مادام Combact إذا ن close و إيه
+
+649
+00:47:47,230 --> 00:47:50,550
+إيش؟ Abounded ما هو ال Combact الست إيش معناه؟
+
+650
+00:47:50,550 --> 00:47:55,810
+Closed و Abounded طيب الآن مادام Closed و Abounded
+
+651
+00:47:55,810 --> 00:48:02,190
+إذا صار عندي الـ infimum للـ T of M موجود وين؟ في
+
+652
+00:48:02,190 --> 00:48:09,940
+الـ T of M Closedbounded than الانفمام موجود و
+
+653
+00:48:09,940 --> 00:48:13,400
+closed الانفمام وين حيكون؟ في جواهات الست الماخدين
+
+654
+00:48:13,400 --> 00:48:17,500
+لها الانفمام و ال superman برضه وين حيكون؟ نفس
+
+655
+00:48:17,500 --> 00:48:20,540
+الأشياء حيكون ال superman موجود مذان bounded و هو
+
+656
+00:48:20,540 --> 00:48:25,840
+حيكون مذان closed وين موجود؟ في ال T of Mإذاً then
+
+657
+00:48:25,840 --> 00:48:29,600
+the inverse image of two points consists of points
+
+658
+00:48:29,600 --> 00:48:34,600
+of mean of M الـ infimum لهدي و المحيكون في الـ T
+
+659
+00:48:34,600 --> 00:48:37,920
+of M يعني إيش معناة الـ infimum .. خلّيني أخد
+
+660
+00:48:37,920 --> 00:48:42,340
+واحدة و تانية زيها الـ infimum للـ T of M إيش
+
+661
+00:48:42,340 --> 00:48:46,800
+معناته موجود في الـ T of M؟ يعني هذا عبارة على
+
+662
+00:48:46,800 --> 00:48:52,820
+صورة عنصر اسمه TX موجود في الـ T of M إذاً هذا الـ
+
+663
+00:48:52,820 --> 00:48:58,570
+X وين موجود؟في الـ M اللي عندي معايا؟ إذا صار عندي
+
+664
+00:48:58,570 --> 00:49:04,910
+الـ T of X هو الـ infimum يعني بمعنى آخر صار الـ T
+
+665
+00:49:04,910 --> 00:49:11,650
+of X عند النقطة هذه اللي هنا is the minimum point
+
+666
+00:49:11,650 --> 00:49:15,870
+يعني صار الآن الـ T attains its minimum عند نقطة
+
+667
+00:49:15,870 --> 00:49:21,170
+وين موجودة في الـ M Similarly اللي هو ال supremum
+
+668
+00:49:21,170 --> 00:49:27,220
+موجود للـ T of Mموجود في الـ T of M إذا صار في
+
+669
+00:49:27,220 --> 00:49:32,220
+عنده نقطة اللي هي اسمها T و T مثلا X برا X naught
+
+670
+00:49:32,220 --> 00:49:37,300
+هي اللي بتساوي ال supremum هذه الـ T هي ال maximum
+
+671
+00:49:37,300 --> 00:49:40,380
+عند ال X naught ال maximum إذا برضه ال X naught
+
+672
+00:49:40,380 --> 00:49:44,500
+موجودة في ال M و ال T maximum عندها يعني ال T
+
+673
+00:49:44,500 --> 00:49:49,060
+attains its maximum and its minimum on points in
+
+674
+00:49:49,060 --> 00:49:55,320
+meanان ام وهو المطلوب وهيك ممكن فلسنا اللي هو هذا
+
+675
+00:49:55,320 --> 00:49:58,380
+ال section وإلى لقاء آخر السلام عليكم ورحمة الله
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Iph5MyF7UCE_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Iph5MyF7UCE_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..de537dd3a425c4ab52ec10399ca87db481dc4aa8
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Iph5MyF7UCE_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2261, "start": 5.09, "end": 22.61, "text": "بسم الله الرحمن الرحيم الحمد لله رب العالمين والصلاة والسلام على سيدنا محمد وعلى أهله وصحبه أجمعين هذه هي المحاضرة الرابعة مساق تحليل اقتراني او تحليل دالي لطلب وطالبات الجامعة الإسلامية لطلبة الماجستير", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21542, 2304, 3215, 24976, 3224, 12602, 3555, 18863, 45340, 9957, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 5551, 3224, 43761, 4032, 9381, 5016, 3555, 3224, 5551, 7435, 2304, 3615, 9957, 29538, 39896, 9673, 5016, 46958, 25720, 34892, 16758, 27884, 47524, 995, 4587, 6055, 5016, 20292, 1211, 1975, 38149, 2288, 7649, 1829, 1975, 2407, 6055, 5016, 20292, 1211, 11778, 6027, 1829, 5296, 9566, 46152, 4032, 9566, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 5296, 9566, 46152, 3660, 9673, 26108, 14851, 13546], "avg_logprob": -0.09010922069688446, 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سيدنا", "probability": 0.9905598958333334}, {"start": 9.47, "end": 9.85, "word": " محمد", "probability": 0.98388671875}, {"start": 9.85, "end": 10.09, "word": " وعلى", "probability": 0.8650716145833334}, {"start": 10.09, "end": 10.37, "word": " أهله", "probability": 0.921875}, {"start": 10.37, "end": 10.89, "word": " وصحبه", "probability": 0.95693359375}, {"start": 10.89, "end": 11.41, "word": " أجمعين", "probability": 0.98173828125}, {"start": 11.41, "end": 12.11, "word": " هذه", "probability": 0.8896484375}, {"start": 12.11, "end": 12.33, "word": " هي", "probability": 0.46630859375}, {"start": 12.33, "end": 13.09, "word": " المحاضرة", "probability": 0.9840087890625}, {"start": 13.09, "end": 13.91, "word": " الرابعة", "probability": 0.9651692708333334}, {"start": 13.91, "end": 14.49, "word": " مساق", "probability": 0.90673828125}, {"start": 14.49, "end": 14.99, "word": " تحليل", "probability": 0.9847412109375}, {"start": 14.99, "end": 15.73, "word": " اقتراني", "probability": 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بدنا نكمل اليوم اللي حكيناه اللي بدناه المرة الماضية وحكينا عن الاتصال أيضا ووصلنا لعند التعريف اللي هو 113 الان بدنا نعرف حاجة اسمها ال closure وقبل هنعرف حاجة اسمها ال accumulation point", "tokens": [7649, 13412, 16606, 21984, 8032, 1863, 24793, 1211, 13672, 1829, 47525, 8315, 3224, 9673, 5016, 46958, 25720, 34892, 4587, 2304, 6055, 1211, 9307, 3660, 9673, 25720, 9673, 46958, 10632, 9122, 8315, 11331, 995, 4117, 9957, 18871, 2423, 1269, 6352, 4032, 3615, 23942, 13672, 1829, 31439, 2423, 7630, 4032, 3615, 23942, 13672, 1829, 31439, 2423, 5395, 6352, 6156, 6027, 7649, 47525, 8315, 8717, 24793, 1211, 45595, 20498, 13672, 1829, 11331, 4117, 1829, 8315, 3224, 13672, 1829, 47525, 8315, 3224, 9673, 25720, 9673, 46958, 10632, 4032, 5016, 4117, 1829, 8315, 18871, 2423, 9307, 9381, 6027, 36632, 11242, 995, 4032, 2407, 36520, 8315, 5296, 3615, 41260, 16712, 3615, 16572, 5172, 13672, 1829, 31439, 2975, 18, 2423, 7649, 47525, 8315, 8717, 3615, 28480, 11331, 26108, 3660, 24525, 2304, 11296, 2423, 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{"start": 44.98, "end": 46.12, "word": " 113", "probability": 0.523681640625}, {"start": 46.12, "end": 47.32, "word": " الان", "probability": 0.65185546875}, {"start": 47.32, "end": 47.56, "word": " بدنا", "probability": 0.94189453125}, {"start": 47.56, "end": 47.92, "word": " نعرف", "probability": 0.9641927083333334}, {"start": 47.92, "end": 48.3, "word": " حاجة", "probability": 0.9899088541666666}, {"start": 48.3, "end": 48.72, "word": " اسمها", "probability": 0.9635416666666666}, {"start": 48.72, "end": 48.9, "word": " ال", "probability": 0.8701171875}, {"start": 48.9, "end": 49.32, "word": " closure", "probability": 0.8583984375}, {"start": 49.32, "end": 50.1, "word": " وقبل", "probability": 0.904296875}, {"start": 50.1, "end": 50.66, "word": " هنعرف", "probability": 0.73822021484375}, {"start": 50.66, "end": 50.98, "word": " حاجة", "probability": 0.9879557291666666}, {"start": 50.98, "end": 51.34, "word": " اسمها", "probability": 0.9052734375}, {"start": 51.34, "end": 51.48, 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"end": 83.03, "word": " countable", "probability": 0.949951171875}, {"start": 83.03, "end": 83.59, "word": " subset", "probability": 0.9189453125}, {"start": 83.59, "end": 84.25, "word": " which", "probability": 0.89013671875}, {"start": 84.25, "end": 84.63, "word": " is", "probability": 0.9560546875}, {"start": 84.63, "end": 85.03, "word": " dense", "probability": 0.94921875}, {"start": 85.03, "end": 85.33, "word": " in", "probability": 0.921875}, {"start": 85.33, "end": 85.75, "word": " main", "probability": 0.71435546875}, {"start": 85.75, "end": 86.21, "word": " M", "probability": 0.73193359375}, {"start": 86.21, "end": 86.45, "word": " X", "probability": 0.7666015625}, {"start": 86.45, "end": 86.63, "word": " إذا", "probability": 0.5472412109375}, {"start": 86.63, "end": 86.81, "word": " في", "probability": 0.580078125}, {"start": 86.81, "end": 87.11, "word": " عندى", "probability": 0.5914306640625}, {"start": 87.11, "end": 87.71, "word": " مفهومين", "probability": 0.9384765625}, {"start": 87.71, "end": 88.57, "word": " المفهوم", "probability": 0.9560546875}, {"start": 88.57, "end": 89.01, "word": " الأول", "probability": 0.983154296875}, {"start": 89.01, "end": 89.27, "word": " أنه", "probability": 0.652099609375}, {"start": 89.27, "end": 89.63, "word": " بنقول", "probability": 0.58050537109375}, {"start": 89.63, "end": 90.09, "word": " M", "probability": 0.841796875}, {"start": 90.09, "end": 91.39, "word": " dense", "probability": 0.7841796875}], "temperature": 1.0}, {"id": 5, "seek": 11887, "start": 92.27, "end": 118.87, "text": "fix معناته الام مقلوجر لها بساوي مين بساوي كل x هذا ما هو معناته اللي هو اللي هي dense اللي أنا بقول عن ال space x نفسه انه separable إذا كدرنا نلاقي subset منه countable اللي هو و تكون هذه countable اللي مقلوجر لها إيش بساوي بساوي ال x فهذا الحالة بنسمي اللي هو ال space هذا إيش ماله is a separable إيش", "tokens": [69, 970, 3714, 3615, 8315, 47395, 2423, 10943, 3714, 4587, 1211, 29245, 2288, 5296, 11296, 4724, 3794, 995, 45865, 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"end": 821.2, "text": "المثال الأول هو هذا يعني باعتبار معلومة ان انت بتعرفوها", "tokens": [6027, 2304, 12984, 6027, 16247, 12610, 31439, 23758, 37495, 22653, 4724, 995, 34268, 3555, 9640, 20449, 1211, 20498, 3660, 16472, 16472, 2655, 39894, 3615, 28480, 2407, 11296], "avg_logprob": -0.3325892814568111, "compression_ratio": 1.2784810126582278, "no_speech_prob": 1.3232231140136719e-05, "words": [{"start": 816.54, "end": 817.38, "word": "المثال", "probability": 0.568084716796875}, {"start": 817.38, "end": 817.62, "word": " الأول", "probability": 0.884765625}, {"start": 817.62, "end": 817.88, "word": " هو", "probability": 0.5556640625}, {"start": 817.88, "end": 818.1, "word": " هذا", "probability": 0.53076171875}, {"start": 818.1, "end": 818.68, "word": " يعني", "probability": 0.7626953125}, {"start": 818.68, "end": 819.28, "word": " باعتبار", "probability": 0.9361328125}, {"start": 819.28, "end": 820.28, "word": " معلومة", "probability": 0.9552001953125}, {"start": 820.28, "end": 820.42, "word": " ان", "probability": 0.375}, {"start": 820.42, "end": 820.46, "word": " انت", "probability": 0.668701171875}, {"start": 820.46, "end": 821.2, "word": " بتعرفوها", "probability": 0.845556640625}], "temperature": 1.0}, {"id": 37, "seek": 84910, "start": 823.16, "end": 849.1, "text": "لأنه ذكرتها قبل ما أبدأ أسجل خلّيني أقولكم إياها الآن عندي اللي هو the real line R إيش ماله is اللي هو separable ليش separable لإن أنا ده عارف من زمان يعني من تحليل واحد إنه ال Q count بال 6 وهي dense in من R الكلوجر لها إيش بساوي بساوي اللي هو من R", "tokens": [1211, 33456, 3224, 29910, 37983, 2655, 11296, 12174, 36150, 19446, 5551, 44510, 10721, 5551, 3794, 7435, 1211, 16490, 1211, 11703, 9957, 1829, 5551, 39648, 24793, 11933, 25528, 11296, 6024, 48506, 18871, 16254, 13672, 1829, 31439, 264, 957, 1622, 497, 11933, 1829, 8592, 3714, 6027, 3224, 307, 13672, 1829, 31439, 3128, 712, 32239, 8592, 3128, 712, 5296, 28814, 1863, 41850, 11778, 3224, 6225, 9640, 5172, 9154, 30767, 2304, 7649, 37495, 22653, 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أقولكم", "probability": 0.768798828125}, {"start": 826.34, "end": 826.62, "word": " إياها", "probability": 0.90234375}, {"start": 826.62, "end": 827.02, "word": " الآن", "probability": 0.73779296875}, {"start": 827.02, "end": 828.36, "word": " عندي", "probability": 0.78955078125}, {"start": 828.36, "end": 829.02, "word": " اللي", "probability": 0.923095703125}, {"start": 829.02, "end": 829.36, "word": " هو", "probability": 0.9873046875}, {"start": 829.36, "end": 829.88, "word": " the", "probability": 0.482421875}, {"start": 829.88, "end": 830.16, "word": " real", "probability": 0.953125}, {"start": 830.16, "end": 830.48, "word": " line", "probability": 0.9599609375}, {"start": 830.48, "end": 830.74, "word": " R", "probability": 0.79248046875}, {"start": 830.74, "end": 831.0, "word": " إيش", "probability": 0.7908528645833334}, {"start": 831.0, "end": 831.48, "word": " ماله", "probability": 0.892578125}, {"start": 831.48, "end": 832.7, "word": " is", "probability": 0.3671875}, {"start": 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837.32, "word": " من", "probability": 0.9326171875}, {"start": 837.32, "end": 838.16, "word": " تحليل", "probability": 0.9503173828125}, {"start": 838.16, "end": 838.5, "word": " واحد", "probability": 0.9931640625}, {"start": 838.5, "end": 838.88, "word": " إنه", "probability": 0.4864501953125}, {"start": 838.88, "end": 839.02, "word": " ال", "probability": 0.86083984375}, {"start": 839.02, "end": 839.48, "word": " Q", "probability": 0.432861328125}, {"start": 839.48, "end": 840.94, "word": " count", "probability": 0.83642578125}, {"start": 840.94, "end": 841.24, "word": " بال", "probability": 0.64794921875}, {"start": 841.24, "end": 841.6, "word": " 6", "probability": 0.43994140625}, {"start": 841.6, "end": 843.18, "word": " وهي", "probability": 0.6956380208333334}, {"start": 843.18, "end": 843.66, "word": " dense", "probability": 0.80859375}, {"start": 843.66, "end": 844.02, "word": " in", "probability": 0.6083984375}, {"start": 844.02, "end": 844.36, "word": " من", "probability": 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نقعد نحكي فيه كمان مرة اللي هذاك اللي بيضل معاكم اللي هو exercise ال Q closure ايش بيساوي بيساوي R و Q is countable اذا صار عند ال R عبارة عن اللي هي separable space اللي زي يمين", "tokens": [2407, 23032, 3555, 3615, 995, 23758, 2423, 28820, 10943, 1975, 12984, 3555, 2655, 8315, 3224, 37495, 22653, 4032, 3714, 12984, 3555, 2655, 8978, 6055, 5016, 20292, 1211, 36764, 24401, 6055, 3555, 3615, 2423, 25947, 311, 6156, 15042, 41185, 8592, 11778, 45761, 1829, 5296, 8315, 8717, 4587, 22488, 8717, 5016, 4117, 1829, 8978, 3224, 9122, 2304, 7649, 3714, 25720, 13672, 1829, 8032, 8848, 995, 4117, 13672, 1829, 4724, 1829, 11242, 1211, 20449, 995, 24793, 13672, 1829, 31439, 5380, 2423, 1249, 24653, 1975, 1829, 8592, 4724, 1829, 3794, 995, 45865, 4724, 1829, 3794, 995, 45865, 497, 4032, 1249, 307, 1207, 712, 1975, 15730, 20328, 9640, 43242, 2423, 497, 6225, 3555, 9640, 3660, 18871, 13672, 1829, 39896, 3128, 712, 1901, 13672, 1829, 30767, 1829, 7251, 2304, 9957], "avg_logprob": -0.22287499809265138, 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بديه بزغره جد ما بدي بيصير عندي أصغر برضه من مين من يبسلون بيه على مين على اتنين إذا صار في عندي أمرين هاي الأمر الأول", "tokens": [39974, 300, 13672, 1829, 31439, 36145, 11296, 39894, 5016, 4587, 4587, 36145, 3224, 2031, 1718, 8717, 995, 4587, 9381, 46810, 5551, 3794, 4724, 1829, 9154, 10874, 1829, 3224, 9154, 36764, 24401, 30731, 3714, 6027, 3224, 8717, 11296, 10632, 5551, 9381, 17082, 2288, 9154, 3714, 9957, 9154, 36632, 6225, 3215, 3215, 8978, 32748, 22653, 995, 4724, 16254, 3224, 4724, 11622, 17082, 2288, 3224, 10874, 3215, 19446, 4724, 16254, 4724, 1829, 9381, 13546, 18871, 16254, 5551, 9381, 17082, 2288, 4724, 43042, 3224, 9154, 3714, 9957, 9154, 7251, 3555, 3794, 1211, 11536, 4724, 1829, 3224, 15844, 3714, 9957, 15844, 1975, 2655, 1863, 9957, 11933, 15730, 20328, 9640, 8978, 18871, 16254, 5551, 29973, 9957, 8032, 47302, 16247, 29973, 16247, 12610], "avg_logprob": -0.22809829569270468, "compression_ratio": 1.8465116279069766, "no_speech_prob": 1.627206802368164e-05, "words": 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"لاحظوا أن أي XY مختلفة هيكون اللي هو بلاج بول حوالينها دي و بول حوالينها دي أشمالهم disjoint نكمل القصة، شوف إيش اللي بدهوا إياه يا عزيزي hence we have uncountable number of balls that are not intersect", "tokens": [1211, 39319, 19913, 14407, 14739, 36632, 48826, 3714, 46456, 46538, 3660, 39896, 30544, 13672, 1829, 31439, 4724, 1211, 26108, 4724, 12610, 11331, 2407, 6027, 9957, 11296, 11778, 1829, 4032, 4724, 12610, 11331, 2407, 6027, 9957, 11296, 11778, 1829, 5551, 8592, 2304, 6027, 16095, 717, 48613, 8717, 24793, 1211, 25062, 9381, 3660, 12399, 13412, 38688, 11933, 1829, 8592, 13672, 1829, 47525, 3224, 14407, 11933, 25528, 3224, 35186, 6225, 11622, 1829, 11622, 1829, 16678, 321, 362, 6219, 792, 712, 1230, 295, 9803, 300, 366, 406, 27815], "avg_logprob": -0.3441176596809836, "compression_ratio": 1.463768115942029, "no_speech_prob": 9.5367431640625e-06, "words": [{"start": 2947.08, "end": 2947.82, "word": "لاحظوا", "probability": 0.735595703125}, {"start": 2947.82, "end": 2948.52, 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" في", "probability": 0.88134765625}, {"start": 3021.99, "end": 3022.37, "word": " الام", "probability": 0.5572509765625}, {"start": 3022.37, "end": 3022.65, "word": " إيش", "probability": 0.7427571614583334}, {"start": 3022.65, "end": 3022.91, "word": " فيه", "probability": 0.738525390625}, {"start": 3022.91, "end": 3023.13, "word": " عندي", "probability": 0.6324462890625}, {"start": 3023.13, "end": 3024.05, "word": " uncountable", "probability": 0.7615559895833334}, {"start": 3024.05, "end": 3024.39, "word": " number", "probability": 0.96484375}, {"start": 3024.39, "end": 3024.65, "word": " of", "probability": 0.9755859375}, {"start": 3024.65, "end": 3025.11, "word": " points", "probability": 0.95166015625}], "temperature": 1.0}, {"id": 135, "seek": 304460, "start": 3025.92, "end": 3044.6, "text": "إذا بدأت بم dense ووصلت مدامة م dense إذا تحتوي on countable number of elements إذا هذا بيقول لي إنه there is no countable dense subset من ال L infinity ومعناته إن ال V is not separable", 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Iph5MyF7UCE_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Iph5MyF7UCE_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..84e9982674575be3f81679cc6a8c09dc731201fb
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Iph5MyF7UCE_raw.srt
@@ -0,0 +1,2580 @@
+1
+00:00:05,090 --> 00:00:07,870
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,870 --> 00:00:10,890
+والصلاة والسلام على سيدنا محمد وعلى أهله وصحبه
+
+3
+00:00:10,890 --> 00:00:15,730
+أجمعين هذه هي المحاضرة الرابعة مساق تحليل اقتراني
+
+4
+00:00:15,730 --> 00:00:21,930
+او تحليل دالي لطلب وطالبات الجامعة الإسلامية لطلبة
+
+5
+00:00:21,930 --> 00:00:27,220
+الماجستيران شاء الله هنكمل اللي بدناه المحاضرة
+
+6
+00:00:27,220 --> 00:00:30,940
+الرقم تلاتة المرة الماضية كنا حاكين عن ال open
+
+7
+00:00:30,940 --> 00:00:35,980
+sets وعلى اللي هو ال neighborhood وعلى اللي هو ال
+
+8
+00:00:35,980 --> 00:00:39,140
+closed sets فالان بدنا نكمل اليوم اللي حكيناه اللي
+
+9
+00:00:39,140 --> 00:00:43,420
+بدناه المرة الماضية وحكينا عن الاتصال أيضا ووصلنا
+
+10
+00:00:43,420 --> 00:00:48,720
+لعند التعريف اللي هو 113 الان بدنا نعرف حاجة اسمها
+
+11
+00:00:48,720 --> 00:00:51,840
+ال closure وقبل هنعرف حاجة اسمها ال accumulation
+
+12
+00:00:51,840 --> 00:00:56,740
+pointأو الـ Limit Points أو اللي هي الـ Cluster
+
+13
+00:00:56,740 --> 00:01:01,020
+Points كلها نفس المفهوم اللي هي نقطة الإلتصاق أو
+
+14
+00:01:01,020 --> 00:01:04,980
+نقطة التجميع A subset M of a metric space X is
+
+15
+00:01:04,980 --> 00:01:10,540
+said to be dense in X بنقول أنه اللي هو الـ M هذه
+
+16
+00:01:10,540 --> 00:01:13,500
+اللي هي subset من X إنها تتمتع بخاصية الكثافة
+
+17
+00:01:13,500 --> 00:01:17,800
+dense in X if اللي هو الـ M closure أيش بيساوي؟
+
+18
+00:01:17,800 --> 00:01:22,470
+بيساوي Xالأن X is said to be separable if it has a
+
+19
+00:01:22,470 --> 00:01:26,810
+countable subset which is dense in main M X إذا في
+
+20
+00:01:26,810 --> 00:01:32,890
+عندى مفهومين المفهوم الأول أنه بنقول M densefix
+
+21
+00:01:32,890 --> 00:01:37,990
+معناته الام مقلوجر لها بساوي مين بساوي كل x هذا ما
+
+22
+00:01:37,990 --> 00:01:42,010
+هو معناته اللي هو اللي هي dense اللي أنا بقول عن
+
+23
+00:01:42,010 --> 00:01:46,870
+ال space x نفسه انه separable إذا كدرنا نلاقي
+
+24
+00:01:46,870 --> 00:01:51,210
+subset منه countable اللي هو و تكون هذه countable
+
+25
+00:01:51,210 --> 00:01:54,130
+اللي مقلوجر لها إيش بساوي بساوي ال x فهذا الحالة
+
+26
+00:01:54,130 --> 00:01:58,250
+بنسمي اللي هو ال space هذا إيش ماله is a separable
+
+27
+00:01:58,250 --> 00:02:03,880
+إيشاللي هو is inseparable الـ space لأن شو معناه M
+
+28
+00:02:03,880 --> 00:02:07,060
+closure إيش أمعنى M closure اللي بدو يزوّبنا عليه
+
+29
+00:02:07,060 --> 00:02:11,340
+اللي هو التعريف اللي جابله اللي هو تلاتة تسعة واحد
+
+30
+00:02:11,340 --> 00:02:14,540
+تلاتة تسعة لت M لإنه ماحكينا عن الشيء برضه المرة
+
+31
+00:02:14,540 --> 00:02:19,380
+الماضية لت M بيقصب situometric space X منقول X0
+
+32
+00:02:19,380 --> 00:02:23,020
+المتين X is called an accumulation point اللي هي
+
+33
+00:02:23,020 --> 00:02:28,200
+نقطة تجميع أو cluster point أو limit pointof M إذا
+
+34
+00:02:28,200 --> 00:02:32,500
+كان every neighborhood M of X0 of X0 اللي هو لو
+
+35
+00:02:32,500 --> 00:02:36,220
+شيلته من ال X0 تقاطع ال M أيش ماله؟ اللي هو يساوي
+
+36
+00:02:36,220 --> 00:02:43,990
+Phi إذا اللي بنقوله بالظبط هنا لو أجيناأخدنا X0 في
+
+37
+00:02:43,990 --> 00:02:49,050
+الـ X بنقول عن هذه الـ X0 إنها accumulation point
+
+38
+00:02:49,050 --> 00:02:54,590
+أو نقطة تجميع للـ X وكانت هذه الـ X مثلا وهي X0
+
+39
+00:02:54,590 --> 00:02:57,790
+فيها بنقول إنها X0 is accumulation point أو limit
+
+40
+00:02:57,790 --> 00:03:01,010
+point أو cluster point إذا كان إيدينا أخدنا أي
+
+41
+00:03:01,010 --> 00:03:05,410
+جوار حواليها أو بنوب عنه بأي open ball حواليها
+
+42
+00:03:05,410 --> 00:03:10,830
+اللي هو تكون هذه ال open ball تحتوي من إيه؟ من X
+
+43
+00:03:10,830 --> 00:03:15,080
+يعني ال open ball هذهمع الـ X Note لأي نصف خطر Y
+
+44
+00:03:15,080 --> 00:03:20,980
+شيلوا منه الـ X Note تقاطع الـ M إيش ماله؟ لا
+
+45
+00:03:20,980 --> 00:03:24,420
+يساوي إيش؟ لا يساوي Phi الـ M أي إن كانت اللي هي
+
+46
+00:03:24,420 --> 00:03:29,700
+الـ M اللي هي ثابتة من Xإذا الـ X node هي عبارة عن
+
+47
+00:03:29,700 --> 00:03:35,540
+accumulation point للـ M إذا بنقدر اللي هو أي أي
+
+48
+00:03:35,540 --> 00:03:39,140
+neighborhood أو أي اللي هو open ball حوالين الـ X
+
+49
+00:03:39,140 --> 00:03:45,680
+node فقاطع الـ M على الأقل بيكون المقطة مين اللي
+
+50
+00:03:45,680 --> 00:03:48,940
+هو X node كمان مقطة يعني بمعنى أخر لو شيلت ال X
+
+51
+00:03:48,940 --> 00:03:53,180
+node تقاطع ال M أشمله لا يساوي 5 هذا معناته اللي
+
+52
+00:03:53,180 --> 00:03:58,170
+هواللي هي انه x not عبارة عن accumulation point
+
+53
+00:03:58,170 --> 00:04:05,550
+لمن لاللي هي ال set M الان ال closure لل M هو
+
+54
+00:04:05,550 --> 00:04:10,570
+عبارة عن is the set consisting of M مع مين ماهي ال
+
+55
+00:04:10,570 --> 00:04:13,990
+accumulation points إلها إذا ال M من الآن وطالع
+
+56
+00:04:13,990 --> 00:04:19,050
+بدنا نعرفها M closure بتساوي M اتحاد مجموعة ال
+
+57
+00:04:19,050 --> 00:04:22,150
+limit points او ال accumulation points اللي عادة
+
+58
+00:04:22,150 --> 00:04:28,520
+الناس برمزولها بMإبراهيم إذا الست المتكونة من M مع
+
+59
+00:04:28,520 --> 00:04:30,700
+ال limit points لها هي اللي بنسميها إيش معناه يا
+
+60
+00:04:30,700 --> 00:04:38,340
+جماعة؟ بنسميها اللي هي ال closure للـ Mملاحظة لإن
+
+61
+00:04:38,340 --> 00:04:42,040
+احنا نستخدمها P of X0 و R الـ closure هذه إلها
+
+62
+00:04:42,040 --> 00:04:46,580
+عارفينها P of X0 و R need not equal to P of X0 و
+
+63
+00:04:46,580 --> 00:04:51,460
+مين و R الآن P تلدة of X0 و R يعني اللي بيقول اللي
+
+64
+00:04:51,460 --> 00:04:57,240
+بيقوله اللي بيقوله إنه قد
+
+65
+00:04:57,240 --> 00:05:02,100
+يتمدى إلى الذهب للبعض إنه لو أجينا أخدنا ال P تلدة
+
+66
+00:05:03,480 --> 00:05:08,960
+of X0 OR الـ B تلد هي إيش هذه الـ closed ball
+
+67
+00:05:08,960 --> 00:05:14,960
+مظبوط قد يتبادل لديهم ويقول لك إن هي نفسهاالبول
+
+68
+00:05:14,960 --> 00:05:18,340
+للـ X note وR ال open ball بس ناخده ماهي إيش ال
+
+69
+00:05:18,340 --> 00:05:22,520
+closure هذا الكلام ممكن يظبط في الـR في الـR وفي
+
+70
+00:05:22,520 --> 00:05:26,080
+الـR تربيع وفي الـR كده لكن in general need not to
+
+71
+00:05:26,080 --> 00:05:29,200
+be true in general يعني هذا الكلام في صورة عامة
+
+72
+00:05:29,200 --> 00:05:34,160
+إيش ماله ليس صحيحا وماخدلك مثال ماخدلك مثال أكيد
+
+73
+00:05:34,160 --> 00:05:36,580
+اللي هو المثال المشهور اللي هو بظله حياته اللي هو
+
+74
+00:05:36,580 --> 00:05:38,840
+discrete metric SBS
+
+75
+00:05:44,530 --> 00:05:50,090
+لو انت اجيت اخدت اللي هو X عبارة عن ال discrete
+
+76
+00:05:50,090 --> 00:05:57,890
+metric space ماشي الحال لو اجيت اخدت ال ball اللي
+
+77
+00:05:57,890 --> 00:06:05,810
+ب X نوت و R ب X نوت و R هذه ال ball اللي لان هي
+
+78
+00:06:05,810 --> 00:06:11,070
+عبارة عن كل ال R ايش بتاخدها انتوا متذكرين ايش ال
+
+79
+00:06:11,070 --> 00:06:15,000
+metric اللي عليها يا واحد يا ايشبتاخد الحرفة اللي
+
+80
+00:06:15,000 --> 00:06:20,000
+هو مين بتاخد اللي هو إيش بتساوي واحد ال ball هذه
+
+81
+00:06:20,000 --> 00:06:23,300
+اللي عبارة عن فيه عارفين إيش تعرف هي عبارة عن كل
+
+82
+00:06:23,300 --> 00:06:27,920
+ال Xات اللي في ال X حيث المسافة بين X note و X
+
+83
+00:06:27,920 --> 00:06:32,280
+بتكون أصغر من مين من واحد و المصفات عارفين احنا يا
+
+84
+00:06:32,280 --> 00:06:34,900
+واحد يا سفر بدنا أصغر من واحد دلوقتي بس بيظل عندنا
+
+85
+00:06:34,900 --> 00:06:39,600
+مين السفر يعني مين بيظل هذه بس فيهاالمقطة X0 لأن
+
+86
+00:06:39,600 --> 00:06:41,900
+لا يوجد أحد يبدأ بالـ X0 نفسه لغاية السفر اللي هي
+
+87
+00:06:41,900 --> 00:06:47,420
+X0 نفسها إذاً هذا اللي هو الـ ball للـ X0 بواحد
+
+88
+00:06:47,420 --> 00:06:52,800
+إيش بساوي اللي هو المقطة Singleton X0 الآن الـ
+
+89
+00:06:52,800 --> 00:06:59,500
+closure له اللي هو عبارة عن الـ closure لهذه هيطلع
+
+90
+00:06:59,500 --> 00:07:05,730
+نفس المقطة X0 لأنه في الـ discrete metric spaceكل
+
+91
+00:07:05,730 --> 00:07:12,510
+set موجودة closed و open وبرهانها
+
+92
+00:07:12,510 --> 00:07:16,150
+سهل حتى المرة الماضية احنا حكينا على انه كيف
+
+93
+00:07:16,150 --> 00:07:21,270
+نبرهنها بتبقى معاكم هذه الهمورك مش صعبة سهل يعني
+
+94
+00:07:21,630 --> 00:07:26,530
+فبيبقى عنده الـ closure لكلوة الست إيش بيطلع الست
+
+95
+00:07:26,530 --> 00:07:30,550
+نفسها إذا اللي هو في هذه الحالة بتطلع البون اللي
+
+96
+00:07:30,550 --> 00:07:34,570
+أمامي اللي هي ال closure إليها إيش بيطلع ال
+
+97
+00:07:34,570 --> 00:07:40,610
+singleton it's notبينما .. بينما .. لو جيت أخدت
+
+98
+00:07:40,610 --> 00:07:46,390
+انت الآن الـ B تلدة الـ B تلدة لل X نقطه A واحد
+
+99
+00:07:46,390 --> 00:07:50,870
+ايش تعريف عرفناه المرة الماضية؟ هي عبارة عن كل
+
+100
+00:07:50,870 --> 00:07:58,730
+النقاط X في الـ Xحيث المسافة بين X و X not أصغر أو
+
+101
+00:07:58,730 --> 00:08:02,730
+يساوي واحد أصغر أو يساوي واحد معناته أشمالنا جدنا
+
+102
+00:08:02,730 --> 00:08:07,970
+كل الست لأن المسافة تانية ياسفر يمين يواحد فبتطلع
+
+103
+00:08:07,970 --> 00:08:12,980
+عند كل الست مين Xفلو احنا من البداية أخدنا الـ X
+
+104
+00:08:12,980 --> 00:08:17,960
+بتحتوي على أكثر من عنصر فبصير قطعاً قطعاً قطعاً
+
+105
+00:08:17,960 --> 00:08:21,140
+اللي هي الـ P X not واحد اللي هي هذه بتطلع ال
+
+106
+00:08:21,140 --> 00:08:25,720
+singleton لا تساومين ال X اللي فيها عنصرين فبتكون
+
+107
+00:08:25,720 --> 00:08:31,900
+عندي هذا مثال على اللي هو metric space بيكون عندي
+
+108
+00:08:31,900 --> 00:08:37,420
+ال closed ball need not to equal to the closure of
+
+109
+00:08:37,420 --> 00:08:46,370
+the open ball واضح؟5 then
+
+110
+00:08:47,340 --> 00:08:51,060
+إذا عرفنا إيش معنات accumulation point أو limit
+
+111
+00:08:51,060 --> 00:08:55,960
+point أو cluster point منه عرفنا ال closure منه
+
+112
+00:08:55,960 --> 00:09:01,020
+عرفنا اللي هو ال dense شو معناته dense اللي هو
+
+113
+00:09:01,020 --> 00:09:04,500
+عرفنا منه اللي هو شو معناته separable و separable
+
+114
+00:09:04,500 --> 00:09:07,940
+قولنا انه countable dense subset تكون موجودة في ال
+
+115
+00:09:07,940 --> 00:09:12,520
+space فبكون عندي ال space ال separable ناخد أمثلة
+
+116
+00:09:12,520 --> 00:09:19,330
+الآن المثال الأولبس في ملاحظة هنا عندنا قبل المثال
+
+117
+00:09:19,330 --> 00:09:24,010
+الأول بيقول لي M is dense if and only if every
+
+118
+00:09:24,010 --> 00:09:31,330
+ball in X will contains points of mean of M ده نجف
+
+119
+00:09:31,330 --> 00:09:41,090
+عند هذا الملاحظة شوية الان
+
+120
+00:09:41,090 --> 00:09:48,080
+M is dense أيش معناتها؟اللي هو معناته تكافئ أن الـ
+
+121
+00:09:48,080 --> 00:09:53,440
+M closure إيش بيساوي بيساوي X هذا بيقول لي if and
+
+122
+00:09:53,440 --> 00:09:58,640
+only if if and only if أي open ball أي open ball
+
+123
+00:09:58,640 --> 00:10:07,340
+بيكس وإبسلون اللي هي تقاطع الـ M لا يساوي إيش لا
+
+124
+00:10:07,340 --> 00:10:09,220
+يساوي Phi ماشي الحال
+
+125
+00:10:13,710 --> 00:10:20,530
+لو كانت الـ M closure بيساوي X في عندي بالنسبة
+
+126
+00:10:20,530 --> 00:10:25,570
+لهذه حالتين الحال الأولى أعطيكم وانت على الكلام مش
+
+127
+00:10:25,570 --> 00:10:32,770
+صعب الحال الأولى ان X not في الـ M و X not ايش
+
+128
+00:10:32,770 --> 00:10:35,830
+مالها برّت لها بهذه الحالتين اللي ممكن تحدث لها لل
+
+129
+00:10:35,830 --> 00:10:42,800
+X ماشي الحال الان لو X not في الـ Mقطعاً هيكون BND
+
+130
+00:10:42,800 --> 00:10:46,760
+بي X وY فقطع ال M إيه إيه إيه إيه إيه إيه إيه إيه
+
+131
+00:10:46,760 --> 00:10:48,080
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+132
+00:10:48,080 --> 00:10:48,200
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+133
+00:10:48,200 --> 00:10:55,340
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+134
+00:10:55,340 --> 00:10:55,720
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+135
+00:10:55,720 --> 00:11:08,940
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+136
+00:11:08,940 --> 00:11:13,620
+إأي neighborhood و أي ball حوالين الـ X و الـ Y و
+
+137
+00:11:13,620 --> 00:11:19,500
+الـ X note اللي أخدتها و الـ Y تقاطع الـ M برضه مش
+
+138
+00:11:19,500 --> 00:11:23,720
+هيسوي فعي لأنه من التعريف اللي قلناه قبل شوية اللي
+
+139
+00:11:23,720 --> 00:11:25,640
+هو شيلوا منه ال X note
+
+140
+00:11:29,190 --> 00:11:32,870
+وقطعوها معاها بيظل لا يساوي فيه طب هي الاصلة من
+
+141
+00:11:32,870 --> 00:11:35,370
+الـ X نوت مش بروحة الام مش في الأمن مش هي اللي في
+
+142
+00:11:35,370 --> 00:11:39,290
+الطيارات دا فبيظل أش ماله في عندي أش فقطحها لا
+
+143
+00:11:39,290 --> 00:11:43,010
+يساوي من أمنه إيش تعريفنا بيقول إيش تعريف اللي هو
+
+144
+00:11:43,010 --> 00:11:47,590
+limit point هي فوق يا جماعة مالكم فوق إن ال
+
+145
+00:11:47,590 --> 00:11:50,310
+neighbor هتشيله ال X نوت وقطعوه مع الام إيش ماله
+
+146
+00:11:50,310 --> 00:11:56,940
+يساوي فيه مدام إحنا الآنمدام اكس نوت مش في الام
+
+147
+00:11:56,940 --> 00:12:00,420
+اذا زي ما قولنا اكس نوت موجودة في الام برايل
+
+148
+00:12:00,420 --> 00:12:03,460
+المدام limit point مدام limit point اذا اي
+
+149
+00:12:03,460 --> 00:12:08,360
+neighborhood او اي وابن بول هذي شيل منها ال اكس
+
+150
+00:12:08,360 --> 00:12:12,380
+نوت وخطعها مع الام اشمالها مش هيساوي فارقة حسب
+
+151
+00:12:12,380 --> 00:12:16,660
+التعريف طب ما هي هذي مش فارقة معها لان اصلا ان
+
+152
+00:12:16,660 --> 00:12:23,160
+عندي الاملأن في نقطة في الـ M غير مين الـ X note
+
+153
+00:12:23,160 --> 00:12:27,740
+والـ M مش في الـ X note إذا أكيد تقطحين لما تشيل
+
+154
+00:12:27,740 --> 00:12:31,960
+هذه تقطحين برضه أشماله مش هيساوي Phi لأن في نقطة
+
+155
+00:12:31,960 --> 00:12:34,860
+غير مين الـ X note اللي هي في التقطع
+
+156
+00:12:37,370 --> 00:12:41,750
+إذاً الآن لو الـ M closure بساوء الـ X معناته هذا
+
+157
+00:12:41,750 --> 00:12:47,010
+إيش معنو؟ لا يساوي اللي هو فال في الجهتين لأي X في
+
+158
+00:12:47,010 --> 00:12:51,010
+الـ X non و ال conversely بنفس الأسلوب تاخد ال X
+
+159
+00:12:51,010 --> 00:12:55,620
+جوا ال M و X برا ال Mأه اللي هو بيكون عنده اللي هو
+
+160
+00:12:55,620 --> 00:12:58,480
+ال .. ال .. ال .. ال X في هذا الحالة يا في اللي بت
+
+161
+00:12:58,480 --> 00:13:02,120
+point يا في مين يا في ال M يعني في النهاية تاخدوا
+
+162
+00:13:02,120 --> 00:13:04,900
+أي X هتكون يا براها يا جوا اللي براها هتكون اللي
+
+163
+00:13:04,900 --> 00:13:08,480
+بت point و اللي .. و اللي جواها ال M هتكون اللي هي
+
+164
+00:13:08,480 --> 00:13:11,100
+في ال M إذا اللي هو ال M ال closure حسه و ال X
+
+165
+00:13:11,100 --> 00:13:18,100
+تابعوا تفاصيلة بتكتبوها انتوا طيب
+
+166
+00:13:18,100 --> 00:13:20,380
+ليه جدا اللي بعدها
+
+167
+00:13:36,540 --> 00:13:40,460
+المثال الأول هو هذا يعني باعتبار معلومة ان انت
+
+168
+00:13:40,460 --> 00:13:46,340
+بتعرفوهالأنه ذكرتها قبل ما أبدأ أسجل خلّيني أقولكم
+
+169
+00:13:46,340 --> 00:13:51,480
+إياها الآن عندي اللي هو the real line R إيش ماله
+
+170
+00:13:51,480 --> 00:13:56,400
+is اللي هو separable ليش separable لإن أنا ده عارف
+
+171
+00:13:56,400 --> 00:14:01,600
+من زمان يعني من تحليل واحد إنه ال Q count بال 6
+
+172
+00:14:01,600 --> 00:14:08,060
+وهي dense in من R الكلوجر لها إيش بساوي بساوي اللي
+
+173
+00:14:08,060 --> 00:14:13,530
+هو من Rو طبعا هذا الكلام اثبتناه يعني و مثبت في
+
+174
+00:14:13,530 --> 00:14:16,910
+تحليل واحد تبع ال bachelor's فمافيش داعي لنا نقعد
+
+175
+00:14:16,910 --> 00:14:20,330
+نحكي فيه كمان مرة اللي هذاك اللي بيضل معاكم اللي
+
+176
+00:14:20,330 --> 00:14:25,210
+هو exercise ال Q closure ايش بيساوي بيساوي R و Q
+
+177
+00:14:25,210 --> 00:14:29,310
+is countable اذا صار عند ال R عبارة عن اللي هي
+
+178
+00:14:29,310 --> 00:14:34,570
+separable space اللي زي يمينالـ C اللي هو the
+
+179
+00:14:34,570 --> 00:14:39,070
+complex plane C اللي هو برضه اسمه الـ inseparable
+
+180
+00:14:39,070 --> 00:14:43,250
+الان inseparable انتوا عارفين الـ C هي عبارة عن كل
+
+181
+00:14:43,250 --> 00:14:47,710
+الأعداد على صورة X ذات IY حيث اللي هو I انتوا
+
+182
+00:14:47,710 --> 00:14:49,910
+عارفين جدر نقص واحد والـ X وY عبارة عن real
+
+183
+00:14:49,910 --> 00:14:56,670
+numbers فالان اللي مؤهلة انها تكون اللي هي dense
+
+184
+00:14:57,530 --> 00:15:02,810
+Accountable اللي هي الست مين M اللي هناخده M اللي
+
+185
+00:15:02,810 --> 00:15:06,530
+هي مستقام المين من ال rational هي عبارة عن كل
+
+186
+00:15:06,530 --> 00:15:15,450
+الأعداد اللي هي المركبة على صورة R1 زاد IR2 حيث R1
+
+187
+00:15:15,450 --> 00:15:20,550
+وR2 element المين NQأول حاجة وهذه countable
+
+188
+00:15:20,550 --> 00:15:24,710
+countable set ليش countable؟ لأنه الأم لو جيته ك
+
+189
+00:15:24,710 --> 00:15:29,150
+set theory هتلاقوها equivalent للـ Q1 across مين
+
+190
+00:15:29,150 --> 00:15:33,070
+الـ Q2 تقدر تعملوا one to one onto function بينهم
+
+191
+00:15:33,070 --> 00:15:36,650
+اللي هو تاخدوا اللي هو أي element هنا لهنا و
+
+192
+00:15:36,650 --> 00:15:41,110
+تفهمتوا أنها إيش مالها one to one أو onto إذن هذه
+
+193
+00:15:41,110 --> 00:15:46,830
+إيش مالها is a countable setالان الـ closure لها
+
+194
+00:15:46,830 --> 00:15:53,230
+الـ closure لها انت لو جيته طبعا استخدمنا انه الـ
+
+195
+00:15:53,230 --> 00:15:58,550
+Q نفسها is dense الـ Q نفسها is dense في الـ R
+
+196
+00:15:58,550 --> 00:16:03,870
+فالان اي element في الـ R بقدر الاقي اشمله element
+
+197
+00:16:03,870 --> 00:16:08,970
+هنا اللي هو في حواليه يعني بمعنى اخر لو جيت اخدته
+
+198
+00:16:08,970 --> 00:16:15,870
+اي الآن Zفي الـ R أي Z في الـ R احنا بنعرف مسبقا
+
+199
+00:16:15,870 --> 00:16:20,230
+الـ Z إيش ماله هيكون على صورة X زائد IY بحكي بلغة
+
+200
+00:16:20,230 --> 00:16:26,970
+الـ Sequences هو نفس الاشي بقدر ألاقي Sequence RN
+
+201
+00:16:26,970 --> 00:16:32,130
+زائد R'NI
+
+202
+00:16:33,360 --> 00:16:38,520
+اللي هو converge لـ X زائد مين IY من وين تبتعد عن
+
+203
+00:16:38,520 --> 00:16:43,220
+خاصية الكثافة تبعت مين تبعت Q لإيش؟ لأن X في ال ..
+
+204
+00:16:43,220 --> 00:16:46,360
+في ال .. X ماله عبارة عن real number إذا بقدر
+
+205
+00:16:46,360 --> 00:16:49,360
+أجيله sequence من ال real number .. من ال rational
+
+206
+00:16:49,360 --> 00:16:52,640
+numbers converge ال X هذه معلومة أخدتها في ال real
+
+207
+00:16:52,640 --> 00:16:57,840
+ونفس الاشي هذا ما هو اللي هو عبارة عناللي هو real
+
+208
+00:16:57,840 --> 00:17:02,420
+number إذا بقدر ألاقي برضه R prime I أو N زي ما
+
+209
+00:17:02,420 --> 00:17:07,220
+نسميها بتروح من مين للأن لأن متنتقل مع بعض
+
+210
+00:17:07,220 --> 00:17:12,900
+باستخدام ال continuity تبعت الجامعة و بيصير عندي R
+
+211
+00:17:12,900 --> 00:17:19,760
+N زاد R N prime converge في I converge ده ال X زاد
+
+212
+00:17:19,760 --> 00:17:25,460
+I Y اللي هو مين اللي هي Zإذا صار عندي لكل element
+
+213
+00:17:25,460 --> 00:17:30,340
+في الـ C بقدر ألاقي sequence converge لهذا وهذا
+
+214
+00:17:30,340 --> 00:17:35,180
+يعني إنه صارت إيش مالها dense في مين في الـ C
+
+215
+00:17:35,180 --> 00:17:39,260
+طبعاً هذا الكلام الفدوى اللي .. اللي .. اللي احنا
+
+216
+00:17:39,260 --> 00:17:44,100
+.. احنا طبعاً عرفنا الـ Depth على أساس اللي هو الـ
+
+217
+00:17:44,100 --> 00:17:46,660
+Neighborhoods ما هو الـ Neighborhoods ما هو أصلا
+
+218
+00:17:46,660 --> 00:17:51,040
+لما نقول هذه converge لهذهبصير limit لها موجودة،
+
+219
+00:17:51,040 --> 00:17:55,300
+يعني هلاقي حوالين أي نقطة .. حوالين النقطة هذه بأي
+
+220
+00:17:55,300 --> 00:18:01,060
+نفس الخطور لازم ألاقي نقاط موجودة منها دي لإنه عند
+
+221
+00:18:01,060 --> 00:18:05,960
+ال limit .. لإن مش واضح حالي، ال limit للـ Rn زائد
+
+222
+00:18:05,960 --> 00:18:13,760
+I Rn برايم بتسوء X زائد I Y إذا لكل يبسلون أكبر من
+
+223
+00:18:13,760 --> 00:18:15,560
+سفر there exist
+
+224
+00:18:20,270 --> 00:18:26,110
+There exists a element in N such that اللي هو
+
+225
+00:18:26,110 --> 00:18:36,150
+البسافة بين RN زيدي RN' ناقص X زيدي IYأصغر من مين
+
+226
+00:18:36,150 --> 00:18:40,570
+من إبسلون وهذه أصلا ترجنها لمين لـ neighborhood
+
+227
+00:18:40,570 --> 00:18:48,590
+بيكس وزاد اي وإبسلون ان هذه في عندك لكل أكبر شومين
+
+228
+00:18:48,590 --> 00:18:54,010
+K يعني من عند K وK زاد واحد وK زاد اتنين كلهم
+
+229
+00:18:54,010 --> 00:18:57,250
+المسافة بينهم أصغر من إبسلون يعني كلهم موجود وينه
+
+230
+00:18:57,250 --> 00:19:01,390
+في هذا ال neighborhood يعني شيلوا منه X زاد IY
+
+231
+00:19:02,130 --> 00:19:05,590
+بيظلوا تقاطعوا مع ال .. مع اللي أخدناها مين هي ال
+
+232
+00:19:05,590 --> 00:19:09,510
+set M هذه اللي هي ال sequence منها لا يساوي إياش
+
+233
+00:19:09,510 --> 00:19:14,650
+فإذا أكيد أكيد أكيد اللي هي هتكون و موجودة اللي هو
+
+234
+00:19:14,650 --> 00:19:20,090
+كل ال X هذا أخدنا Z arbitrarily ملخص الحديث أخدنا
+
+235
+00:19:20,090 --> 00:19:26,810
+Z arbitrarily و موجودة في ال Cلجينا انه اي open
+
+236
+00:19:26,810 --> 00:19:34,670
+ball اللي هو حوالين ال X Z I Y هنلاقي فيها
+
+237
+00:19:34,670 --> 00:19:39,190
+elements من ال .. بالظبط من هم ال elements اللي هو
+
+238
+00:19:39,190 --> 00:19:44,350
+ال elements اللي .. اللي .. اللي .. اللي هي هذاK
+
+239
+00:19:44,350 --> 00:19:48,270
+وK زائد واحد وK زائد اتنين كل ال sequence هذه كلها
+
+240
+00:19:48,270 --> 00:19:52,010
+اللي دي في وين في هذه المنطقة فاهمين ايش بحكيه
+
+241
+00:19:52,010 --> 00:19:55,690
+فبصير عندي هذا نقص هذا لا يساوي في معناته رجعنا
+
+242
+00:19:55,690 --> 00:20:00,090
+للملاحظة اللي قبل بشوية اللي حكيتها ان M is dense
+
+243
+00:20:00,090 --> 00:20:11,570
+in X if and only if اللي هو every ball تحتوي نقاط
+
+244
+00:20:11,570 --> 00:20:15,900
+من Mأو تقطحها مع ام يشماله لا يساوي فاي وهذا فعلا
+
+245
+00:20:15,900 --> 00:20:22,700
+أثبتته اخدت اي Z limited in C لجأت انه اي open
+
+246
+00:20:22,700 --> 00:20:27,300
+ball حوالين الـ Z هذه هي X Z I Y شيل منها النقطة
+
+247
+00:20:27,300 --> 00:20:31,180
+هيكون تقطحها مع ام لا يساوي فاي وطبيعي زي ما قلنا
+
+248
+00:20:31,180 --> 00:20:34,940
+قبل في حالتين ام هذه جوا ام او برا ام بيطلع اللي
+
+249
+00:20:34,940 --> 00:20:39,580
+هو تقطع اللي هو لا يساوي فاي دائما وبيكون هيك احنا
+
+250
+00:20:39,580 --> 00:20:45,620
+أثبتنا ان ال closureللأمبساوسية هذا exercise معاكم
+
+251
+00:20:45,620 --> 00:20:49,000
+اديروا بالكم هذا exercise عشان هيك انا ماكتبتوش
+
+252
+00:20:49,000 --> 00:20:51,960
+الكلام بترتبوه و بتكتبوه قبرهان
+
+253
+00:20:56,240 --> 00:21:00,120
+هذا المفروض كلها معلومات سابقة لكن خلّينا نيجي
+
+254
+00:21:00,120 --> 00:21:04,000
+الآن للإشي الجديد اللي هو كيف نرتبه و نحكي فيه
+
+255
+00:21:04,000 --> 00:21:10,220
+بالتفصيل نبدأ في ال metric space الان a discrete
+
+256
+00:21:10,220 --> 00:21:14,620
+metric space is
+
+257
+00:21:14,620 --> 00:21:20,920
+separable if and only if x أشمالها is countable
+
+258
+00:21:22,920 --> 00:21:26,900
+عندى الان هو مبرهن برهانه اللى .. البرهان اللى
+
+259
+00:21:26,900 --> 00:21:33,100
+موجود هنا فيه انه .. خلّيني أقول برهانين البرهان
+
+260
+00:21:33,100 --> 00:21:41,340
+هذا اعتمد على انه ال M is closed if and only if ال
+
+261
+00:21:41,340 --> 00:21:46,380
+M closure بتسوى ال X او
+
+262
+00:21:46,380 --> 00:21:49,520
+في حالة ال M is closed بتكون ال M closure بتسوى X
+
+263
+00:21:50,710 --> 00:21:56,090
+أنا الي خاطر أبرهن من نقطة السفر خليني أشوف كيف
+
+264
+00:21:56,090 --> 00:22:00,390
+ايش اللي بقوله a discrete metric space X is
+
+265
+00:22:00,390 --> 00:22:05,150
+separable if and only if X أشمالها is countable
+
+266
+00:22:05,150 --> 00:22:09,330
+يعني و كأنه بيقوللي انه discrete metric space
+
+267
+00:22:10,690 --> 00:22:13,970
+Superable if and only if لما الـ X نفسها شمالها
+
+268
+00:22:13,970 --> 00:22:17,330
+تكون countable لسبب بسيط كل هذا لأنه بس خلّيني على
+
+269
+00:22:17,330 --> 00:22:20,090
+جهة هذا الكلام لأنه هذا بده تفصيل احنا أصلا في الـ
+
+270
+00:22:20,090 --> 00:22:22,730
+Discrete Metric Space اللي .. اللي عندنا اللي
+
+271
+00:22:22,730 --> 00:22:25,770
+عندنا اللي هو ال .. ال sets اللي موجودة كلها
+
+272
+00:22:25,770 --> 00:22:29,560
+closed و كلها openيعني لأن هو عبارة عن ال .. ال ..
+
+273
+00:22:29,560 --> 00:22:31,300
+ال .. ال .. بيعمل discrete topology و discrete
+
+274
+00:22:31,300 --> 00:22:33,100
+topology هذا اللي بيعرف topology و discrete
+
+275
+00:22:33,100 --> 00:22:37,940
+topology كل ال sets اللي موجودة فيها closed و open
+
+276
+00:22:37,940 --> 00:22:43,440
+لأنه كلشي بيحتوي ماشي الحال طيب الآن بناء عليه
+
+277
+00:22:43,440 --> 00:22:47,660
+فبكون عندي لو بدها considerable معناته في
+
+278
+00:22:47,660 --> 00:22:52,050
+countable setالـ Closure لها إيش بيساوي؟ بيساوي
+
+279
+00:22:52,050 --> 00:22:55,230
+الـ X طيب هنا كلهم Closed يعني أي واحدة proper
+
+280
+00:22:55,230 --> 00:22:58,850
+subset الـ Closure لها نفسها يعني مش هتصل لمين لـ
+
+281
+00:22:58,850 --> 00:23:03,490
+X مافيش حد هيصل لـ X إلى مين الـ X نفسها ماشي
+
+282
+00:23:03,490 --> 00:23:06,290
+الحال خلّيني أقول هذا الكلام على جهة خلّيني أجيل
+
+283
+00:23:06,290 --> 00:23:09,250
+البرهان اللي عند هذا و برجعلكم كمان البرهان تاني
+
+284
+00:23:10,430 --> 00:23:13,730
+Suppose that X is separable ما زم X is separable
+
+285
+00:23:13,730 --> 00:23:18,590
+إذا أكيد في countable subset M of X بحيث أن ال M
+
+286
+00:23:18,590 --> 00:23:23,190
+closure إيش بتساوي؟ بتساوي X ماشي الحال لكن
+
+287
+00:23:23,190 --> 00:23:26,530
+however any subset of a discrete metric space is
+
+288
+00:23:26,530 --> 00:23:33,870
+closedمعنى T-Close؟ معناته أن الـ M موجهة لها
+
+289
+00:23:33,870 --> 00:23:36,430
+بساوي نفسها
+
+290
+00:23:40,350 --> 00:23:44,890
+إذا صارت عندي ال X نفسها is countable هيا مش هيك
+
+291
+00:23:44,890 --> 00:23:48,150
+بنقول مش احنا فرضنا separable إذا there is M
+
+292
+00:23:48,150 --> 00:23:51,670
+countable إذا في النهاية وصلنا ل M بساوة X معناته
+
+293
+00:23:51,670 --> 00:23:54,490
+صارت ال X نفسها إشمالها countable conversely
+
+294
+00:23:54,490 --> 00:24:00,210
+suppose that X إشمالها is countable then أكيد ال X
+
+295
+00:24:00,210 --> 00:24:03,310
+كلوجيا اللي هي إيش بيساوي إذا X إشمالها is
+
+296
+00:24:03,310 --> 00:24:08,710
+countable التجارة التانية سهلةطيب خلّينا في .. في
+
+297
+00:24:08,710 --> 00:24:13,710
+شغل انا حابب ا .. افصلها لأنه مش اتفصلتش هنا انه
+
+298
+00:24:13,710 --> 00:24:19,830
+يعني ان انا لو قولنا بدنا نعمل remark هنا ونقول
+
+299
+00:24:19,830 --> 00:24:32,410
+the only .. the only .. the onlyاللي هي dense
+
+300
+00:24:32,410 --> 00:24:40,950
+subset of X is X itself وهذا اللي اعتمدنا عليها
+
+301
+00:24:40,950 --> 00:24:44,830
+اصلا هنا the only dense subset of X أشمالها is X
+
+302
+00:24:44,830 --> 00:24:49,170
+itself يعني الآن أي proper subset منها مستحيل تكون
+
+303
+00:24:49,170 --> 00:24:50,650
+dense approved
+
+304
+00:24:52,690 --> 00:24:56,550
+منقول هدف وين في الـ discrete metric space بدي
+
+305
+00:24:56,550 --> 00:25:00,590
+أقول suppose that
+
+306
+00:25:00,590 --> 00:25:12,850
+M is a proper subset of X and M closure بساوة إيه
+
+307
+00:25:12,850 --> 00:25:17,450
+إيش؟ بساوة X مش الحالة دي نسي انا بدي أسألك
+
+308
+00:25:17,450 --> 00:25:17,970
+contradiction
+
+309
+00:25:20,810 --> 00:25:25,050
+الان مدام أن مقروبر subset من X اذا اكيد اكيد اكيد
+
+310
+00:25:25,050 --> 00:25:32,470
+في X element او X note element in X but X note is
+
+311
+00:25:32,470 --> 00:25:38,970
+not element المين in M ماشي مش في ال M بتثبتلك ان
+
+312
+00:25:38,970 --> 00:25:42,550
+ال X note هدو مش هتكون في ال limit point ا افامش
+
+313
+00:25:42,550 --> 00:25:45,350
+في ال limit point، معناته إيش ماله؟ مستحيل ال M
+
+314
+00:25:45,350 --> 00:25:48,450
+closure إيش مالها؟ تساول X، اللي هو ال M Closure،
+
+315
+00:25:48,450 --> 00:25:51,170
+هي عبارة عن M إتحاد M إبراهيم، مدام M مش في ال ..
+
+316
+00:25:51,170 --> 00:25:53,290
+X not مش في ال M موجودة، أثبت لك إن M مش في ال M
+
+317
+00:25:53,290 --> 00:25:55,970
+إبراهيم، بدون خلاص، في Contradiction ده مافيش ..
+
+318
+00:25:55,970 --> 00:26:00,250
+اللي ممكن يكون بس dense subset of X في إن هو X
+
+319
+00:26:00,250 --> 00:26:07,130
+itself، طيبالان عندى x not limit in x but x not is
+
+320
+00:26:07,130 --> 00:26:12,250
+not a limit in x نعم خدوا ال distance بين x not او
+
+321
+00:26:12,250 --> 00:26:15,730
+x أو خلّيني ناخد ال ball ليش ال distance ناخد ال
+
+322
+00:26:15,730 --> 00:26:19,550
+ball خدوا ال ball ال ball أكيد عرفته إيش بده أعمل
+
+323
+00:26:19,550 --> 00:26:23,700
+ال ball x notمش أحنا بنقول عشان تكون في ال M prime
+
+324
+00:26:23,700 --> 00:26:29,260
+لازم يكون أي ball حواليها بأي نصف خطر لازم يقاطع
+
+325
+00:26:29,260 --> 00:26:32,280
+ال M في نقطة غير ال X0؟ هيك معناه ال limit points
+
+326
+00:26:32,280 --> 00:26:36,820
+أنا بدي أعطيك اللي هو P of X0 و نص مثلا أو طول أو
+
+327
+00:26:36,820 --> 00:26:44,100
+ربع شيلوا منه ال X0 تقاطع ال M إيش حالة جيه بساوي؟
+
+328
+00:26:44,590 --> 00:26:48,630
+فاي لإيش لإن المقاطع اللي بتبعد عن اكس نوت اصغر
+
+329
+00:26:48,630 --> 00:26:53,170
+منه اللي هو أدل من مُص بس الـ X note لإن المسافتين
+
+330
+00:26:53,170 --> 00:26:58,270
+عندنا يا سفر يا واحد إذا كانت المسافة أصغر من واحد
+
+331
+00:26:58,270 --> 00:27:01,770
+معناته سفر إذا صارت اليادي بس بتحتوي على من ال
+
+332
+00:27:01,770 --> 00:27:04,770
+single to ال X note لما تشيلوا X note منه تقعطوا
+
+333
+00:27:04,770 --> 00:27:08,970
+اللي هم إيش حيساويفهي اذا اكيد اكيد ال X نوت اللي
+
+334
+00:27:08,970 --> 00:27:13,750
+مش في ال M مش limit point كمان ماشي والسبب اللي
+
+335
+00:27:13,750 --> 00:27:17,350
+قلناه قبل شهر ان M في الواقع هي closed ما زم M
+
+336
+00:27:17,350 --> 00:27:21,450
+closed اذا ال M prime ال M closure اللي هي نفسها M
+
+337
+00:27:21,450 --> 00:27:27,350
+طيب الان اثبتنا ان the only thing subset of X mean
+
+338
+00:27:27,350 --> 00:27:31,530
+is X itself خليني اعتبد على هدف البرهان طبعا هو
+
+339
+00:27:31,530 --> 00:27:36,910
+البرهان اللي هنا بشكل اوضح الان بدأ اقولطبعا من
+
+340
+00:27:36,910 --> 00:27:40,450
+اتجاه ال time لو كانت x countable اللي هو
+
+341
+00:27:40,450 --> 00:27:44,130
+separable سهلة لان نفترض انها separable نقول
+
+342
+00:27:44,130 --> 00:27:52,150
+suppose suppose that x is separable مادام
+
+343
+00:27:52,150 --> 00:27:56,050
+separable then there exist M such that M closure
+
+344
+00:27:56,050 --> 00:28:02,970
+ايش بيساوي بيساوي xلما الملاحظة اللي فوق XM must
+
+345
+00:28:02,970 --> 00:28:08,930
+be X ليه؟ because the only subset .. دي ال subset
+
+346
+00:28:08,930 --> 00:28:12,750
+of Xاشم هتكون اللي هي ال X نفسها إذا صارت ال M
+
+347
+00:28:12,750 --> 00:28:16,930
+بساوي ال X و ال M is countable إذا ال X is
+
+348
+00:28:16,930 --> 00:28:20,890
+countable بس اللي هي توضيح ل .. اللي هي الثغرة
+
+349
+00:28:20,890 --> 00:28:23,990
+اللي هي .. أو اللي مش موجودة هناطيب اللي بعدها
+
+350
+00:28:23,990 --> 00:28:29,290
+نيجي لان اثبتنا انه discrete metric space بكون
+
+351
+00:28:29,290 --> 00:28:33,970
+separable if and only if X is countable نيجي لان
+
+352
+00:28:33,970 --> 00:28:39,030
+لحاجة اسمها ال LB spaces ركزوا ال LB spaces احنا
+
+353
+00:28:39,030 --> 00:28:44,690
+حكيناها حكيناها دبل هيكبدنا نثبت لكم ان الـ LB
+
+354
+00:28:44,690 --> 00:28:49,650
+spaces الـ B بين الواحد وبين ال infinity is
+
+355
+00:28:49,650 --> 00:28:54,750
+separable تقريبا اللي هو مستقى من اللي قبل بشوية
+
+356
+00:28:54,750 --> 00:29:01,070
+حكينا عنه في الحالة ال complex الآن بدي أجيب 6Mو
+
+357
+00:29:01,070 --> 00:29:03,390
+تكون condensed في مين؟ في الـ LB، انت عارفين ايش
+
+358
+00:29:03,390 --> 00:29:07,590
+الـ LB؟ هي عبارة عن Space of Sequences الصممش لـ
+
+359
+00:29:07,590 --> 00:29:12,090
+Sequence Xi I أُس B أُس 1 على B is finite، ماشي
+
+360
+00:29:12,090 --> 00:29:17,960
+الحال، طيب، صلوا عنا بقالهخدوا الان ال 6M اللي هي
+
+361
+00:29:17,960 --> 00:29:22,420
+عبارة عن عنصرها R1,R2,R3 اللي عند RN والباقي إيش
+
+362
+00:29:22,420 --> 00:29:28,360
+ماله؟ أسفر هذا أكيد وين ما نوجودة في القلبي والـRI
+
+363
+00:29:28,360 --> 00:29:31,380
+كله إيه شماله؟ الـRational Numbers والـN إيه
+
+364
+00:29:31,380 --> 00:29:36,040
+شماله؟ Element N يعني بمعنى أخر هذه ال6 فيها اللي
+
+365
+00:29:36,040 --> 00:29:41,750
+هي كل الـR1والباقي أسفار كل ال R واحد والR اتنين
+
+366
+00:29:41,750 --> 00:29:44,850
+والباقي أسفار كل ال R واحد والR اتنين والR تلاتة
+
+367
+00:29:44,850 --> 00:29:48,330
+والباقي أسفار كل ال finite number of elements
+
+368
+00:29:48,330 --> 00:29:54,970
+والباقي أسفار لأي N كانت فواضح أن هذه اللي هي ال 6
+
+369
+00:29:54,970 --> 00:29:57,850
+بالشكل هذا is equipotent
+
+370
+00:30:01,460 --> 00:30:09,260
+Countable number of كروس كروس كروس
+
+371
+00:30:14,800 --> 00:30:18,200
+اللي هى لو كل واحدة countable اذا اكيد هيكون ان اي
+
+372
+00:30:18,200 --> 00:30:22,900
+شمالها is equipotent للكيو معناته اخر اي شمالهن is
+
+373
+00:30:22,900 --> 00:30:27,120
+countable اذا ال set M عبارة عن countable set
+
+374
+00:30:27,120 --> 00:30:30,660
+الدور الآن بدنا نثبت ان الكيو والنكولوجر ايش
+
+375
+00:30:30,660 --> 00:30:34,420
+بتساوي .. آسف ال M نكولوجر بتساوي اللى هى ال LB
+
+376
+00:30:34,420 --> 00:30:40,300
+بتثبتلكم
+
+377
+00:30:40,300 --> 00:30:47,710
+الآنالأم اللي عندي هذه أم closure لها بساوي القلبي
+
+378
+00:30:47,710 --> 00:30:54,370
+نشوف
+
+379
+00:30:54,370 --> 00:31:00,630
+طبعا هذه subset من هذه طبيعي لأنه من أين بدي أجيب
+
+380
+00:31:00,630 --> 00:31:03,650
+ال limits الآن بدي أخد أي element هنا و بدي أثبت
+
+381
+00:31:03,650 --> 00:31:06,250
+لكم يا ال element هذا يا حكومي limit point يا
+
+382
+00:31:06,250 --> 00:31:12,010
+حكومي فلان مظبوط ولا لا طب خليني نشوفيعني بمعنى
+
+383
+00:31:12,010 --> 00:31:16,750
+اخر اللي قولنا قبل شوية انه ممكن نروح باتجاه انه
+
+384
+00:31:16,750 --> 00:31:19,830
+اي element في القلبي اللي لاجي اللي هو ball حواليه
+
+385
+00:31:19,830 --> 00:31:22,270
+اللي لاجي اي ball حواليه .. اي ball حواليه اسف ..
+
+386
+00:31:22,270 --> 00:31:25,190
+اي ball حواليه تقاطع ال .. ال .. ال .. ال .. ال ..
+
+387
+00:31:25,190 --> 00:31:25,350
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+388
+00:31:25,350 --> 00:31:25,410
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+389
+00:31:25,410 --> 00:31:25,730
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+390
+00:31:25,730 --> 00:31:25,770
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+391
+00:31:25,770 --> 00:31:26,350
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+392
+00:31:26,350 --> 00:31:27,050
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+393
+00:31:27,050 --> 00:31:27,190
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+394
+00:31:27,190 --> 00:31:36,030
+..
+
+395
+00:31:36,030 --> 00:31:40,270
+ال .. ال ..الأن we show that any closure element
+
+396
+00:31:40,270 --> 00:31:44,670
+بتساوي مين؟ قلبي عشان نثبت هيك قولنا ناخد أي X وين
+
+397
+00:31:44,670 --> 00:31:48,430
+موجودة في القلبي ال X كيف شكلها عبارة عن sequence
+
+398
+00:31:48,430 --> 00:31:51,730
+ماحنا عارفين اللي هو شكل العناصر اللي موجودة في
+
+399
+00:31:51,730 --> 00:31:55,750
+القلبي عبارة عن sequences يعني بمعنى آخر عند ال X
+
+400
+00:31:55,750 --> 00:32:02,750
+ال X اللي في القلبياللي هي عبارة عن sequence xi I
+
+401
+00:32:02,750 --> 00:32:05,570
+I من واحد إلى ما لا نهاية وبكون عشان تكون في
+
+402
+00:32:05,570 --> 00:32:09,590
+القلبي summation xi I أس بي I من واحد إلى ما لا
+
+403
+00:32:09,590 --> 00:32:14,210
+نهاية is finite أو converge متفقين عليها هذا من
+
+404
+00:32:14,210 --> 00:32:21,230
+قبل احنا نيجي الآن يا جماعة خدولي أي ي أكبر من مين
+
+405
+00:32:21,230 --> 00:32:26,770
+من سفراللي أنا بقوللي then there is n بسواة n
+
+406
+00:32:26,770 --> 00:32:31,830
+وإبسالون n element in n such that الصماشن x j of b
+
+407
+00:32:31,830 --> 00:32:35,110
+j من عند n زاد واحد إلى infinity أصغر من مين من
+
+408
+00:32:35,110 --> 00:32:38,890
+إبسالون بي على اتنين هذا يسي معناته هيها من هان
+
+409
+00:32:38,890 --> 00:32:44,650
+هدي هدي هدي من هان لعنزل هان إيش معناته أنا مش
+
+410
+00:32:44,650 --> 00:32:53,540
+عمال بقول إنه الصماشن هذا is finiteبالظبط لا يعني
+
+411
+00:32:53,540 --> 00:33:00,500
+بمعنى اخر ان ال limit للصممش XI I قص بي I من واحد
+
+412
+00:33:00,500 --> 00:33:05,360
+لعند K مثلا او لعند M زي ما بدناه as M goes to
+
+413
+00:33:05,360 --> 00:33:11,350
+infinity بساوي ايشعدد اللي هو بيساوي هذا اللي
+
+414
+00:33:11,350 --> 00:33:16,090
+نسميها ده مثلا عدد اسمه مين اسمه العدد ماشي بيساوي
+
+415
+00:33:16,090 --> 00:33:20,530
+L أو بيساوي summation Xi I أس بي I من عند واحد إلى
+
+416
+00:33:20,530 --> 00:33:24,430
+ملارها تعرف اللي متشهو معناته وصيرنا نحكي عن أرقام
+
+417
+00:33:24,430 --> 00:33:27,610
+لأن هذا رقم وهذا رقم ماشي الحال اللي بنحكي في R
+
+418
+00:33:27,610 --> 00:33:32,310
+ثانوية أو في Z أو في C لأن for every أكبر أكبر من
+
+419
+00:33:32,310 --> 00:33:38,670
+0There exist N أو K element in N such that for
+
+420
+00:33:38,670 --> 00:33:44,640
+every N أكبر شو Kهذا اللي هو ال term اللي هو مثلا
+
+421
+00:33:44,640 --> 00:33:48,360
+نسميه SM أو اللي بدنا ياه و SM اللي بدنا ياه اللي
+
+422
+00:33:48,360 --> 00:33:53,320
+هو هذا ال term هذا ال term اللي هو ال summation xi
+
+423
+00:33:53,320 --> 00:33:59,780
+I أس بي I من عند واحد لعند اللي هو أخدتها أنا اللي
+
+424
+00:33:59,780 --> 00:34:06,100
+هي N ناقص ال summation xi I أس بي I من واحد إلى
+
+425
+00:34:06,100 --> 00:34:10,840
+مانا نهاية أصغر من أي أبسلون في الدنياأنا بتاخد
+
+426
+00:34:10,840 --> 00:34:14,740
+الـY أنا حر اسمها Y-B على 2 على 2 عشان الحسابات
+
+427
+00:34:14,740 --> 00:34:20,420
+عندى أصغر من Y-B على 2 هذا من اللي هو أصلا هذا
+
+428
+00:34:20,420 --> 00:34:23,520
+عبارة هذا الكلام صحيح لكل N أكبر شوكة وهي اللي
+
+429
+00:34:23,520 --> 00:34:30,090
+أخدتها وخلصتها أخدت 4N واحدةfor every n بخلّيني
+
+430
+00:34:30,090 --> 00:34:35,310
+أسميها أكبر سوء n عشان أبدأ في اللي بديها بيصير
+
+431
+00:34:35,310 --> 00:34:38,910
+عند ال n هذا ناقص هذا ايش بيكون عبارة عن ال
+
+432
+00:34:38,910 --> 00:34:43,530
+summation اللي هو xi من عند n خلصنا ال n هذولا
+
+433
+00:34:43,530 --> 00:34:47,630
+شيلناهم ضال عند من مين n زائد واحد إلى ما لنهاية
+
+434
+00:34:47,630 --> 00:34:53,050
+xi I أس بي أصغر من و أس بي على مينعلى اتنين واضحت
+
+435
+00:34:53,050 --> 00:34:57,230
+هذه اذا صار عند الان for every y أكبر من 0 there
+
+436
+00:34:57,230 --> 00:35:01,230
+exists an unlimited n such that اللي هو xij أسبي j
+
+437
+00:35:01,230 --> 00:35:07,300
+من n زي 1 من نهاية أصغر من y بي على اتنينأي سؤال
+
+438
+00:35:07,300 --> 00:35:11,800
+من جهة أخرى من جهة أخرى أنا بعرف أنه ال rational
+
+439
+00:35:11,800 --> 00:35:16,980
+numbers اللي أنا أصلا باني قصد عليها اللي هي لأن
+
+440
+00:35:16,980 --> 00:35:20,660
+since the rational numbers are dense in R بدلاً من
+
+441
+00:35:20,660 --> 00:35:26,040
+أنها دنسة في R إذا أقنع بقدر أزغر المسافةاللي هو
+
+442
+00:35:26,040 --> 00:35:31,020
+بين اللي هو الـ XII و أي rational number بقى او او
+
+443
+00:35:31,020 --> 00:35:32,940
+او او او او او او او او او او او او او او او او او
+
+444
+00:35:32,940 --> 00:35:33,020
+او او او او او او او او او او او او او او او او او
+
+445
+00:35:33,020 --> 00:35:33,640
+او او او او او او او او او او او او او او او او او
+
+446
+00:35:33,640 --> 00:35:33,680
+او او او او او او او او او او او او او او او او او
+
+447
+00:35:33,680 --> 00:35:33,680
+او او او او او او او او او او او او او او او او او
+
+448
+00:35:33,680 --> 00:35:39,800
+او او او او او او او او او او او او او او او او
+
+449
+00:35:40,420 --> 00:35:44,560
+بقدر أجيب rational number is very closed له لأن
+
+450
+00:35:44,560 --> 00:35:48,420
+احنا بنعرف أنه dense يعني بنلاقي انه sequence من
+
+451
+00:35:48,420 --> 00:35:51,980
+ال rationales كلها رايحة لكساي I إذا بلاقي ر I
+
+452
+00:35:51,980 --> 00:35:56,940
+بحيث أنه المسافة بينهم أصغر ما يكون ماشي الحال هذا
+
+453
+00:35:56,940 --> 00:36:01,260
+بعمله لكساي 1 و لكساي 2 و لكساي 3 و لكساي 4 و لهم
+
+454
+00:36:01,260 --> 00:36:07,280
+كلهم بعملهم واضح؟ إذا بقدر ألاقي الآن اللي هو
+
+455
+00:36:08,570 --> 00:36:12,470
+بخاصية الكثافة للـ Q في R بقدر ألاقي rational
+
+456
+00:36:12,470 --> 00:36:19,950
+numbers ر I لـ close to mean to xi Isuch that اللي
+
+457
+00:36:19,950 --> 00:36:27,850
+هو إنها بتحقق إنه xij ناقص RJ أس بي من جيه من واحد
+
+458
+00:36:27,850 --> 00:36:31,670
+إلى ماله نهاية أصغر من مين من أي عدد في الدنيا
+
+459
+00:36:31,670 --> 00:36:35,890
+بديه بزغره جد ما بدي بيصير عندي أصغر برضه من مين
+
+460
+00:36:35,890 --> 00:36:39,170
+من يبسلون بيه على مين على اتنين إذا صار في عندي
+
+461
+00:36:39,170 --> 00:36:46,770
+أمرين هاي الأمر الأولوهي الأمر الثاني الان هذولة
+
+462
+00:36:46,770 --> 00:36:52,230
+هيوصلني للي بديها لحظة انا ايش لجيت انا بدأت في ال
+
+463
+00:36:52,230 --> 00:37:00,010
+X هيها هيها ال X والان بدأت اركب من خاصية الكثافة
+
+464
+00:37:00,010 --> 00:37:08,570
+ل ال Q بدأت الاقي اللي هو sequence من ال RJ ال RJ
+
+465
+00:37:08,570 --> 00:37:13,500
+الان هذه J من 1 إلى ملا نهايةإيش مالها المسافة
+
+466
+00:37:13,500 --> 00:37:18,800
+أصغر من ي من ي بي على اتنين هذه اللي هتمثل لين؟ Y
+
+467
+00:37:18,800 --> 00:37:24,520
+إذا hence we can find Y element in M satisfying
+
+468
+00:37:24,520 --> 00:37:32,260
+the following المسافة
+
+469
+00:37:32,260 --> 00:37:37,000
+بين
+
+470
+00:37:37,000 --> 00:37:43,660
+X و Y هتكون بتساوياللي هو طبعا اسمه عشان مانديش
+
+471
+00:37:43,660 --> 00:37:47,860
+اعملاش واحد على بيه بتساوي ال summation هذا زي اد
+
+472
+00:37:47,860 --> 00:37:55,140
+مين ال summation اللي عندها معايا هذا
+
+473
+00:37:55,140 --> 00:37:59,180
+ال summation طبعا هذا خليه لعند هنا بيقل عندي اللي
+
+474
+00:37:59,180 --> 00:38:06,160
+هو جاي من عند واحد لعند n هذي لعند n بكفينا لعند n
+
+475
+00:38:07,490 --> 00:38:12,850
+عارفين ليه؟ عشان ادنى بتكون هنا لإن هنا أشمالها R1
+
+476
+00:38:12,850 --> 00:38:17,510
+وR2 وR3 والباقي أشمالهم أسفار ماشي الحال فبصير
+
+477
+00:38:17,510 --> 00:38:22,770
+عندي الآن طبعا بسهل عليه أكتر لإن الباقي كله
+
+478
+00:38:22,770 --> 00:38:26,640
+أشماله خلاص بقت خلاص منه إيش بده فيهطيب فبصير عندى
+
+479
+00:38:26,640 --> 00:38:29,360
+اللى هو المسافة بين هذه و هذه عبارة عن هذه زائد
+
+480
+00:38:29,360 --> 00:38:34,160
+هذه عارفين ليش لأن الباقى هان اشماله أسفار يعني ال
+
+481
+00:38:34,160 --> 00:38:38,300
+summation جسمته جسمين المسافة بين X و Y اللى هى Y
+
+482
+00:38:38,300 --> 00:38:46,710
+عندك R1وR2 وR3 لعند RN والباقي إيش ماله أصفر
+
+483
+00:38:46,710 --> 00:38:50,830
+فالمسافة هذه هتروح اللي هي الـRI هتبقى اللي هي
+
+484
+00:38:50,830 --> 00:38:54,430
+أشبه سجادة اللي هي الـXY جاي لحالها واللي هي أصلا
+
+485
+00:38:54,430 --> 00:38:58,110
+أنا مهتلها من الأصل جا جيتها وخلصنا فبصير هذا
+
+486
+00:38:58,110 --> 00:39:02,990
+المسافة التنين بتساوي هذا زائد هذا وهذا أصغر من
+
+487
+00:39:02,990 --> 00:39:06,230
+مين من يبسلون أس بي على اتنين ويبسلون أس بي على
+
+488
+00:39:06,230 --> 00:39:08,810
+اتنين اتنين أصغر من مين من يبسلون
+
+489
+00:39:16,460 --> 00:39:26,590
+ماذا فعلت؟ انا اخدت اي element x في القلبانتبهوا
+
+490
+00:39:26,590 --> 00:39:30,790
+عشان نعرف الـ X الكلي أي X في القلبي و لـ gate Y
+
+491
+00:39:30,790 --> 00:39:36,970
+في الـ M بحيث ان المسافة بين X و Y أصغر من مين من
+
+492
+00:39:36,970 --> 00:39:43,310
+إبسلون لأي إبسلون مين في الدنيا بمعنى آخر لأي ball
+
+493
+00:39:43,310 --> 00:39:52,770
+حوالين ال X أه و بنصف خطر أي نصف خطر تقاطع ال Mالـ
+
+494
+00:39:52,770 --> 00:39:58,170
+YP لا يساوي فاي وهذا ايش معناته؟ معناته صارت اللي
+
+495
+00:39:58,170 --> 00:40:04,810
+هي الـ LB closure .. آسف الـ LB بيساوي الـ M إيش؟
+
+496
+00:40:04,810 --> 00:40:05,310
+Closure
+
+497
+00:40:10,220 --> 00:40:16,460
+هذه اللى عندى لقيت اللى هو الـ M closure بساوى
+
+498
+00:40:16,460 --> 00:40:24,000
+القلبي بدأت في ال X في القلبي وانتهيت ان ال X كانت
+
+499
+00:40:24,000 --> 00:40:28,000
+موجودة في ال M closureوالـ LB صارت جزئية من الـ M
+
+500
+00:40:28,000 --> 00:40:30,500
+closure وزي ما قلنا في الأول الـ M closure دايما
+
+501
+00:40:30,500 --> 00:40:33,840
+جزئية من الـ LB إذا صارت التنتين متساوياتين إذا
+
+502
+00:40:33,840 --> 00:40:38,720
+صرت ملاقي countable subset اللي هي M of LB which
+
+503
+00:40:38,720 --> 00:40:41,940
+is dense in LB إذا صار الـ LB is a separable space
+
+504
+00:40:41,940 --> 00:40:46,820
+نجي الأن ناخد مثال على non-separable space ومثال
+
+505
+00:40:46,820 --> 00:40:53,380
+مهم برضه مثال مهم برضه
+
+506
+00:40:53,380 --> 00:40:57,620
+هتلاقوني اعتمادت على ملاحظةبرجو في كتاب التحليل
+
+507
+00:40:57,620 --> 00:41:03,120
+اللي أتخذناها في ال baccalaureate كتاب بارتل عن
+
+508
+00:41:03,120 --> 00:41:06,640
+اللي
+
+509
+00:41:06,640 --> 00:41:15,400
+هو ال binary representation للعدد وكف ياندي one to
+
+510
+00:41:15,400 --> 00:41:21,220
+one onto function بينهم خليني أشوفها ملاحظة قبل ما
+
+511
+00:41:21,220 --> 00:41:28,370
+نبدأ بالمثالبقول لي for any y element in 0,1 يعني
+
+512
+00:41:28,370 --> 00:41:33,530
+i,y اللي هي بين السفر و بين الواحد there is اللي
+
+513
+00:41:33,530 --> 00:41:38,670
+هو a sequence xii such that xii element in 0,1 for
+
+514
+00:41:38,670 --> 00:41:46,510
+all iلأي Y المتن Zero و واحد بلاقي Sequence Xi I
+
+515
+00:41:46,510 --> 00:41:51,510
+عناصرها يا سفر يا واحد هذه سفر واحد بتذكرنا في
+
+516
+00:41:51,510 --> 00:41:55,210
+اللي هي عناصر اللي هو ال ال ال ال ال binary
+
+517
+00:41:55,210 --> 00:41:59,870
+operation ال binary operation يا Zero يا واحدكلنا
+
+518
+00:41:59,870 --> 00:42:04,350
+أخدنا نظرية أعداد for all i and y ايش بيساوي كصاي
+
+519
+00:42:04,350 --> 00:42:06,710
+واحد على اتنين كصاي اتنين على اتنين ترجل كصاي تلتة
+
+520
+00:42:06,710 --> 00:42:08,210
+تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة
+
+521
+00:42:08,210 --> 00:42:08,530
+تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة
+
+522
+00:42:08,530 --> 00:42:11,310
+تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة
+
+523
+00:42:11,310 --> 00:42:18,410
+تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة
+
+524
+00:42:18,410 --> 00:42:28,630
+تلتة تل
+
+525
+00:42:28,800 --> 00:42:32,280
+اللي هو بقدر أجيله اللي هو الـBinary
+
+526
+00:42:32,280 --> 00:42:38,960
+Representation اللي هو للـY بساوي اللي هو XI I على
+
+527
+00:42:38,960 --> 00:42:44,140
+Y أتنين زاد XI I على 2 تربيع زاد او هي واحد آسف
+
+528
+00:42:44,140 --> 00:42:50,170
+اتنين إلى اخرى إلى مانا نهايةالان و ال .. و ال ..
+
+529
+00:42:50,170 --> 00:42:55,930
+و ال .. و الويات المختلفة هتلاقيهم بمثل ايش أعداد
+
+530
+00:42:55,930 --> 00:43:01,970
+مختلفة منها يعني هذه التمثيل اللي هو بنظام ال
+
+531
+00:43:01,970 --> 00:43:07,450
+decimal يكافئ تماما one to one correspondence مع
+
+532
+00:43:07,450 --> 00:43:10,350
+التمثيل بإيش بال binary operation خليني أنا أخد
+
+533
+00:43:10,350 --> 00:43:14,530
+على فترة سنة واحد اللي بتلزمنيماشي؟ اذا for any y
+
+534
+00:43:14,530 --> 00:43:17,010
+element in 0,1 there is a sequence xi,i such that
+
+535
+00:43:17,010 --> 00:43:21,590
+xi,i of 0,1 for all i and y بتساوي كده is a binary
+
+536
+00:43:21,590 --> 00:43:24,290
+representation of y moreover اللي قلت قبل شوية
+
+537
+00:43:24,290 --> 00:43:29,050
+different y's element in كده have different binary
+
+538
+00:43:29,050 --> 00:43:32,350
+representations اذا انا مرتاح فاش اشي بتكرر هدولة
+
+539
+00:43:32,350 --> 00:43:35,150
+هنا نفسهم بس هدول اسمهم decimal و هدول اسمهم ايش
+
+540
+00:43:35,150 --> 00:43:39,200
+معلوم binary representationاللي حابب يطلع حيثي
+
+541
+00:43:39,200 --> 00:43:43,320
+introduction to a real analysis لبارتيل وشيربرت
+
+542
+00:43:43,320 --> 00:43:49,330
+اللي بندرسه في ال baccalaureateاللي هي الـ space
+
+543
+00:43:49,330 --> 00:43:53,890
+اللي أمامي the space L infinity is not separable
+
+544
+00:43:53,890 --> 00:43:58,310
+is not separable يعني بدنا نقول مش هنقدر نلاقي
+
+545
+00:43:58,310 --> 00:44:03,110
+countable dense set في الـ L infinity لو بدك تيجي
+
+546
+00:44:03,110 --> 00:44:06,830
+تقول والله بدي أفترض let M be any dense subset of
+
+547
+00:44:06,830 --> 00:44:09,770
+L بيه اللي متاعها L infinity مش هتطلع إيش مالها
+
+548
+00:44:09,770 --> 00:44:15,560
+countable بس باختصار هي الحكيمة الآن عياز سريعlet
+
+549
+00:44:15,560 --> 00:44:19,800
+n be anything subset of main of n infinity طيب ال
+
+550
+00:44:19,800 --> 00:44:23,740
+infinity لأنه بيقولك خد s رعبان عن x i i اللي
+
+551
+00:44:23,740 --> 00:44:27,640
+بتنقل ال infinity و ال x i i اللي بتنزيره main و
+
+552
+00:44:27,640 --> 00:44:30,960
+واحد هذولة يعني ال sequence اللي موجودة في ال
+
+553
+00:44:30,960 --> 00:44:33,400
+infinity على صراية واحد وصفر واحد وصفر واحد وأكيد
+
+554
+00:44:33,400 --> 00:44:36,160
+في ال infinity لأن كيف تكون في ال infinity ال
+
+555
+00:44:36,160 --> 00:44:41,040
+sequence اللي هو تكون bounded sequence يعني ال x i
+
+556
+00:44:41,040 --> 00:44:43,660
+ايات هذولة حطيناها ان جوا absolute value هيكون
+
+557
+00:44:43,660 --> 00:44:47,030
+أصغر من some عددودول هي صفرها واحد إذا أكيد إيش
+
+558
+00:44:47,030 --> 00:44:51,070
+مالها is bounded إذا عندك xi I وين موجودة في الأقل
+
+559
+00:44:51,070 --> 00:44:55,050
+infinity أكيد اللي هي ال xi I المتكونة من اللي هو
+
+560
+00:44:55,050 --> 00:44:59,790
+01 يعني مثلا 10000011100
+
+561
+00:44:59,790 --> 00:45:04,590
+كل هدول ال elements وين موجودات في الأقل infinity
+
+562
+00:45:06,870 --> 00:45:13,550
+شوفوا لها since 01 is uncountable أكيد ما احنا
+
+563
+00:45:13,550 --> 00:45:17,350
+عارفين هدم علوة سابقة and for each y element in 01
+
+564
+00:45:17,350 --> 00:45:21,610
+بنقدر نلاقي their correspondence xi i element in S
+
+565
+00:45:21,610 --> 00:45:27,110
+هدم هي من اللي حكينا عنهم قبل شوية and different
+
+566
+00:45:27,110 --> 00:45:31,690
+y's in 01 have different sequences in S إذا هتطلع
+
+567
+00:45:31,690 --> 00:45:39,120
+ال S هذه اللي هي is uncountable set ماشي؟لأنه عندى
+
+568
+00:45:39,120 --> 00:45:44,280
+اللي هي هذه اللي هي أي element في الـ zero والواحد
+
+569
+00:45:44,280 --> 00:45:48,780
+بقدر أجيله representation هنالأن الـ 01 01 01 01
+
+570
+00:45:48,780 --> 00:45:51,380
+01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
+
+571
+00:45:51,380 --> 00:45:52,240
+01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
+
+572
+00:45:52,240 --> 00:45:57,320
+01 01 01 01 01 01 01 01 01 01 01
+
+573
+00:45:57,320 --> 00:45:58,080
+01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
+
+574
+00:45:58,080 --> 00:45:58,100
+01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
+
+575
+00:45:58,100 --> 00:45:58,140
+01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
+
+576
+00:45:58,140 --> 00:45:58,140
+01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
+
+577
+00:45:58,140 --> 00:45:59,240
+01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
+
+578
+00:45:59,240 --> 00:46:00,400
+01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
+
+579
+00:46:00,400 --> 00:46:00,460
+01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
+
+580
+00:46:00,460 --> 00:46:04,940
+01 01 01 01 01 01 01 01 01 01 01 01 01
+
+581
+00:46:04,940 --> 00:46:04,940
+01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
+
+582
+00:46:04,940 --> 00:46:04,940
+01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
+
+583
+00:46:04,940 --> 00:46:15,680
+01 01
+
+584
+00:46:15,680 --> 00:46:20,760
+01 01 01Hence, S is uncountable إلى أن خدوا أي X
+
+585
+00:46:20,760 --> 00:46:25,940
+وY وإن موجودة XII وYI وإن موجودات وGamma I في الـ
+
+586
+00:46:25,940 --> 00:46:32,700
+S أي تنتج وخدوه المختلفات مدام هم مختلفات إذا في
+
+587
+00:46:32,700 --> 00:46:35,720
+واحد من ال interest اللي بينهم مختلف عن التاني على
+
+588
+00:46:35,720 --> 00:46:39,820
+الأقل في واحد يمكن في أكتر من واحدوالـ interest
+
+589
+00:46:39,820 --> 00:46:44,280
+اللي فيه مثلا لو قلنا هذا اللي رقمه خمسة بختلف عن
+
+590
+00:46:44,280 --> 00:46:49,140
+اللي رقمه خمسة يعني فبصير حاصل طرحل لأبسولوت
+
+591
+00:46:49,140 --> 00:46:53,900
+الواحد لأن ولا .. فش عنها ال X هي Zero و واحد فدي
+
+592
+00:46:53,900 --> 00:46:56,920
+كان Zero و واحد فأكيد واحد بينهم بختلف عن التاني
+
+593
+00:46:56,920 --> 00:46:59,720
+إذا المسافة بيننا إيش بساوي واحد إذا انصارة ال
+
+594
+00:46:59,720 --> 00:47:02,920
+distance بين ال X و ال Y في حالة الاختلاف إيش
+
+595
+00:47:02,920 --> 00:47:07,720
+بساوي بساوي اللي هو إيه شمالها بساوي واحديعني
+
+596
+00:47:07,720 --> 00:47:14,200
+بمعنى آخر الـ ball لل X و تلت لل X و تلت تقاطع ال
+
+597
+00:47:14,200 --> 00:47:22,040
+ball لل Y و تلت أكيد هيسوف Y ليش؟ لأنه الآن ال
+
+598
+00:47:22,040 --> 00:47:30,200
+ball لل X و Y لل X و تلتتقاطع الـ ball للـ Y تلت
+
+599
+00:47:30,200 --> 00:47:35,200
+أو نصف اللي بيدك إياه اللي هو بساوي فاي لو بدنا
+
+600
+00:47:35,200 --> 00:47:40,700
+نقول خلّينا نفترض إنه Z فيها إنه Z هنا Z هنا
+
+601
+00:47:40,700 --> 00:47:48,240
+معناته Z في الـ B X و تلت andزد element بي و أيه
+
+602
+00:47:48,240 --> 00:47:52,740
+تلت صح ولا لأ نقول أيه تساوي فيه إذا مساعدت
+
+603
+00:47:52,740 --> 00:47:59,150
+المسافة بين ال X و ال Z بساوي أيه معله تلتإذا مدام
+
+604
+00:47:59,150 --> 00:48:03,690
+بتساوى تلت وانا بعرف المسافات بين أي عنصرين هتكون
+
+605
+00:48:03,690 --> 00:48:06,850
+يا صفر يا مين حسب اللي هم .. انتوا عارفين ايش ال
+
+606
+00:48:06,850 --> 00:48:11,130
+metric هنا اللي هو عبارة عن supremum لل XII ناقص
+
+607
+00:48:11,130 --> 00:48:16,150
+القمر هذوله .. هذوله المسافات بينهم اللي هو يا صفر
+
+608
+00:48:16,150 --> 00:48:20,890
+يا واحد لو بده يكون واحد الان لو بده يكون واحد مش
+
+609
+00:48:20,890 --> 00:48:25,750
+هيكون .. مش .. مش .. مش هيظبط فالان هذه بساللي هو
+
+610
+00:48:25,750 --> 00:48:28,850
+دي زد ودي إكس بيساوي تولك معناته إن زد إيش هتساوي
+
+611
+00:48:28,850 --> 00:48:34,970
+الإكس بس في هذه الحالة الآن التاني لو زد هنا إيش
+
+612
+00:48:34,970 --> 00:48:40,060
+هيعطيني هذا إن زد إيش بتساويمن الجهتين عشان تكون
+
+613
+00:48:40,060 --> 00:48:43,460
+هدي فيه هدي و فيه هدي لازم نزل ال X عشان بتساوي و
+
+614
+00:48:43,460 --> 00:48:47,320
+أنا باعدى بال X و ال Y أشمالهم نختلفت إذا قطعا
+
+615
+00:48:47,320 --> 00:48:51,800
+قطعا يا جماعة البول هدي تقاطع البول هدي لشوفاني
+
+616
+00:48:51,800 --> 00:48:58,740
+أصلا بي X و تلت فش فيها لغير X و ال BY تلت فش فيها
+
+617
+00:48:58,740 --> 00:49:04,020
+لغير ال Y و ال X مابتساوي شوية لازم تقاطع طيب ماشي
+
+618
+00:49:04,020 --> 00:49:12,480
+الحاجة إذا صار عندىلاحظوا أن أي XY مختلفة هيكون
+
+619
+00:49:12,480 --> 00:49:18,000
+اللي هو بلاج بول حوالينها دي و بول حوالينها دي
+
+620
+00:49:18,000 --> 00:49:22,540
+أشمالهم disjoint نكمل القصة، شوف إيش اللي بدهوا
+
+621
+00:49:22,540 --> 00:49:25,720
+إياه يا عزيزي hence we have uncountable number of
+
+622
+00:49:25,720 --> 00:49:33,870
+balls that are not intersectمستحيل يتقاطعي اذا
+
+623
+00:49:33,870 --> 00:49:37,590
+الان how though m is dense in l infinity لكن احنا
+
+624
+00:49:37,590 --> 00:49:40,950
+بنقول قاعدين ان m ايش ما لها dense in l infinity
+
+625
+00:49:40,950 --> 00:49:45,410
+اذا each of the above balls اللي حكينا عنها must
+
+626
+00:49:45,410 --> 00:49:49,410
+contain an element of مين فعلا عشان تكون ان هي
+
+627
+00:49:49,410 --> 00:49:52,790
+dense بظبط مش احنا بنقول m is dense ايش معنات m
+
+628
+00:49:52,790 --> 00:49:58,030
+بيبقى معناه عندنا m is dense in اللي هو مين قلبي
+
+629
+00:49:58,890 --> 00:50:08,290
+إذا أي بول حوالين أي نقطة
+
+630
+00:50:08,290 --> 00:50:17,550
+X وأنا أخدت مثلا تلت تقاطه الأم أشماله ليسوا فايل
+
+631
+00:50:17,550 --> 00:50:21,830
+وهذه العدد الأشمال هي الـ uncountable درنا إذا صار
+
+632
+00:50:21,830 --> 00:50:25,110
+في الام إيش فيه عندي uncountable number of points
+
+633
+00:50:25,920 --> 00:50:32,060
+إذا بدأت بم dense ووصلت
+
+634
+00:50:32,060 --> 00:50:34,560
+مدامة م dense إذا تحتوي on countable number of
+
+635
+00:50:34,560 --> 00:50:37,600
+elements إذا هذا بيقول لي إنه there is no
+
+636
+00:50:37,600 --> 00:50:42,540
+countable dense subset من ال L infinity ومعناته إن
+
+637
+00:50:42,540 --> 00:50:46,430
+ال V is not separableإذن، لذلك، لدينا عدد غير
+
+638
+00:50:46,430 --> 00:50:50,950
+مقارنة من حجمين لا يتعامل مع بعضهم، ولكن M هو نسبة
+
+639
+00:50:50,950 --> 00:50:55,090
+لـInfinity، وكما قلت، فكل حجم من الأعلى يجب أن
+
+640
+00:50:55,090 --> 00:51:00,170
+يحتوي على حجم M، لذلك M نفسية شمالها لديها عدد غير
+
+641
+00:51:00,170 --> 00:51:03,770
+مقارنة من حجمين، ومنذ أن M كانت عبارة عن نفسها،
+
+642
+00:51:03,770 --> 00:51:08,560
+فInfinity ليستالـ separable و بيكون .. هيك احنا
+
+643
+00:51:08,560 --> 00:51:12,120
+خلصنا المحاضرة الرابعة و عندنا ال homework اللي هي
+
+644
+00:51:12,120 --> 00:51:15,800
+star اللي هي ستة واربعتاش و ان شاء الله إلى لقاء
+
+645
+00:51:15,800 --> 00:51:17,640
+آخر السلام عليكم و رحمة الله و بركاته
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/J7SCFPaCRLU.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/J7SCFPaCRLU.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8463ce4af118b36b0978310dd8b85857aa8df513
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/J7SCFPaCRLU.srt
@@ -0,0 +1,2387 @@
+1
+00:00:05,690 --> 00:00:08,790
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,790 --> 00:00:11,910
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:11,910 --> 00:00:17,250
+آله وصحبه أجمعين هذه المحاضرة التاسعة مساق تحليل 
+
+4
+00:00:17,250 --> 00:00:20,150
+دالي أو تحليل اقتراني لطلاب وطالبات الجامعة
+
+5
+00:00:20,150 --> 00:00:24,470
+الإسلامية ماجستير رياضيات اليوم إن شاء الله هنكمل 
+
+6
+00:00:24,470 --> 00:00:27,830
+اللي هو في الـ section نبدأ في الـ section اللي هو
+
+7
+00:00:27,830 --> 00:00:32,070
+اثنين ثلاثة اللي هو further properties of normed
+
+8
+00:00:32,070 --> 00:00:37,220
+spaces اللي هيخليني أحكي عن خواص أخرى اللي هو للـ 
+
+9
+00:00:37,220 --> 00:00:41,720
+Normed Space الآن نبدأ اللي هو بالتعريف التالي
+
+10
+00:00:41,720 --> 00:00:47,300
+التعريف اللي هو كمّيًّا بيقول لي a subspace Y of a
+
+11
+00:00:47,300 --> 00:00:51,000
+normed space X is a subset of X considered as a 
+
+12
+00:00:51,000 --> 00:00:54,440
+vector space with a norm in Y obtained by
+
+13
+00:00:54,440 --> 00:00:58,960
+restricting the norm in X to Y يعني 
+
+14
+00:00:58,960 --> 00:01:03,240
+الـ X-normed space لأن لو كانت عندي Y مجموعة جزئية 
+
+15
+00:01:03,240 --> 00:01:07,720
+من X والـ Y اللي هو الـ .. الـ .. الـ norm اللي عليها هو
+
+16
+00:01:07,720 --> 00:01:09,860
+الـ norm اللي .. اللي .. اللي .. اللي هي الـ norm
+
+17
+00:01:09,860 --> 00:01:14,680
+الأصلي تبع X وكانت Y نفسها subspace as a vector 
+
+18
+00:01:14,680 --> 00:01:18,160
+space من X فبكون عندي في هذه الحالة بنسمي Y
+
+19
+00:01:18,160 --> 00:01:24,880
+نسميها as a normed subspace من مين؟ من اللي هو X
+
+20
+00:01:25,500 --> 00:01:30,340
+هذا تعريف اللي هو normed subspace نطلع في نظرية
+
+21
+00:01:30,340 --> 00:01:35,220
+أخذناها إحنا في اللي هو 148 نظرية كانت بتقول إن هو
+
+22
+00:01:35,220 --> 00:01:38,560
+subspace M of a complete metric space في الـ metric 
+
+23
+00:01:38,560 --> 00:01:42,720
+space X is itself complete if and only if the
+
+24
+00:01:42,720 --> 00:01:47,500
+subset M is closed in X الآن ما إحنا عارفين إن كل
+
+25
+00:01:47,500 --> 00:01:51,300
+normed space عبارة عن metric space إذًا اللي بنطبق
+
+26
+00:01:51,300 --> 00:01:54,200
+على الـ metric space أكيد بنطبق على مين؟ على الـ
+
+27
+00:01:54,200 --> 00:01:58,180
+normed space يعني بمعنى آخر، الآن النظرية 3
+
+28
+00:01:58,180 --> 00:02:01,380
+اثنين ثلاثة automatic هتيجيني من مين؟ من 
+
+29
+00:02:01,380 --> 00:02:05,060
+النظرية واحد أربعة ثمانية، إيش بتقول هذه النظرية؟
+
+30
+00:02:05,060 --> 00:02:09,140
+إن a subspace Y of Banach space X، طبعًا Banach space
+
+31
+00:02:09,140 --> 00:02:12,080
+معناها complete normed space، يعني complete metric
+
+32
+00:02:12,080 --> 00:02:17,880
+space اللي هي a subspace Y of Banach space X is
+
+33
+00:02:17,880 --> 00:02:22,180
+complete اللي هي هذه اللي هي Y complete if and 
+
+34
+00:02:22,180 --> 00:02:26,860
+only if إيش مالها Y is closed اللي هي subspace من
+
+35
+00:02:26,860 --> 00:02:30,980
+من من الـ X إذًا هذه النظرية ما هي إلا حالة خاصة من 
+
+36
+00:02:30,980 --> 00:02:34,020
+النظرية 148 النظرية 148 على metric space in 
+
+37
+00:02:34,020 --> 00:02:37,680
+general هذه عالمين على اللي هو واحد من الـ metric 
+
+38
+00:02:37,680 --> 00:02:41,480
+spaces اللي هو الـ metric space المولّد أو الـ 
+
+39
+00:02:41,480 --> 00:02:46,040
+induced by the norm ماشي الحال إذًا هذه automatic من 
+
+40
+00:02:46,040 --> 00:02:50,520
+1 4 8 يعني نيجي الآن لبعض الملاحظات اللي بدنا 
+
+41
+00:02:50,520 --> 00:02:55,120
+نحكي فيها عشان تلزمنا اللي هو لاحقًا الآن a 
+
+42
+00:02:55,120 --> 00:02:58,540
+sequence xn in a normed space x is convergent 
+
+43
+00:02:58,540 --> 00:03:02,940
+if there is x a limit in x such that limit norm الـ 
+
+44
+00:03:02,940 --> 00:03:07,280
+xn ناقص x يساوي 0 as n goes to infinity مش جديد هذا
+
+45
+00:03:07,280 --> 00:03:10,820
+يا جماعة إحنا لما عرفنا الـ sequence إنّها converge
+
+46
+00:03:10,820 --> 00:03:16,170
+xn converge لـ x في metric space X والـ D إيش قلنا
+
+47
+00:03:16,170 --> 00:03:22,370
+إنّه اللي هو limit للـ distance بين xn و x as n 
+
+48
+00:03:22,370 --> 00:03:26,150
+goes to infinity إيش يساوي؟ يساوي صفر طيب ما هو الـ
+
+49
+00:03:26,150 --> 00:03:30,890
+norm اللي عندنا إحنا هنا هو عبارة عن metric يعني 
+
+50
+00:03:30,890 --> 00:03:34,590
+الآن لو بدنا نطبق هذا الكلام على الـ metric اللي
+
+51
+00:03:34,590 --> 00:03:38,590
+عندنا اللي هو norm ما هو هذا إيش بيمثل؟ بيمثل
+
+52
+00:03:38,590 --> 00:03:43,400
+عبارة عن norm الـ xn ناقص x اللي هو limit له as n 
+
+53
+00:03:43,400 --> 00:03:46,980
+goes to infinity يساوي صفر إذًا التعريف هذا مش 
+
+54
+00:03:46,980 --> 00:03:51,280
+تعريف جديد ما هو إلا عبارة عن تطبيق لتعريف سابق
+
+55
+00:03:51,280 --> 00:03:53,520
+أخذناه في الـ metric space شو معناه الـ xn 
+
+56
+00:03:53,520 --> 00:03:58,560
+converge لـ some x اللي هو بيكون limit لـ اللي هو الـ 
+
+57
+00:03:58,560 --> 00:04:02,400
+norm اللي هو الـ distance بين xn و x as n goes to
+
+58
+00:04:02,400 --> 00:04:06,360
+infinity يساوي صفر بس كتبناه بلغة الـ norm على أساس
+
+59
+00:04:06,360 --> 00:04:10,300
+إنّه هنقدر نشتغل عليه الآن بناءً على هذا التعريف 
+
+60
+00:04:12,030 --> 00:04:16,970
+إحنا خلّيني نقول عرفنا اللي هو شو معناه xn 
+
+61
+00:04:16,970 --> 00:04:20,510
+-convergent طيب إذا في شيء ثاني دائماً بنحكي و
+
+62
+00:04:20,510 --> 00:04:24,210
+بنتهدّى له اللي هو لشيء ثاني بنحكي فيه اللي هو شو 
+
+63
+00:04:24,210 --> 00:04:26,330
+معناه للـ sequence كوشي يعني بنحكي عن
+
+64
+00:04:26,330 --> 00:04:29,030
+الـ convergent وبنحكي عن مين الـ convergence وبنحكي
+
+65
+00:04:29,030 --> 00:04:32,910
+عن الـ Cauchy sequence لأن a sequence xn in
+
+66
+00:04:32,910 --> 00:04:37,120
+a normed space x is a كوشي sequence if for every
+
+67
+00:04:37,120 --> 00:04:40,060
+ε أكبر من 0 there exists k element in n such that 
+
+68
+00:04:40,060 --> 00:04:44,160
+norm xn ناقص xm أصغر من ε لكل n و m أكبر من
+
+69
+00:04:44,160 --> 00:04:48,440
+k برضه مش جديد إحنا كنا نقول xn is Cauchy في الـ
+
+70
+00:04:48,440 --> 00:04:51,840
+metric إذا كانت اللي هو for every ε أكبر من 0
+
+71
+00:04:51,840 --> 00:04:55,480
+there exists k element in n such that norm x أي 
+
+72
+00:04:55,480 --> 00:04:59,500
+اللي هو الـ distance بين xn و xm يكون أصغر من ε
+
+73
+00:04:59,500 --> 00:05:04,460
+لكل n أكبر من مين من k أو أكبر أو يساوي k لأن الـ
+
+74
+00:05:04,460 --> 00:05:07,700
+norm الـ metric اللي عندنا اليوم بيشتغل عليه هو 
+
+75
+00:05:07,700 --> 00:05:12,700
+عبارة عن الـ norm xn ناقص xm لأن هذا الـ metric اللي 
+
+76
+00:05:12,700 --> 00:05:16,100
+عندنا اليوم هو الـ induced by the norm إذن برضه مش 
+
+77
+00:05:16,100 --> 00:05:19,940
+تعريف جديد ولكن تطبيق على الـ metric اللي مولّد من 
+
+78
+00:05:19,940 --> 00:05:24,290
+الـ norm طيب نيجي للتعريف اللي بعده بناءً عليه طبعًا 
+
+79
+00:05:24,290 --> 00:05:27,150
+إحنا لإن إحنا في normed space يا جماعة ما دام 
+
+80
+00:05:27,150 --> 00:05:31,050
+في normed space إذًا هو عبارة عن vector space 
+
+81
+00:05:31,050 --> 00:05:33,450
+يعني عملية الجمع وعملية الـ scalar multiplication 
+
+82
+00:05:33,450 --> 00:05:37,590
+كلها مشروعة عشان هيك الآن إحنا أكثر
+
+83
+00:05:37,590 --> 00:05:41,570
+حرية قبل كنا نأخذ لما نأخذ نأخذ metric space بيكون
+
+84
+00:05:41,570 --> 00:05:45,890
+عنده X و D X مجرد set فما أقدرش أحكي عن مجموع عناصر 
+
+85
+00:05:45,890 --> 00:05:48,770
+بينها أو scalar multiplication لا لا لا لا 
+
+86
+00:05:48,770 --> 00:05:53,520
+الآن صار عندنا اللي هو عبارة عن norm وهذا عبارة عن
+
+87
+00:05:53,520 --> 00:05:58,000
+norm فهذا عبارة عن vector space مشرّع إلى الحديث
+
+88
+00:05:58,000 --> 00:06:02,160
+عن الجمع وعن الـ scalar multiplication بناءً عليه
+
+89
+00:06:02,160 --> 00:06:06,820
+بنفع أقول الآن على مجموع عناصر يعني بنفع أروح 
+
+90
+00:06:06,820 --> 00:06:11,800
+باتجاه اللي هو series نشوف كيف let xn be a
+
+91
+00:06:11,800 --> 00:06:17,370
+sequence in a normed space X and let S1 be a 
+
+92
+00:06:17,370 --> 00:06:22,030
+sequence of partial sums يعني S1 يساوي x1 S2
+
+93
+00:06:22,030 --> 00:06:28,030
+يساوي x1 زائد x2 S3 يساوي x1 زائد x2 زائد x3 Sn in
+
+94
+00:06:28,030 --> 00:06:32,370
+general x1 زائد x2 زائد xn صارت هذه الـ Sn عبارة عن
+
+95
+00:06:32,370 --> 00:06:36,070
+sequence of partial sums زي اللي أخذناها في
+
+96
+00:06:36,070 --> 00:06:39,230
+الكالكولس العادي بس كنا إحنا اللي عارية نشتغل 
+
+97
+00:06:44,560 --> 00:06:48,900
+إذا كان الـ Sn مرتبط بـ S فإن الـ Infinite Series 
+
+98
+00:06:48,900 --> 00:06:53,860
+Summation xn قد يكون مرتبط بـ S و Sn يسمى بالنسبة
+
+99
+00:06:53,860 --> 00:06:57,520
+للعدد من السلاسل ويقال Sn بالسلمانية xn يعني اللي
+
+100
+00:06:57,520 --> 00:07:07,300
+بيقوله لو عندي أن أعرف شو معنى السلاسل مرتبط الآن 
+
+101
+00:07:07,300 --> 00:07:11,340
+عند الـ sequence of partial sums Sn اللي هي الـ Sn
+
+102
+00:07:11,340 --> 00:07:16,180
+n تساوي x1 زائد xn هذا كله اللي موجود في الـ
+
+103
+00:07:16,180 --> 00:07:22,580
+normed space طيب بنقول إن Sn بتروح لـ S يعني
+
+104
+00:07:22,580 --> 00:07:26,320
+converges to some element اسمه S وبنكتبه summation
+
+105
+00:07:26,320 --> 00:07:30,940
+xn i من عند واحد لما إنه تروح لما نهاية as n goes 
+
+106
+00:07:30,940 --> 00:07:34,060
+to infinity يعني بيصير summation بدل لـ Sn هذا 
+
+107
+00:07:34,060 --> 00:07:38,640
+عبارة عن summation xn i من عند واحد لعند n لأن as 
+
+108
+00:07:38,640 --> 00:07:40,720
+n goes to infinity بيصير الـ summation هذا i من
+
+109
+00:07:40,720 --> 00:07:45,580
+واحد إلى ما لا نهاية بنسميه S يساوي S وبنقول 
+
+110
+00:07:45,580 --> 00:07:48,960
+عنه الـ sequence الـ series في هذه الحالة converges
+
+111
+00:07:48,960 --> 00:07:54,120
+to sum اللي هو element S هذا اللي هو sum of the 
+
+112
+00:07:54,120 --> 00:08:00,600
+series طيب إذا كان الـ norm لـ x1 زائد norm لـ x2
+
+113
+00:08:00,600 --> 00:08:05,180
+زائد norm لـ x3 إلى ما لا نهاية بدل ما أجمع الـ x1 و
+
+114
+00:08:05,180 --> 00:08:08,940
+x2 و x3 بأجمع مين الـ normات اللي هين و أساريتي اللي
+
+115
+00:08:08,940 --> 00:08:12,380
+هي جمع أعداد حقيقية موجبة إذا كان مجموع هدول 
+
+116
+00:08:12,380 --> 00:08:17,900
+exists بنقول summation xn is absolutely convergent 
+
+117
+00:08:17,900 --> 00:08:21,280
+زي ما كنا بالضبط نقول في الـ real إن الـ absolute 
+
+118
+00:08:21,280 --> 00:08:24,620
+value x1 absolute value x2 زائد إلى آخره يكون 
+
+119
+00:08:24,620 --> 00:08:27,480
+convergent بنقول الـ series الأصلية تبعت اللي هي
+
+120
+00:08:27,480 --> 00:08:31,240
+الـ real absolutely convergent وهنا إحنا اللي هو 
+
+121
+00:08:31,240 --> 00:08:34,540
+بنفس الطريقة بتعميم أكبر بدل من نأخذ على الـ R 
+
+122
+00:08:34,540 --> 00:08:38,980
+نفسها بنأخذ على أي normed space ففي هذه الحالة 
+
+123
+00:08:38,980 --> 00:08:41,660
+بنسميها اللي هي absolutely convergent زي ما قلنا 
+
+124
+00:08:42,280 --> 00:08:46,100
+نأخذ الـ definition الآن الـ definition بدنا نعرف 
+
+125
+00:08:46,100 --> 00:08:50,000
+حاجة if a normed space X contains a sequence en
+
+126
+00:08:50,000 --> 00:08:53,640
+ركزوا، إيش الـ sequence هذه؟ with the property 
+
+127
+00:08:53,640 --> 00:08:57,360
+that for every x element in X there exists a 
+
+128
+00:08:57,360 --> 00:09:01,000
+unique sequence of scalars αn such that اللي
+
+129
+00:09:01,000 --> 00:09:05,420
+هو x limit x ناقص α1 e1 α2 e2 زائد αn en as n
+
+130
+00:09:05,420 --> 00:09:10,620
+goes to infinity يساوي صفر ثم αn 
+
+131
+00:09:10,620 --> 00:09:15,360
+بيكون نسميها إيش مالها a Schauder basis for X the
+
+132
+00:09:15,360 --> 00:09:19,740
+series summation xn αi ei i من واحد لإنفينيتي 
+
+133
+00:09:19,740 --> 00:09:23,180
+is called the expansion of x with respect to 
+
+134
+00:09:23,180 --> 00:09:28,060
+αn إذًا الآن في عندنا حاجة اسمها إيش هي Schauder
+
+135
+00:09:28,060 --> 00:09:33,340
+basis إيش Schauder basis كمان مرة؟ هي كتالوج إذا 
+
+136
+00:09:33,340 --> 00:09:40,800
+أخذنا عندي x element in X arbitrary arbitrary و
+
+137
+00:09:40,800 --> 00:09:51,780
+لجينا sequence αn of scalars ماشي الحال بحيث إنّه
+
+138
+00:09:51,780 --> 00:09:58,690
+اللي هي يكون عندها limit للـ norm من الـ x ناقص α
+
+139
+00:09:58,690 --> 00:10:04,550
+1 e1 إيش e1 هنّ جهّزها ونقول لك زائد α2 
+
+140
+00:10:04,550 --> 00:10:09,810
+e2 زائد αn en as n goes to infinity
+
+141
+00:10:09,810 --> 00:10:15,550
+infinity لجناه بيساوي صفر معناته بنقول عن ال
+
+142
+00:10:15,550 --> 00:10:22,260
+sequence هذه اللي هي E1، E2، E3، E4
+
+143
+00:10:22,260 --> 00:10:27,000
+إلى ما لها نهاية اللي بنسميها En بنقول عنها is a
+
+144
+00:10:27,000 --> 00:10:33,770
+Schauder basis for ال space اللي عند X و في
+
+145
+00:10:33,770 --> 00:10:37,650
+هذه الحالة as n goes to infinity بيصير وكأنه
+
+146
+00:10:37,650 --> 00:10:42,650
+بنقول ال norm للـ X ناقص ال summation للـ αi Ei
+
+147
+00:10:42,650 --> 00:10:46,390
+i من عند واحد لعند n لما تروح إلى ما لها نهاية و
+
+148
+00:10:46,390 --> 00:10:49,250
+كأنه بيصير اللي هو مدام ال limit هذا بيساوي صفر و
+
+149
+00:10:49,250 --> 00:10:54,270
+كأنه بنقول X بتساوي ال summation αi Ei i من
+
+150
+00:10:54,270 --> 00:10:59,390
+واحد إلى ما لها نهاية يعني بمعنى آخر بنقول En is a
+
+151
+00:10:59,390 --> 00:11:05,030
+Schauder basis للـ X إذا كان كل X في الـ X بنقدر
+
+152
+00:11:05,030 --> 00:11:10,410
+نلاقي sequence of scalars αn بحيث إنه الـ X
+
+153
+00:11:10,410 --> 00:11:14,790
+هذا انكتبت على صورة Infinite Series αi Ei i
+
+154
+00:11:14,790 --> 00:11:20,930
+من واحد عند مين لعند اللي هو Infinity أي سؤال؟
+
+155
+00:11:24,480 --> 00:11:27,380
+طيب طبعاً هذه الـ sequence اللي جاية unique
+
+156
+00:11:27,380 --> 00:11:32,460
+sequence تنسوش إنه صورة وحيدة على أساس إن كل واحد
+
+157
+00:11:32,460 --> 00:11:40,720
+يطلع له بصيغة مختلفة طبعاً لكل X في unique sequence
+
+158
+00:11:40,720 --> 00:11:43,240
+of scalars αn such that X بالصيغة ال
+
+159
+00:11:43,240 --> 00:11:46,300
+summation هذا مفادلة حول ما نسميه En as a Schauder 
+
+160
+00:11:46,300 --> 00:11:50,430
+basis طيب ناخد مثال مثال على الـ Schauder bases
+
+161
+00:11:50,430 --> 00:11:55,730
+الآن example En is a Schauder basis for الـ
+
+162
+00:11:55,730 --> 00:12:00,270
+lP نشوف إيش En الـ lP عارفينه أنتو وإحنا حكينا عنه
+
+163
+00:12:00,270 --> 00:12:02,930
+بالتفصيل
+
+164
+00:12:03,580 --> 00:12:08,980
+E1 هو عبارة عن واحد والباقي صفار E2 صفر والـ ثاني
+
+165
+00:12:08,980 --> 00:12:13,660
+واحد والباقي صفار E3 صفر صفر واحد والباقي صفار
+
+166
+00:12:13,660 --> 00:12:18,240
+En in general صفر صفر صفر En ناقص واحد من العناصر
+
+167
+00:12:18,240 --> 00:12:22,620
+صفار وبعدين الرقم الـ entry N بتكون واحد والباقي
+
+168
+00:12:22,620 --> 00:12:27,330
+إيش مالهأ صفر هذه الآن اللي هي sequence of elements
+
+169
+00:12:27,330 --> 00:12:30,730
+أكيد وين موجودة؟ موجودة في الـ lP لإن ال summation
+
+170
+00:12:30,730 --> 00:12:35,790
+لها عبارة عن واحد بس فـ finite ده موجود وين في
+
+171
+00:12:35,790 --> 00:12:40,730
+الـ lP مافي أي مشكلة بدنا نثبت إن هذه بتعمل
+
+172
+00:12:40,730 --> 00:12:44,090
+Schauder basis إيش بدنا ناخد؟ بدنا ناخد أي X 
+
+173
+00:12:44,090 --> 00:12:49,070
+arbitrary element ونلاقي ال sequence ناخد X أي 
+
+174
+00:12:49,070 --> 00:12:55,360
+element في الـ lP أيوة يا جماعة بدنا ناخد X أي 
+
+175
+00:12:55,360 --> 00:13:00,220
+element في الـ lP ونلاقي ال sequence of scalars αn 
+
+176
+00:13:00,220 --> 00:13:04,620
+مثلاً أو اللي نسميها بعد شوية بحيث إنه اللي هو 
+
+177
+00:13:04,620 --> 00:13:07,100
+sequence وحيدة إن X نقدر نكتبها على صورة
+
+178
+00:13:07,100 --> 00:13:12,760
+summation αn في En n من واحد إلى وين إلى ما لها
+
+179
+00:13:12,760 --> 00:13:19,160
+نهاية ده نشوف كده خلّا مع بعض الآن let X be any
+
+180
+00:13:19,160 --> 00:13:23,880
+fixed element in lP طبعاً كيف شكله الـ X في الـ lP
+
+181
+00:13:23,880 --> 00:13:28,020
+sequence يعني X1، X2، X3، X4
+
+182
+00:13:28,020 --> 00:13:30,920
+إلى ما لا نهاية إذن X any fixed element in
+
+183
+00:13:30,920 --> 00:13:34,940
+lP إذن مدام في الـ lP إذن أكيد ال summation
+
+184
+00:13:34,940 --> 00:13:39,180
+الـ Xi i، i من واحدة and infinity الـ lP إيش ماله؟
+
+185
+00:13:39,180 --> 00:13:43,380
+is finite، convergent، عشان اللي هو شروط وجوده في
+
+186
+00:13:43,380 --> 00:13:47,640
+الـ lP مدام هيك إذا then there is a sequence Xi i
+
+187
+00:13:47,640 --> 00:13:50,820
+of scalars such that أنا بدعي الآتي إنه بقدر
+
+188
+00:13:50,820 --> 00:13:54,560
+ألاقي sequence of scalars Xi i من وين جبتها اللي
+
+189
+00:13:54,560 --> 00:13:57,960
+هي عناصر ال sequence اللي هاني يعني أخدت X1 و X2 و
+
+190
+00:13:57,960 --> 00:14:02,440
+X3 و X4 هي اللي هي من ال sequence of scalars اللي
+
+191
+00:14:02,440 --> 00:14:08,060
+أنا بديها such that الـ X ناقص بقعد بطبق في التعريف
+
+192
+00:14:08,060 --> 00:14:13,060
+Xi 1 E 1 زي Xi 2 E 2 زي Xi N E N نحسبها مع بعض
+
+193
+00:14:13,570 --> 00:14:18,270
+ونشوف كيف نوصل إن ال limit لهذه بيساوي صفر نكون
+
+194
+00:14:18,270 --> 00:14:21,750
+خلصت، نكون أثبتت إنه فيه وموجود، وبعدين نثبت إنه
+
+195
+00:14:21,750 --> 00:14:27,530
+إيش وحيد، طيب، بساوي، الآن X نفسها عبارة عن مين؟
+
+196
+00:14:27,530 --> 00:14:31,850
+عن E1، E2، En، En، X1، En، X2، sequence إلى ما لا
+
+197
+00:14:31,850 --> 00:14:38,350
+نهاية طيب هيها الـ ||X|| طيب ناقص الآن α1 E1
+
+198
+00:14:39,220 --> 00:14:45,140
+اللي عبارة عن α1 E 1 + α2 E 2 +
+
+199
+00:14:45,140 --> 00:14:51,200
+αn En ماعملتش فيها ولا شيء لسه ماهي الحال و
+
+200
+00:14:51,200 --> 00:14:58,580
+يساوي الآن خلينا نحسبها هذه نحسب هذه الآن نحسب هذه
+
+201
+00:14:58,580 --> 00:15:07,640
+نحسب α1 E 1 لعند αn En لعند هذه نشوف
+
+202
+00:15:07,640 --> 00:15:13,850
+إيش هي α1 E1 + α2 E2
+
+203
+00:15:13,850 --> 00:15:20,970
++ αn En ويساوي α Xi1 في Xi1
+
+204
+00:15:20,970 --> 00:15:21,210
+n
+
+205
+00:15:25,070 --> 00:15:30,130
+في E1 E1 يعني عبارة عن 1 0 0 إلى ما لا نهاية
+
+206
+00:15:30,130 --> 00:15:37,750
++ ال Xi2 في 0 1 0 0 + لما أصل
+
+207
+00:15:37,750 --> 00:15:44,870
+للأخيرة اللي هي Xin في 0 0 لما أصل لل term N
+
+208
+00:15:44,870 --> 00:15:51,390
+اللي هو 1 والباقي أشمله صفر ويساوي نيجي نحسب
+
+209
+00:15:51,390 --> 00:15:58,020
+إن Xi 1 وهدولة صفار صفار Xi 2 والباقي
+
+210
+00:15:58,020 --> 00:16:02,280
+صفار لما أصل عند مين Xi n واللي بعدهم كلهم
+
+211
+00:16:02,280 --> 00:16:08,700
+إيش يا جماعة صفار طيب الآنصار هذا عبارة عن هذا ..
+
+212
+00:16:08,700 --> 00:16:14,640
+هذا اللي مهشر عليه اللي هو X1 و X2 و X3 و Xn و
+
+213
+00:16:14,640 --> 00:16:19,800
+الباقي 0 لما أطرح حد ناقص هذا هيروح من الأولانيات
+
+214
+00:16:19,800 --> 00:16:24,420
+هيطلع 0 .. 0 .. 0 .. 0 ويضل مين اللي هي ال
+
+215
+00:16:24,420 --> 00:16:27,460
+terms دولة لأنهم لما نطرح منهم الأسفار بيضل هنا
+
+216
+00:16:27,460 --> 00:16:32,070
+Xn X1 Xn X2 إلى ما لا نهاية واضح حاصل طرح
+
+217
+00:16:32,070 --> 00:16:36,750
+الجهتين هذا الآن مجموعته إيش بيساوي بيساوي مجموعته
+
+218
+00:16:36,750 --> 00:16:41,150
+اللي هو الـ ||.|| ||.|| أنا وين بشتغل في الـ lP و
+
+219
+00:16:41,150 --> 00:16:44,490
+الـ lP norm إيش ماله ال summation للـ absolute values
+
+220
+00:16:44,490 --> 00:16:48,890
+ده دول ال terms أس p الكل 1/p هي Xi i
+
+221
+00:16:48,890 --> 00:16:52,930
+أس p الكل 1/p i الأولانيات من واحد لأم
+
+222
+00:16:52,930 --> 00:16:56,470
+نصفار إذا بيبدأ ال summation هنا زائد واحد أمين
+
+223
+00:16:56,470 --> 00:17:01,090
+لما لها نهاية as n goes to infinity هذا ال summation
+
+224
+00:17:01,090 --> 00:17:04,890
+بتلاشى as n goes to infinity هيروح لوين لعين صفر
+
+225
+00:17:04,890 --> 00:17:07,410
+لما قلت روح لما قلت هذا ال summation هيتلاشى ويروح
+
+226
+00:17:07,410 --> 00:17:11,970
+لـ 0 as n goes to infinity إذا إن أنا اللي جيت
+
+227
+00:17:11,970 --> 00:17:23,130
+سويته إن أنا اللي سويته أثبتت لك إنه limit||X||
+
+228
+00:17:23,130 --> 00:17:29,790
+ناقص summation Xi i Ei i من عند واحد لعند n as n
+
+229
+00:17:29,790 --> 00:17:34,730
+goes to infinity إيش بيساوي؟ بيساوي 0 دل أثبت إنه
+
+230
+00:17:34,730 --> 00:17:38,570
+وحيدة اللي هي ال sequence of scalars وحيدة يعني ال
+
+231
+00:17:38,570 --> 00:17:42,850
+sequence of scalars اللي جيت Xi i هذه اللي هي نفس
+
+232
+00:17:42,850 --> 00:17:46,670
+تركيبة مين الـ X اللي جوا اللي أخدتها منها اللي هي
+
+233
+00:17:46,670 --> 00:17:52,940
+هتكون إيه أشماله as unique اطلع لفوق Now assume
+
+234
+00:17:52,940 --> 00:17:56,980
+that there is a sequence ثانية αi of scalars such
+
+235
+00:17:56,980 --> 00:18:03,740
+that X - α1 E1 + α2 E2 + αn En بتروح لـ 0 إذن
+
+236
+00:18:03,740 --> 00:18:08,080
+اجثمين تنفيذ لان افترض إن هي أشماله في واحدة ثانية
+
+237
+00:18:08,080 --> 00:18:11,700
+بتحقق نفس الشروط الأولى وبعدين اثبت لك إنه هتطلع
+
+238
+00:18:11,700 --> 00:18:16,520
+حد الـ sequence αi هي نفسها مين لـ Xi i فبتكون خلاص
+
+239
+00:18:16,520 --> 00:18:19,830
+is unique إلى and then الـ absolute value للـ
+
+240
+00:18:19,830 --> 00:18:22,990
+summation هذا هو عبارة عن إيش عبارة عن الـ
+
+241
+00:18:22,990 --> 00:18:27,470
+summation Xi i - αi Ei i من عند واحد لعند
+
+242
+00:18:27,470 --> 00:18:33,890
+مين لعند n هذه حسبتها ||X|| نحسب لكم إياها هنا
+
+243
+00:18:41,120 --> 00:18:54,240
+ممكن تحسبوها لحالكم لكن خلّينا نحسب الهدف
+
+244
+00:18:54,240 --> 00:18:57,520
+اللي فرضناه ونحسب هذه الهدف عشان نوصلها لما نريده
+
+245
+00:18:59,970 --> 00:19:03,390
+الـ Xi i - αi في Ei i من عند واحد لعند n
+
+246
+00:19:03,390 --> 00:19:08,370
+بدنا نفردها الـ Ei هدولة scalars والـ E1 عبارة
+
+247
+00:19:08,370 --> 00:19:12,010
+عن 1 0 0 0 ولا أخرى بيصير هذه عبارة
+
+248
+00:19:12,010 --> 00:19:23,020
+عن Xi i أبدا بالأولى i أبدا
+
+249
+00:19:23,020 --> 00:19:25,480
+بالأولى i أبدا بالأولى i أبدا بالأولى i أبدا
+
+250
+00:19:25,480 --> 00:19:26,260
+بالأولى i أبدا بالأولى i أبدا بالأولى i أبدا
+
+251
+00:19:26,260 --> 00:19:26,300
+بالأولى i أبدا بالأولى i أبدا بالأولى i أبدا
+
+252
+00:19:26,300 --> 00:19:26,420
+بالأولى i أبدا بالأولى i أبدا بالأولى i أبدا
+
+253
+00:19:26,420 --> 00:19:26,440
+بالأولى i أبدا بالأولى i أبدا بالأولى i أبدا
+
+254
+00:19:26,440 --> 00:19:26,560
+بالأولى i أبدا بالأولى i أبدا بالأولى i أبدا
+
+255
+00:19:26,560 --> 00:19:35,040
+بالأولى i أبدا بالأولى i أبدا بالأولى X - اللي
+
+256
+00:19:35,040 --> 00:19:40,680
+هو الأولى اللي هي هذه + 
+
+257
+00:19:40,680 --> 00:19:45,100
+اللي هو ||X|| الثانية X - مين الثانية يعني ضفت X
+
+258
+00:19:45,100 --> 00:19:48,520
+وطرحت مين X واستخدمت الـ triangle inequality طب
+
+259
+00:19:48,520 --> 00:19:53,380
+الآن هذه ما هي من الحالة الأولى ما هي X كتبت على
+
+260
+00:19:53,380 --> 00:19:58,800
+صورة الـ summation هذا يعني بمعنى آخر هذا الـ
+
+261
+00:19:58,800 --> 00:20:01,620
+limit له بيساوي صفر وهذا ال limit بيساوي صفر اللي
+
+262
+00:20:01,620 --> 00:20:05,520
+فرضته هنا إذا صار ال limit لهذا كله أشمله بيساوي
+
+263
+00:20:05,520 --> 00:20:11,650
+صفر إذا as n goes to infinity بيصير هذا المقدار i من
+
+264
+00:20:11,650 --> 00:20:15,550
+عند واحد إلى ما لا نهاية بيساوي صفر اطلع لفوق then
+
+265
+00:20:15,550 --> 00:20:19,090
+as n goes to infinity هذا المقدار بيروح للصفر
+
+266
+00:20:19,090 --> 00:20:22,170
+معناته إيش معناته هذا لما قالنا تروح إلى ما لا
+
+267
+00:20:22,170 --> 00:20:26,970
+نهاية يعني i من واحد إلى ما لا نهاية Xi i Ei - 
+
+268
+00:20:26,970 --> 00:20:31,810
+الـ αi Ei إيش بيساوي بيساوي اللي هو صفر هذا إيش هو في
+
+269
+00:20:31,810 --> 00:20:39,310
+الواقع اللي هو Xi i - αi as a sequence كيف؟
+
+270
+00:20:39,310 --> 00:20:45,790
+لأن هذا ال summation عبارة عن Xi i - Ei - 
+
+271
+00:20:45,790 --> 00:20:51,580
+αi في i ال summation i من واحد إلى ما لها نهاية
+
+272
+00:20:51,580 --> 00:20:56,620
+خلّينا نفردها بيساوي الآن الأولى عبارة عن Xi 1
+
+273
+00:20:56,620 --> 00:21:01,140
+- α1 في E1 هتطلع والباقي صفار
+
+274
+00:21:01,140 --> 00:21:07,520
+ماشي + الثانية صفر Xi 2 - α2
+
+275
+00:21:07,520 --> 00:21:13,230
+والباقي إيش صفار الآن اللي عند ما أصل عند آخر
+
+276
+00:21:13,230 --> 00:21:18,270
+واحدة 0 0 0 عند n من العناصر بيصير Xi n
+
+277
+00:21:18,270 --> 00:21:24,450
+- En - αn والباقي صفار مافي الحال و
+
+278
+00:21:24,450 --> 00:21:27,170
+بيضلوا إلى ما لا نهاية هذا في الواقع إيش هيكون
+
+279
+00:21:27,170 --> 00:21:31,410
+عبارة عن الـ .. هي عبارة عن صفر إيش مالها اللي هي
+
+280
+00:21:31,410 --> 00:21:36,390
+مجموعه مع بعض هي عبارة عن || اللي هو Xi 1 -
+
+281
+00:21:36,390 --> 00:21:44,620
+Alpha 1 Xi 2 نقص ألف اتنين مجمعين مجمعين و XI تلاتة
+
+282
+00:21:44,620 --> 00:21:50,780
+نقص ألف تلاتة و XI N نقص ألف N وهذا بيضلوا إلى مين
+
+283
+00:21:50,780 --> 00:21:53,980
+إلى مالة نهاية إذا في الواقع هذه اللي جوايا شمالها
+
+284
+00:21:53,980 --> 00:21:59,280
+هي ال sequence هذه XI I نقص ألف I لأن هذه صارت
+
+285
+00:21:59,280 --> 00:22:03,460
+بتساوي صفر معناته مدام النور بيساوي صفر إذا اللي
+
+286
+00:22:03,460 --> 00:22:06,640
+جوا بيساوي صفر معناته أن ال sequence هذه بتساوي ال
+
+287
+00:22:06,640 --> 00:22:09,860
+sequence هذه ومعناته اللي هو ال E أنصار إيش ماله
+
+288
+00:22:09,860 --> 00:22:14,660
+is a Schauder basis لإنه حقق الشرطين إن لكل X في
+
+289
+00:22:14,660 --> 00:22:18,750
+القلبي there exists a unique اللي هي مين اللي هي
+
+290
+00:22:18,750 --> 00:22:22,110
+sequence of scalars such that الـ X can be written
+
+291
+00:22:22,110 --> 00:22:28,150
+as a summation of Alpha N في اللي هي E N أو Xi N
+
+292
+00:22:28,150 --> 00:22:31,950
+في E N من N من 1 إلى ما لا نهاية إذا صارت الـ E N is
+
+293
+00:22:31,950 --> 00:22:38,250
+a Schauder basis نيجي الآن لاللي هو النظرية
+
+294
+00:22:38,250 --> 00:22:42,650
+التالية اللي هي completion of a normed space
+
+295
+00:22:48,170 --> 00:22:53,190
+في الواقع هي هذه امتداد للنظرية اللي أخدناها في
+
+296
+00:22:53,190 --> 00:22:59,050
+اللي هي section 16 هي عندي اللي هو theorem اللي هو
+
+297
+00:22:59,050 --> 00:23:05,910
+162 أخدنا اللي هو النظرية كانت انه for any metric
+
+298
+00:23:05,910 --> 00:23:10,250
+space X وD بنقدر نلاجي completion metric space X
+
+299
+00:23:10,250 --> 00:23:16,650
+hat وD hat which has a subspace W as isometric with
+
+300
+00:23:16,650 --> 00:23:21,470
+X and is dense in X hat وقلنا هذا اللي هو X hat is
+
+301
+00:23:21,470 --> 00:23:26,330
+unique up to isomorphism هذه شرحناها بشكل كامل
+
+302
+00:23:26,330 --> 00:23:31,990
+في المحاضرة اللي هو السابعة عشان هيك أنا بفضل إن أنت
+
+303
+00:23:31,990 --> 00:23:35,330
+مجرد ما بدك تسمع هذه المحاضرة لليوم إنك تروح
+
+304
+00:23:35,330 --> 00:23:39,820
+للمحاضرة السابعة وتحضرها ومن ثم أكمل على الكلام
+
+305
+00:23:39,820 --> 00:23:41,860
+اللي بدأ أحكيه لأنه أنا بدأ أكمل على البرهان اللي
+
+306
+00:23:41,860 --> 00:23:46,840
+هنا هذا البرهان كان اللي هو عبارة عن عن اللي هي
+
+307
+00:23:46,840 --> 00:23:51,240
+للنظرية اللي هي on metric space أن any metric
+
+308
+00:23:51,240 --> 00:23:55,240
+space can be completed الآن بدأ أقول أن any normed
+
+309
+00:23:55,240 --> 00:23:58,220
+space can be completed ترجع لي على ال .. على
+
+310
+00:23:58,220 --> 00:24:03,660
+النظرية تبعتنا اليوم خلينا نشوف اللي هو الكلام
+
+311
+00:24:03,660 --> 00:24:09,980
+اللي بدنا نحكيه الآن اللي هو بيقول لي theorem اللي
+
+312
+00:24:09,980 --> 00:24:15,340
+هو 236 completion يعني لو أخدنا X بي A
+
+313
+00:24:15,340 --> 00:24:22,220
+normed space then there is a Banach space X hat and is
+
+314
+00:24:22,220 --> 00:24:26,400
+an isometry A from X to a subspace and to a subspace
+
+315
+00:24:26,400 --> 00:24:31,300
+W of X hat which is dense in X hat the space X hat
+
+316
+00:24:31,300 --> 00:24:35,100
+is unique except for isometries أنا في الواقع هذه
+
+317
+00:24:35,100 --> 00:24:40,000
+النظرية مبرهنها لإيش؟ مبرهنها في حال أن X metric
+
+318
+00:24:40,000 --> 00:24:45,500
+space يعني الآن كل ما يتعلق بوجود الـ X hat موجود
+
+319
+00:24:45,500 --> 00:24:50,350
+من الأصل بس موجود as a metric space أنا الآن إيش
+
+320
+00:24:50,350 --> 00:24:56,850
+دوري بدي أسويه بدي أخلي اللي هو اللي هو ال X هذا
+
+321
+00:24:56,850 --> 00:25:01,010
+ال X هذا بدي أركبه الآن as a normed space إذا
+
+322
+00:25:01,010 --> 00:25:05,750
+انبقى علي أني أشوف ال X hat أن أعملها vector space
+
+323
+00:25:05,750 --> 00:25:09,010
+يعني معناته بدي أعرف scalar multiplication و بدي
+
+324
+00:25:09,010 --> 00:25:12,210
+أعرف اللي هو vector addition بالاستعانة بال X
+
+325
+00:25:12,210 --> 00:25:17,400
+الأصلية والآن اللي هي الشغلة الثانية ال isometric
+
+326
+00:25:17,400 --> 00:25:23,820
+اللي كان بين ال W و ال X اللي هي W و ال X كان جاب لي
+
+327
+00:25:23,820 --> 00:25:27,340
+اللي هو بس one to one  onto function و preserves
+
+328
+00:25:27,340 --> 00:25:30,790
+the distance اللي هي preserves the norm الآن بده
+
+329
+00:25:30,790 --> 00:25:35,130
+شرط ثالث إنه بده يحافظ على اللي هو الأنصار اللي هي
+
+330
+00:25:35,130 --> 00:25:38,810
+ال isometric بين vector space و vector space إذا
+
+331
+00:25:38,810 --> 00:25:41,850
+بده ينقل عملية الجمع و عملية ال scalar
+
+332
+00:25:41,850 --> 00:25:45,610
+multiplication عشان يسميه isometry يعني بمعنى آخر
+
+333
+00:25:45,610 --> 00:25:52,750
+الآن ال isometry T بين X لعين W أول شيء Preserve
+
+334
+00:25:52,750 --> 00:25:55,150
+the norm أو Preserve the distance اللي قلناه المرة
+
+335
+00:25:55,150 --> 00:25:59,410
+الفاية و one to one و onto وهذا مثبت من قبل
+
+336
+00:25:59,410 --> 00:26:04,710
+الشيء الثاني يجب أن نثبت أن T تحافظ على Alpha X
+
+337
+00:26:06,420 --> 00:26:11,200
+زائد Y بتساوي اللي هو إيه شمالها اللي هو Alpha في
+
+338
+00:26:11,200 --> 00:26:16,840
+TX زائد TY يعني بتحافظ على العملية الجامعة ب
+
+339
+00:26:16,840 --> 00:26:20,760
+preserve the operation يعني بمفهوم اللي هو الجبر
+
+340
+00:26:20,760 --> 00:26:24,780
+الخطي Linear اللي هو تكون T Linear و تحافظ على ال
+
+341
+00:26:24,780 --> 00:26:27,760
+scalar multiplication إذا هي اللي بدنا نسويها بس
+
+342
+00:26:27,760 --> 00:26:30,640
+إحنا بدنا نكمل على اللي هو السابق خلينا نشوف مع
+
+343
+00:26:30,640 --> 00:26:36,000
+بعض طيب الآن by theorem 162 there is a complete
+
+344
+00:26:36,000 --> 00:26:39,600
+metric space X hat ال metric هنا اللي هو induced
+
+345
+00:26:39,600 --> 00:26:47,340
+by the norm there is a metric space X hat المقصود
+
+346
+00:26:47,340 --> 00:26:51,520
+أنه ال metric اللي بدو ييجي هنا اللي هو اعتمد على
+
+347
+00:26:51,520 --> 00:26:54,700
+ال metric اللي في ال X اللي هو اللي induced by the
+
+348
+00:26:54,700 --> 00:27:00,410
+norm and an isometry A من X لعين W اللي سميناها في
+
+349
+00:27:00,410 --> 00:27:04,390
+حين و إيه شمالها A of X و كنا عارفين كيف أرسلناها
+
+350
+00:27:04,390 --> 00:27:08,430
+راجعوا المحاضرة where A where W is dense in X hat
+
+351
+00:27:08,430 --> 00:27:14,450
+and X hat أثبتناها as A is unique except
+
+352
+00:27:14,450 --> 00:27:19,380
+for isometries طيب، الآن هذا الكلام كله من المحاضرة
+
+353
+00:27:19,380 --> 00:27:22,460
+السابقة وفصلنا تفصيل وأخذنا محاضرة كاملة بيجي
+
+354
+00:27:22,460 --> 00:27:26,300
+حوالي ساعة و نص أو أكثر على برهان النظرية الآن
+
+355
+00:27:26,300 --> 00:27:30,100
+بدنا نكمل بما يتعلق بال normed space بدأ أبدأ
+
+356
+00:27:30,100 --> 00:27:34,040
+أعرف لك اللي هو عملية جمع وعملية scalar
+
+357
+00:27:34,040 --> 00:27:36,920
+multiplication على مين على ال X hat عشان هذا أقول لك
+
+358
+00:27:36,920 --> 00:27:41,620
+إن X hat هتمثل لي vector من S base طيب كيف بدأ
+
+359
+00:27:41,620 --> 00:27:49,290
+أعملها؟ عندي let X hat و Y hat element in X hat إذا
+
+360
+00:27:49,290 --> 00:27:52,310
+بتذكروا إحنا الـ X hat كانت عبارة عن equivalency
+
+361
+00:27:52,310 --> 00:27:55,390
+class اللي هي ال equivalency class كانت اللي هي في
+
+362
+00:27:55,390 --> 00:27:57,810
+داخلها أو اللي عامل اللي هي مين هي Cauchy
+
+363
+00:27:57,810 --> 00:28:00,470
+sequences وكلنا الـ Cauchy sequences اللي هي
+
+364
+00:28:00,470 --> 00:28:03,450
+العلاقة في بعض كان في نفس مين ال equivalency class
+
+365
+00:28:03,450 --> 00:28:07,530
+هذا كله شرحناه المرة الماضية الآن بتاخد أي X n
+
+366
+00:28:07,530 --> 00:28:10,230
+موجودة في الـ X hat sequence إنه equivalency class
+
+367
+00:28:10,750 --> 00:28:16,310
+الآن و Y n و Y n موجودة في الـ Y hat ماشي الآن بدي
+
+368
+00:28:16,310 --> 00:28:21,530
+أعرف الآن اللي هو احصل على اللي هي Z hat مستوى X
+
+369
+00:28:21,530 --> 00:28:27,100
+hat زائد Y hat كيف بدي احصلها ركزوا معي الآن عندي
+
+370
+00:28:27,100 --> 00:28:30,560
+لو جيت لحظة تشوف الـ Cauchy Sequences الـ Z n تين
+
+371
+00:28:30,560 --> 00:28:35,420
+هدولة لو جمعتها لبعض وسميتها Z n إيش بيكون هدولة الـ
+
+372
+00:28:35,420 --> 00:28:39,760
+Z n الجديدة؟ بتكون الـ Z n عبارة عن Cauchy اللي هو
+
+373
+00:28:39,760 --> 00:28:43,460
+إيش Sequence ليش؟ لأن X n Cauchy و Y n Cauchy
+
+374
+00:28:43,460 --> 00:28:46,020
+مجموعته Cauchy Sequences إيش هيطلع؟ Cauchy
+
+375
+00:28:46,020 --> 00:28:50,500
+Sequence إذا الآن Z n Cauchy Sequence الآن بما إنه
+
+376
+00:28:50,500 --> 00:28:54,780
+زي ما بقول لك X N and Y N are Cauchy Sequences إذن Z N
+
+377
+00:28:54,780 --> 00:28:59,640
+is a Cauchy Sequence الآن define Z hat بتساوي X
+
+378
+00:28:59,640 --> 00:29:04,680
+hat زائد Y hat كيف؟ مين هي ال Z hat؟ هذه ال Z hat
+
+379
+00:29:04,680 --> 00:29:08,600
+اللي هي بدها تتحقق equivalency class اللي بدها
+
+380
+00:29:08,600 --> 00:29:12,740
+تتحدد هويتها بواسطة من ال Z N يعني ال Cauchy
+
+381
+00:29:12,740 --> 00:29:16,680
+Sequence اللي طلعت من مجمع هذه زائد هذه ال
+
+382
+00:29:16,680 --> 00:29:21,240
+equivalence class تبعي تاخدها وسميها إيش مالها Z
+
+383
+00:29:21,240 --> 00:29:25,020
+hat إذا عملية الجمع صارت واضحة في ال X hat في ال X
+
+384
+00:29:25,020 --> 00:29:28,080
+hat عملية الجمع كده باجي باجمع باخد X hat
+
+385
+00:29:28,080 --> 00:29:32,470
+arbitrary هات و Y hat arbitrary هات إنما بقول X hat
+
+386
+00:29:32,470 --> 00:29:36,970
+زائد Y hat إيش بيساوي Z hat طب مين Z hat هذه؟ هذه
+
+387
+00:29:36,970 --> 00:29:43,110
+Z hat اللي هي بتساوي Z N اللي هي ال equivalence
+
+388
+00:29:43,110 --> 00:29:47,330
+class لها طب مين Z N هذه؟ Z N هي اللي ناتجة من
+
+389
+00:29:47,330 --> 00:29:52,370
+sequence من هنا زائد sequence من هنا إذن صارت الآن
+
+390
+00:29:52,370 --> 00:29:56,590
+اللي هي عملية الجمع تمدت على جمالية الجمع الأصلية
+
+391
+00:29:56,590 --> 00:29:59,430
+اللي بين اللي هي ال sequences اللي في ال space الأصل
+
+392
+00:29:59,430 --> 00:30:04,050
+هو ال X هذا عملية الجمع الآن طب هذه العملية ال well
+
+393
+00:30:04,050 --> 00:30:08,750
+defined يعني بمعنى آخر لو أنا أخدت X n و Y n و جه
+
+394
+00:30:08,750 --> 00:30:12,990
+واحد ثاني قال أنا بدي أخد W n موجودة في ال X hat و
+
+395
+00:30:12,990 --> 00:30:16,330
+K n موجودة في ال Y hat و جيت جماعة ثاني و طلع ليها
+
+396
+00:30:16,330 --> 00:30:20,690
+sequence هل هذه ال sequence هيكون ال equivalency
+
+397
+00:30:20,690 --> 00:30:25,070
+class لها نفس هذه أنا بقول لك أه و عشان هيك بدي أكون
+
+398
+00:30:25,070 --> 00:30:28,010
+well defined و شوف كيف بدنا نثبت أنها well defined
+
+399
+00:30:28,010 --> 00:30:34,590
+اطلع لفوق طيب this definition is independent of the
+
+400
+00:30:34,590 --> 00:30:38,950
+choice of the Cauchy sequences in X hat and Y hat
+
+401
+00:30:38,950 --> 00:30:44,390
+ماشي نشوف كده in fact لو أنت اخترت عشان الجامع
+
+402
+00:30:44,390 --> 00:30:48,930
+اللي قولنا عنه قبل شوية X N واخترت W N معناته
+
+403
+00:30:48,930 --> 00:30:51,870
+التنتين في نفس ال equivalence class معناته related
+
+404
+00:30:51,870 --> 00:30:55,180
+حسب ال relation اللي عرفناها المرة الماضية و جيت
+
+405
+00:30:55,180 --> 00:31:00,420
+أنت اخترت في ال Y hat Y N و أنا اخترت V N أو W N أو
+
+406
+00:31:00,420 --> 00:31:03,680
+اللي هي V N اللي هي طبعا مادام إن في نفس ال
+
+407
+00:31:03,680 --> 00:31:06,760
+equivalency class إذا التنتين شمالين related حسب
+
+408
+00:31:06,760 --> 00:31:11,200
+الخاصية أو حسب العلاقة اللي عرفناها المرة الماضية
+
+409
+00:31:11,200 --> 00:31:15,140
+طيب طب هذولة متى بيكون ال X N لما تكون X N related
+
+410
+00:31:15,140 --> 00:31:18,880
+to W N إيش قلنا بيكون X N عرفنا ال relation المرة
+
+411
+00:31:18,880 --> 00:31:24,860
+الماضية related to W N في حال كانت ال limit لل
+
+412
+00:31:24,860 --> 00:31:29,560
+distance بين ال X N و ال W N إيش هتساوي؟ هتساوي صفر
+
+413
+00:31:29,560 --> 00:31:32,420
+طب ما هي ال distance الآن إحنا بنحكي عن اللي هو
+
+414
+00:31:32,420 --> 00:31:36,880
+norm ال metric هذا اللي الآن induced by the norm
+
+415
+00:31:36,880 --> 00:31:41,200
+يعني بمعنى آخر norm ال X N نقص W N إيش هيساوي؟
+
+416
+00:31:41,200 --> 00:31:47,060
+limitه هيساوي صفر إذا لما X N related to W N معناته
+
+417
+00:31:47,060 --> 00:31:54,280
+أصبح limit X N نقص W N بيساوي صفر و limit Y N نقص V N
+
+418
+00:31:54,280 --> 00:32:00,620
+بيساوي صفر شوف الآن اللي بدأ أصل إليه أنا بدأ أصل إن
+
+419
+00:32:00,620 --> 00:32:04,600
+جوابي و جوابكم نفس الشيء اللي هو عند Normal X N
+
+420
+00:32:04,600 --> 00:32:08,440
+زائد Y N ناقص W N زائد V N هذا بالـ Triangling
+
+421
+00:32:08,440 --> 00:32:14,260
+Quality أصغر يساوي Normal X<sub>N</sub> ناقص W<sub>N</sub> زائد Y<sub>N</sub> ناقص
+
+422
+00:32:14,260 --> 00:32:18,840
+من V<sub>N</sub> لأن بما أنه اللي هو التمتين هذوله في نفس ال
+
+423
+00:32:18,840 --> 00:32:21,560
+equivalency class زي ما قلنا إذا هذه as n goes to 
+
+424
+00:32:21,560 --> 00:32:24,100
+infinity بتروح للصفر وهذه as n goes to infinity
+
+425
+00:32:24,100 --> 00:32:28,440
+بتروح للصفر بمعنى آخر هذه ال limit اللي هتروح لمين
+
+426
+00:32:28,440 --> 00:32:33,480
+للصفر يعني بمعنى آخر ال sequence ال X<sub>n</sub> زي Y<sub>n</sub> اللي 
+
+427
+00:32:33,480 --> 00:32:38,170
+اعتمدت عليه جوابهاللي هو و ال sequence هذه related
+
+428
+00:32:38,170 --> 00:32:41,950
+يعني بمعنى آخر التنتين في نفس ال equivalency class
+
+429
+00:32:41,950 --> 00:32:46,110
+يعني بمعنى آخر ال Z^ تبعته هي نفس ال Z^
+
+430
+00:32:46,110 --> 00:32:49,910
+تبعتك لإن هدولة هيكون التنتين في نفس ال
+
+431
+00:32:49,910 --> 00:32:54,370
+equivalency class فبكون في هذه الحالة إنه فعلا ال
+
+432
+00:32:54,370 --> 00:32:58,470
+Z^ بيساوي X^ زي Y^ is well defined اطلع
+
+433
+00:32:58,470 --> 00:33:04,720
+لفوق شويةإذا نخلصنا من عملية الجمع اللي مبنية على
+
+434
+00:33:04,720 --> 00:33:10,900
+اللي عندنا Similarly بالنسبة لمين we define the
+
+435
+00:33:10,900 --> 00:33:16,500
+product αX^ اللي هيكون element من X^ of 
+
+436
+00:33:16,500 --> 00:33:20,340
+a scalar α and X^ to be the equivalence
+
+437
+00:33:20,340 --> 00:33:23,800
+class for which αX^ is representative إيش
+
+438
+00:33:23,800 --> 00:33:29,240
+يعني؟ يعني بنفس الطريقةعشان اعرف اللي هو شو معناته
+
+439
+00:33:29,240 --> 00:33:36,560
+اخد X^ element in X^ واخد α scalar بده
+
+440
+00:33:36,560 --> 00:33:40,940
+اعرف الآن عملية ال scalar multiplication في داخل
+
+441
+00:33:40,940 --> 00:33:45,530
+ال X^ وين رايح أنا عشان أثبت لكم إنه هذا X^
+
+442
+00:33:45,530 --> 00:33:49,350
+هيطلع في vector space عرفنا الجامع والأن بنعرف مين
+
+443
+00:33:49,350 --> 00:33:54,450
+ال scalar multiplication الآن α في ال X^
+
+444
+00:33:54,450 --> 00:33:59,270
+بدي أعرفها عبارة عن اللي هي ال .. ال .. ال .. ال
+
+445
+00:33:59,270 --> 00:34:02,850
+.. طبعا مدامة ال X^ في ال X^ إذا أكيد في
+
+446
+00:34:02,850 --> 00:34:07,450
+sequence X<sub>N</sub> موجودة في ال X^ هذا اللي هي البنت
+
+447
+00:34:07,450 --> 00:34:09,290
+عليها ال equivalence class الـ Cauchy sequence
+
+448
+00:34:09,290 --> 00:34:14,070
+الان α في X<sub>n</sub> برضه هتطلع Cauchy sequence بدام
+
+449
+00:34:14,070 --> 00:34:18,090
+X<sub>n</sub> الان ال Cauchy sequence هذه ال equivalence
+
+450
+00:34:18,090 --> 00:34:22,790
+class هي اللي بتسميها α في مين؟ في X^ يعني
+
+451
+00:34:22,790 --> 00:34:26,910
+بمعنى أخر α في X^ بدي أعرفها على أساس α
+
+452
+00:34:26,910 --> 00:34:31,630
+في X لكل ^ يعني هذه إيش بترمز؟ بترمز The set of 
+
+453
+00:34:31,630 --> 00:34:36,150
+all equivalency classes اللي هي αX<sub>N</sub> حيث X<sub>N</sub> is
+
+454
+00:34:36,150 --> 00:34:40,410
+a Cauchy sequence in X^ Similarly زي اللي قبل
+
+455
+00:34:40,410 --> 00:34:46,840
+بالظبط الآن هذه تحت هذا ال product Similarly as in
+
+456
+00:34:46,840 --> 00:34:50,640
+the definition above nationalيد الطريقة المباشرة
+
+457
+00:34:50,640 --> 00:34:54,020
+of addition one can see that the definition of a
+
+458
+00:34:54,020 --> 00:34:57,240
+product is independent of the choice of
+
+459
+00:34:57,240 --> 00:35:02,760
+representative of etc يعني بمعنى أخر انت أخدتفي
+
+460
+00:35:02,760 --> 00:35:07,220
+الـ X^ X<sub>N</sub> كوشي سيكوانس وواحد تاني أخد Y<sub>N</sub> في
+
+461
+00:35:07,220 --> 00:35:11,240
+الكوشي سيكوانس X^ هيطلع عند الألفة في ال X<sub>N</sub>
+
+462
+00:35:11,240 --> 00:35:14,180
+والألفة في ال Y<sub>N</sub> ال equivalency classes انهم زي
+
+463
+00:35:14,180 --> 00:35:18,220
+بعض يعني بمعنى جوابي وجوابك زي بعض عشان هيك اللي
+
+464
+00:35:18,220 --> 00:35:22,400
+هو ال scalar multiplication برضه ايه شمالها is
+
+465
+00:35:22,400 --> 00:35:27,930
+well defined الان بالاستعانة
+
+466
+00:35:27,930 --> 00:35:37,110
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+467
+00:35:37,110 --> 00:35:39,430
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+468
+00:35:39,430 --> 00:35:40,370
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+469
+00:35:40,370 --> 00:35:40,630
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+470
+00:35:40,630 --> 00:35:40,650
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+471
+00:35:40,650 --> 00:35:40,710
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+472
+00:35:40,710 --> 00:35:41,370
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+473
+00:35:41,370 --> 00:35:42,230
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+474
+00:35:42,230 --> 00:35:46,070
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة انت
+
+475
+00:35:46,070 --> 00:35:50,830
+الآن لو جيت على حسب التعريف و جيت على كل خواص الـ
+
+476
+00:35:50,830 --> 00:35:54,490
+vector space هتلاقيها متحققة على العملية وهذه
+
+477
+00:35:54,490 --> 00:35:58,390
+بتظلها حسابات عندكم بتعملوها لحالكم اتحققوا العشر
+
+478
+00:35:58,390 --> 00:36:02,890
+شروط تبعات ال vector space يعني بمعنى اخر انا الآن
+
+479
+00:36:02,890 --> 00:36:07,330
+اثبتت ان X^ شمالها is a vector space و الـ
+
+480
+00:36:07,330 --> 00:36:12,520
+zero elementللـ X^ is the equivalence class
+
+481
+00:36:12,520 --> 00:36:15,360
+contains all Cauchy sequences which converge to 0
+
+482
+00:36:15,360 --> 00:36:19,900
+منطقي، ليش؟ الآن الـ zero element هان الـ zero
+
+483
+00:36:19,900 --> 00:36:24,040
+element هان، بدي أسميه الـ zero^ مين الـ zero
+
+484
+00:36:24,040 --> 00:36:27,700
+^؟ اللي هو اللي في ال equivalence class له Zero
+
+485
+00:36:27,700 --> 00:36:31,640
+Zero، Zero، Zero، هد Cauchy sequence ولا لأ؟ أكيد
+
+486
+00:36:31,640 --> 00:36:34,900
+Cauchy sequence اللي هن كل ال .. ال .. ال .. ال ..
+
+487
+00:36:34,900 --> 00:36:39,210
+Cauchy sequences اللي converge لـ Zero converge to
+
+488
+00:36:39,210 --> 00:36:43,230
+zero هيكون in hand فهادي اللي هي الـ zero^
+
+489
+00:36:43,230 --> 00:36:47,990
+عبارة عن the set of all كوشي sequences that
+
+490
+00:36:47,990 --> 00:36:52,430
+converge to zero ماشي زي هذه فبكون هذا هو مين هو
+
+491
+00:36:52,430 --> 00:36:58,030
+الـ zero element اللي هو اللي لدك إذا صار عندي
+
+492
+00:36:58,030 --> 00:37:03,490
+land in X^ under these operations is a vector
+
+493
+00:37:03,490 --> 00:37:06,730
+space how؟ إلكم
+
+494
+00:37:09,170 --> 00:37:16,810
+الأن نيجي نشوف اللي هو زي ما وعدناكم بدنا اللي هو
+
+495
+00:37:16,810 --> 00:37:22,970
+نثبت انه اللي هو زي ما قلنا ال isometry في هذه
+
+496
+00:37:22,970 --> 00:37:27,630
+الحالة اللي هي التلت حالات اللي هي one to one و
+
+497
+00:37:27,630 --> 00:37:30,570
+one to two و preserve the distance اللي هي
+
+498
+00:37:30,570 --> 00:37:33,970
+preserve the norm اللي قلته سابقاً و الأخيرة اللي
+
+499
+00:37:33,970 --> 00:37:39,490
+هو linear بتثبت انه T اللي هو طبعا احنا بسميه A A
+
+500
+00:37:39,490 --> 00:37:43,430
+في αX زائد Y بيسوا A α في A X زائد مين A
+
+501
+00:37:43,430 --> 00:37:47,650
+في Y يعني بمعنى آخر برضه ب preserve the mean the
+
+502
+00:37:47,650 --> 00:37:56,890
+distances the operations طيب by using الان X هاد
+
+503
+00:37:56,890 --> 00:37:59,890
+under these operations قولنا vector space لان let
+
+504
+00:37:59,890 --> 00:38:06,020
+α be an scalar and X وY any elements in X ثم
+
+505
+00:38:06,020 --> 00:38:10,900
+يوجد سيكوينس x<sub>1</sub> و y<sub>1</sub> في الـ x مثلًا مادان x و y في
+
+506
+00:38:10,900 --> 00:38:15,420
+الـ x إذا بقدر ألاقي x unconverged لل x و y
+
+507
+00:38:15,420 --> 00:38:21,220
+unconverged لمن؟ لل y ماشي الحال الان عندى ..
+
+508
+00:38:21,220 --> 00:38:26,980
+بتقولي كيف نلاقي؟وهو اللي فيه أسهل منها اخد مين؟
+
+509
+00:38:26,980 --> 00:38:30,660
+اخد الـ sequence X و X و X و X و X Converged للـ X
+
+510
+00:38:30,660 --> 00:38:33,780
+ولا لا؟ أكيد Converged للـ X وعصرها دولة من وين؟
+
+511
+00:38:33,780 --> 00:38:37,000
+من الـ X لأننا بدأت الـ X من وين؟ من الـ X ونفس
+
+512
+00:38:37,000 --> 00:38:40,540
+الشيء للـ Y إذا أكيد أكيد أكيد هلاقي اللي هو
+
+513
+00:38:40,540 --> 00:38:44,680
+Sequences X unconverged لل X و Y unconverged لل Y
+
+514
+00:38:44,680 --> 00:38:49,040
+وقلنا على سبيل المثال الـ sequence اللي فيها X X X
+
+515
+00:38:49,040 --> 00:38:56,050
+X هي متقدرة للعرب الان let X<sub>N</sub> element in X^ و Y<sub>N</sub>
+
+516
+00:38:56,050 --> 00:39:00,270
+element in Y^ اللي هي الـ X^ اللي هي
+
+517
+00:39:00,270 --> 00:39:06,460
+equivalence classesاللي related to x and الـ y^
+
+518
+00:39:06,460 --> 00:39:09,560
+هي عبارة عن كل الـ sequences related للـ y<sub>n</sub> by
+
+519
+00:39:09,560 --> 00:39:12,180
+using the definition of scalar product and vector
+
+520
+00:39:12,180 --> 00:39:15,260
+addition اللي حكينا عنه قبل شوية in excel we have
+
+521
+00:39:15,260 --> 00:39:20,280
+نحسب الآن احسبلي الآن α في AX زائد A من AY
+
+522
+00:39:20,280 --> 00:39:27,200
+الان عندي بساوي ال A من وين جاية يا جماعة ال A
+
+523
+00:39:27,200 --> 00:39:32,220
+اللي هي هذهجاية من X لعند مين؟ W و الـ W إذا
+
+524
+00:39:32,220 --> 00:39:35,520
+بتتذكروا عملناها construction كانت سبسيط من مين؟
+
+525
+00:39:35,520 --> 00:39:40,500
+من X^ يعني عاصرها اللي هنا عبارة عن equivalency
+
+526
+00:39:40,500 --> 00:39:43,140
+classes اللي هنا يعني الصور هذه equivalency
+
+527
+00:39:43,140 --> 00:39:47,600
+classes إذا α في AX اللي عبارة عن α في X
+
+528
+00:39:47,600 --> 00:39:52,200
+^ ال X^ .. ال X^ ده .. ال A .. ال AX وين
+
+529
+00:39:52,200 --> 00:39:56,610
+هي تروح؟لـ Element في داخل الـ Main الـ W و الـ W
+
+530
+00:39:56,610 --> 00:39:59,730
+لما كنا أخدنا الـ Element أخدناها الـ Main كل ال
+
+531
+00:39:59,730 --> 00:40:03,850
+equivalency classes X و X و X و X و X ده بتتذكروا
+
+532
+00:40:03,850 --> 00:40:10,350
+يعني بمعنى أخر اللي هي ال A X هي نفسها مين ال X
+
+533
+00:40:10,350 --> 00:40:18,020
+^ هي عرفناها زائد A of Y مين هي ال Y^ قابل
+
+534
+00:40:18,020 --> 00:40:20,700
+بشوية من عملية الجامعة .. العملية الجامعة قلنا
+
+535
+00:40:20,700 --> 00:40:24,940
+α في X^ زائد Y^ كله بيساوين α في X
+
+536
+00:40:24,940 --> 00:40:31,680
+زائد Y كل ماله .. كل ^ عرفنا عملية الجامعة قابل
+
+537
+00:40:31,680 --> 00:40:35,400
+بشوية ويساوي الآن هذا عبارة عن mean هذا اللي جوا
+
+538
+00:40:35,400 --> 00:40:38,600
+هو عبارة من تعريف ال function A هو عبارة عن A
+
+539
+00:40:38,600 --> 00:40:43,400
+αX زائد mean زائد Y إذاً واضح إن الـ A is
+
+540
+00:40:43,400 --> 00:40:47,540
+linear يعني الـ A is an isometry that preserves
+
+541
+00:40:47,540 --> 00:40:50,620
+the algebraic operations isometry من المرة الفاتتة
+
+542
+00:40:50,620 --> 00:40:54,540
+و preserves the algebraic operations إذاً صارت اللي
+
+543
+00:40:54,540 --> 00:41:01,780
+هي ال W والـ X زي بعض بس هدولة اللي هي اسم و هدولة
+
+544
+00:41:01,780 --> 00:41:04,480
+اللي هي اسم أخر لكن في one to one non to function
+
+545
+00:41:04,480 --> 00:41:08,220
+وفي اللي هو preserve the distance وفي preserve the
+
+546
+00:41:08,220 --> 00:41:13,980
+operations فكتو vector spaces اتن تين نفس الشيء
+
+547
+00:41:13,980 --> 00:41:19,300
+ولكن بالاسماء متغيرة اسم هناك هات وهنا اسم هنا أو
+
+548
+00:41:19,300 --> 00:41:22,140
+اسم هناك equivalence classes وهنا اسم هنا elements
+
+549
+00:41:22,140 --> 00:41:29,190
+اللي هي جزء من ال .. اللي هي اللي من ال X طيب بدنا
+
+550
+00:41:29,190 --> 00:41:32,910
+أخر إشي ماحنا .. عن إيش احنا خلصنا احنا الآن هذه
+
+551
+00:41:32,910 --> 00:41:36,930
+vector space و خلصنا ال isometry ضال اللي هو ال X
+
+552
+00:41:36,930 --> 00:41:40,350
+^ بعد ما فبتناها vector space بده عرف عليها norm
+
+553
+00:41:40,350 --> 00:41:45,030
+بده عرف عليها norm شوف كده عرف عليها norm الآن أول
+
+554
+00:41:45,030 --> 00:41:52,050
+إشي احنا عارفين ال W جزء من مين؟ من ال X^ طيب
+
+555
+00:41:53,750 --> 00:41:57,650
+من المرة الماضية بقى ايضا عندي لان خلينا ناخد بس
+
+556
+00:41:57,650 --> 00:42:02,550
+هالشغل قبل for Y^ بتساوي AY ال AY ايش بنسميها
+
+557
+00:42:02,550 --> 00:42:07,410
+احنا؟ Y^ Y^ مين هي؟ هي عبارة عن ال
+
+558
+00:42:07,410 --> 00:42:11,430
+equivalency class إذا بتتذكروا لما ركّبناها الـ Y
+
+559
+00:42:11,430 --> 00:42:17,230
+^ عبارة عن ال equivalency class ل S Y و Y و Y و
+
+560
+00:42:17,230 --> 00:42:21,150
+Y اللي converge ل من؟ ل الـ Zero ل الـ Yات اللي من 
+
+561
+00:42:21,150 --> 00:42:25,430
+من؟ اللي من X ماشي هذا حكيناه المرة الماضية فالآن
+
+562
+00:42:25,430 --> 00:42:30,470
+Y hat بيساوي A Y we have بدنا نعرف الـ norm 1 هالمين
+
+563
+00:42:30,470 --> 00:42:37,330
+على W كيف بده اعرفه Normal y hat على w بيساوي Normal
+
+564
+00:42:37,330 --> 00:42:45,110
+mean الـ y Normal y الآن لاحظ لما انعرفت هنا عند هذا
+
+565
+00:42:45,110 --> 00:42:51,350
+طبعا و هذا نورم كامل فعلى طول هذا هيحقق كل مين كل
+
+566
+00:42:51,350 --> 00:42:55,750
+خواص الـ norm الآن هذا معناته preserved distances
+
+567
+00:42:55,750 --> 00:42:59,710
+لأنه بيصير الـ distance بين اللي هو اللي هي اللي
+
+568
+00:42:59,710 --> 00:43:04,630
+احنا عارفين الـ distance preserved by من W ل X فهذه
+
+569
+00:43:04,630 --> 00:43:07,930
+اللي هي بتمثل الـ distance بين Y hat و Zero hat
+
+570
+00:43:07,930 --> 00:43:12,760
+وهذه الـ distance بين Y و Zero و preserves في الأصل
+
+571
+00:43:12,760 --> 00:43:16,340
+لما أثبتناها المرة الماضية إذا الـ norm بيساوي الـ
+
+572
+00:43:16,340 --> 00:43:20,400
+norm مافيش فيها مشكلة الان the corresponding
+
+573
+00:43:20,400 --> 00:43:24,580
+metric on w is the restriction of d hat to w اللي
+
+574
+00:43:24,580 --> 00:43:27,300
+هو الـ d hat لما عرفناها عرفته زي ما قلت قبل بشوية
+
+575
+00:43:27,300 --> 00:43:31,600
+المرة الماضية الـ d hat اللي هي كان اللي هو عبارة
+
+576
+00:43:31,600 --> 00:43:37,200
+عن اللي أخدناها اللي هي الـ preserve d hat of اللي
+
+577
+00:43:37,200 --> 00:43:42,730
+هي ay وأي element تاني أو العناصر اللي هنا بيساوي الـ
+
+578
+00:43:42,730 --> 00:43:46,850
+D بين العناصر اللي موجودة صورهم أو أصولهم اللي
+
+579
+00:43:46,850 --> 00:43:50,870
+موجودة في الـ X إذاً هذا عندي صار عندي الـ D hat
+
+580
+00:43:50,870 --> 00:43:59,230
+متلائم مع اللي اللي هو عرفناه اليوم الآن بنقدر الآن
+
+581
+00:43:59,230 --> 00:44:03,750
+.. هذا الكلام كان عرفه عالمياً على اللي هو الـ W
+
+582
+00:44:03,750 --> 00:44:08,030
+بنعمله extension الآن بالاستعانة باللي احنا اللي
+
+583
+00:44:08,030 --> 00:44:13,850
+هي عملناها هذا اللي هو الجديد هذا هو عبارة عن لمن
+
+584
+00:44:13,850 --> 00:44:19,400
+متناسق مع الـ D hat عرّف للـ X عباق العناصر اللي
+
+585
+00:44:19,400 --> 00:44:22,680
+موجودة في الـ .. في الـ .. في الـ X hat ككل مش في
+
+586
+00:44:22,680 --> 00:44:25,960
+الـ W في الـ X hat عرّفه كالتالي الـ X hat 2
+
+587
+00:44:25,960 --> 00:44:30,300
+بيساوي الـ distance hat بين 0 و 10 والـ X hat for
+
+588
+00:44:30,300 --> 00:44:34,840
+all X elements in X hat نورم الـ X2 هذا هتلاقي إيش
+
+589
+00:44:34,840 --> 00:44:37,500
+ما له نورم و هيحقق الشروط اللي إحنا بنعرفها
+
+590
+00:44:37,500 --> 00:44:41,720
+Therefore صار عندي X hat اللي هو صار عندي normed
+
+591
+00:44:41,720 --> 00:44:45,420
+space و vector space و من ثم normed space و كان
+
+592
+00:44:45,420 --> 00:44:50,950
+عندي الـ isometry بين اللي هو الـ W والـ X بكل شروطه
+
+593
+00:44:50,950 --> 00:44:54,350
+اللي هي السابقة بالاضافة لـ Linearity تبعت اليوم
+
+594
+00:44:54,350 --> 00:44:58,450
+بكون حصلنا على الـ X hat is the third اللي هو
+
+595
+00:44:58,450 --> 00:45:03,730
+Space بكون هي كقولنا أو وصلنا انه every complete
+
+596
+00:45:03,730 --> 00:45:08,030
+.. every normed space can be completed وإلى لقاء
+
+597
+00:45:08,030 --> 00:45:09,490
+آخر السلام عليكم ورحمة الله
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/J7SCFPaCRLU_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/J7SCFPaCRLU_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f0f44f5eefb50a7eb074258749459cec7fb8585d
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/J7SCFPaCRLU_postprocess.srt
@@ -0,0 +1,2388 @@
+1
+00:00:05,690 --> 00:00:08,790
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,790 --> 00:00:11,910
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:11,910 --> 00:00:17,250
+آله وصحبه أجمعين هذه المحاضرة التاسعة مساق تحليل
+
+4
+00:00:17,250 --> 00:00:20,150
+دالي أو تحليل اقتراني لطلاب طالبات الجامعة
+
+5
+00:00:20,150 --> 00:00:24,470
+الإسلامية ماجستير رياضيات اليوم ان شاء الله هنكمل
+
+6
+00:00:24,470 --> 00:00:27,830
+اللي هو في ال section نبدأ في ال section اللي هو
+
+7
+00:00:27,830 --> 00:00:32,070
+اتنين تلاتة اللي هو further properties of normed
+
+8
+00:00:32,070 --> 00:00:37,220
+spaces اللي هيخلّيني أحكي عن خواص أخرى اللي هو للـ
+
+9
+00:00:37,220 --> 00:00:41,720
+Normed Space الأن نبدأ اللي هو بالتعريف التالي
+
+10
+00:00:41,720 --> 00:00:47,300
+التعريف اللي هو كميالي بيقول لي a subspace Y of a
+
+11
+00:00:47,300 --> 00:00:51,000
+normed space X is a subset of X considered as a
+
+12
+00:00:51,000 --> 00:00:54,440
+vector space with a norm in Y obtained by
+
+13
+00:00:54,440 --> 00:00:58,960
+restricting the norm in X to mean to Yعندي اللي هو
+
+14
+00:00:58,960 --> 00:01:03,240
+الـ X-normed space لأن لو كانت عندي Y مجموعة جزئية
+
+15
+00:01:03,240 --> 00:01:07,720
+من X وY اللي هو ال .. ال .. ال norm اللي عليها هو
+
+16
+00:01:07,720 --> 00:01:09,860
+ال norm اللي .. اللي .. اللي .. اللي هي ال norm
+
+17
+00:01:09,860 --> 00:01:14,680
+الأصلي تبع X وكانت Y نفسها subspace as a vector
+
+18
+00:01:14,680 --> 00:01:18,160
+space من X فبكون عندي في هذه الحياة بنسمي Y
+
+19
+00:01:18,160 --> 00:01:24,880
+أشمالها as a normed subspace من مين؟ من اللي هو X
+
+20
+00:01:25,500 --> 00:01:30,340
+هذا تعريف اللي هو normed subspace نطلع في نظرية
+
+21
+00:01:30,340 --> 00:01:35,220
+أخدناها احنا في اللي هو 148 نظرية كانت بتقول ان هو
+
+22
+00:01:35,220 --> 00:01:38,560
+subspace M of a complete metric space في ال metric
+
+23
+00:01:38,560 --> 00:01:42,720
+space X is itself complete if and only if the
+
+24
+00:01:42,720 --> 00:01:47,500
+situation is closed in Mالان ما احنا عارفين ان كل
+
+25
+00:01:47,500 --> 00:01:51,300
+normed space عبارة عن metric space اذا اللي بنطبق
+
+26
+00:01:51,300 --> 00:01:54,200
+على ال metric space اكيد بنطبق على مين؟ على ال
+
+27
+00:01:54,200 --> 00:01:58,180
+normed space يعني بمعنى اخر، الان النظرية تلت
+
+28
+00:01:58,180 --> 00:02:01,380
+اتنين تلت اتنين automatic هتيجيني من مين؟ من
+
+29
+00:02:01,380 --> 00:02:05,060
+النظرية احد اربعة تمانية، ايش بتقول هذه النظرية؟
+
+30
+00:02:05,060 --> 00:02:09,140
+ان ا sub space Y of بنخ space X، طبعا بنخ space
+
+31
+00:02:09,140 --> 00:02:12,080
+معناته complete normed space، يعني complete metric
+
+32
+00:02:12,080 --> 00:02:17,880
+spaceاللي هي a subspace Y of بنخ space X is
+
+33
+00:02:17,880 --> 00:02:22,180
+complete اللي هي هذه اللي هي Y complete if and
+
+34
+00:02:22,180 --> 00:02:26,860
+only if إيش ما لها Y is closed اللي هي subspace من
+
+35
+00:02:26,860 --> 00:02:30,980
+من من الـ X إذا هذه النظرية ما هي إلا حالة خاصة من
+
+36
+00:02:30,980 --> 00:02:34,020
+النظرية الفجوة النظرية الفجوة على metric space in
+
+37
+00:02:34,020 --> 00:02:37,680
+general هذه عالمين على اللي هو واحد من ال metric
+
+38
+00:02:37,680 --> 00:02:41,480
+spaces اللي هو ال metric space المولد أو ال
+
+39
+00:02:41,480 --> 00:02:46,040
+induced by the normماشي الحال إذا هذه automatic من
+
+40
+00:02:46,040 --> 00:02:50,520
+1 4 8 يعني نيجي الآن ليه بعض الملاحظات اللي بدنا
+
+41
+00:02:50,520 --> 00:02:55,120
+نحكي فيها عشان تلزمنا اللي هو لاحقا الان a
+
+42
+00:02:55,120 --> 00:02:58,540
+sequence xn in a norm of this base x is convergent
+
+43
+00:02:58,540 --> 00:03:02,940
+if there is x a limit in x such that limit norm ال
+
+44
+00:03:02,940 --> 00:03:07,280
+xn ناقص x بسوء 0 as n goes to infinity مش جديد هذا
+
+45
+00:03:07,280 --> 00:03:10,820
+يا جماعة احنا لما نعرفنا ال sequence انها converge
+
+46
+00:03:10,820 --> 00:03:16,170
+xn converge ده ال xفي metric space X وD ايش قلنا
+
+47
+00:03:16,170 --> 00:03:22,370
+انه اللي هو limit لل distance بين X و N و X as N
+
+48
+00:03:22,370 --> 00:03:26,150
+minus infinity ايش يساوي؟ ساوي سفر طيب ما هو ال
+
+49
+00:03:26,150 --> 00:03:30,890
+norm اللي عندنا احنا هنا هو عبارة عن metric يعني
+
+50
+00:03:30,890 --> 00:03:34,590
+الآن لو بدنا نطبق هذا الكلام على ال metric اللي
+
+51
+00:03:34,590 --> 00:03:38,590
+عندنا اللي هو norm ما هو هذا ايش بيمثل؟ بيمثل
+
+52
+00:03:38,590 --> 00:03:43,400
+عبارة عن norm ال X N ناقص X اللي هو limit لهas n
+
+53
+00:03:43,400 --> 00:03:46,980
+goes to infinity بساوة سفر إذا التعريف هذا مش
+
+54
+00:03:46,980 --> 00:03:51,280
+تعريف جديد ما هو إلا عبارة عن تطبيق لتعريف سابق
+
+55
+00:03:51,280 --> 00:03:53,520
+أخدناه في الـ metric space شو معناته الـ xn
+
+56
+00:03:53,520 --> 00:03:58,560
+converge ل some x اللي هو بيكون limit لاللي هو ال
+
+57
+00:03:58,560 --> 00:04:02,400
+norm اللي هو ال distance بين xn و x as n goes to
+
+58
+00:04:02,400 --> 00:04:06,360
+infinity بساوة سفر بس كتبناه بلغة ال norm على أساس
+
+59
+00:04:06,360 --> 00:04:10,300
+إنه هنقدرنا نشتغل عليه الآن بناء على هذا التعريف
+
+60
+00:04:12,030 --> 00:04:16,970
+أحنا خلّيني نقول عرفنا اللي هو شو معناه xn
+
+61
+00:04:16,970 --> 00:04:20,510
+-convergent طيب إذا في إشي تاني دايما بنحكي و
+
+62
+00:04:20,510 --> 00:04:24,210
+بنتهدأك اللي هو لأ إشي تاني بنحكي فيه اللي هو شو
+
+63
+00:04:24,210 --> 00:04:26,330
+معناته للـsequence كوشي يعني بنحكي عن
+
+64
+00:04:26,330 --> 00:04:29,030
+الـconvergent و بنحكي عن مين ال convergence و
+
+65
+00:04:29,030 --> 00:04:32,910
+بنحكي عن الكوشي sequence لأن a sequence xn in
+
+66
+00:04:32,910 --> 00:04:37,120
+around this base x is a كوشي sequenceif for every
+
+67
+00:04:37,120 --> 00:04:40,060
+y أكبر من 0 there exists k element in n such that
+
+68
+00:04:40,060 --> 00:04:44,160
+normal xn ناقص xn أصغر من 100 من y كل n وأكبر من
+
+69
+00:04:44,160 --> 00:04:48,440
+100 برضه مش جديد احنا كنا نقول xn is Cauchy في ال
+
+70
+00:04:48,440 --> 00:04:51,840
+metric إذا كانت اللي هو for every xn أكبر من 0
+
+71
+00:04:51,840 --> 00:04:55,480
+there exists k element in n such that normal x أي
+
+72
+00:04:55,480 --> 00:04:59,500
+اللي هو ال distance في ال xn و ال xيكون أصغر من Y
+
+73
+00:04:59,500 --> 00:05:04,460
+لكل N أكبر من مين من K أو أكبر أو سوء K لأن ال
+
+74
+00:05:04,460 --> 00:05:07,700
+norm ال metric اللي عندنا اليوم بيشتغل عليه هو
+
+75
+00:05:07,700 --> 00:05:12,700
+عبارة عن ال norm XN ناقص XN لأن هذا ال metric اللي
+
+76
+00:05:12,700 --> 00:05:16,100
+عندنا اليوم هو ال induced by the norm إذن برضه مش
+
+77
+00:05:16,100 --> 00:05:19,940
+تعريف جديد ولكن تطبيق على ال metric اللي مولد من
+
+78
+00:05:19,940 --> 00:05:24,290
+ال norm طيبنجي للتعريف اللي بعده بناء عليه طبعا
+
+79
+00:05:24,290 --> 00:05:27,150
+احنا لان احنا في norm of the space يا جماعة مادام
+
+80
+00:05:27,150 --> 00:05:31,050
+في norm of the space اذا هو عبارة عن vector space
+
+81
+00:05:31,050 --> 00:05:33,450
+يعني عملية الجمع وعملية ال scale and
+
+82
+00:05:33,450 --> 00:05:37,590
+multiplication كلها مشرعة عشان هيك الان احنا اكثر
+
+83
+00:05:37,590 --> 00:05:41,570
+حرية قبل كنا ناخد لما ناخد ناخد metric space هيكون
+
+84
+00:05:41,570 --> 00:05:45,890
+عنده X وD X مجرد 6 فمقدرش احكي عن مجموع عناصر
+
+85
+00:05:45,890 --> 00:05:48,770
+بينها او scale and multiplication لالا لالا لالا
+
+86
+00:05:48,770 --> 00:05:53,520
+الان صار عندنا اللي هوعبارة عن norm وهذا عبارة عن
+
+87
+00:05:53,520 --> 00:05:58,000
+norm فهذا عبارة عن vector space مشرّع إلى الحديث
+
+88
+00:05:58,000 --> 00:06:02,160
+عن الجمع وعن الـ scalar multiplication بناء عليه
+
+89
+00:06:02,160 --> 00:06:06,820
+بنفع أقول الآن على مجموع عناصر يعني بنفع أروح
+
+90
+00:06:06,820 --> 00:06:11,800
+باتجاه اللي هو series نشوف كيف let xn be a
+
+91
+00:06:11,800 --> 00:06:17,370
+sequence in a normed space Xand let S1 be a
+
+92
+00:06:17,370 --> 00:06:22,030
+sequence of partial sums يعني S1 بيساوي X1 S2
+
+93
+00:06:22,030 --> 00:06:28,030
+بيساوي X1 زي X2 S3 بيساوي X1 زي X2 زي X3 S1 in
+
+94
+00:06:28,030 --> 00:06:32,370
+general X1 زي X2 زي XN صارت هذه الـ S1 عبارة عن
+
+95
+00:06:32,370 --> 00:06:36,070
+sequence of partial sums زي اللي أخدناها في
+
+96
+00:06:36,070 --> 00:06:39,230
+الكالكولاست العادى بس كنا احنا اللي عارية نشتغل
+
+97
+00:06:44,560 --> 00:06:48,900
+إذا كان الـ S مرتبط بـ S فإن الـ Infinite Series
+
+98
+00:06:48,900 --> 00:06:53,860
+Summation XI قد يكون مرتبط بـ S وS يسمى بالنسبة
+
+99
+00:06:53,860 --> 00:06:57,520
+للعدة من السلسلين وقال S بالسلمانية XI يعني اللي
+
+100
+00:06:57,520 --> 00:07:07,300
+بيقوله لو عندي أن أعرف شو معنات السلسلين مرتبطالان
+
+101
+00:07:07,300 --> 00:07:11,340
+عند الـ sequence of partial sums S N اللي هي الـ S
+
+102
+00:07:11,340 --> 00:07:16,180
+N بتساوي X 1 زائد X N هذا كله اللي موجود في الـ
+
+103
+00:07:16,180 --> 00:07:22,580
+normed space طيب بنقول ان S N بتروح ل Sيعني
+
+104
+00:07:22,580 --> 00:07:26,320
+converts to some element اسمه S و بنكتبه summation
+
+105
+00:07:26,320 --> 00:07:30,940
+XI I من عند واحد لما انه تروح لما نهاية as N goes
+
+106
+00:07:30,940 --> 00:07:34,060
+to infinity يعني بيصير summation بدل لـ Sn هذا
+
+107
+00:07:34,060 --> 00:07:38,640
+عبارة عن summation XI I من عند واحد لعند N لأن as
+
+108
+00:07:38,640 --> 00:07:40,720
+N goes to infinity بيصير ال summation هذا I من
+
+109
+00:07:40,720 --> 00:07:45,580
+واحد إلى ما لنهاية بنسميه أش بساوي بساوي S و بنقول
+
+110
+00:07:45,580 --> 00:07:48,960
+عنه ال sequenceالـ series في هذه الحالة converts
+
+111
+00:07:48,960 --> 00:07:54,120
+to sum اللي هو element S هذا اللي هو sum of the
+
+112
+00:07:54,120 --> 00:08:00,600
+series طيب إذا كان ال norm لـ X1 زاد norm لـ X2
+
+113
+00:08:00,600 --> 00:08:05,180
+زاد norm لـ X3 إلى ما لا نهاية بدل ما أجمع ال X1 و
+
+114
+00:08:05,180 --> 00:08:08,940
+X2 و X3 بأجمع مين ال normات اللي هين و أسارتي اللي
+
+115
+00:08:08,940 --> 00:08:12,380
+هى جمع عداد حقيقية موجبة إذا كان مجموح إن هدولة
+
+116
+00:08:12,380 --> 00:08:17,900
+existبنقول summation xi is absolutely convergent
+
+117
+00:08:17,900 --> 00:08:21,280
+زي ما كنا بالظبط نقول في الريال إن ال absolute
+
+118
+00:08:21,280 --> 00:08:24,620
+value x1 absolute value x2 زائد إلى آخر يكون
+
+119
+00:08:24,620 --> 00:08:27,480
+convergent بنقول ال series الأصلية تبعت اللي هي
+
+120
+00:08:27,480 --> 00:08:31,240
+الريال absolutely convergent وهنا إحنا اللي هو
+
+121
+00:08:31,240 --> 00:08:34,540
+بنفس الطريقة بستعميم أكبر بدء من ناخد على ال R
+
+122
+00:08:34,540 --> 00:08:38,980
+نفسها بناخد على أي norm this base ففي هذا الحالة
+
+123
+00:08:38,980 --> 00:08:41,660
+بنسميها اللي هي absolutely convergent زي ما قلنا
+
+124
+00:08:42,280 --> 00:08:46,100
+ناخد الـ definition الآن الـ definition بدنا نعرف
+
+125
+00:08:46,100 --> 00:08:50,000
+حاجة if a normed space X contains a sequence E N
+
+126
+00:08:50,000 --> 00:08:53,640
+ركزه، إيش ال sequence هذه؟ with the probability
+
+127
+00:08:53,640 --> 00:08:57,360
+that for every X element in X there exists a
+
+128
+00:08:57,360 --> 00:09:01,000
+unique sequence of scalars Alpha N such that اللي
+
+129
+00:09:01,000 --> 00:09:05,420
+هو X limit X ناقصة للألف واحد E1 ألف اتنين E2 نزلت
+
+130
+00:09:05,420 --> 00:09:10,620
+ألف ن E N as N goes to infinity بساوي سفرثم aₙ
+
+131
+00:09:10,620 --> 00:09:15,360
+بيكون نسميها ايش ما لها a Schauder basis for X the
+
+132
+00:09:15,360 --> 00:09:19,740
+series summation XI ألف I EI I من واحد لإنفينيتي
+
+133
+00:09:19,740 --> 00:09:23,180
+is called the expansion of X with respect to mean
+
+134
+00:09:23,180 --> 00:09:28,060
+to aₙ إذا الآن في عنا حاجة اسمها إيش هي Schauder
+
+135
+00:09:28,060 --> 00:09:33,340
+basis إيش Schauder basis كمان مرة؟ هي كتالة إذا
+
+136
+00:09:33,340 --> 00:09:40,800
+أخدنا عندي X element in X arbitraryarbitrary و
+
+137
+00:09:40,800 --> 00:09:51,780
+لجينا sequence αن of scalars ماشي الحال بحيث انه
+
+138
+00:09:51,780 --> 00:09:58,690
+اللي هي يكون عنده limit للنور من ال X ناقصالفا
+
+139
+00:09:58,690 --> 00:10:04,550
+واحد في اي واحد ايش اي واحد هتجهب ونقولك زائد الفا
+
+140
+00:10:04,550 --> 00:10:09,810
+اتنين اي اتنين زائد الفا ان اي ان as n goes to
+
+141
+00:10:09,810 --> 00:10:15,550
+infinity لجناه بيساوي سفر معناته بنقول عن ال
+
+142
+00:10:15,550 --> 00:10:22,260
+sequence هذه اللي هي اي واحد اي اتنين اي تلاتةE4
+
+143
+00:10:22,260 --> 00:10:27,000
+إلى مالة نهاية اللي بنسميها EN بنقول عنها is a
+
+144
+00:10:27,000 --> 00:10:33,770
+shoulder bases forming for ال space اللي عند Xو في
+
+145
+00:10:33,770 --> 00:10:37,650
+هذه الحالة as n goes to infinity بيصير و كأنه
+
+146
+00:10:37,650 --> 00:10:42,650
+بنقول ال norm لل X ناقص ال summation لل alpha I EI
+
+147
+00:10:42,650 --> 00:10:46,390
+I من عند واحد لعند n لما تروح إلى مالة نهاية و
+
+148
+00:10:46,390 --> 00:10:49,250
+كأنه بيصير اللي هو مدام ال limit هذا بيساوي سفر و
+
+149
+00:10:49,250 --> 00:10:54,270
+كأنه بنقول X بتساوي ال summation alpha I EI I من
+
+150
+00:10:54,270 --> 00:10:59,390
+واحد إلى مالة نهاية يعني بمعنى آخربنقول E N is a
+
+151
+00:10:59,390 --> 00:11:05,030
+Schauder basis لـ X إذا كان كل X في الـ X بنقدر
+
+152
+00:11:05,030 --> 00:11:10,410
+نلاقي sequence of scalars Alpha N بحيث إنه الـ X
+
+153
+00:11:10,410 --> 00:11:14,790
+هاد انكتبت على صورة Infinite Series Alpha I E I I
+
+154
+00:11:14,790 --> 00:11:20,930
+من واحد عند مين لعند اللي هو Infinity أي سؤال؟
+
+155
+00:11:24,480 --> 00:11:27,380
+طيب طبعا هذه الـ sequensation اللي جيها unique
+
+156
+00:11:27,380 --> 00:11:32,460
+sequence تنسوش انه صورة وحيدة على اساس ان كل واحد
+
+157
+00:11:32,460 --> 00:11:40,720
+يطلعله بصيغة مختلفة طبعا لكل X في unique sequence
+
+158
+00:11:40,720 --> 00:11:43,240
+of scalars alpha n such that X بالصيغة ال
+
+159
+00:11:43,240 --> 00:11:46,300
+summation هذا مفادلة حول ما نسميه E n as a show of
+
+160
+00:11:46,300 --> 00:11:50,430
+numbers طيب ناخد مثالمثال على الـ show their bases
+
+161
+00:11:50,430 --> 00:11:55,730
+الان example en is a show their bases for البي
+
+162
+00:11:55,730 --> 00:12:00,270
+نشوف ايش en البي عارفينه انتوا واحنا حكينا عنه
+
+163
+00:12:00,270 --> 00:12:02,930
+بالتفصيل
+
+164
+00:12:03,580 --> 00:12:08,980
+E1 هو عبارة عن واحد و الباقي صفار E2 صفر و التاني
+
+165
+00:12:08,980 --> 00:12:13,660
+واحد و الباقي صفار E3 صفر صفر واحد و الباقي صفار
+
+166
+00:12:13,660 --> 00:12:18,240
+EN in general صفر صفر صفر EN ناقص واحد من العناصر
+
+167
+00:12:18,240 --> 00:12:22,620
+صفار و بعدين الرقم ال entry N بتكون واحد و الباقي
+
+168
+00:12:22,620 --> 00:12:27,330
+ايش مالهأصفر هذه الان اللي هي sequence of elements
+
+169
+00:12:27,330 --> 00:12:30,730
+أكيد وين موجودة؟ موجودة في القلبي لإن ال summation
+
+170
+00:12:30,730 --> 00:12:35,790
+إلها عبارة عن واحد بس ف finite ده موجود وين في
+
+171
+00:12:35,790 --> 00:12:40,730
+القلبي مافي أي مشكلة بدنا نثبت إن هذه بتعمل
+
+172
+00:12:40,730 --> 00:12:44,090
+shoulder bases إيش بدنا ناخد؟ بدنا ناخد أي X
+
+173
+00:12:44,090 --> 00:12:49,070
+arbitrary element ونلاقي ال sequence ناخد X أي
+
+174
+00:12:49,070 --> 00:12:55,360
+element في القلبيأيوة يا جماعة بدنا ناخد X أي
+
+175
+00:12:55,360 --> 00:13:00,220
+element في الـ LB ونلاقي ال sequence of scalars αN
+
+176
+00:13:00,220 --> 00:13:04,620
+مثلا أو اللي نسميها بعد شوية بحيث انه اللي هو
+
+177
+00:13:04,620 --> 00:13:07,100
+sequence وحيدة انه X نقدر نكتبها على سورة
+
+178
+00:13:07,100 --> 00:13:12,760
+summation αN في EN N من واحد إلى وين إلى مالة
+
+179
+00:13:12,760 --> 00:13:19,160
+نهاية ده نشوف كده خلّا مع بعضالأن let X be any
+
+180
+00:13:19,160 --> 00:13:23,880
+fixed element in B طبعاً كيف شكله الـ X في القلبي
+
+181
+00:13:23,880 --> 00:13:28,020
+Sequences يعني XI واحد، XI اتنين، XI تلت، XI
+
+182
+00:13:28,020 --> 00:13:30,920
+أربعة، إلى ما لنهاية، إذن X any fixed element in
+
+183
+00:13:30,920 --> 00:13:34,940
+قلبي إذن مدامه في القلبي، إذن أكيد الـ summation
+
+184
+00:13:34,940 --> 00:13:39,180
+الـ XI I، I من واحدة and infinity الـ B إيش ماله؟
+
+185
+00:13:39,180 --> 00:13:43,380
+is finite، convergent، عشان اللي هو شروط وجوده في
+
+186
+00:13:43,380 --> 00:13:47,640
+القلبيمدام هيك إذا then there is a sequence Xi I
+
+187
+00:13:47,640 --> 00:13:50,820
+of scalars such that أنا بتدعي الآتي أنه بقدر
+
+188
+00:13:50,820 --> 00:13:54,560
+ألاقي sequence of scalars Xi I من وين جبتها اللي
+
+189
+00:13:54,560 --> 00:13:57,960
+هي عناصر ال sequence اللي هاني يعني أخدت X1 و X2 و
+
+190
+00:13:57,960 --> 00:14:02,440
+X3 و X4 هي اللي هي من ال sequence of scalars اللي
+
+191
+00:14:02,440 --> 00:14:08,060
+أنا بديها such that ال X ناقص بقعد بطبق في التعريف
+
+192
+00:14:08,060 --> 00:14:13,060
+Xi 1 E 1 زي Xi 2 E 2 زي Xi N E N نحسبها مع بعض
+
+193
+00:14:13,570 --> 00:14:18,270
+ونشوف كيف نوصل إن ال limit لهذه بيساوي سفر نكون
+
+194
+00:14:18,270 --> 00:14:21,750
+خلصت، نكون أثبتت إنه فيه وموجود، وبعدين نثبت إنه
+
+195
+00:14:21,750 --> 00:14:27,530
+إيش وحيد، طيب، بساوي، الآن X نفسها عبارة عن مين؟
+
+196
+00:14:27,530 --> 00:14:31,850
+عن E1, E2, EN, EN, Z1, EN, Z2، Sequence إلى ما لا
+
+197
+00:14:31,850 --> 00:14:38,350
+نهاية، طيب هيها ال CLX، طيب، ناقص، الآن Alpha 1 E1
+
+198
+00:14:39,220 --> 00:14:45,140
+اللي عبارة عن Alpha 1 E 1 زائد Alpha 2 E 2 زائد
+
+199
+00:14:45,140 --> 00:14:51,200
+Alpha N E N ماعملتش فيها ولا شي لسه ماهي الحال و
+
+200
+00:14:51,200 --> 00:14:58,580
+يساوي الآن خلينا نحسبها هذه نحسب هذه الآن نحسب هذه
+
+201
+00:14:58,580 --> 00:15:07,640
+نحسب Alpha 1 E 1 لعند Alpha N E N لعند هذه نشوف
+
+202
+00:15:07,640 --> 00:15:13,850
+إيش هيالفا واحد اي واحد زائد الفا اتنين اي اتنين
+
+203
+00:15:13,850 --> 00:15:20,970
+زائد الفا ان اي ان ويساوي الفا اكساي واحد في اكساي
+
+204
+00:15:20,970 --> 00:15:21,210
+ان
+
+205
+00:15:25,070 --> 00:15:30,130
+في E1 E1 يعني عبارة عن واحد صفر صفر إلى مانا نهاية
+
+206
+00:15:30,130 --> 00:15:37,750
+زائد ال XI2 في Zero واحد Zero Zero زائد لما أصل
+
+207
+00:15:37,750 --> 00:15:44,870
+للأخيرة اللي هي XIN في Zero Zero لما أصل لل term N
+
+208
+00:15:44,870 --> 00:15:51,390
+اللي هو واحد والباقي أشمله أصفر ويسافر نيجي نحسب
+
+209
+00:15:51,390 --> 00:15:58,020
+ان XI واحدو هدولة صفراء إسفار إكساي اتنين والباقي
+
+210
+00:15:58,020 --> 00:16:02,280
+إسفار لما أصل عند مين إكساي أن واللي بعدهم كلهم
+
+211
+00:16:02,280 --> 00:16:08,700
+إيش يا جماعة إسفار طيب الأنصار هذا عبارة عنهذا ..
+
+212
+00:16:08,700 --> 00:16:14,640
+هذا اللي مهشر عليه اللي هو x1 و x2 و x3 و xn و
+
+213
+00:16:14,640 --> 00:16:19,800
+الباقي 0 لما أطرح حد ناقص هذا هيروح من الأولانيات
+
+214
+00:16:19,800 --> 00:16:24,420
+هيطلع 0 .. 0 .. 0 .. 0 و يضل المين اللي هي ال
+
+215
+00:16:24,420 --> 00:16:27,460
+interest دولة لأنهم لما نطرح منهم الأسفار بيضل هنا
+
+216
+00:16:27,460 --> 00:16:32,070
+xn زي 1 و xn زي 2 إلى ما لنهايةواضح حاصل طرح
+
+217
+00:16:32,070 --> 00:16:36,750
+الجهتين هذا الان مجموعه ايش بيساوي بيساوي مجموعه
+
+218
+00:16:36,750 --> 00:16:41,150
+اللي هو ال normه normه انا وين بشتغل في ال ال B و
+
+219
+00:16:41,150 --> 00:16:44,490
+ال B norm ايش معله ال summation لل absolute values
+
+220
+00:16:44,490 --> 00:16:48,890
+ده دول ال interest أس بي الكلس واحد على بي هي xi I
+
+221
+00:16:48,890 --> 00:16:52,930
+أس بي الكلس واحد على بي I الأولميات من واحد لأم
+
+222
+00:16:52,930 --> 00:16:56,470
+نصفار اذا بيبدأ ال summation هنا زاد واحد أمين
+
+223
+00:16:56,470 --> 00:17:01,090
+لماله نهيئةas n goes to infinity هذا ال summation
+
+224
+00:17:01,090 --> 00:17:04,890
+بتلاشى as n goes to infinity هيروح لوين لعين سفر
+
+225
+00:17:04,890 --> 00:17:07,410
+لما قلت روح لما قلت هذا ال summation هيتلاشى ويروح
+
+226
+00:17:07,410 --> 00:17:11,970
+ل zero as n goes to infinity اذا ان انا اللي اجيت
+
+227
+00:17:11,970 --> 00:17:23,130
+سويته ان انا اللي سويته اثبتتلك انه limitNormal X
+
+228
+00:17:23,130 --> 00:17:29,790
+ناقص summation XII EI I من عند واحد لعند N as N
+
+229
+00:17:29,790 --> 00:17:34,730
+goes to infinity ايش بيساوي؟ بيساوي 0 دل أثبت انه
+
+230
+00:17:34,730 --> 00:17:38,570
+وحيدة اللي هي ال sequence of scalars وحيدة يعني ال
+
+231
+00:17:38,570 --> 00:17:42,850
+sequence of scalars اللي جيت XII هذه اللي هي نفس
+
+232
+00:17:42,850 --> 00:17:46,670
+تركيبة مين ال X اللي جوا اللي أخدتها منها اللي هي
+
+233
+00:17:46,670 --> 00:17:52,940
+هتكون ايه اشمالها as unique اطلع لفوقNow assume
+
+234
+00:17:52,940 --> 00:17:56,980
+that there is a sequence تانية αI of scalars such
+
+235
+00:17:56,980 --> 00:18:03,740
+that X- α1 E1 زائد α2 E2 زائد αN EN بتروح لـ 0 أزن
+
+236
+00:18:03,740 --> 00:18:08,080
+جثمين تنفيذ لان افترض انها اشمالها في واحدة تانية
+
+237
+00:18:08,080 --> 00:18:11,700
+بتحقق نفس الشروط الأولى و بعدين اثبتلك انه هتطلع
+
+238
+00:18:11,700 --> 00:18:16,520
+حد ال sequence αI هي نفسها مين لـ Xi I فبتكون خلاص
+
+239
+00:18:16,520 --> 00:18:19,830
+is uniqueإلى and then ال absolute value لل
+
+240
+00:18:19,830 --> 00:18:22,990
+summation هذا هو عبارة عن إيش عبارة عن ال
+
+241
+00:18:22,990 --> 00:18:27,470
+summation xi i ناقص alpha i ei i من عند واحد لعند
+
+242
+00:18:27,470 --> 00:18:33,890
+مين لعند n هذه حسبتها normal x نحسبلكم إياها هان
+
+243
+00:18:41,120 --> 00:18:54,240
+ممكن تحسبوها لحالكم لكن خلّين نحسب الهدف
+
+244
+00:18:54,240 --> 00:18:57,520
+اللي فرضناه و نحسب هذه الهدف عشان نوصلها لما نريده
+
+245
+00:18:59,970 --> 00:19:03,390
+الـ Xi I ناقص Alpha I في EI I من عند واحد لعندان
+
+246
+00:19:03,390 --> 00:19:08,370
+بدنا نفردها ال EI هدولة scalars وال EI ال E1 عبارة
+
+247
+00:19:08,370 --> 00:19:12,010
+عن واحد زيرو زيرو زيرو و لا اخرى بيصير هدى عبارة
+
+248
+00:19:12,010 --> 00:19:23,020
+عن XiI أبدا بالأولى I أبدا
+
+249
+00:19:23,020 --> 00:19:25,480
+بالأولى I أبدا بالأولى I أبدا بالأولى I أبدا
+
+250
+00:19:25,480 --> 00:19:26,260
+بالأولى I أبدا بالأولى I أبدا بالأولى I أبدا
+
+251
+00:19:26,260 --> 00:19:26,300
+بالأولى I أبدا بالأولى I أبدا بالأولى I أبدا
+
+252
+00:19:26,300 --> 00:19:26,420
+بالأولى I أبدا بالأولى I أبدا بالأولى I أبدا
+
+253
+00:19:26,420 --> 00:19:26,440
+بالأولى I أبدا بالأولى I أبدا بالأولى I أبدا
+
+254
+00:19:26,440 --> 00:19:26,560
+بالأولى I أبدا بالأولى I أبدا بالأولى I أبدا
+
+255
+00:19:26,560 --> 00:19:35,040
+بالأولى I أبدا بالأولى I أبدا بالأولىX ناقص اللي
+
+256
+00:19:35,040 --> 00:19:40,680
+هو الأولى اللي هي هذه زائد
+
+257
+00:19:40,680 --> 00:19:45,100
+اللي هو X norm التاني X ناقص مين التاني يعني ضفت X
+
+258
+00:19:45,100 --> 00:19:48,520
+و طرحت مين X و استخدمت ال triangle inequalityطب
+
+259
+00:19:48,520 --> 00:19:53,380
+الآن هذه ما هي من الحالة الأولى ما هي X كتبت على
+
+260
+00:19:53,380 --> 00:19:58,800
+صورة الـ Submission هذا يعني بمعنى أخر هذا ال
+
+261
+00:19:58,800 --> 00:20:01,620
+limit له بساوة سفر وهذا ال limit بساوة سفر اللي
+
+262
+00:20:01,620 --> 00:20:05,520
+فرضته هان إذا صار ال limit لهذا كله أشمله بساوة
+
+263
+00:20:05,520 --> 00:20:11,650
+سفر إذا as n goes to infinity بصير هذا المقدارI من
+
+264
+00:20:11,650 --> 00:20:15,550
+عند واحد إلى ما لا نهاية بساوي سفر اطلع لفوق then
+
+265
+00:20:15,550 --> 00:20:19,090
+as n goes to infinity هذا المقدار بيروح للسفر
+
+266
+00:20:19,090 --> 00:20:22,170
+معناته ايش معناته هذا لما قالنا تروح إلى ما لا
+
+267
+00:20:22,170 --> 00:20:26,970
+نهاية يعني I من واحد إلى ما لا نهاية XII EI ناقص
+
+268
+00:20:26,970 --> 00:20:31,810
+الف I EI ايش بساوي بساوي اللي هو سفر هذا ايش هو في
+
+269
+00:20:31,810 --> 00:20:39,310
+الواقعاللي هو xi i ناقص alpha i as a sequence كيف؟
+
+270
+00:20:39,310 --> 00:20:45,790
+لأن هذا ال summation عبارة عن xi i ناقص ei ناقص
+
+271
+00:20:45,790 --> 00:20:51,580
+alpha iفي I ال summation I من واحد إلى مانع نهائية
+
+272
+00:20:51,580 --> 00:20:56,620
+خلّينا نفردها بساوى الآن الأولى عبارة عن XI واحد
+
+273
+00:20:56,620 --> 00:21:01,140
+ناقص Alpha واحد في E واحد هتطلع و الباقي أسفار
+
+274
+00:21:01,140 --> 00:21:07,520
+ماشي زائد التانية السفر XI اتنين ناقص Alpha اتنين
+
+275
+00:21:07,520 --> 00:21:13,230
+و الباقي ايش أسفارالان اللى عند ما اصل عند اخر
+
+276
+00:21:13,230 --> 00:21:18,270
+واحدة Zero Zero Zero عند N من العناصر بيصير Xi N
+
+277
+00:21:18,270 --> 00:21:24,450
+ناقص E N ناقص Alpha N و الباقى أسفار مافي الحال و
+
+278
+00:21:24,450 --> 00:21:27,170
+بيضلوا إلى ما لا نهاية هذا في الواقع ايش هيكون
+
+279
+00:21:27,170 --> 00:21:31,410
+عبارة عن ال .. هي عبارة عن سارة ايش مالها اللى هى
+
+280
+00:21:31,410 --> 00:21:36,390
+مجموحة مع بعض هي عبارة عن norm اللى هو Xi 1 ناقص
+
+281
+00:21:36,390 --> 00:21:44,620
+Alpha 1 Xi 2نقص ألف اتنين مجمحين مجمحين و XI تلاتة
+
+282
+00:21:44,620 --> 00:21:50,780
+نقص ألف تلاتة و XI N نقص ألف N وهذا بيضلوا إلى مين
+
+283
+00:21:50,780 --> 00:21:53,980
+إلى مالة نهاية إذا في الواقع هذه اللي جوايا شمالها
+
+284
+00:21:53,980 --> 00:21:59,280
+هي ال sequence هذه XI I نقص ألف I لأن هذه صارت
+
+285
+00:21:59,280 --> 00:22:03,460
+بتساوي سفرمعناته مدام النور بيساوي سفر إذا اللي
+
+286
+00:22:03,460 --> 00:22:06,640
+جوا بيساوي سفر معناته أن ال sequence هذه بتساوي ال
+
+287
+00:22:06,640 --> 00:22:09,860
+sequence هذه ومعناته اللي هو ال E أنصار إيش ماله
+
+288
+00:22:09,860 --> 00:22:14,660
+is a shoulder basis لإنه حقق الشرطين إن لكل X في
+
+289
+00:22:14,660 --> 00:22:18,750
+القلبي there exists a unique اللي هي ميناللي هي
+
+290
+00:22:18,750 --> 00:22:22,110
+sequence of scalars such that الـ X can be written
+
+291
+00:22:22,110 --> 00:22:28,150
+as a summation of Alpha N في اللي هي E N أو Xi N
+
+292
+00:22:28,150 --> 00:22:31,950
+في E N من N من 1 إلى ما لنهاية إذا صارت الـ E N is
+
+293
+00:22:31,950 --> 00:22:38,250
+a Schauder basis نيجي الآن لاللي هو النظرية
+
+294
+00:22:38,250 --> 00:22:42,650
+التالية اللي هي completion of a normed space
+
+295
+00:22:48,170 --> 00:22:53,190
+في الواقع هي هذه امتداد للنظرية اللي أخدناها في
+
+296
+00:22:53,190 --> 00:22:59,050
+اللي هي section 16 هي عندي اللي هو theorem اللي هو
+
+297
+00:22:59,050 --> 00:23:05,910
+162 أخدنا اللي هو النظرية كانت انه for any metric
+
+298
+00:23:05,910 --> 00:23:10,250
+space X وD بنقدر اللاجئ completion metric space X
+
+299
+00:23:10,250 --> 00:23:16,650
+hat وD hatwhich has a subspace W as isometric with
+
+300
+00:23:16,650 --> 00:23:21,470
+X and is dense in X hat وقلنا هذا اللي هو X hat is
+
+301
+00:23:21,470 --> 00:23:26,330
+unique up to isomorphism هذه شرحناها بشكل كامل
+
+302
+00:23:26,330 --> 00:23:31,990
+المحاضرة اللي هو السابعة عشان هيك أنا بفضل ان انت
+
+303
+00:23:31,990 --> 00:23:35,330
+مجرد ما بدك تسمح هذه المحاضرة لليوم انك تروح
+
+304
+00:23:35,330 --> 00:23:39,820
+للمحاضرة السابعةوتحضرها ومن ثم اتكمل على الكلام
+
+305
+00:23:39,820 --> 00:23:41,860
+اللي بدأ احكيه لأنه انا بدأ اكمل على البروحان اللي
+
+306
+00:23:41,860 --> 00:23:46,840
+هنا هذا البروحان كان اللي هو عبارة عن عن اللي هي
+
+307
+00:23:46,840 --> 00:23:51,240
+للنظرية اللي هي on metric space ان any metric
+
+308
+00:23:51,240 --> 00:23:55,240
+space can be completed الآن بدأ اقول ان any normed
+
+309
+00:23:55,240 --> 00:23:58,220
+space can be completed ترجعلي على ال .. على
+
+310
+00:23:58,220 --> 00:24:03,660
+النظرية تبعتنا اليوم خلينا نشوف اللي هو الكلام
+
+311
+00:24:03,660 --> 00:24:09,980
+اللي بدنا نحكيهالآن اللي هو بيقوللي theorem اللي
+
+312
+00:24:09,980 --> 00:24:15,340
+هو اتنين تلاتة ستة completion يعني لو أخدنا x بي a
+
+313
+00:24:15,340 --> 00:24:22,220
+normed space then there is a بنخ space x hatand is
+
+314
+00:24:22,220 --> 00:24:26,400
+isometry A from X to a subspace and to a subspace
+
+315
+00:24:26,400 --> 00:24:31,300
+W of X hat which is dense in X hat the space X hat
+
+316
+00:24:31,300 --> 00:24:35,100
+is unique except for isometries أنا في الواقع هذه
+
+317
+00:24:35,100 --> 00:24:40,000
+النظرية مبرهنها لإيش؟ مبرهنها في حال أن X metric
+
+318
+00:24:40,000 --> 00:24:45,500
+space يعني الآن كل ما يتعلق بوجود الـ X hat موجود
+
+319
+00:24:45,500 --> 00:24:50,350
+من الأصل بس موجود as a metric spaceأنا الآن إيش
+
+320
+00:24:50,350 --> 00:24:56,850
+دوري بدي أسويه بدي أخلي اللي هو اللي هو ال X هذا
+
+321
+00:24:56,850 --> 00:25:01,010
+ال X هذا بدي أركبها الآن as a normed space إذا
+
+322
+00:25:01,010 --> 00:25:05,750
+انضل علي أني أشوف ال X hat أن أعملها vector space
+
+323
+00:25:05,750 --> 00:25:09,010
+يعني معناته بدي أعرف scalar multiplication و بدي
+
+324
+00:25:09,010 --> 00:25:12,210
+أعرف اللي هو vector addition بالاستعانة بال X
+
+325
+00:25:12,210 --> 00:25:17,400
+الأصليةوالان اللى هى الشغله الثانيه ال isometric
+
+326
+00:25:17,400 --> 00:25:23,820
+اللى كان بين ال W و ال X اللى هى W و ال X كان جابل
+
+327
+00:25:23,820 --> 00:25:27,340
+اللى هو بس one to one one to function و preserves
+
+328
+00:25:27,340 --> 00:25:30,790
+the distance اللى هى preserves the normالان بده
+
+329
+00:25:30,790 --> 00:25:35,130
+شرط ثالث انه بده يحافظ على اللي هو الانصار اللي هي
+
+330
+00:25:35,130 --> 00:25:38,810
+ال isometric بين vector space و vector space اذا
+
+331
+00:25:38,810 --> 00:25:41,850
+بده ينقل عملية الجمع و عملية ال scalar
+
+332
+00:25:41,850 --> 00:25:45,610
+multiplication عشان يسميه isometry يعني بمعنى اخر
+
+333
+00:25:45,610 --> 00:25:52,750
+الان ال isometry T بين X لعين Wأول شيء Preserve
+
+334
+00:25:52,750 --> 00:25:55,150
+the norm أو Preserve the distance اللي قلناه المرة
+
+335
+00:25:55,150 --> 00:25:59,410
+الفاتة و one to one و one to two وهذا مثبت من قبل
+
+336
+00:25:59,410 --> 00:26:04,710
+الشيء الثاني يجب أن نثبت أن T تحافظ على Alpha X
+
+337
+00:26:06,420 --> 00:26:11,200
+زائد Y بتساوي اللي هو إيه شمالها اللي هو Alpha في
+
+338
+00:26:11,200 --> 00:26:16,840
+TX زائد TY يعني بتحافظ على العملية الجامعة ب
+
+339
+00:26:16,840 --> 00:26:20,760
+preserve the operation يعني بمفهوم اللي هو الجبر
+
+340
+00:26:20,760 --> 00:26:24,780
+الخط Linear اللي هو تكون T Linear و تحافظ على ال
+
+341
+00:26:24,780 --> 00:26:27,760
+scalar multiplication إذا هي اللي بدنا نسويه بس
+
+342
+00:26:27,760 --> 00:26:30,640
+احنا بدنا نكمل على اللي هو السابق خلينا نشوف مع
+
+343
+00:26:30,640 --> 00:26:36,000
+بعضطيب الآن by theorem 162 there is a complete
+
+344
+00:26:36,000 --> 00:26:39,600
+metric space X hat ال metric هنا اللي هو induced
+
+345
+00:26:39,600 --> 00:26:47,340
+by the norm there is a metric space X hat المقصود
+
+346
+00:26:47,340 --> 00:26:51,520
+أنه ال metric اللي بدو ييجي هنا اللي هو اعتمد على
+
+347
+00:26:51,520 --> 00:26:54,700
+ال metric اللي في ال X اللي هو اللي induced by the
+
+348
+00:26:54,700 --> 00:27:00,410
+normand an isometry a من x لعن و اللي سمناها في
+
+349
+00:27:00,410 --> 00:27:04,390
+حين و أيه اشمالها a of x و كنا عارفين كيف أرسلناها
+
+350
+00:27:04,390 --> 00:27:08,430
+راجعوا المحاضرة where a where w is dense in mean
+
+351
+00:27:08,430 --> 00:27:14,450
+in x hat and x hat أثبتناها as a is unique except
+
+352
+00:27:14,450 --> 00:27:19,380
+for isometriesطيب، الآن هذا الكلام كله من المحاضرة
+
+353
+00:27:19,380 --> 00:27:22,460
+السابقة وفصلنا تفصيل واخدنا محاضرة كاملة بيجي
+
+354
+00:27:22,460 --> 00:27:26,300
+حوالي ساعة و نص أو أكتر على البرهان النظرية الآن
+
+355
+00:27:26,300 --> 00:27:30,100
+بدنا نكمل بما يتعلق بال normed space بدأ أبدأ
+
+356
+00:27:30,100 --> 00:27:34,040
+أعرفلك اللي هو عملية جمع وعملية scalar
+
+357
+00:27:34,040 --> 00:27:36,920
+multiplication على مين على ال X hat عشان هذا أقولك
+
+358
+00:27:36,920 --> 00:27:41,620
+إن X hat هتمثل لي vector من S base طيب كيف بدأ
+
+359
+00:27:41,620 --> 00:27:49,290
+أعملها؟ عنديlet x hat و y hat element in x hat إذا
+
+360
+00:27:49,290 --> 00:27:52,310
+بتذكروا إحنا الـ x hat كانت عبارة عن equivalency
+
+361
+00:27:52,310 --> 00:27:55,390
+class اللي هي ال equivalency class كانت اللي هي في
+
+362
+00:27:55,390 --> 00:27:57,810
+داخلها أو اللي عامل اللي هي مين هي Cauchy
+
+363
+00:27:57,810 --> 00:28:00,470
+sequences وكلنا الـ Cauchy sequences اللي هي
+
+364
+00:28:00,470 --> 00:28:03,450
+العلاقة في بعض كان في نفس مين ال equivalency class
+
+365
+00:28:03,450 --> 00:28:07,530
+هذا كله شرحناه المرة الماضية الآن بتاخد أي x أنف
+
+366
+00:28:07,530 --> 00:28:10,230
+موجودة في الـ x hat sequence إنه equivalency class
+
+367
+00:28:10,750 --> 00:28:16,310
+الان وي ان وين موجودة في الـ y hat ماشي الان بدي
+
+368
+00:28:16,310 --> 00:28:21,530
+اعرف الان اللي هو احصل على اللي هي z hat مستوى x
+
+369
+00:28:21,530 --> 00:28:27,100
+hat زايد y hat كيف بدي احصلها ركزوا معاياالآن عندي
+
+370
+00:28:27,100 --> 00:28:30,560
+لو جيت لحظة تشوف الـ Cauchy Sequences الـ Zن تين
+
+371
+00:28:30,560 --> 00:28:35,420
+هدولة لو جمعتها لبعض وسمتها Zn إيش بيكون هدولة الـ
+
+372
+00:28:35,420 --> 00:28:39,760
+Zn الجديدة؟ بتكون الـ Zn عبارة عن Cauchy اللي هو
+
+373
+00:28:39,760 --> 00:28:43,460
+إيش Sequence ليش؟ لأن Xn Cauchy و Yn Cauchy
+
+374
+00:28:43,460 --> 00:28:46,020
+مجموعته Cauchy Sequences إيش هيطلع؟ Cauchy
+
+375
+00:28:46,020 --> 00:28:50,500
+Sequence إذا الآن Zn Cauchy Sequenceالان بما انه
+
+376
+00:28:50,500 --> 00:28:54,780
+زي ما بقولك XN and YN are Cauchy Sequences دين ZN
+
+377
+00:28:54,780 --> 00:28:59,640
+is a Cauchy Sequence الان define Z hat بتساوي X
+
+378
+00:28:59,640 --> 00:29:04,680
+hat زائد Y hat كيف؟ مين هي ال Z hat؟ هذه ال Z hat
+
+379
+00:29:04,680 --> 00:29:08,600
+اللي هي بدها تتحقق equivalency class اللي بدها
+
+380
+00:29:08,600 --> 00:29:12,740
+تتحدد هويتها بواسطة من ال ZN يعني ال Cauchy
+
+381
+00:29:12,740 --> 00:29:16,680
+Sequence اللي طلعت من المجموح هذه زائد هذهالـ
+
+382
+00:29:16,680 --> 00:29:21,240
+equivalence class تبعي تاخدها وسميها إيش مالها Z
+
+383
+00:29:21,240 --> 00:29:25,020
+hat إذا عملية الجمع صارت واضحة في ال X hat في ال X
+
+384
+00:29:25,020 --> 00:29:28,080
+hat عملية الجمع كده باجي باجمع باخد X hat
+
+385
+00:29:28,080 --> 00:29:32,470
+arbitrary هات و Y hat arbitrary هاتإنما بقول X hat
+
+386
+00:29:32,470 --> 00:29:36,970
+زائد Y hat إيش بيساوي Z hat طب مين Z hat هذه؟ هذه
+
+387
+00:29:36,970 --> 00:29:43,110
+Z hat L اللي هي بتساوي Zn اللي هي ال equivalence
+
+388
+00:29:43,110 --> 00:29:47,330
+class لها طب مين Zn هذه؟ Zn هي اللي ناتجة من
+
+389
+00:29:47,330 --> 00:29:52,370
+sequence من هنا زائد sequence من هنا إذن صارت الآن
+
+390
+00:29:52,370 --> 00:29:56,590
+اللي هي عملية الجمع تمدت على جمالية الجمع الأصلية
+
+391
+00:29:56,590 --> 00:29:59,430
+اللي بين اللي هي ال sequences L في ال space الأصل
+
+392
+00:29:59,430 --> 00:30:04,050
+هو ال Xهذا عملية الجمع الان طب هذه العملية ال well
+
+393
+00:30:04,050 --> 00:30:08,750
+defined يعني بمعنى آخر لو أنا أخدت xn و yn و جه
+
+394
+00:30:08,750 --> 00:30:12,990
+واحد تاني قال أنا بدي أخد wn موجودة في ال x hat و
+
+395
+00:30:12,990 --> 00:30:16,330
+kn موجودة في ال y hat و جيت جماعة تاني و طلع ليها
+
+396
+00:30:16,330 --> 00:30:20,690
+sequence هل هذه ال sequence هيكون ال equivalency
+
+397
+00:30:20,690 --> 00:30:25,070
+class لها نفس هذه أنا بقولك أه و عشان هيك بدي أكون
+
+398
+00:30:25,070 --> 00:30:28,010
+well defined وشوف كيف بدنا نثبت أنها well defined
+
+399
+00:30:28,010 --> 00:30:34,590
+اطلع لفوقطيب this definition is independent of the
+
+400
+00:30:34,590 --> 00:30:38,950
+choice of the Cauchy sequences in X hat and Y hat
+
+401
+00:30:38,950 --> 00:30:44,390
+ماشي نشوف كده in fact لو انت اخترت عشان الجامع
+
+402
+00:30:44,390 --> 00:30:48,930
+اللي قولنا عنه قبل شوية XN واخترت WN معناته
+
+403
+00:30:48,930 --> 00:30:51,870
+التنتين في نفس ال equivalence class معناته related
+
+404
+00:30:51,870 --> 00:30:55,180
+حسب ال relation اللي عرفناها المرة الماضيةو جيت
+
+405
+00:30:55,180 --> 00:31:00,420
+انت اخترت في ال Y hat YN و انا اخترت VN او WN او
+
+406
+00:31:00,420 --> 00:31:03,680
+اللي هي VN اللي هي طبعا مادامن في نفس ال
+
+407
+00:31:03,680 --> 00:31:06,760
+equivalency class اذا التنتين اشمالين related حسب
+
+408
+00:31:06,760 --> 00:31:11,200
+الخاصية او حسب العلاقة اللي عرفناها المرة الماضية
+
+409
+00:31:11,200 --> 00:31:15,140
+طيب طب هذولة متى بيكون ال XN لما تكون XN related
+
+410
+00:31:15,140 --> 00:31:18,880
+to WN ايش قلنا بيكون XN عرفنا ال relation المرة
+
+411
+00:31:18,880 --> 00:31:24,860
+الماضية related to WNفي حال كانت ال limit لل
+
+412
+00:31:24,860 --> 00:31:29,560
+distance بين ال Xn و ال Wn إيش هتساوي؟ هتساوي سفر
+
+413
+00:31:29,560 --> 00:31:32,420
+طب ما هي ال distance الآن إحنا بنحكي عن اللي هو
+
+414
+00:31:32,420 --> 00:31:36,880
+norm ال metric هذا اللي الآن induced by the norm
+
+415
+00:31:36,880 --> 00:31:41,200
+يعني بمعنى آخر norm ال Xn نقص Wn إيش هيساوي؟
+
+416
+00:31:41,200 --> 00:31:47,060
+limitه هيساوي سفر إذا لما Xnrelated to wn معناته
+
+417
+00:31:47,060 --> 00:31:54,280
+اصبح limit xn نقص wn بساوي سفر و limit yn نقص vn
+
+418
+00:31:54,280 --> 00:32:00,620
+بساوي سفر شوف الآناللي بدأ أصل إليه أنا بدأ أصل إن
+
+419
+00:32:00,620 --> 00:32:04,600
+جوابي و جوابكم نفس الاشي اللي هو عند Normal XN
+
+420
+00:32:04,600 --> 00:32:08,440
+زائد YN ناقص WN زائد VN هذا بالـ Triangling
+
+421
+00:32:08,440 --> 00:32:14,260
+Quality أصغر يساوي Normal XN ناقص WN زائد YN ناقص
+
+422
+00:32:14,260 --> 00:32:18,840
+من VNلأن بما أنه اللي هو التمتين هذوله في نفس ال
+
+423
+00:32:18,840 --> 00:32:21,560
+equivalency class زي ما قلنا إذا هذه as n goes to
+
+424
+00:32:21,560 --> 00:32:24,100
+infinity بتروح للصفر وهذه as n goes to infinity
+
+425
+00:32:24,100 --> 00:32:28,440
+بتروح للصفر بمعنى آخر هذه ال limit اللي هتروح لمين
+
+426
+00:32:28,440 --> 00:32:33,480
+للصفر يعني بمعنى آخر ال sequence ال Xn زي Yn اللي
+
+427
+00:32:33,480 --> 00:32:38,170
+اعتمدت عليه جوابهاللي هو و ال sequence هذه related
+
+428
+00:32:38,170 --> 00:32:41,950
+يعني بمعنى آخر التنتين في نفس ال equivalency class
+
+429
+00:32:41,950 --> 00:32:46,110
+يعني بمعنى آخر ال Z hat تبعته هي نفس ال Z hat
+
+430
+00:32:46,110 --> 00:32:49,910
+تبعتك لإن هدولة هيكون التنتين في نفس ال
+
+431
+00:32:49,910 --> 00:32:54,370
+equivalency class فبكون في هذه الحالة إنه فعلا ال
+
+432
+00:32:54,370 --> 00:32:58,470
+Z hat بيساوي X hat زي Y hat is well defined اطلع
+
+433
+00:32:58,470 --> 00:33:04,720
+لفوق شويةإذا نخلصنا من عملية الجمع اللي مبنية على
+
+434
+00:33:04,720 --> 00:33:10,900
+اللي عندنا Similarly بالنسبة لمين we define the
+
+435
+00:33:10,900 --> 00:33:16,500
+product Alpha X hat اللي هيكون element من X hat of
+
+436
+00:33:16,500 --> 00:33:20,340
+a scalar Alpha and X hat to be the equivalence
+
+437
+00:33:20,340 --> 00:33:23,800
+class for which Alpha X hat is representative إيش
+
+438
+00:33:23,800 --> 00:33:29,240
+يعني؟ يعني بنفس الطريقةعشان اعرف اللي هو شو معناته
+
+439
+00:33:29,240 --> 00:33:36,560
+اخد x hat element in x hat واخد alpha scalar بده
+
+440
+00:33:36,560 --> 00:33:40,940
+اعرف الآن عملية ال scalar multiplication في داخل
+
+441
+00:33:40,940 --> 00:33:45,530
+ال x hatوين رايح أنا عشان أثبت لكم إنه هذا X hat
+
+442
+00:33:45,530 --> 00:33:49,350
+هيطلع في vector space عرفنا الجامع والأن بنعرف مين
+
+443
+00:33:49,350 --> 00:33:54,450
+ال scalar multiplication الآن Alpha في ال X hat
+
+444
+00:33:54,450 --> 00:33:59,270
+بدي أعرفها عبارة عن اللي هي ال .. ال .. ال .. ال
+
+445
+00:33:59,270 --> 00:34:02,850
+.. طبعا مدامة ال X hat في ال X hat إذا أكيد في
+
+446
+00:34:02,850 --> 00:34:07,450
+sequence XN موجودة في ال X hatهذا اللي هي البنت
+
+447
+00:34:07,450 --> 00:34:09,290
+عليها ال equivalence class الـ Cauchy sequence
+
+448
+00:34:09,290 --> 00:34:14,070
+الان Alpha في Xn برضه هتطلع Cauchy sequence بدام
+
+449
+00:34:14,070 --> 00:34:18,090
+Xn الان ال Cauchy sequence هذه ال equivalence
+
+450
+00:34:18,090 --> 00:34:22,790
+class هي اللي بتسميها Alpha في مين؟ في X hatيعني
+
+451
+00:34:22,790 --> 00:34:26,910
+بمعنى أخر Alpha في X hat بدي أعرفها على أساس Alpha
+
+452
+00:34:26,910 --> 00:34:31,630
+في X لكل hat يعني هذه إيش بترمز؟ بترمز The set of
+
+453
+00:34:31,630 --> 00:34:36,150
+all equivalency classes اللي هي Alpha XN حيث XN is
+
+454
+00:34:36,150 --> 00:34:40,410
+a Cauchy sequence in X hat Similarly زي اللي قبل
+
+455
+00:34:40,410 --> 00:34:46,840
+بالظبط الآن هذه تحت هذا ال productSimilarly as in
+
+456
+00:34:46,840 --> 00:34:50,640
+the definition above nationalيد الطريقة المباشرة
+
+457
+00:34:50,640 --> 00:34:54,020
+of addition one can see that the definition of a
+
+458
+00:34:54,020 --> 00:34:57,240
+product is independent of the choice of
+
+459
+00:34:57,240 --> 00:35:02,760
+representative of etc يعني بمعنى أخر انت أخدتفي
+
+460
+00:35:02,760 --> 00:35:07,220
+الـ X hat XN كوشي سيكوانس وواحد تاني أخد YN في
+
+461
+00:35:07,220 --> 00:35:11,240
+الكوشي سيكوانس X hat هيطلع عند الألفة في ال XN
+
+462
+00:35:11,240 --> 00:35:14,180
+والألفة في ال YN ال equivalency classes انهم زي
+
+463
+00:35:14,180 --> 00:35:18,220
+بعض يعني بمعنى جوابي وجوابك زي بعض عشان هيك اللي
+
+464
+00:35:18,220 --> 00:35:22,400
+هو ال scalar multiplication برضه ايه شمالها is
+
+465
+00:35:22,400 --> 00:35:27,930
+well definedالان بالاستعانة
+
+466
+00:35:27,930 --> 00:35:37,110
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+467
+00:35:37,110 --> 00:35:39,430
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+468
+00:35:39,430 --> 00:35:40,370
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+469
+00:35:40,370 --> 00:35:40,630
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+470
+00:35:40,630 --> 00:35:40,650
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+471
+00:35:40,650 --> 00:35:40,710
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+472
+00:35:40,710 --> 00:35:41,370
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+473
+00:35:41,370 --> 00:35:42,230
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+474
+00:35:42,230 --> 00:35:46,070
+بالاستعانة بالاستعانة بالاستعانة بالاستعانةانت
+
+475
+00:35:46,070 --> 00:35:50,830
+الآن لو جيت على حسب التعريف و جيت على كل خواص الـ
+
+476
+00:35:50,830 --> 00:35:54,490
+vector space هتلاقيها متحققة على العملية وهذه
+
+477
+00:35:54,490 --> 00:35:58,390
+بتظلها حسابات عندكم بتعملوها لحالكم اتحققوا العشر
+
+478
+00:35:58,390 --> 00:36:02,890
+شروط تبعات ال vector space يعني بمعنى اخر انا الآن
+
+479
+00:36:02,890 --> 00:36:07,330
+اثبتت ان X hat اشمالها is a vector space و الـ
+
+480
+00:36:07,330 --> 00:36:12,520
+zero elementللـ X hat is the equivalence class
+
+481
+00:36:12,520 --> 00:36:15,360
+contains all Cauchy sequences which converge to 0
+
+482
+00:36:15,360 --> 00:36:19,900
+منطقي، ليش؟ الآن الـ zero element هان الـ zero
+
+483
+00:36:19,900 --> 00:36:24,040
+element هان، بدي أسميه الـ zero hat مين الـ zero
+
+484
+00:36:24,040 --> 00:36:27,700
+hat؟ اللي هو اللي في ال equivalence class له Zero
+
+485
+00:36:27,700 --> 00:36:31,640
+Zero، Zero، Zero، هد Cauchy sequence ولا لأ؟ أكيد
+
+486
+00:36:31,640 --> 00:36:34,900
+Cauchy sequence اللي هن كل ال .. ال .. ال .. ال ..
+
+487
+00:36:34,900 --> 00:36:39,210
+Cauchy sequences اللي converge لـ Zeroconverge to
+
+488
+00:36:39,210 --> 00:36:43,230
+zero هيكون in hand فهادي اللي هي الـ zero hat
+
+489
+00:36:43,230 --> 00:36:47,990
+عبارة عن the set of all كوشي sequences that
+
+490
+00:36:47,990 --> 00:36:52,430
+converge to zero ماشي زي هذه فبكون هذا هو مين هو
+
+491
+00:36:52,430 --> 00:36:58,030
+الـ zero element اللي هو اللي لدك إذا صار عندي
+
+492
+00:36:58,030 --> 00:37:03,490
+land in X hat under these operations is a vector
+
+493
+00:37:03,490 --> 00:37:06,730
+space how؟ إلكم
+
+494
+00:37:09,170 --> 00:37:16,810
+الأن نيجي نشوف اللي هو زي ما وعدناكم بدنا اللي هو
+
+495
+00:37:16,810 --> 00:37:22,970
+نثبت انه اللي هو زي ما قلنا ال isometry في هذه
+
+496
+00:37:22,970 --> 00:37:27,630
+الحالة اللي هي التلت حالات اللي هي one to one و
+
+497
+00:37:27,630 --> 00:37:30,570
+one to two و preserve the distance اللي هي
+
+498
+00:37:30,570 --> 00:37:33,970
+preserve the norm اللي قلته سابقاً و الأخيرة اللي
+
+499
+00:37:33,970 --> 00:37:39,490
+هو linear بتثبت انه T اللي هو طبعا احنا بسميه AA
+
+500
+00:37:39,490 --> 00:37:43,430
+في Alpha X زائد Y بيسوا A Alpha في A X زائد مين A
+
+501
+00:37:43,430 --> 00:37:47,650
+في Y يعني بمعنى آخر برضه ب preserve the mean the
+
+502
+00:37:47,650 --> 00:37:56,890
+distances the operations طيب by using الان X هاد
+
+503
+00:37:56,890 --> 00:37:59,890
+under these operations قولنا vector space لان let
+
+504
+00:37:59,890 --> 00:38:06,020
+Alpha be an scalar and X وY any elements in Xثم
+
+505
+00:38:06,020 --> 00:38:10,900
+يوجد سيكوينس x1 و y1 في الـ x مثلًا مادان x و y في
+
+506
+00:38:10,900 --> 00:38:15,420
+الـ x إذا بقدر ألاقي x unconverged لل x و y
+
+507
+00:38:15,420 --> 00:38:21,220
+unconverged لمن؟ لل y ماشي الحال الان عندى ..
+
+508
+00:38:21,220 --> 00:38:26,980
+بتقولي كيف نلاقي؟وهو اللي فيه أسهل منها اخد مين؟
+
+509
+00:38:26,980 --> 00:38:30,660
+اخد الـ sequence X و X و X و X و X Converged للـ X
+
+510
+00:38:30,660 --> 00:38:33,780
+ولا لا؟ أكيد Converged للـ X وعصرها دولة من وين؟
+
+511
+00:38:33,780 --> 00:38:37,000
+من الـ X لأننا بدأت الـ X من وين؟ من الـ X ونفس
+
+512
+00:38:37,000 --> 00:38:40,540
+الشيء للـ Y إذا أكيد أكيد أكيد هلاقي اللي هو
+
+513
+00:38:40,540 --> 00:38:44,680
+Sequences X unconverged لل X و Y unconverged لل Y
+
+514
+00:38:44,680 --> 00:38:49,040
+وقلنا على سبيل المثال الـ sequence اللي فيها X X X
+
+515
+00:38:49,040 --> 00:38:56,050
+X هي متقدرة للعربالان let XN element in X hat و YN
+
+516
+00:38:56,050 --> 00:39:00,270
+element in Y hat اللي هي الـ X hat اللي هي
+
+517
+00:39:00,270 --> 00:39:06,460
+equivalence classesاللي related to x and الـ y hat
+
+518
+00:39:06,460 --> 00:39:09,560
+هي عبارة عن كل الـ sequences related للـ yn by
+
+519
+00:39:09,560 --> 00:39:12,180
+using the definition of scalar product and vector
+
+520
+00:39:12,180 --> 00:39:15,260
+addition اللي حكينا عنه قبل شوية in excel we have
+
+521
+00:39:15,260 --> 00:39:20,280
+نحسب الآن احسبلي الآن alpha في ax زائد a من ay
+
+522
+00:39:20,280 --> 00:39:27,200
+الان عندي بساوي ال a من وين جاية يا جماعة ال a
+
+523
+00:39:27,200 --> 00:39:32,220
+اللي هي هذهجاية من X لعند مين؟ W و الـ W إذا
+
+524
+00:39:32,220 --> 00:39:35,520
+بتتذكروا عملناها construction كانت سبسيط من مين؟
+
+525
+00:39:35,520 --> 00:39:40,500
+من X hat يعني عاصرها اللي هنا عبارة عن equivalency
+
+526
+00:39:40,500 --> 00:39:43,140
+classes اللي هنا يعني الصور هذه equivalency
+
+527
+00:39:43,140 --> 00:39:47,600
+classes إذا Alpha في AX اللي عبارة عن Alpha في X
+
+528
+00:39:47,600 --> 00:39:52,200
+hat ال X hat .. ال X hat ده .. ال A .. ال AX وين
+
+529
+00:39:52,200 --> 00:39:56,610
+هي تروح؟لـ Element في داخل الـ Main الـ W و الـ W
+
+530
+00:39:56,610 --> 00:39:59,730
+لما كنا أخدنا الـ Element أخدناها الـ Main كل ال
+
+531
+00:39:59,730 --> 00:40:03,850
+equivalency classes X و X و X و X و X ده بتتذكروا
+
+532
+00:40:03,850 --> 00:40:10,350
+يعني بمعنى أخر اللي هي ال A X هي نفسها مين ال X
+
+533
+00:40:10,350 --> 00:40:18,020
+hat هي عرفناها زائد A of Y مين هي ال Y hatجابل
+
+534
+00:40:18,020 --> 00:40:20,700
+بشوية من عملية الجامعة .. العملية الجامعة قلنا
+
+535
+00:40:20,700 --> 00:40:24,940
+alpha في x hat زائد y hat كله بيساوين alpha في x
+
+536
+00:40:24,940 --> 00:40:31,680
+زائد y كل ماله .. كل hat عرفنا عملية الجامعة جابل
+
+537
+00:40:31,680 --> 00:40:35,400
+بشوية ويساوي الآن هذا عبارة عن mean هذا اللي جوا
+
+538
+00:40:35,400 --> 00:40:38,600
+هو عبارة من تعريف ال function a هو عبارة عن a
+
+539
+00:40:38,600 --> 00:40:43,400
+alpha x زائد mean زائد yإذاً واضح إن الـ A is
+
+540
+00:40:43,400 --> 00:40:47,540
+linear يعني الـ A is an isometry that preserves
+
+541
+00:40:47,540 --> 00:40:50,620
+the algebraic operations isometry من المرة الفاتتة
+
+542
+00:40:50,620 --> 00:40:54,540
+وpreserves the algebraic operations إذاً صارت اللي
+
+543
+00:40:54,540 --> 00:41:01,780
+هي ال Wوالـ X زي بعض بس هدولة اللي هي اسم و هدولة
+
+544
+00:41:01,780 --> 00:41:04,480
+اللي هي اسم أخر لكن في one to one non to function
+
+545
+00:41:04,480 --> 00:41:08,220
+وفي اللي هو preserve the distance وفي preserve the
+
+546
+00:41:08,220 --> 00:41:13,980
+operations فكتو vector spaces اتن تين نفس الشيء
+
+547
+00:41:13,980 --> 00:41:19,300
+ولكن بالاسماء متغيرة اسم هناك هات وهنا اسم هنا أو
+
+548
+00:41:19,300 --> 00:41:22,140
+اسم هناك equivalence classes وهنا اسم هنا elements
+
+549
+00:41:22,140 --> 00:41:29,190
+اللي هي جزء من ال .. اللي هي اللي من ال Xطيب بدنا
+
+550
+00:41:29,190 --> 00:41:32,910
+أخر إشي ماحنا .. عن إيش احنا خلصنا احنا الآن هذه
+
+551
+00:41:32,910 --> 00:41:36,930
+vector space و خلصنا ال isometry ضال اللي هو ال X
+
+552
+00:41:36,930 --> 00:41:40,350
+hat بعد ما فبتناها vector space بده عرف عليها norm
+
+553
+00:41:40,350 --> 00:41:45,030
+بده عرف عليها norm شوف كده عرف عليها norm الآن أول
+
+554
+00:41:45,030 --> 00:41:52,050
+إشي احنا عارفين ال W جزء من مين؟ من ال X hat طيب
+
+555
+00:41:53,750 --> 00:41:57,650
+من المرة الماضية بقى ايضا عندي لان خلينا ناخد بس
+
+556
+00:41:57,650 --> 00:42:02,550
+هالشغل قبل for y hat بتساوي ay ال ay ايش بنسميها
+
+557
+00:42:02,550 --> 00:42:07,410
+احنا؟ y hat y hat مين هي؟ هي عبارة عن ال
+
+558
+00:42:07,410 --> 00:42:11,430
+equivalency classإذا بتتذكروا لما ركّبناها الـ Y
+
+559
+00:42:11,430 --> 00:42:17,230
+hat عبارة عن ال equivalency class ل S Y و Y و Y و
+
+560
+00:42:17,230 --> 00:42:21,150
+Y اللي converge ل من؟ ل الـ Zero ل الـ Yات اللي من
+
+561
+00:42:21,150 --> 00:42:25,430
+من؟ اللي من X ماشي هذا حكيناه المرة الماضية فالآن
+
+562
+00:42:25,430 --> 00:42:30,470
+Y hat بيساوي A Y we have بدنا نعرف النورم 1 هالمين
+
+563
+00:42:30,470 --> 00:42:37,330
+على Wكيف بده اعرفه Normal y hat على w بساوي Normal
+
+564
+00:42:37,330 --> 00:42:45,110
+mean ال y Normal y الان لاحظ لما انعرفت هناعند هذا
+
+565
+00:42:45,110 --> 00:42:51,350
+طبعا و هذا نورم كامل فعلى طول هذا هيحقق كل مين كل
+
+566
+00:42:51,350 --> 00:42:55,750
+خواص النورم الآن هذا معناته preserved distances
+
+567
+00:42:55,750 --> 00:42:59,710
+لأنه بيصير ال distance بين اللي هو اللي هي اللي
+
+568
+00:42:59,710 --> 00:43:04,630
+احنا عارفين ال distance preserved by من W ل X فهذه
+
+569
+00:43:04,630 --> 00:43:07,930
+اللي هي بتمثل ال distance بين Y هات و Zero هات
+
+570
+00:43:07,930 --> 00:43:12,760
+وهذه ال distance بين Y و Zeroو preserves في الأصل
+
+571
+00:43:12,760 --> 00:43:16,340
+لما أثبتناها المرة الماضية إذا ال norm بيساوي ال
+
+572
+00:43:16,340 --> 00:43:20,400
+norm مافيش فيها مشكلة الان the corresponding
+
+573
+00:43:20,400 --> 00:43:24,580
+metric on w is the restriction of d hat to w اللي
+
+574
+00:43:24,580 --> 00:43:27,300
+هو ال d hat لما عرفناها عرفته زي ما قلت قبل بشوية
+
+575
+00:43:27,300 --> 00:43:31,600
+المرة الماضية ال d hat اللي هي كان اللي هو عبارة
+
+576
+00:43:31,600 --> 00:43:37,200
+عن اللي أخدناها اللي هي ال preserve d hat of اللي
+
+577
+00:43:37,200 --> 00:43:42,730
+هي ayوأي element تاني أو العناصر اللي هنا بساوي ال
+
+578
+00:43:42,730 --> 00:43:46,850
+D بين العناصر اللي موجودة صورهم أو أصولهم اللي
+
+579
+00:43:46,850 --> 00:43:50,870
+موجودة في ال X إذاً هذا عندي صار عندي ال D هات
+
+580
+00:43:50,870 --> 00:43:59,230
+متلائم مع اللي اللي هو عرفناه اليومالآن بنقدر الآن
+
+581
+00:43:59,230 --> 00:44:03,750
+.. هذا الكلام كان عرفه عالمياً على اللي هو الـ W
+
+582
+00:44:03,750 --> 00:44:08,030
+بنعمله extension الآن بالاستعانة باللي احنا اللي
+
+583
+00:44:08,030 --> 00:44:13,850
+هي عملناها هذا اللي هو الجديد هذا هو عبارة عن لمن
+
+584
+00:44:13,850 --> 00:44:19,400
+متناسق مع الـ D hatعرّف للـ X عباق العناصر اللي
+
+585
+00:44:19,400 --> 00:44:22,680
+موجودة في الـ .. في الـ .. في الـ X hat ككل مش في
+
+586
+00:44:22,680 --> 00:44:25,960
+الـ W في الـ X hat عرّفه كالتالي الـ X hat 2
+
+587
+00:44:25,960 --> 00:44:30,300
+بيساوي ال distance hat بين 0 و 10 والـ X hat for
+
+588
+00:44:30,300 --> 00:44:34,840
+all X elements in X hatنورم الـ X2 هذا هتلاقي إيش
+
+589
+00:44:34,840 --> 00:44:37,500
+ما له نورم و هيحقق الشروط اللي إحنا بنعرفها
+
+590
+00:44:37,500 --> 00:44:41,720
+Therefore صار عندي X hat اللي هو صار عندي normed
+
+591
+00:44:41,720 --> 00:44:45,420
+space و vector space و من ثم normed space و كان
+
+592
+00:44:45,420 --> 00:44:50,950
+عندي ال isometry بين اللي هوالـ W والـ X بكل شروطه
+
+593
+00:44:50,950 --> 00:44:54,350
+اللي هي السابقة بالاضافة لـ Linearity تبعت اليوم
+
+594
+00:44:54,350 --> 00:44:58,450
+بكون حصلنا على الـ X hat is the third اللي هو
+
+595
+00:44:58,450 --> 00:45:03,730
+Space بكون هي كقولنا أو وصلنا انه every complete
+
+596
+00:45:03,730 --> 00:45:08,030
+.. every normed space can be completed وإلى لقاء
+
+597
+00:45:08,030 --> 00:45:09,490
+آخر السلام عليكم ورحمة الله
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/J7SCFPaCRLU_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/J7SCFPaCRLU_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..69f1ed874a23122c21710354dd30b44cb0a88b68
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/J7SCFPaCRLU_raw.json
@@ -0,0 +1 @@
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372.74, "end": 373.12, "word": " normed", "probability": 0.9130859375}, {"start": 373.12, "end": 373.4, "word": " space", "probability": 0.783203125}, {"start": 373.4, "end": 373.76, "word": " X", "probability": 0.712890625}], "temperature": 1.0}, {"id": 15, "seek": 39923, "start": 374.47, "end": 399.23, "text": "and let S1 be a sequence of partial sums يعني S1 بيساوي X1 S2 بيساوي X1 زي X2 S3 بيساوي X1 زي X2 زي X3 S1 in general X1 زي X2 زي XN صارت هذه الـ S1 عبارة عن sequence of partial sums زي اللي أخدناها في الكالكولاست العادى بس كنا احنا اللي عارية نشتغل", "tokens": [474, 718, 318, 16, 312, 257, 8310, 295, 14641, 34499, 37495, 22653, 318, 16, 4724, 1829, 3794, 995, 45865, 1783, 16, 318, 17, 4724, 1829, 3794, 995, 45865, 1783, 16, 30767, 1829, 1783, 17, 318, 18, 4724, 1829, 3794, 995, 45865, 1783, 16, 30767, 1829, 1783, 17, 30767, 1829, 1783, 18, 318, 16, 294, 2674, 1783, 16, 30767, 1829, 1783, 17, 30767, 1829, 1783, 45, 20328, 9640, 2655, 29538, 2423, 39184, 318, 16, 6225, 3555, 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"end": 1047.03, "word": " EI", "probability": 0.736572265625}, {"start": 1047.03, "end": 1047.95, "word": " I", "probability": 0.89404296875}, {"start": 1047.95, "end": 1048.15, "word": " من", "probability": 0.94677734375}, {"start": 1048.15, "end": 1048.45, "word": " عند", "probability": 0.9599609375}, {"start": 1048.45, "end": 1048.81, "word": " واحد", "probability": 0.76416015625}, {"start": 1048.81, "end": 1049.17, "word": " لعند", "probability": 0.8561197916666666}, {"start": 1049.17, "end": 1049.39, "word": " N", "probability": 0.68359375}, {"start": 1049.39, "end": 1049.65, "word": " as", "probability": 0.50830078125}, {"start": 1049.65, "end": 1049.79, "word": " N", "probability": 0.93408203125}, {"start": 1049.79, "end": 1050.01, "word": " goes", "probability": 0.8642578125}, {"start": 1050.01, "end": 1050.15, "word": " to", "probability": 0.92333984375}, {"start": 1050.15, "end": 1050.55, "word": " infinity", "probability": 0.75537109375}, {"start": 1050.55, "end": 1051.29, "word": " ايش", "probability": 0.7254638671875}, {"start": 1051.29, "end": 1052.19, "word": " بيساوي؟", "probability": 0.7833658854166666}, {"start": 1052.19, "end": 1052.57, "word": " بيساوي", "probability": 0.96982421875}, {"start": 1052.57, "end": 1052.85, "word": " 0", "probability": 0.2113037109375}, {"start": 1052.85, "end": 1053.57, "word": " دل", "probability": 0.537841796875}, {"start": 1053.57, "end": 1054.23, "word": " أثبت", "probability": 0.926025390625}, {"start": 1054.23, "end": 1054.73, "word": " انه", "probability": 0.6893310546875}, {"start": 1054.73, "end": 1055.65, "word": " وحيدة", "probability": 0.8665771484375}, {"start": 1055.65, "end": 1055.85, "word": " اللي", "probability": 0.827880859375}, {"start": 1055.85, "end": 1055.97, "word": " هي", "probability": 0.9248046875}, {"start": 1055.97, "end": 1056.13, "word": " ال", "probability": 0.485595703125}, {"start": 1056.13, "end": 1056.41, "word": " sequence", "probability": 0.87744140625}, {"start": 1056.41, 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1062.07, "word": " اللي", "probability": 0.9794921875}, {"start": 1062.07, "end": 1062.31, "word": " هي", "probability": 0.94140625}, {"start": 1062.31, "end": 1062.85, "word": " نفس", "probability": 0.976318359375}, {"start": 1062.85, "end": 1063.61, "word": " تركيبة", "probability": 0.9346923828125}, {"start": 1063.61, "end": 1063.93, "word": " مين", "probability": 0.6878662109375}, {"start": 1063.93, "end": 1064.07, "word": " ال", "probability": 0.8623046875}, {"start": 1064.07, "end": 1064.31, "word": " X", "probability": 0.859375}, {"start": 1064.31, "end": 1064.55, "word": " اللي", "probability": 0.97900390625}, {"start": 1064.55, "end": 1064.91, "word": " جوا", "probability": 0.8544921875}, {"start": 1064.91, "end": 1065.53, "word": " اللي", "probability": 0.983154296875}, {"start": 1065.53, "end": 1065.91, "word": " أخدتها", "probability": 0.9263671875}, {"start": 1065.91, "end": 1066.25, "word": " منها", "probability": 0.995361328125}, {"start": 1066.25, "end": 1066.55, 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اثبتلك انه هتطلع حد ال sequence αI هي نفسها مين لـ Xi I فبتكون خلاص is unique", "tokens": [13267, 6552, 300, 456, 307, 257, 8310, 6055, 7649, 10632, 5691, 40, 295, 15664, 685, 1270, 300, 1783, 12, 5691, 16, 462, 16, 30767, 16373, 3215, 5691, 17, 462, 17, 30767, 16373, 3215, 5691, 45, 462, 45, 39894, 32887, 5016, 5296, 39184, 1958, 5551, 11622, 1863, 10874, 12984, 2304, 9957, 6055, 1863, 41185, 8848, 5296, 7649, 1975, 5172, 2655, 43042, 16472, 11296, 1975, 8592, 2304, 6027, 11296, 8978, 36764, 24401, 3660, 6055, 7649, 10632, 39894, 5016, 4587, 4587, 8717, 36178, 25124, 32887, 9566, 16247, 12610, 7578, 4032, 39182, 9957, 1975, 12984, 3555, 2655, 23275, 16472, 3224, 8032, 2655, 9566, 1211, 3615, 11331, 3215, 2423, 8310, 5691, 40, 39896, 8717, 36178, 11296, 3714, 9957, 5296, 39184, 15712, 286, 6156, 3555, 2655, 30544, 16490, 1211, 33546, 307, 3845], "avg_logprob": -0.26476377483427993, "compression_ratio": 1.5263157894736843, "no_speech_prob": 1.1324882507324219e-06, "words": [{"start": 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1076.98, "end": 1077.42, "word": " that", "probability": 0.947265625}, {"start": 1077.42, "end": 1077.92, "word": " X", "probability": 0.72998046875}, {"start": 1077.92, "end": 1078.22, "word": "-", "probability": 0.1943359375}, {"start": 1078.22, "end": 1078.84, "word": " α1", "probability": 0.4991455078125}, {"start": 1078.84, "end": 1079.58, "word": " E1", "probability": 0.6710205078125}, {"start": 1079.58, "end": 1080.54, "word": " زائد", "probability": 0.5519866943359375}, {"start": 1080.54, "end": 1081.02, "word": " α2", "probability": 0.896484375}, {"start": 1081.02, "end": 1081.46, "word": " E2", "probability": 0.953857421875}, {"start": 1081.46, "end": 1081.96, "word": " زائد", "probability": 0.8800455729166666}, {"start": 1081.96, "end": 1082.36, "word": " αN", "probability": 0.863037109375}, {"start": 1082.36, "end": 1082.64, "word": " EN", "probability": 0.89697265625}, {"start": 1082.64, "end": 1083.0, "word": " بتروح", "probability": 0.9005533854166666}, {"start": 1083.0, "end": 1083.24, "word": " لـ", "probability": 0.491943359375}, {"start": 1083.24, "end": 1083.36, "word": " 0", "probability": 0.278076171875}, {"start": 1083.36, "end": 1083.74, "word": " أزن", "probability": 0.66943359375}, {"start": 1083.74, "end": 1084.48, "word": " جثمين", "probability": 0.6583251953125}, {"start": 1084.48, "end": 1085.18, "word": " تنفيذ", "probability": 0.7860107421875}, {"start": 1085.18, "end": 1085.36, "word": " لان", "probability": 0.3826904296875}, {"start": 1085.36, "end": 1085.74, "word": " افترض", "probability": 0.8798828125}, {"start": 1085.74, "end": 1086.22, "word": " انها", "probability": 0.8271484375}, {"start": 1086.22, "end": 1087.26, "word": " اشمالها", "probability": 0.7841796875}, {"start": 1087.26, "end": 1087.42, "word": " في", "probability": 0.91064453125}, {"start": 1087.42, "end": 1087.82, "word": " واحدة", "probability": 0.9630533854166666}, {"start": 1087.82, "end": 1088.08, "word": " تانية", "probability": 0.9973958333333334}, {"start": 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value لل summation هذا هو عبارة عن إيش عبارة عن ال summation xi i ناقص alpha i ei i من عند واحد لعند مين لعند n هذه حسبتها normal x نحسبلكم إياها هان", "tokens": [28814, 23942, 293, 550, 2423, 8236, 2158, 24976, 28811, 23758, 31439, 6225, 3555, 9640, 3660, 18871, 11933, 1829, 8592, 6225, 3555, 9640, 3660, 18871, 2423, 28811, 36800, 741, 8717, 995, 4587, 9381, 8961, 741, 14020, 741, 9154, 43242, 36764, 24401, 5296, 3615, 41260, 3714, 9957, 5296, 3615, 41260, 297, 29538, 11331, 35457, 2655, 11296, 2710, 2031, 8717, 5016, 35457, 23275, 2304, 11933, 25528, 11296, 8032, 7649], "avg_logprob": -0.2735541151530707, "compression_ratio": 1.5149700598802396, "no_speech_prob": 1.1324882507324219e-06, "words": [{"start": 1097.55, "end": 1097.77, "word": "إلى", "probability": 0.509490966796875}, {"start": 1097.77, "end": 1097.95, "word": " and", "probability": 0.8193359375}, {"start": 1097.95, "end": 1098.17, "word": " then", "probability": 0.9267578125}, {"start": 1098.17, "end": 1098.97, "word": " ال", "probability": 0.78125}, {"start": 1098.97, "end": 1099.31, "word": " absolute", "probability": 0.56787109375}, {"start": 1099.31, "end": 1099.69, "word": " value", "probability": 0.99267578125}, {"start": 1099.69, "end": 1099.83, "word": " لل", "probability": 0.77001953125}, {"start": 1099.83, "end": 1100.23, "word": " summation", "probability": 0.51806640625}, {"start": 1100.23, "end": 1100.75, "word": " هذا", "probability": 0.70751953125}, {"start": 1100.75, "end": 1101.37, "word": " هو", "probability": 0.90087890625}, {"start": 1101.37, "end": 1101.71, "word": " عبارة", "probability": 0.9937744140625}, {"start": 1101.71, "end": 1101.85, "word": " عن", "probability": 0.99560546875}, {"start": 1101.85, "end": 1102.19, "word": " إيش", "probability": 0.8263346354166666}, {"start": 1102.19, "end": 1102.77, "word": " عبارة", "probability": 0.86822509765625}, {"start": 1102.77, "end": 1102.91, "word": " عن", "probability": 0.98828125}, {"start": 1102.91, "end": 1102.99, "word": " ال", "probability": 0.79541015625}, {"start": 1102.99, "end": 1103.51, "word": " summation", "probability": 0.9228515625}, {"start": 1103.51, "end": 1104.59, "word": " xi", "probability": 0.485595703125}, {"start": 1104.59, "end": 1105.01, "word": " i", "probability": 0.50146484375}, {"start": 1105.01, "end": 1105.51, "word": " ناقص", "probability": 0.77508544921875}, {"start": 1105.51, "end": 1105.73, "word": " alpha", "probability": 0.430419921875}, {"start": 1105.73, "end": 1105.97, "word": " i", "probability": 0.6845703125}, {"start": 1105.97, "end": 1106.17, "word": " ei", "probability": 0.7275390625}, {"start": 1106.17, "end": 1106.53, "word": " i", "probability": 0.2293701171875}, {"start": 1106.53, "end": 1106.69, "word": " من", "probability": 0.91455078125}, {"start": 1106.69, "end": 1106.87, "word": " عند", "probability": 0.9853515625}, {"start": 1106.87, "end": 1107.17, "word": " واحد", "probability": 0.97509765625}, {"start": 1107.17, "end": 1107.47, "word": " لعند", 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زايد y hat كيف بدي احصلها ركزوا معايا", "tokens": [6027, 7649, 4032, 1829, 16472, 4032, 9957, 3714, 29245, 23328, 3660, 8978, 2423, 39184, 288, 2385, 3714, 33599, 1829, 2423, 7649, 4724, 16254, 1975, 3615, 28480, 2423, 7649, 13672, 1829, 31439, 1975, 5016, 36520, 15844, 13672, 1829, 39896, 710, 2385, 3714, 14851, 2407, 7578, 2031, 2385, 30767, 995, 25708, 288, 2385, 9122, 33911, 4724, 16254, 1975, 5016, 36520, 11296, 12602, 4117, 11622, 14407, 20449, 995, 25528], "avg_logprob": -0.2901119278438056, "compression_ratio": 1.6546762589928057, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1690.75, "end": 1691.23, "word": "الان", "probability": 0.773681640625}, {"start": 1691.23, "end": 1691.53, "word": " وي", "probability": 0.32611083984375}, {"start": 1691.53, "end": 1691.77, "word": " ان", "probability": 0.634765625}, {"start": 1691.77, "end": 1692.05, "word": " وين", "probability": 0.703125}, {"start": 1692.05, "end": 1692.65, "word": " موجودة", "probability": 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"probability": 0.89013671875}, {"start": 1967.87, "end": 1968.59, "word": " التنتين", "probability": 0.849609375}, {"start": 1968.59, "end": 1969.13, "word": " في", "probability": 0.9716796875}, {"start": 1969.13, "end": 1969.69, "word": " نفس", "probability": 0.998291015625}, {"start": 1969.69, "end": 1969.91, "word": " ال", "probability": 0.98681640625}, {"start": 1969.91, "end": 1970.63, "word": " equivalency", "probability": 0.986328125}, {"start": 1970.63, "end": 1971.11, "word": " class", "probability": 0.99169921875}, {"start": 1971.11, "end": 1971.91, "word": " فبكون", "probability": 0.9397786458333334}, {"start": 1971.91, "end": 1972.17, "word": " في", "probability": 0.3388671875}, {"start": 1972.17, "end": 1972.71, "word": " هذه", "probability": 0.55419921875}, {"start": 1972.71, "end": 1973.19, "word": " الحالة", "probability": 0.9842122395833334}, {"start": 1973.19, "end": 1973.55, "word": " إنه", "probability": 0.5245361328125}, {"start": 1973.55, "end": 1974.15, "word": " فعلا", "probability": 0.875}, {"start": 1974.15, "end": 1974.37, "word": " ال", "probability": 0.92333984375}, {"start": 1974.37, "end": 1974.57, "word": " Z", "probability": 0.93115234375}, {"start": 1974.57, "end": 1974.83, "word": " hat", "probability": 0.9892578125}, {"start": 1974.83, "end": 1975.13, "word": " بيساوي", "probability": 0.53182373046875}, {"start": 1975.13, "end": 1975.35, "word": " X", "probability": 0.85498046875}, {"start": 1975.35, "end": 1975.45, "word": " hat", "probability": 0.9619140625}, {"start": 1975.45, "end": 1975.63, "word": " زي", "probability": 0.796142578125}, {"start": 1975.63, "end": 1975.89, "word": " Y", "probability": 0.7080078125}, {"start": 1975.89, "end": 1976.33, "word": " hat", "probability": 0.97900390625}, {"start": 1976.33, "end": 1976.93, "word": " is", "probability": 0.814453125}, {"start": 1976.93, "end": 1977.41, "word": " well", "probability": 0.95947265625}, {"start": 1977.41, "end": 1978.01, "word": " defined", "probability": 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"probability": 0.7607421875}, {"start": 1985.8, "end": 1986.24, "word": " عندنا", "probability": 0.80029296875}, {"start": 1986.24, "end": 1987.56, "word": " Similarly", "probability": 0.3818359375}, {"start": 1987.56, "end": 1989.26, "word": " بالنسبة", "probability": 0.915283203125}, {"start": 1989.26, "end": 1989.74, "word": " لمين", "probability": 0.7685546875}, {"start": 1989.74, "end": 1990.02, "word": " we", "probability": 0.1593017578125}, {"start": 1990.02, "end": 1990.7, "word": " define", "probability": 0.9560546875}, {"start": 1990.7, "end": 1990.9, "word": " the", "probability": 0.83251953125}, {"start": 1990.9, "end": 1991.46, "word": " product", "probability": 0.95068359375}, {"start": 1991.46, "end": 1991.94, "word": " Alpha", "probability": 0.270751953125}, {"start": 1991.94, "end": 1992.42, "word": " X", "probability": 0.853515625}, {"start": 1992.42, "end": 1992.86, "word": " hat", "probability": 0.5673828125}, {"start": 1992.86, "end": 1994.0, "word": " اللي", "probability": 0.7861328125}, {"start": 1994.0, "end": 1994.66, "word": " هيكون", "probability": 0.910888671875}, {"start": 1994.66, "end": 1995.04, "word": " element", "probability": 0.87548828125}, {"start": 1995.04, "end": 1995.28, "word": " من", "probability": 0.521484375}, {"start": 1995.28, "end": 1995.82, "word": " X", "probability": 0.481201171875}, {"start": 1995.82, "end": 1996.18, "word": " hat", "probability": 0.892578125}, {"start": 1996.18, "end": 1996.5, "word": " of", "probability": 0.75732421875}, {"start": 1996.5, "end": 1997.26, "word": " a", "probability": 0.8330078125}, {"start": 1997.26, "end": 1997.68, "word": " scalar", "probability": 0.85888671875}, {"start": 1997.68, "end": 1998.1, "word": " Alpha", "probability": 0.85888671875}, {"start": 1998.1, "end": 1998.4, "word": " and", "probability": 0.81005859375}, {"start": 1998.4, "end": 1998.64, "word": " X", "probability": 0.98828125}, {"start": 1998.64, "end": 1999.0, "word": " hat", "probability": 0.91064453125}, {"start": 1999.0, "end": 1999.46, "word": " to", "probability": 0.83837890625}, {"start": 1999.46, "end": 1999.66, "word": " be", "probability": 0.95361328125}, {"start": 1999.66, "end": 1999.8, "word": " the", "probability": 0.6826171875}, {"start": 1999.8, "end": 2000.34, "word": " equivalence", "probability": 0.877197265625}, {"start": 2000.34, "end": 2000.82, "word": " class", "probability": 0.9609375}, {"start": 2000.82, "end": 2001.08, "word": " for", "probability": 0.93603515625}, {"start": 2001.08, "end": 2001.36, "word": " which", "probability": 0.9130859375}, {"start": 2001.36, "end": 2001.7, "word": " Alpha", "probability": 0.94091796875}, {"start": 2001.7, "end": 2001.88, "word": " X", "probability": 0.96044921875}, {"start": 2001.88, "end": 2002.08, "word": " hat", "probability": 0.822265625}, {"start": 2002.08, "end": 2002.3, "word": " is", "probability": 0.9453125}, {"start": 2002.3, "end": 2003.04, "word": " representative", "probability": 0.751953125}, {"start": 2003.04, "end": 2003.8, "word": " إيش", "probability": 0.74853515625}, {"start": 2003.8, "end": 2004.6, "word": " يعني؟", "probability": 0.9161783854166666}, {"start": 2004.6, "end": 2005.1, "word": " يعني", "probability": 0.91064453125}, {"start": 2005.1, "end": 2005.42, "word": " بنفس", "probability": 0.9833984375}, {"start": 2005.42, "end": 2005.94, "word": " الطريقة", "probability": 0.9871419270833334}], "temperature": 1.0}, {"id": 86, "seek": 202166, "start": 2006.62, "end": 2021.66, "text": "عشان اعرف اللي هو شو معناته اخد x hat element in x hat واخد alpha scalar بده اعرف الآن عملية ال scalar multiplication في داخل ال x hat", "tokens": [3615, 8592, 7649, 1975, 3615, 28480, 13672, 1829, 31439, 13412, 2407, 20449, 8315, 47395, 1975, 9778, 3215, 2031, 2385, 4478, 294, 2031, 2385, 4032, 47283, 3215, 8961, 39684, 47525, 3224, 1975, 3615, 28480, 6024, 48506, 6225, 42213, 10632, 2423, 39684, 27290, 8978, 11778, 47283, 1211, 2423, 2031, 2385], "avg_logprob": 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product and vector addition اللي حكينا عنه قبل شوية in excel we have نحسب الآن احسبلي الآن alpha في ax زائد a من ay الان عندي بساوي ال a من وين جاية يا جماعة ال a اللي هي هذه", "tokens": [6027, 20292, 4077, 281, 2031, 293, 2423, 39184, 288, 2385, 39896, 6225, 3555, 9640, 3660, 18871, 28242, 2423, 39184, 22978, 4077, 24976, 39184, 17861, 538, 1228, 264, 7123, 295, 39684, 1674, 293, 8062, 4500, 13672, 1829, 11331, 4117, 1829, 8315, 18871, 3224, 12174, 36150, 13412, 2407, 10632, 294, 454, 4933, 321, 362, 8717, 5016, 35457, 6024, 48506, 1975, 5016, 35457, 20292, 6024, 48506, 8961, 8978, 6360, 30767, 16373, 3215, 257, 9154, 7494, 2423, 7649, 18871, 16254, 4724, 3794, 995, 45865, 2423, 257, 9154, 4032, 9957, 10874, 995, 10632, 35186, 10874, 15042, 27884, 2423, 257, 13672, 1829, 39896, 29538], "avg_logprob": -0.26420454485247835, "compression_ratio": 1.58, "no_speech_prob": 1.0788440704345703e-05, "words": [{"start": 2342.7, "end": 2343.12, "word": "اللي", "probability": 0.727783203125}, 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"probability": 0.1702880859375}, {"start": 2514.05, "end": 2514.37, "word": " المرة", "probability": 0.939208984375}, {"start": 2514.37, "end": 2514.87, "word": " الماضية", "probability": 0.98876953125}, {"start": 2514.87, "end": 2514.99, "word": " بقى", "probability": 0.8074544270833334}, {"start": 2514.99, "end": 2515.87, "word": " ايضا", "probability": 0.804931640625}, {"start": 2515.87, "end": 2516.47, "word": " عندي", "probability": 0.7509765625}, {"start": 2516.47, "end": 2516.69, "word": " لان", "probability": 0.5947265625}, {"start": 2516.69, "end": 2517.07, "word": " خلينا", "probability": 0.7802734375}, {"start": 2517.07, "end": 2517.43, "word": " ناخد", "probability": 0.9781901041666666}, {"start": 2517.43, "end": 2517.65, "word": " بس", "probability": 0.6015625}, {"start": 2517.65, "end": 2518.23, "word": " هالشغل", "probability": 0.616796875}, {"start": 2518.23, "end": 2518.61, "word": " قبل", "probability": 0.758544921875}, {"start": 2518.61, "end": 2519.35, "word": " for", "probability": 0.697265625}, {"start": 2519.35, "end": 2519.69, "word": " y", "probability": 0.5}, {"start": 2519.69, "end": 2520.01, "word": " hat", "probability": 0.71728515625}, {"start": 2520.01, "end": 2520.51, "word": " بتساوي", "probability": 0.76007080078125}, {"start": 2520.51, "end": 2520.99, "word": " ay", "probability": 0.359130859375}, {"start": 2520.99, "end": 2521.51, "word": " ال", "probability": 0.802734375}, {"start": 2521.51, "end": 2521.79, "word": " ay", "probability": 0.445556640625}, {"start": 2521.79, "end": 2521.97, "word": " ايش", "probability": 0.7923990885416666}, {"start": 2521.97, "end": 2522.55, "word": " بنسميها", "probability": 0.8509521484375}, {"start": 2522.55, "end": 2523.31, "word": " احنا؟", "probability": 0.82952880859375}, {"start": 2523.31, "end": 2523.57, "word": " y", "probability": 0.666015625}, {"start": 2523.57, "end": 2524.01, "word": " hat", "probability": 0.95849609375}, {"start": 2524.01, "end": 2524.65, "word": " y", "probability": 0.449462890625}, {"start": 2524.65, "end": 2525.03, "word": " hat", "probability": 0.98193359375}, {"start": 2525.03, "end": 2525.33, "word": " مين", "probability": 0.9658203125}, {"start": 2525.33, "end": 2526.21, "word": " هي؟", "probability": 0.912841796875}, {"start": 2526.21, "end": 2526.45, "word": " هي", "probability": 0.89208984375}, {"start": 2526.45, "end": 2527.11, "word": " عبارة", "probability": 0.9962158203125}, {"start": 2527.11, "end": 2527.31, "word": " عن", "probability": 0.9853515625}, {"start": 2527.31, "end": 2527.41, "word": " ال", "probability": 0.72314453125}, {"start": 2527.41, "end": 2528.07, "word": " equivalency", "probability": 0.92041015625}, {"start": 2528.07, "end": 2528.81, "word": " class", "probability": 0.99072265625}], "temperature": 1.0}, {"id": 109, "seek": 255113, "start": 2529.27, "end": 2551.13, "text": "إذا بتتذكروا لما ركّبناها الـ Y hat عبارة عن ال equivalency class ل S Y و Y و Y و Y اللي converge ل من؟ ل الـ Zero ل الـ Yات اللي من من؟ اللي من X ماشي هذا حكيناه المرة الماضية فالآن Y hat بيساوي A Y we have بدنا نعرف النورم 1 هالمين على W", "tokens": [28814, 15730, 39894, 2655, 8848, 37983, 14407, 5296, 15042, 12602, 4117, 11703, 3555, 8315, 11296, 2423, 39184, 398, 2385, 6225, 3555, 9640, 3660, 18871, 2423, 9052, 3020, 1508, 5296, 318, 398, 4032, 398, 4032, 398, 4032, 398, 13672, 1829, 41881, 5296, 9154, 22807, 5296, 2423, 39184, 17182, 5296, 2423, 39184, 398, 9307, 13672, 1829, 9154, 9154, 22807, 13672, 1829, 9154, 1783, 3714, 33599, 1829, 23758, 11331, 4117, 1829, 8315, 3224, 9673, 25720, 9673, 46958, 10632, 6156, 6027, 148, 48506, 398, 2385, 4724, 1829, 3794, 995, 45865, 316, 398, 321, 362, 47525, 8315, 8717, 3615, 28480, 28239, 13063, 2304, 502, 8032, 45340, 9957, 15844, 343], "avg_logprob": -0.32797620182945614, "compression_ratio": 1.611353711790393, "no_speech_prob": 1.6689300537109375e-06, "words": [{"start": 2529.27, "end": 2529.53, "word": "إذا", "probability": 0.844482421875}, {"start": 2529.53, 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"probability": 0.958984375}, {"start": 2547.81, "end": 2548.41, "word": " بدنا", "probability": 0.6688232421875}, {"start": 2548.41, "end": 2548.81, "word": " نعرف", "probability": 0.9384765625}, {"start": 2548.81, "end": 2549.43, "word": " النورم", "probability": 0.7952473958333334}, {"start": 2549.43, "end": 2549.79, "word": " 1", "probability": 0.611328125}, {"start": 2549.79, "end": 2550.47, "word": " هالمين", "probability": 0.6905924479166666}, {"start": 2550.47, "end": 2550.69, "word": " على", "probability": 0.84228515625}, {"start": 2550.69, "end": 2551.13, "word": " W", "probability": 0.86474609375}], "temperature": 1.0}, {"id": 110, "seek": 256348, "start": 2551.87, "end": 2563.49, "text": "كيف بده اعرفه Normal y hat على w بساوي Normal mean ال y Normal y الان لاحظ لما انعرفت هنا", "tokens": [4117, 33911, 47525, 3224, 1975, 3615, 28480, 3224, 21277, 288, 2385, 15844, 261, 4724, 3794, 995, 45865, 21277, 914, 2423, 288, 21277, 288, 2423, 7649, 20193, 5016, 19913, 5296, 15042, 16472, 3615, 28480, 2655, 34105], "avg_logprob": -0.527777804268731, "compression_ratio": 1.2149532710280373, "no_speech_prob": 2.7418136596679688e-06, "words": [{"start": 2551.87, "end": 2552.25, "word": "كيف", "probability": 0.583740234375}, {"start": 2552.25, "end": 2552.47, "word": " بده", "probability": 0.3739013671875}, {"start": 2552.47, "end": 2552.91, "word": " اعرفه", "probability": 0.873046875}, {"start": 2552.91, "end": 2553.53, "word": " Normal", "probability": 0.2037353515625}, {"start": 2553.53, "end": 2553.97, "word": " y", "probability": 0.447998046875}, {"start": 2553.97, "end": 2554.23, "word": " hat", "probability": 0.80224609375}, {"start": 2554.23, "end": 2554.45, "word": " على", "probability": 0.509765625}, {"start": 2554.45, "end": 2554.87, "word": " w", "probability": 0.6689453125}, {"start": 2554.87, "end": 2556.91, "word": " بساوي", "probability": 0.65142822265625}, {"start": 2556.91, "end": 2557.33, "word": " Normal", "probability": 0.56298828125}, {"start": 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وصلنا", "probability": 0.9075520833333334}, {"start": 2701.63, "end": 2702.45, "word": " انه", "probability": 0.6087646484375}, {"start": 2702.45, "end": 2703.25, "word": " every", "probability": 0.640625}, {"start": 2703.25, "end": 2703.73, "word": " complete", "probability": 0.422119140625}, {"start": 2703.73, "end": 2703.95, "word": " ..", "probability": 0.299560546875}, {"start": 2703.95, "end": 2704.27, "word": " every", "probability": 0.77880859375}, {"start": 2704.27, "end": 2705.35, "word": " normed", "probability": 0.818359375}, {"start": 2705.35, "end": 2705.75, "word": " space", "probability": 0.8154296875}, {"start": 2705.75, "end": 2706.03, "word": " can", "probability": 0.9345703125}, {"start": 2706.03, "end": 2706.23, "word": " be", "probability": 0.96533203125}, {"start": 2706.23, "end": 2706.89, "word": " completed", "probability": 0.84619140625}, {"start": 2706.89, "end": 2707.63, "word": " وإلى", "probability": 0.7835286458333334}, {"start": 2707.63, "end": 2708.03, "word": " لقاء", "probability": 0.9366861979166666}, {"start": 2708.03, "end": 2708.39, "word": " آخر", "probability": 0.8916015625}, {"start": 2708.39, "end": 2708.73, "word": " السلام", "probability": 0.86767578125}, {"start": 2708.73, "end": 2709.07, "word": " عليكم", "probability": 0.90771484375}, {"start": 2709.07, "end": 2709.29, "word": " ورحمة", "probability": 0.93310546875}, {"start": 2709.29, "end": 2709.49, "word": " الله", "probability": 0.955078125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2709.699, "duration_after_vad": 2658.376874999997}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/KVXWicAzB2A_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/KVXWicAzB2A_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0d94d4eb674ca4291b71992a0e86f1f7e1f82f58
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/KVXWicAzB2A_postprocess.srt
@@ -0,0 +1,3556 @@
+1
+00:00:05,210 --> 00:00:07,970
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,970 --> 00:00:11,030
+والصلاة والسلام على سيد المرسلين سيدنا محمد عليه
+
+3
+00:00:11,030 --> 00:00:15,530
+والصحابي الأجمعين هذه هي المحاضرة رقم 13 مساق
+
+4
+00:00:15,530 --> 00:00:19,670
+تحليل اقتراني أو تحليل دالي طلاب طالبات الجامعة
+
+5
+00:00:19,670 --> 00:00:25,240
+الإسلامية ماجستير رياضيةوصلنا لعند الاتنين سبعة
+
+6
+00:00:25,240 --> 00:00:28,340
+اللي هو تحت عنوان bounded and continuous linear
+
+7
+00:00:28,340 --> 00:00:33,660
+operators لنتعرف على مفهوم اليوم مفهوم مهم وكمان
+
+8
+00:00:33,660 --> 00:00:38,660
+اللي هو بعض خواصه أو البعض النظريات اللي هتكون
+
+9
+00:00:38,660 --> 00:00:42,420
+ملازمانة على طول الفصل اللي هي بما يتعلق شو معنات
+
+10
+00:00:42,420 --> 00:00:46,770
+bounded linear operatorsالـ Bounded Linear
+
+11
+00:00:46,770 --> 00:00:50,110
+Operator احنا عرفناه المرة الماضية وعرفناه كمان في
+
+12
+00:00:50,110 --> 00:00:53,190
+الجبر الخطوة و بنعرفه بالاصل اللي هنعرفه شو معناه
+
+13
+00:00:53,190 --> 00:00:56,230
+Bounded Linear Operator؟ وإيش معناه الـ
+
+14
+00:00:56,230 --> 00:00:58,430
+Continuity؟ طبعا احنا الـ Continuity بنعرفها شو
+
+15
+00:00:58,430 --> 00:01:01,670
+معناه الـ Continuity؟ بنعرفها بدنا نربط شو علاقة
+
+16
+00:01:01,670 --> 00:01:04,830
+الـ Continuous Linear Operator بالـ Bounded Linear
+
+17
+00:01:04,830 --> 00:01:07,610
+Operator وخلينا نشوف هذا الكلام بنجاوب عليه من
+
+18
+00:01:07,610 --> 00:01:12,070
+خلال اللي هو حديثنا اليوم إن شاء اللهالـ
+
+19
+00:01:12,070 --> 00:01:15,330
+Definition الأول لو كان عندي X و Y normed spaces
+
+20
+00:01:15,330 --> 00:01:21,150
+التنين على نفس ال field التنين ياريال يتنين أشمال
+
+21
+00:01:21,150 --> 00:01:25,290
+وكمبليكس و المرة الفاترة قلنا ليش لأن let domain T
+
+22
+00:01:25,290 --> 00:01:29,010
+من domain of T لعند Y بيقى linear operator و ال
+
+23
+00:01:29,010 --> 00:01:33,390
+domain of T ده جزء من من اللي هو normed space X
+
+24
+00:01:33,390 --> 00:01:38,080
+طبعا X عليها نورمها و Y عليها نورمهاThe operator T
+
+25
+00:01:38,080 --> 00:01:41,480
+is said to be bounded منقول عنه bounded linear
+
+26
+00:01:41,480 --> 00:01:45,660
+operator هذا اعرفنا على مين؟ على linear operator
+
+27
+00:01:45,660 --> 00:01:50,920
+منقول عنه bounded if there is a number c such that
+
+28
+00:01:50,920 --> 00:01:56,200
+for all x element in domain of T norm TX أصغر
+
+29
+00:01:56,200 --> 00:02:03,380
+يساوي في مين؟ C في norm LX إذن الآن منقول عن Tمن
+
+30
+00:02:03,380 --> 00:02:08,560
+domain of T جزء من X طبعا لعند Y انه bounded انه
+
+31
+00:02:08,560 --> 00:02:13,900
+يتحقق TX normal طبعا هذا normal موجود في Y أصغر أو
+
+32
+00:02:13,900 --> 00:02:18,560
+ساوى C في norm ال X ال X طبعا هو الموجود في domain
+
+33
+00:02:18,560 --> 00:02:22,780
+of T أو ال norm الموجود على اللي هي ال Xاللي كان
+
+34
+00:02:22,780 --> 00:02:26,320
+هذا الكلام يكون صحيح لكل x و m موجودة في ال domain
+
+35
+00:02:26,320 --> 00:02:29,340
+of D إذا كان هذا صحيح معناته أنه على طول بنقول عن
+
+36
+00:02:29,340 --> 00:02:34,700
+ال T إيش ما لها is a bounded linear operator طبعا
+
+37
+00:02:34,700 --> 00:02:37,800
+هذا ال bounded linear operator بهذا التعريف والاسم
+
+38
+00:02:37,800 --> 00:02:41,760
+نفسه is standard كل الناس بتستخدمه وفي نفس الوقت
+
+39
+00:02:41,760 --> 00:02:46,170
+برضه ال bounded functionالـ bounded as a function
+
+40
+00:02:46,170 --> 00:02:51,050
+برضه standard إذا كانت T بعتبرها as a function من
+
+41
+00:02:51,050 --> 00:02:54,930
+domain of T أو من اللي هي لعند X بقول a bounded
+
+42
+00:02:54,930 --> 00:02:58,590
+function أو لعند Y بنقول a bounded function مقصود
+
+43
+00:02:58,590 --> 00:03:01,810
+فيها في كل ال functions سواء كان اللي هو عند A
+
+44
+00:03:01,810 --> 00:03:05,070
+اللي هي هذا known space أو vector space أو أو
+
+45
+00:03:05,070 --> 00:03:08,030
+الأخرين المهم يكون فيه topology بنقول عنه bounded
+
+46
+00:03:08,030 --> 00:03:13,470
+إذا كان T Xabsolute value او norm او اللي هو اصغر
+
+47
+00:03:13,470 --> 00:03:18,570
+او يساوي اللي هو c for every x element in main in
+
+48
+00:03:18,570 --> 00:03:23,310
+domain of D هذا معناته bounded as a function احنا
+
+49
+00:03:23,310 --> 00:03:27,830
+الآن بنا .. وهذا standardالناس بتستعمله وهذا ال
+
+50
+00:03:27,830 --> 00:03:31,290
+standard الناس بتستعمله الان احنا ال focusing
+
+51
+00:03:31,290 --> 00:03:35,850
+هنعمله على مين على ال bounded linear operator هذا
+
+52
+00:03:35,850 --> 00:03:39,810
+معناته ايش ماله is a bounded linear operator هذي
+
+53
+00:03:39,810 --> 00:03:42,690
+is a bounded as a function عشان ما يشيرش confusion
+
+54
+00:03:42,690 --> 00:03:49,190
+عند الناس او اللي هو اي التباس طيبنجي الآن نشوف
+
+55
+00:03:49,190 --> 00:03:52,710
+ايش الملاحظة اللي .. الملاحظات اللي بحكيها Notes
+
+56
+00:03:52,710 --> 00:03:56,590
+الملاحظة الأولى The smallest c such that the above
+
+57
+00:03:56,590 --> 00:04:00,750
+inequality holds for all and zero excellent in
+
+58
+00:04:00,750 --> 00:04:05,590
+domain of T is defined as norm of T ايش بيقول؟
+
+59
+00:04:05,590 --> 00:04:09,990
+بيقول انت مش بتقول bounded إذا لقينا c بحيث norm
+
+60
+00:04:09,990 --> 00:04:14,740
+of T X أصغر شوه مين؟ C في مين؟ في norm of Xالأن
+
+61
+00:04:14,740 --> 00:04:19,340
+أصغر واحدة في الـCs هذولة أصغر واحدة في الـCs اللي
+
+62
+00:04:19,340 --> 00:04:24,560
+هو بنسميه إيش منها نورمين الـT طب مين أصغر واحدة
+
+63
+00:04:24,560 --> 00:04:29,900
+في الـCs هذه؟ الآن معناته إن نورم الـTX على نورم
+
+64
+00:04:29,900 --> 00:04:33,240
+الـX provided that النورم لا يساوي سفر أصغر أو
+
+65
+00:04:33,240 --> 00:04:37,140
+يساوي C بدي أصغر واحدة في الـCs هذه هذول الـCs
+
+66
+00:04:37,140 --> 00:04:40,800
+كلهم upper bound لهذه الستأصغر واحدة فين؟ إيش
+
+67
+00:04:40,800 --> 00:04:44,260
+هتكون؟ The least upper bound، اللي هو مين؟ بمعنى
+
+68
+00:04:44,260 --> 00:04:51,500
+آخر الـ Supremum لـ Normal T X ع Normal X Such
+
+69
+00:04:51,500 --> 00:04:56,940
+that X element in domain of T ناقص مين؟ السفر هذا
+
+70
+00:04:56,940 --> 00:05:00,420
+اللي هو الـ Supremum اللي هيطلع عن مين هو؟ عبارة
+
+71
+00:05:00,420 --> 00:05:08,270
+عن مين؟ Normal Tالآن إذا كان domain الـ T بيساوي 0
+
+72
+00:05:08,270 --> 00:05:11,850
+يعني مافيش فيلة غير الـ 0 domain الـ T الـ 0 إذا
+
+73
+00:05:11,850 --> 00:05:15,170
+أي function بتعملها عليها تنجل الـ 0 لميلا الـ 0
+
+74
+00:05:15,170 --> 00:05:19,610
+عشان تكون linear إذا حيكون بنعرف في هذه الحالة
+
+75
+00:05:19,610 --> 00:05:23,610
+نورم الـ T إيش بيساوي بيساوي 0 أما أي linear
+
+76
+00:05:23,610 --> 00:05:28,470
+operator domainه لا يساوي 0 على طول norm الـ T
+
+77
+00:05:28,470 --> 00:05:33,250
+تبعته اللي هي ال operatorالنوم لمين لـ Operator
+
+78
+00:05:33,250 --> 00:05:38,510
+اللي هو بيساوي هذا الكلامهذا اللي عندي نورم الـ T
+
+79
+00:05:38,510 --> 00:05:43,210
+أنا مسميه نورم الـ T هو في الواقع هيحقق شروط
+
+80
+00:05:43,210 --> 00:05:47,850
+النورم كلها عشان هيك اسمه بنسميه نورم فهو فعلاً
+
+81
+00:05:47,850 --> 00:05:52,830
+هيعمل نورم نورم عالمين يعني الآن احنا و كإني جاعد
+
+82
+00:05:52,830 --> 00:05:56,590
+انا ما احنا كنا نعمل نورم نورم احنا عالمين احنا
+
+83
+00:05:56,590 --> 00:06:02,760
+ناخد X as a vector space و نعمل عليه مينnorm طب
+
+84
+00:06:02,760 --> 00:06:06,040
+هذا ال norm على مين؟ أنا و كإني بقول the
+
+85
+00:06:06,040 --> 00:06:12,540
+collection of all bounded linear operators بعرف
+
+86
+00:06:12,540 --> 00:06:15,960
+عليه ال norm المهم الآن طبعا هذا جايين الكلام الآن
+
+87
+00:06:15,960 --> 00:06:20,120
+هذا norm ال T بعرف واش بساوي بساوي المقدار هذا طيب
+
+88
+00:06:20,120 --> 00:06:23,220
+from
+
+89
+00:06:23,220 --> 00:06:27,800
+the definition above من التعريف above norm ال T X
+
+90
+00:06:30,910 --> 00:06:34,830
+أحنا بنقول أصغر أو يساوي C في ميان في normal X
+
+91
+00:06:34,830 --> 00:06:40,950
+نورم ال T واحدة منهم مش ال T the smallest one
+
+92
+00:06:40,950 --> 00:06:47,590
+هيكون عندي نورم ال T X أصغر أو يساوي نورم ال T في
+
+93
+00:06:47,590 --> 00:06:53,850
+ميانفى norm ال X ومن هنا كمان اللى هو norm ال T فى
+
+94
+00:06:53,850 --> 00:06:58,190
+X على norm ال X هيكون اللى هو طبيعى أصغر أو سوى
+
+95
+00:06:58,190 --> 00:07:01,930
+مين norm ال T فأدور بالطرفين فبطلع norm ال T X
+
+96
+00:07:01,930 --> 00:07:05,070
+أصغر أو سوى C اللى هو norm ال T فى norm ال X أي
+
+97
+00:07:05,070 --> 00:07:10,990
+سؤال؟ طيب الآن نيجينا اللمّة الأولى اطلع لفوق
+
+98
+00:07:10,990 --> 00:07:19,790
+بالله اللمّة الأولى إيش بتقول اللمّة؟لما بتقول
+
+99
+00:07:19,790 --> 00:07:24,450
+مرايالي انه
+
+100
+00:07:24,450 --> 00:07:29,750
+let T من domain of T لعند ال while اللي قلت قبل
+
+101
+00:07:29,750 --> 00:07:36,940
+شوية be bounded linear operatorثم نورم الـ T
+
+102
+00:07:36,940 --> 00:07:40,660
+بيساوي supremum لـ T X X element in domain و T
+
+103
+00:07:40,660 --> 00:07:45,500
+وخدت مين الآن على نورمك لـ X بس إيش اللي بيساوي؟
+
+104
+00:07:45,500 --> 00:07:52,360
+واحد، بتدعي .. بتدعي إن هذا هيعمل لي نورم و T
+
+105
+00:07:52,360 --> 00:07:56,720
+هيكون satisfied من واحد عند أربعة يعني و كإن بيقول
+
+106
+00:07:56,720 --> 00:08:04,310
+لي في هذه النظرية إن نورم الـ T بيساوي supremumلـ
+
+107
+00:08:04,310 --> 00:08:10,930
+Tx as a norm such that norm ال X بتسوي واحد و ال X
+
+108
+00:08:10,930 --> 00:08:19,810
+في domain ال T يكافئ ال supremum لnorm ال Tx على
+
+109
+00:08:19,810 --> 00:08:28,830
+norm ال X such that X element in domain of TX
+
+110
+00:08:28,830 --> 00:08:33,130
+element in domain of T وإثباته مش صعب لأن نثبت أنه
+
+111
+00:08:33,130 --> 00:08:36,610
+norm بده يحقق الأربع شروط والأربع شروط يعني اللي
+
+112
+00:08:36,610 --> 00:08:39,850
+هي سهلة يعني مافيش فيها إشكالية الآن إنه هذا
+
+113
+00:08:39,850 --> 00:08:47,030
+بيساوي هذا برضه اللي هو عنده لو أخدنا أي X في في
+
+114
+00:08:47,030 --> 00:08:51,610
+domain T هنلاقي اللي هو ال X ع نورمها موجود في
+
+115
+00:08:51,610 --> 00:08:55,480
+domain Tفلو سميتها y بيصير normal y هنا بيساوي
+
+116
+00:08:55,480 --> 00:08:58,280
+واحد و عليها بتشتغلوا فبتقولوا هذا اللي هو أصغر
+
+117
+00:08:58,280 --> 00:09:00,980
+يساوي هذا و هذا أصغر يساوي هذا و بطلع اللي هي
+
+118
+00:09:00,980 --> 00:09:04,060
+المساوية المهم exercise عشان هي كانت سهلة بقولكم
+
+119
+00:09:04,060 --> 00:09:11,770
+طيبالنهائي هو الـ Example الـ Examples لن تثبت أن
+
+120
+00:09:11,770 --> 00:09:17,250
+كلها مرتبطة لأن ما سيثبتهم قدام الـ Boundedness
+
+121
+00:09:17,250 --> 00:09:20,410
+سيغنون عن هؤلاء الذين يشعرون أن هؤلاء سهلات
+
+122
+00:09:20,410 --> 00:09:25,050
+بالنسبة له وسيكونون على طول بالثبتين الآن Zero
+
+123
+00:09:25,050 --> 00:09:29,940
+Operatorواحد من أمثلة اللي هو الـ Bounded Linear
+
+124
+00:09:29,940 --> 00:09:33,580
+Operator ايش الـ Zero Operator؟ الـ Zero Operator
+
+125
+00:09:33,580 --> 00:09:37,480
+زي Zero من X لعند Y on a normed space X is a
+
+126
+00:09:37,480 --> 00:09:41,320
+Bounded Linear Operator وإيش اللي هو الـ Zero
+
+127
+00:09:41,320 --> 00:09:44,620
+Operator؟ بياخد كل Element لـ 100 للصفراللي هو هذا
+
+128
+00:09:44,620 --> 00:09:49,560
+norm وإيش هيطلع عبارة عن سفر bounded أو linear ال
+
+129
+00:09:49,560 --> 00:09:52,640
+linear اللي احنا حكينا المرة الفاتة عن بعض الأمثلة
+
+130
+00:09:52,640 --> 00:09:56,680
+وهو اثباته انه linear سهل واثباته bounded برضه
+
+131
+00:09:56,680 --> 00:10:02,450
+مافيش فيه إشكاليةاللي بعده خلّيني أشوف المثال اللي
+
+132
+00:10:02,450 --> 00:10:07,070
+بعده let x اللي بنسميه differentiation operator
+
+133
+00:10:07,070 --> 00:10:10,230
+differentiation operator خلّيني أبرهنه و أريكم
+
+134
+00:10:10,230 --> 00:10:15,090
+أمور البرهان سهلا ان شاء الله البرهان بقصده اللي
+
+135
+00:10:15,090 --> 00:10:19,710
+هو برهان اللي هي أن ال operator اللي بنعرضه أنه
+
+136
+00:10:19,710 --> 00:10:22,330
+bounded هناخدكم عدة أمثلة الآن و نبرهنها
+
+137
+00:10:23,470 --> 00:10:27,310
+differentiation operator اللي هو let x be a norm
+
+138
+00:10:27,310 --> 00:10:30,670
+of the space of all polynomials أخدنا مين؟ اللي هو
+
+139
+00:10:30,670 --> 00:10:35,530
+space of all polynomials on الفترة 0 و 1 و ال norm
+
+140
+00:10:35,530 --> 00:10:38,490
+ال x إيش بناخده؟ اللي هو ال maximum اللي أخدناه
+
+141
+00:10:38,490 --> 00:10:41,330
+قبل هيك هاد عملنا norm of the space عمليا اللي هو
+
+142
+00:10:41,330 --> 00:10:44,530
+اللي بيساوي طبعا هذه أخدت أنا مين؟ هي norm of the
+
+143
+00:10:44,530 --> 00:10:48,050
+space of all polynomials إذا بتذكر و أثبتنا إن هذا
+
+144
+00:10:48,050 --> 00:10:52,030
+مش completeالان with norm ال X بيساوي ال maximum
+
+145
+00:10:52,030 --> 00:10:54,750
+ال absolute value X of T T element in J the
+
+146
+00:10:54,750 --> 00:10:58,150
+differential operator T من X لعندي X ده عارف
+
+147
+00:10:58,150 --> 00:11:02,190
+operator بياخد من X ل X ايش بيسوي بيجي اللي هو
+
+148
+00:11:02,190 --> 00:11:07,510
+بياخد اي element هنا الى تفاضله يعني بياخد اي T X
+
+149
+00:11:07,510 --> 00:11:10,790
+of T ال X of T هدي يشملها polynomial ايش بيساوي
+
+150
+00:11:10,790 --> 00:11:16,050
+صورتها X prime of Tis an unbounded linear operator
+
+151
+00:11:16,050 --> 00:11:19,650
+مثلًا على مين؟ على unbounded linear operator نحن
+
+152
+00:11:19,650 --> 00:11:22,750
+ناخده لكم برضه على bounded linear operator شوفوا
+
+153
+00:11:22,750 --> 00:11:25,850
+الآن كيف نثبت أنه unbounded linear operator ال
+
+154
+00:11:25,850 --> 00:11:31,630
+linearity سهلة لو أثبتوها لحالكم بتنفع عشان
+
+155
+00:11:31,630 --> 00:11:37,150
+أورجيكم أنه أنا فعلاً لما أقولكم سهلة هي سهلة خدوا
+
+156
+00:11:37,150 --> 00:11:40,330
+الآن for all x y element in x and all scalars
+
+157
+00:11:40,330 --> 00:11:44,200
+alpha بدأ أثبتلكم أنها linearأيش اللي هي T of α X
+
+158
+00:11:44,200 --> 00:11:48,480
+زي Y بدأت بتبت سواء α T X زي الـ T Y هذا مناط
+
+159
+00:11:48,480 --> 00:11:53,260
+اللينيه شوفوا الآن T of α X زي Y شو معناته هذه
+
+160
+00:11:53,260 --> 00:11:58,300
+بترسل إلى α X زي Y prime of مين لأن هذه عبارة عن
+
+161
+00:11:58,300 --> 00:12:00,820
+بلونوميا لو هذه بلونوميا لو Alpha مضروبة فيها
+
+162
+00:12:00,820 --> 00:12:05,480
+الاخره عبارة عن ال .. ال .. ال .. ال operator تبعي
+
+163
+00:12:05,480 --> 00:12:09,960
+وظيفته أنه يفاضل هيك هواللي هو صار عندى Alpha زياد
+
+164
+00:12:09,960 --> 00:12:14,320
+X وPrime T وانا بعرف ان الـ Linearity .. ال .. ال
+
+165
+00:12:14,320 --> 00:12:17,760
+.. التفاضل Linear اللي هي بمعنى آخر بيصير Alpha في
+
+166
+00:12:17,760 --> 00:12:22,020
+X Prime of T زياد Y Prime of V of T الأولى هي
+
+167
+00:12:22,020 --> 00:12:25,440
+عبارة عن Alpha T X والتانى عبارة عن T Y معناته T
+
+168
+00:12:25,440 --> 00:12:28,380
+is Linear إذا الموضوع سهل وما بدناش نظلنا .. اللي
+
+169
+00:12:28,380 --> 00:12:31,620
+هو .. نحكي فيه سرنا اللي هو تجاوزنا هذه المرحلة
+
+170
+00:12:31,620 --> 00:12:38,750
+احنا نيجي الآنهنثبت أنه اللي هو unbounded بدأ أثبت
+
+171
+00:12:38,750 --> 00:12:42,150
+لكم unbounded بدأ أجيلكم sequence احنا لازم نلاقي
+
+172
+00:12:42,150 --> 00:12:47,730
+إيش عشان نثبت bounded أنه نثبت أنه norm TX أصغر أو
+
+173
+00:12:47,730 --> 00:12:52,850
+سوء C في norm X لكل X موجودة في domain T بدأ
+
+174
+00:12:52,850 --> 00:12:57,170
+أجيلكم sequence أو جزء من هال Xات اللي هنا يستحيل
+
+175
+00:12:57,170 --> 00:13:01,490
+ينطبق عليها مستحيل يجيلها C تنفع لهم كلهم أو نلاقي
+
+176
+00:13:01,490 --> 00:13:06,250
+C اللي هو بتنفعأو نجيه لـ C مهما كانت كبيرة تشوفوا
+
+177
+00:13:06,250 --> 00:13:12,710
+كيف الأمر بسيط let XN of T ايش بتساوي؟ T أوسان
+
+178
+00:13:12,710 --> 00:13:17,290
+بولونوميا مظهوطة لا لا بولونوميا البسيطة كمانwhere
+
+179
+00:13:17,290 --> 00:13:21,350
+n element in N ثم دور بالـ Xn إيش هيساوي حسب اللي
+
+180
+00:13:21,350 --> 00:13:25,150
+إحنا عارفينه اللي هو maximum لل Xn of T من ال Xn
+
+181
+00:13:25,150 --> 00:13:29,070
+of T اللي هي T أس N يعني بدي maximum لل T أس N لل
+
+182
+00:13:29,070 --> 00:13:32,790
+T اللي هو الموجودة في الـ J والـ J إيش هي ماخدينها
+
+183
+00:13:32,790 --> 00:13:38,330
+01 إذا ال maximum لل T أس N لكل T هناالـ maximum
+
+184
+00:13:38,330 --> 00:13:46,730
+بيساوي واحد إذا ال norm لكل ال Xn بيساوي واحد إذا
+
+185
+00:13:46,730 --> 00:13:51,350
+ال norm هذه لكل ال Xn لجته بيساوي واحد
+
+186
+00:13:54,070 --> 00:13:59,450
+الان شوفوا تي اكس ان تي اكس ان ايش هو normal بساوي
+
+187
+00:13:59,450 --> 00:14:03,290
+ال maximum لأ لأنه برضه في وين برمي وين من
+
+188
+00:14:03,290 --> 00:14:08,430
+polynomial ل polynomial لنفس ال space اللي هو صورة
+
+189
+00:14:08,430 --> 00:14:10,850
+تي اكس ان اللي هي ان في تي اكس ان نقص واحد مش
+
+190
+00:14:10,850 --> 00:14:16,320
+دقتهاالان norm ال maximum له هذا المقدار اللي هو
+
+191
+00:14:16,320 --> 00:14:21,500
+عندك ال T المقصة نقص واحد في T limited J واحد اللي
+
+192
+00:14:21,500 --> 00:14:25,240
+هو maximum لها وفي عندك N إيش بدي يطلع بسوءًا إذا
+
+193
+00:14:25,240 --> 00:14:31,660
+طلع عندي norm T X N بسوءًا معناته إن norm T X N
+
+194
+00:14:31,660 --> 00:14:36,260
+على X N إيش بساوي بسوءًا لا يمكن بأي حال من
+
+195
+00:14:36,260 --> 00:14:42,380
+الأحوال إن اللي جيلنا C بحيث أنه يكون normالـ T X
+
+196
+00:14:42,380 --> 00:14:47,740
+N على Normal X N يكون أصغر أوي سوى C لكل أنوية
+
+197
+00:14:47,740 --> 00:14:54,200
+موجودة في الـ N أو لكل X N موجودة في الـ Space مين
+
+198
+00:14:54,200 --> 00:14:59,160
+مش ممكن لأن الـ N إيش هنا عندي هذا طلع إيش بتساوي
+
+199
+00:14:59,160 --> 00:15:03,860
+بساوة N فش C تكون أكبر من الـ N زي اللي في الدنيا
+
+200
+00:15:03,860 --> 00:15:07,360
+لأ لإن أحنا بنعرف أصلا The set of all natural
+
+201
+00:15:07,360 --> 00:15:13,670
+numbers is unboundedفهذا اللي هو بناء عليه لا يمكن
+
+202
+00:15:13,670 --> 00:15:17,790
+إيجاد such C إذا therefore T is not bounded إذا
+
+203
+00:15:17,790 --> 00:15:24,350
+هذا مثال على Unbounded Linear Operator اطلع لفوق
+
+204
+00:15:24,350 --> 00:15:29,450
+الآن Integral Operator لناخد T برضه من ال
+
+205
+00:15:29,450 --> 00:15:31,990
+continuous functions لل continuous functions كلها
+
+206
+00:15:33,970 --> 00:15:38,070
+be defined by T X of T بساوية ال integration من
+
+207
+00:15:38,070 --> 00:15:42,910
+صفر لعين لواحد K of T وTau X of Tau D من D Tau
+
+208
+00:15:42,910 --> 00:15:45,970
+where K اللي هي هذه is a continuous is a given
+
+209
+00:15:45,970 --> 00:15:47,870
+continuous function يعني اللي كنا نسميه kernel
+
+210
+00:15:47,870 --> 00:15:51,590
+زمان في المعادلة التكملية أو المعادلة التفاضلية
+
+211
+00:15:51,590 --> 00:15:58,000
+هذا الآن عندي اللي هي دالة متصلةاللي هي داية متصلة
+
+212
+00:15:58,000 --> 00:16:03,080
+معينة K الان صورة X of T هي عبارة عن ال
+
+213
+00:16:03,080 --> 00:16:06,380
+integration من صفر إلى واحد للدالة اللي أنا أخدتها
+
+214
+00:16:06,380 --> 00:16:11,060
+اللي نسميها kernel مضروبة في مين في ال X اللي هي
+
+215
+00:16:11,060 --> 00:16:15,560
+اللي بدأت أكملها of Tau دي مين Tau يعني هي دي
+
+216
+00:16:15,560 --> 00:16:18,320
+function of two variables وانا ماعطيكم إنه دي
+
+217
+00:16:18,320 --> 00:16:22,950
+continuous functionماشي الحال continuous على اللي
+
+218
+00:16:22,950 --> 00:16:25,550
+هي طبعا هدى واضح انها function of two variables
+
+219
+00:16:25,550 --> 00:16:29,810
+continuous على الـG cross G معايا عشان اضمن انه
+
+220
+00:16:29,810 --> 00:16:32,450
+هدى متصلة و هدى متصلة اذا الـTin-Tin متصلات
+
+221
+00:16:32,450 --> 00:16:35,350
+بالنسبة لتاو اللي بده كامل إليها معناته التكامل
+
+222
+00:16:35,350 --> 00:16:40,530
+المضمون انه ايش ماله موجود طيب اذا صارت هدى T X of
+
+223
+00:16:40,530 --> 00:16:46,250
+T بسوء كده اللي هو فعلا اشي اللي هو معرف تعريفا
+
+224
+00:16:46,250 --> 00:16:51,540
+تماماwhich is called the kernel on D of T مش مشكلة
+
+225
+00:16:51,540 --> 00:16:55,500
+هذي then T is a bounded linear operator ليها مثال
+
+226
+00:16:55,500 --> 00:16:59,940
+عالمين a bounded linear operator اطلع على فوق اطلع
+
+227
+00:16:59,940 --> 00:17:04,940
+على فوق الان نيجي نشوف طبعا احنا ال C01 اتفاجنا ال
+
+228
+00:17:04,940 --> 00:17:10,400
+C01 عبارة عن ال space ال norms space ال continuous
+
+229
+00:17:10,400 --> 00:17:13,480
+functions مين ال normal اللي عليه ال maximum ماشي
+
+230
+00:17:13,480 --> 00:17:16,180
+ال normal اللي عليه ال maximum وهذا ال space
+
+231
+00:17:16,180 --> 00:17:22,500
+completeبالمناسبة اه طيبfor all x,y elements in C0
+
+232
+00:17:22,500 --> 00:17:22,980
+,1
+
+233
+00:17:50,230 --> 00:17:53,270
+الـ Scale of Multiplication و الـ Additivity اللي
+
+234
+00:17:53,270 --> 00:17:56,490
+هو الـ Integration بتوزع عليها و يساوي هذه اللي هي
+
+235
+00:17:56,490 --> 00:18:02,410
+TX و التانية TY إذا صارت اللي هو T is Linear الآن
+
+236
+00:18:02,410 --> 00:18:05,830
+بتثبتلكم أنه اللي هو ال .. ال .. ال .. ال operator
+
+237
+00:18:05,830 --> 00:18:11,990
+اللي عندنا اللي هو TX TX بساوي ال Integration من
+
+238
+00:18:11,990 --> 00:18:19,070
+صفر اللي عنده واحد K T و Tau X of TauD τاو انها
+
+239
+00:18:19,070 --> 00:18:24,470
+ايش معناها is bounded يعني بمعنى اخر نورم ال TX
+
+240
+00:18:24,470 --> 00:18:30,350
+على نورم ال X أصغر يساوي some C انشوف ايش هي ال C
+
+241
+00:18:30,350 --> 00:18:35,110
+اللي بحكي عنها صلى على النبي عليه الصلاة والسلام
+
+242
+00:18:35,110 --> 00:18:41,160
+نيجي الأن أول إشيعندي اللي هو الـ Kernel الـ
+
+243
+00:18:41,160 --> 00:18:47,000
+Kernel اللي هو الـ K of K الـ K هذه is continuous
+
+244
+00:18:47,000 --> 00:18:50,720
+على closed bounded square G اللي اتفاجنا على انه
+
+245
+00:18:50,720 --> 00:18:54,120
+معرفين على G cross G و G اللي هو عبارة عن اللي هي
+
+246
+00:18:54,120 --> 00:18:57,320
+closed interval و G cross G بيصير bounded closed
+
+247
+00:18:57,320 --> 00:19:02,350
+اللي هي إياش squareإذن بمعنى أخر continuous على
+
+248
+00:19:02,350 --> 00:19:07,470
+closed bounded region إذن أكيد هتكون اللي هي ال K
+
+249
+00:19:07,470 --> 00:19:12,390
+نفسها bounded نظرية دي اللي بدكم then K is bounded
+
+250
+00:19:12,390 --> 00:19:16,310
+ماشي الحال as a function that is there is C أكبر
+
+251
+00:19:16,310 --> 00:19:19,530
+من صفر such that ال absolute value لل K of T وTau
+
+252
+00:19:19,530 --> 00:19:23,190
+أصغر أو ساوى مين أصغر أو ساوى C على كل المنطقة
+
+253
+00:19:23,190 --> 00:19:26,610
+المعرفة عليها لإنها continuous على closed bounded
+
+254
+00:19:26,610 --> 00:19:32,680
+regionfurthermore ال absolute value لل X of T اللي
+
+255
+00:19:32,680 --> 00:19:35,980
+هي أكيد واحدة منهن أصغر أو شاو ال maximum عليهم
+
+256
+00:19:35,980 --> 00:19:40,300
+كلهن عالميا عند ال T معينة X of T عند T معينة أصغر
+
+257
+00:19:40,300 --> 00:19:43,440
+أو شاو ال maximum يعني بمعنى أخر ال X of T أكيد
+
+258
+00:19:43,440 --> 00:19:49,950
+أصغر أو شاو من نورمها يعني الآن X of TX of T هذي
+
+259
+00:19:49,950 --> 00:19:53,530
+أصغر أو يساوي Normal X لأن Normal X هو ال maximum
+
+260
+00:19:53,530 --> 00:19:59,410
+لكل هذولة معناه أن Normal X أكبر يساوي X of T لكل
+
+261
+00:19:59,410 --> 00:20:04,950
+T في الفترة 0 و 1 اللي بشتغل عليها إذا خذوا
+
+262
+00:20:04,950 --> 00:20:08,690
+المعلومتين المعلومة باتجاه ال kernel و المعلومة
+
+263
+00:20:08,690 --> 00:20:13,900
+باتجاه X of T هنسوا الآنالـ .. الـ norm لـ T of
+
+264
+00:20:13,900 --> 00:20:17,300
+Xاش بيساوي الـ TX ما هي بترمي وين برضه في ال
+
+265
+00:20:17,300 --> 00:20:20,580
+continuous إذن هيطلع عبارة عن .. طبعا هذه function
+
+266
+00:20:20,580 --> 00:20:25,680
+of V هتطلع of T تاوة هتطلع اللي هي عدد .. هت ..
+
+267
+00:20:25,680 --> 00:20:28,640
+هتروح .. إذن هتبقى لها function في مين بس؟ في T
+
+268
+00:20:28,640 --> 00:20:33,300
+إذن الآن norm الـ TX أو الـ TX بيساوي هذا norm هو
+
+269
+00:20:33,300 --> 00:20:37,640
+ال maximum للقيمة هذه على الـ T اللي وين ما لها
+
+270
+00:20:37,640 --> 00:20:41,930
+الـ Ts اللي موجودة في الـ Jاللي هي أكيد أصغر أو
+
+271
+00:20:41,930 --> 00:20:45,550
+يساوي بما أن هذا absolute value أصغر أو يساوي ال
+
+272
+00:20:45,550 --> 00:20:49,010
+integration لل absolute value صح؟ أصغر أو يساوي ال
+
+273
+00:20:49,010 --> 00:20:51,130
+integration ال absolute value في ال absolute value
+
+274
+00:20:51,130 --> 00:20:56,150
+الآن هذه من فوق أثبتت أنها أشمالها أصغر أو يساوي C
+
+275
+00:20:56,150 --> 00:21:00,710
+وهذه أصغر أو يساوي 100 اللي هو اللي هو النور،
+
+276
+00:21:00,710 --> 00:21:05,570
+مظبوط؟معايا هايها ال X و T أصغر أو أصغر منين ال
+
+277
+00:21:05,570 --> 00:21:09,830
+norm إذا بشيل هذه بحط مكانها ال C وهذه بشيلها بحط
+
+278
+00:21:09,830 --> 00:21:13,910
+مكانها اللي هو ال norm فبصير ال integration اللي
+
+279
+00:21:13,910 --> 00:21:17,310
+هو هذا أصغر أو أصغر منين ال integration C في نورم
+
+280
+00:21:17,310 --> 00:21:21,430
+ال X بطلع برا برضه لأنه عدد من Zero ل واحد دي Tau
+
+281
+00:21:21,430 --> 00:21:25,050
+ومن Zero ل واحد دي Tau إيش قيمته واحد إلا إذا بصير
+
+282
+00:21:25,050 --> 00:21:30,090
+C في نورم ال X يعني بمعنى آخر أثبتت الآن أن نورم
+
+283
+00:21:30,090 --> 00:21:37,080
+ال TXأصغر أو سوى C في نور مين ال X لكل X وين
+
+284
+00:21:37,080 --> 00:21:41,400
+موجودة في domain T وهذا يعني أن T is bounded أي
+
+285
+00:21:41,400 --> 00:21:49,180
+سؤال المفروض أن الكلام بدأ يحلو يعني نيجي الآن
+
+286
+00:21:49,180 --> 00:21:59,620
+نشوف اللي هو نعرف functionمن Rn لعند Rm بالاستعانة
+
+287
+00:21:59,620 --> 00:22:03,180
+.. وهذا مثال موجود في الجبر الخاطي بالاستعانة ..
+
+288
+00:22:03,180 --> 00:22:07,000
+بالاستعانة بالـ matrix اللي بيحول ال element من
+
+289
+00:22:07,000 --> 00:22:11,720
+هنا إلى element وين في الـ Rmالنورم اللي على
+
+290
+00:22:11,720 --> 00:22:15,520
+القرار نعرفينه اللي هو الجدر التربيعي x1 تربيع زاد
+
+291
+00:22:15,520 --> 00:22:20,920
+x2 تربيع زاد xn تربيع لأن عناصرها إيش هذه؟ x1, x2,
+
+292
+00:22:21,020 --> 00:22:26,840
+x3 و xn هذه عناصرها x1, x2, x3 و xm إذا نورمها هذا
+
+293
+00:22:26,840 --> 00:22:31,580
+هو الجدر التربيعي ل x1 تربيع زاد x2 تربيع زاد xn
+
+294
+00:22:31,580 --> 00:22:34,970
+تربيع وهذه كانت نورمها مشابهاللي هم بيقولي لو
+
+295
+00:22:34,970 --> 00:22:38,110
+أخدنا Matrix هذا الـ Matrix الـ Real Matrix اللي
+
+296
+00:22:38,110 --> 00:22:42,390
+هو أداة تعريف ال .. ال .. ال .. ال function اللي
+
+297
+00:22:42,390 --> 00:22:45,490
+عندي أو ال operator اللي عنده أخدت A بتساوي Alpha
+
+298
+00:22:45,490 --> 00:22:50,990
+J K ب M by N Matrix M by N عشان يناسب مين اللي هو
+
+299
+00:22:50,990 --> 00:22:55,270
+في حالة الضرب اللي هو ال Rn و ال Rm و ينجلي من Rn
+
+300
+00:22:55,270 --> 00:23:02,660
+لمين لعند RmDefined by TXاش بساوي FX الـ X من وين
+
+301
+00:23:02,660 --> 00:23:06,940
+عبارة عن element اللي هو XI واحد و XI اتنين و XI N
+
+302
+00:23:06,940 --> 00:23:11,600
+ماشي الحل الان بقولك إذا T is a bounded linear
+
+303
+00:23:11,600 --> 00:23:14,640
+operator إذا الـ linear و A شماله abounded خلّينا
+
+304
+00:23:14,640 --> 00:23:21,290
+نشوفلكل x و y element in Rn and all scalars α T of
+
+305
+00:23:21,290 --> 00:23:25,430
+α x زائد y ايش بيساوي؟ بيساوي هذا ولا طبعا هذا
+
+306
+00:23:25,430 --> 00:23:28,790
+اللي هو عبارة عن element في Rn وهذا element في Rn
+
+307
+00:23:28,790 --> 00:23:32,290
+هذا ال A matrix اشمله M by N matrix خلّينا نجوه
+
+308
+00:23:32,290 --> 00:23:39,990
+عشان ال A عبارة عن ألف واحد واحد لما نقصل Mby N
+
+309
+00:23:39,990 --> 00:23:45,550
+أكم عمود N من الأعمدة لعند Alpha 1 N مظبوط و بمشي
+
+310
+00:23:45,550 --> 00:23:52,490
+من هنا Alpha M 1 لعند Alpha M N هاي ال matrix اللي
+
+311
+00:23:52,490 --> 00:23:58,530
+عندى مش الحال الآن هذا ال matrix بدي أضربه في اللي
+
+312
+00:23:58,530 --> 00:24:06,110
+هو مين عندى T من R Nلعند RM بسمحولي بس أكتب على
+
+313
+00:24:06,110 --> 00:24:08,970
+صورة أعمدة اللي هي ال RN اللي هي اللي في ال RN
+
+314
+00:24:08,970 --> 00:24:14,810
+اللي هو عبارة عن Xi 1 لعند Xi N بدها ترمي وين؟ في
+
+315
+00:24:14,810 --> 00:24:21,910
+جامعة 1 لمين؟ لجامعة M ماشي؟ شوفوا الآن T
+
+316
+00:24:25,140 --> 00:24:31,940
+T of هذه الـ X التي هي XI واحد لعند XI N ما هي
+
+317
+00:24:31,940 --> 00:24:37,400
+ساوي الماتريكس هذا مضروب في XI واحد لعند XI N
+
+318
+00:24:37,400 --> 00:24:43,810
+معاياعملية الضرب هذا هيجيب ال element كله وبعدين
+
+319
+00:24:43,810 --> 00:24:46,210
+هذا هيجيب ال element لما أصل للأخر بيجيب ال
+
+320
+00:24:46,210 --> 00:24:49,930
+element أما كم element هنجيب M من ال elements هذا
+
+321
+00:24:49,930 --> 00:24:53,710
+هيجيب واحد هذا اتنين العديش لما أصل عند ال M إذا
+
+322
+00:24:53,710 --> 00:25:01,230
+هيطلع عندي عبارة عن جامعة واحد عند جامعةإذا فعلاً
+
+323
+00:25:01,230 --> 00:25:04,710
+هذا اللي هو بيعمل ليه linear operator من A بيعمل
+
+324
+00:25:04,710 --> 00:25:08,390
+ليه operator من RN لعند RM Linear اه Linear ليش
+
+325
+00:25:08,390 --> 00:25:11,930
+Linear لأن لو أخدت T of Alpha X زائد Y تنسوش أن
+
+326
+00:25:11,930 --> 00:25:16,130
+هذا Matrix وهذا Matrix كلهم Matrixالأن إيش هيساوي
+
+327
+00:25:16,130 --> 00:25:21,410
+حسب القانون A matrix في هدولة Alpha scalar ماشي
+
+328
+00:25:21,410 --> 00:25:24,570
+الحال في ضرب ال matrices ال alpha ال scalar بتطلع
+
+329
+00:25:24,570 --> 00:25:27,190
+برا عن المشترك بتظهر اللي هو A في X و بقى دي A في
+
+330
+00:25:27,190 --> 00:25:32,030
+Y اللي هو عبارة عن AX اللي هو ال TX وال AY ال TY
+
+331
+00:25:32,030 --> 00:25:36,580
+إذا صارت عبارة عن linear operator طيبلأن .. ال ..
+
+332
+00:25:36,580 --> 00:25:41,060
+ضال عليا أستخدم مين الآن؟ أثبت مين؟ أثبت أنه is
+
+333
+00:25:41,060 --> 00:25:44,920
+bounded بدي أستخدم في .. في أثبات ال boundedness
+
+334
+00:25:44,920 --> 00:25:48,320
+الكوششوارزينكواليتي مذاكرين الكوششوارزينكواليتي ال
+
+335
+00:25:48,320 --> 00:25:53,340
+summation xi i gamma i أصغر أو ساوي ال summation
+
+336
+00:25:53,340 --> 00:25:59,520
+xi i تربيع الكل أص نص في ال summation gamma i
+
+337
+00:25:59,520 --> 00:26:03,850
+تربيع الكل أشماله أص نصليه استخدمها؟ خلّيني نشوف
+
+338
+00:26:03,850 --> 00:26:06,670
+إيش اللي .. إيش .. إيش اللي بدي أعمله الموضوع
+
+339
+00:26:06,670 --> 00:26:10,990
+حسابات الآن وحسابات سهلة إن شاء الله خدوا الآن زي
+
+340
+00:26:10,990 --> 00:26:14,650
+ما قلنا خدوا أي X موجودة في ال domain الـR of T هي
+
+341
+00:26:14,650 --> 00:26:19,450
+كولوم Matrix أخدته Xi واحد and Xi N وحسبوه لنورم
+
+342
+00:26:19,450 --> 00:26:22,390
+الـTX اللي هو تربيع عشان اللي هو تسهيل عملية
+
+343
+00:26:22,390 --> 00:26:26,870
+الحسابات أخدت التربيع بساوي نورم الـX الكلمين
+
+344
+00:26:26,870 --> 00:26:32,270
+تربيع لأن الـTX مش بساوي A في X تربيعالان ax هي ال
+
+345
+00:26:32,270 --> 00:26:36,310
+a وهي ال x نضربهم نضرب اللي هو السطر الأول في
+
+346
+00:26:36,310 --> 00:26:40,430
+العمود الأول بطلع summation للضرب هذا اه اللي هو
+
+347
+00:26:40,430 --> 00:26:44,570
+بطلع ال .. اطلع لفوق شوية لفوق شوية اه بس خلي بس
+
+348
+00:26:44,570 --> 00:26:48,570
+اظهر هنا بطلع ال summation الأول summation اللي هو
+
+349
+00:26:48,570 --> 00:26:52,170
+السطر الأول في العمود الأولفي العمود نفسه هاي ال
+
+350
+00:26:52,170 --> 00:26:55,870
+entry الأول الان ال summation هذا العمود التاني في
+
+351
+00:26:55,870 --> 00:26:59,210
+السطر التاني في العمود اللي عندى هاي و بطلع لما
+
+352
+00:26:59,210 --> 00:27:03,950
+أصل لأخر واحد اللي هو بيجيب هذا طيب هذول الآن
+
+353
+00:27:03,950 --> 00:27:08,230
+عبارة عن Gamma 1 و Gamma 2 و Gamma 3 و Gamma M ايش
+
+354
+00:27:08,230 --> 00:27:11,870
+form هنا بشغل في الأرقام الآن اللي هو تربيح هذا و
+
+355
+00:27:11,870 --> 00:27:15,470
+تربيح هذا و تربيح هذا و كل انتحت مين الجدر و بجمحل
+
+356
+00:27:15,470 --> 00:27:19,920
+صح بجمحل و أخد انتحت الجدر معايا كيف؟بصير الآن
+
+357
+00:27:19,920 --> 00:27:24,000
+عبارة عن summation مجموح هذا اللي هو لكل واحد
+
+358
+00:27:24,000 --> 00:27:30,200
+تربيع آسف اه هنا اللي هي هذا تربيع اه و هذا تربيع
+
+359
+00:27:30,200 --> 00:27:33,700
+و هذا تربيع و هذا تربيع و بعدين ماله بجمحها و الكل
+
+360
+00:27:33,700 --> 00:27:38,140
+تحت الجذر من المناخ التربيع فاهمين اه؟اللي هو هذا
+
+361
+00:27:38,140 --> 00:27:41,800
+أصغر أو ساوي بالـ Schwarz inequality بدي أطبّقها
+
+362
+00:27:41,800 --> 00:27:44,620
+على اللي جوا على هذه الـSchwarz inequality هذه
+
+363
+00:27:44,620 --> 00:27:49,700
+تربيع أص نص تربيع أص نص وهذه تربيع أص نص والباقي
+
+364
+00:27:49,700 --> 00:27:54,580
+فوق أيضا أيش ماله تربية معايا واضح هذا أصغر أو
+
+365
+00:27:54,580 --> 00:27:58,420
+ساوي الآن لو جينا شوفنا هذه هذه بتمثل مين يا جماعة
+
+366
+00:27:58,420 --> 00:28:02,970
+اللي جواNormal X صح ولا لأ وهي فيه تربيع بتطلع
+
+367
+00:28:02,970 --> 00:28:06,770
+Normal X ماله تربيع بيظل ال summation لل summation
+
+368
+00:28:06,770 --> 00:28:10,450
+لأن هذا ثابت بيصير بيطلع برا فبيصير Normal X تربيع
+
+369
+00:28:10,450 --> 00:28:14,530
+في ال summation اللي عند double summation هذا في
+
+370
+00:28:14,530 --> 00:28:18,850
+النهاية عدد لأن هذا من هو هذا جاي من ال matrix
+
+371
+00:28:18,850 --> 00:28:22,150
+اللي أنا استخدمته في تعريف الدالة يعني إيش محدد
+
+372
+00:28:22,150 --> 00:28:26,110
+يعني هيكون عبارة عن إيش قيمة عددية إذا صار عندي
+
+373
+00:28:26,110 --> 00:28:31,670
+Normal TXتربيع أصغر أو شويه Normal X تربيع في مين؟
+
+374
+00:28:31,670 --> 00:28:36,850
+في some constant C يلا
+
+375
+00:28:36,850 --> 00:28:40,470
+اللي بعده اطلع لفوق اطلع لفوق فبصير عندي Normal T
+
+376
+00:28:40,470 --> 00:28:43,370
+X تربيع أصغر أو شويه اللي هو C تربيع في Normal X
+
+377
+00:28:43,370 --> 00:28:45,710
+حيث و C تربيع بالساوية ال summation اللي قلنا عنه
+
+378
+00:28:45,710 --> 00:28:51,070
+إذن و هذا يعني T is bounded إذن عبارة عن bounded
+
+379
+00:28:51,070 --> 00:28:54,850
+linear operator اللي أثبتناه نأتي إلى نظرية
+
+380
+00:28:57,850 --> 00:29:03,610
+لو انتوا لاحظته بس قبل احكيها النظرية theorem if
+
+381
+00:29:03,610 --> 00:29:06,850
+and only if this base X is finite dimensional then
+
+382
+00:29:06,850 --> 00:29:10,970
+every linear operator on X أشماله is bounded كلام
+
+383
+00:29:10,970 --> 00:29:17,270
+خطيرإنه أي Linear Operator في الدنيا على finite
+
+384
+00:29:17,270 --> 00:29:20,970
+dimensional space هيطلع bounded linear EIH
+
+385
+00:29:20,970 --> 00:29:24,930
+Operator يعني اللي جاب البشوية هدولة تبع الـRN وRK
+
+386
+00:29:24,930 --> 00:29:28,110
+خلاص ما هو bounded linear operator على .. linear
+
+387
+00:29:28,110 --> 00:29:31,230
+operator على اللي هو finite dimensional space لأن
+
+388
+00:29:31,230 --> 00:29:34,230
+automatic هيكون إيش ماله؟ bounded linear operator
+
+389
+00:29:35,250 --> 00:29:39,590
+بدنا نبرهنها لان لو اتيت و لاحظته يمكن برهنها بيجي
+
+390
+00:29:39,590 --> 00:29:42,770
+تلت نظريات جابلها دي او نظريتين على الـ finite
+
+391
+00:29:42,770 --> 00:29:47,670
+dimensional و فيهم كلهم يمكن نروح لبرهان واحدة
+
+392
+00:29:47,670 --> 00:29:52,430
+كلهم استخدمنا فرضنا ال bases و استخدمنا اللمّة
+
+393
+00:29:52,430 --> 00:29:56,230
+اللي احنا تبعت اللي هي summation أكبر أو يساوي
+
+394
+00:29:56,230 --> 00:30:00,250
+اللي هو C في اللي هو اللي هي كتلة ال scalars،
+
+395
+00:30:00,250 --> 00:30:06,640
+مظبوط؟ عساس انه يعني لتتكارب البرهانطيب، الآن
+
+396
+00:30:06,640 --> 00:30:09,360
+خلّينا نفترض أن الـ dimension للـ space اللي عنده
+
+397
+00:30:09,360 --> 00:30:14,240
+X يش بيساوي N ونفترض ال basis تبعته E1 وE2 وEN بيه
+
+398
+00:30:14,240 --> 00:30:18,200
+a basis for X then every X element in X has a
+
+399
+00:30:18,200 --> 00:30:20,500
+unique representation عارفينه هذا الكلام من الجبر
+
+400
+00:30:20,500 --> 00:30:25,940
+الخطي اللي هي بغسط أي X في الـ X عشانه basis بنكد
+
+401
+00:30:25,940 --> 00:30:29,040
+و أسوء as a linear combination من العناصر هدولة
+
+402
+00:30:29,040 --> 00:30:34,340
+ووحيد و اللي بيبطل basisالفا واحد اي واحد زي الفا
+
+403
+00:30:34,340 --> 00:30:37,400
+اتنين اي اتنين زي الفا ان اياش اي ان هاد ال X
+
+404
+00:30:37,400 --> 00:30:41,120
+where الفا واحد و الفا اتنين are mean scalar by
+
+405
+00:30:41,120 --> 00:30:44,160
+linearity of T لأن هو مفترض اياش ماله linear و بدك
+
+406
+00:30:44,160 --> 00:30:48,940
+تثبت انه اياش bounded شوفوا كيف نورم ال TX ايش
+
+407
+00:30:48,940 --> 00:30:55,100
+هيساوي اللي هو ال summation لل alpha I TEI اكيد
+
+408
+00:30:55,770 --> 00:31:01,630
+Txاش بيساوي .. Txاش بيساوي اللي هو T لهذا إذا
+
+409
+00:31:01,630 --> 00:31:04,690
+Alpha واحد تي واحد زاد Alpha اتنين تي اتنين زاد
+
+410
+00:31:04,690 --> 00:31:08,690
+Alpha N تي N اللي هو هذا بحطه جوا تمين norm الان
+
+411
+00:31:08,690 --> 00:31:13,960
+أنا شغلي وين الان هذا normalإذا أصغر أوي و ساوي
+
+412
+00:31:13,960 --> 00:31:17,760
+اللي هو ال .. ال .. ال .. ال .. ال .. ال triangle
+
+413
+00:31:17,760 --> 00:31:21,380
+inequality اللي هو norm ال .. ال .. ال .. الأول
+
+414
+00:31:21,380 --> 00:31:24,820
+زاد التاني زاد التالت زاد مية norm هنا أصغر أوي و
+
+415
+00:31:24,820 --> 00:31:26,700
+ساوي نورم الأول زاد نورم التاني و زاد نورم الأخر
+
+416
+00:31:26,700 --> 00:31:30,440
+هذا اللي استخدمته إذا ال norm للمجموع أصغر أوي
+
+417
+00:31:30,440 --> 00:31:34,590
+مجموع لل normالآن الـ α I اللي هي scalar فبتدخل و
+
+418
+00:31:34,590 --> 00:31:37,750
+بتخرج من برا النورم بإيش ما لها ب absolute value
+
+419
+00:31:37,750 --> 00:31:41,630
+فاهمين اللي بحكيه؟ summation في نورمين اللي بيظل
+
+420
+00:31:41,630 --> 00:31:46,720
+نورمين الـ T E Iإذا الـ T I أكم واحدة هنا معروف أن
+
+421
+00:31:46,720 --> 00:31:50,380
+طبعا الـ E 1 و E 2 و E N بحكي عن إشي محدد اللي
+
+422
+00:31:50,380 --> 00:31:53,660
+وعددهن N من العناصر إذا أكيد فيه أكبر واحدة فيهم
+
+423
+00:31:53,660 --> 00:31:57,540
+أكيد لأن هدول أعداد مودبة أكبر ساو سيفر خدوا ال
+
+424
+00:31:57,540 --> 00:32:02,580
+maximum الهن هدولة فبصير هذا المقدار أصغر أو يساوي
+
+425
+00:32:02,580 --> 00:32:05,740
+ال maximum الهن في ال main في ال summation اللي
+
+426
+00:32:05,740 --> 00:32:10,560
+عندي اطلعي لفوق الان من لمة اتنين اربعة واحد اللي
+
+427
+00:32:10,560 --> 00:32:14,430
+وعدتكم فيهابدي اتخلص من هذولة بدي اتخلص من هذه
+
+428
+00:32:14,430 --> 00:32:19,060
+انزلينبدا تخلص منها الـ scalars اللي موجودة و تبدأ
+
+429
+00:32:19,060 --> 00:32:26,100
+تبدأ تبدأ تبدأ تبدأ تبدأ
+
+430
+00:32:26,100 --> 00:32:28,600
+تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ
+
+431
+00:32:28,600 --> 00:32:31,920
+تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ
+
+432
+00:32:31,920 --> 00:32:31,940
+تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ
+
+433
+00:32:31,940 --> 00:32:44,340
+تبدأ تبدأ
+
+434
+00:32:44,340 --> 00:32:50,360
+تماشي هذه اللي ما الان بتربط هذه مع الاولى صار هذا
+
+435
+00:32:50,360 --> 00:32:55,140
+ال summation اصغر او يساوي normal x على ال c انزل
+
+436
+00:32:55,140 --> 00:32:59,060
+لتحت .. انزل لتحت بدي اللي هو اخد .. اخد خلص من
+
+437
+00:32:59,060 --> 00:33:02,760
+هذه بيصير اصغر او يساوي هذا في normal x على مين؟
+
+438
+00:33:02,760 --> 00:33:07,000
+على ال c اطلع لفوق قدر من واحد و اللي عندي هذه
+
+439
+00:33:07,000 --> 00:33:11,020
+بقدر اقول normal T x اصغر يساوي واحد على c في ال
+
+440
+00:33:11,020 --> 00:33:17,040
+maximum هذا في normal x هذا كله على بعضثابت لأن
+
+441
+00:33:17,040 --> 00:33:20,880
+هذا عبارة عن قيمة عددية و 1 على C قيمة عددية إذا
+
+442
+00:33:20,880 --> 00:33:24,680
+نورم الـ TX أصغر يساوي some number M في نورم الـ X
+
+443
+00:33:24,680 --> 00:33:28,520
+إذا صار عنده و الـ M طبعا هذه المشمولة هي هذه M
+
+444
+00:33:28,520 --> 00:33:32,800
+مشمولة تغيروا هذا M كم تهلل الفعل بساوي 1 على C في
+
+445
+00:33:32,800 --> 00:33:39,060
+ال maximum للنورم hence T أشمالها is bounded يلّا
+
+446
+00:33:39,060 --> 00:33:43,440
+لبعده نيجي
+
+447
+00:33:43,440 --> 00:33:44,180
+نشوف
+
+448
+00:33:49,850 --> 00:33:57,170
+Theorem 279 إعلان كبير إعلان بقولكم باختصارلما
+
+449
+00:33:57,170 --> 00:33:59,690
+يكون عندنا linear operator لما يكون عندنا linear
+
+450
+00:33:59,690 --> 00:34:04,190
+operator هتلاقوا مفهوم ال boundedness هو نفس مفهوم
+
+451
+00:34:04,190 --> 00:34:08,250
+ال continuity هو نفس مفهوم ال continuity عند نقطة
+
+452
+00:34:08,250 --> 00:34:12,390
+يعني لو كان عندك linear operator و كانت continuous
+
+453
+00:34:12,390 --> 00:34:16,250
+عند نقطة توكل على الله continuous على كل مين على
+
+454
+00:34:16,250 --> 00:34:19,770
+كل ال domain و هيكون bounded و لو كان bounded
+
+455
+00:34:19,770 --> 00:34:21,850
+هيكون continuous عند كل ال domain و هيكون
+
+456
+00:34:21,850 --> 00:34:25,090
+continuous عند مين عند كل نقطة كلام خوى .. خوى جدا
+
+457
+00:34:25,950 --> 00:34:29,230
+ومريح let T من domain of T لعند Y بيقالينا
+
+458
+00:34:29,230 --> 00:34:32,310
+operator where domain of T subset من X and X and Y
+
+459
+00:34:32,310 --> 00:34:36,450
+are normed spaces then T is continuous if and only
+
+460
+00:34:36,450 --> 00:34:40,530
+if T is bounded هاي واحدة اتنين إذا كانت T
+
+461
+00:34:40,530 --> 00:34:45,030
+continuous عند بس نقطة هتلاقيها نقلها continuous
+
+462
+00:34:45,030 --> 00:34:51,730
+على كل ال domain يلا نشوف بدنا نبرهن ال theorem
+
+463
+00:34:51,730 --> 00:34:57,310
+ناخد اتجاه الأول اتجاه التاني و بعدين ناخد Bطيب
+
+464
+00:34:57,310 --> 00:35:07,370
+سلّع على النبي عليه الصلاة والسلام شوفوا
+
+465
+00:35:07,370 --> 00:35:13,610
+خلّينا نشوف اللي بحكيهاالان بس بدنا نشيل هال سفر
+
+466
+00:35:13,610 --> 00:35:16,430
+من عندنا عشان لو بدنا نجسم على سفر كده نجسم على T
+
+467
+00:35:16,430 --> 00:35:20,750
+مايكون مرتاحين نفش نجسم على سفر الـ 4T بيساوي سفر
+
+468
+00:35:20,750 --> 00:35:23,110
+ال .. ال .. ال .. ال .. ال .. ال linear operator
+
+469
+00:35:23,110 --> 00:35:25,850
+اللي هو ال zero linear operator هذا linear و
+
+470
+00:35:25,850 --> 00:35:28,530
+bounded و كل الدنيا حلوة فيه و كنتوا حلوة فيهfor T
+
+471
+00:35:28,530 --> 00:35:33,130
+بيساوى 0 the statement is trivial لأن لت لا تساوي
+
+472
+00:35:33,130 --> 00:35:38,370
+0 نفترض انه مش هو ال zero operator ماشي الان مدام
+
+473
+00:35:38,370 --> 00:35:41,470
+مش هو ال zero operator اذا اكيد ال norm لت اشماله
+
+474
+00:35:41,470 --> 00:35:45,910
+مش سفر ماشي الحال طيب لان اصلا من تعريف ال norm ال
+
+475
+00:35:45,910 --> 00:35:48,190
+norm ت بيساوى سفر if and only if ت اللي جوه بيساوي
+
+476
+00:35:48,190 --> 00:35:53,250
+سفر طيب اذا ال norm ت لا يساوي سفر لان نفترض ت is
+
+477
+00:35:53,250 --> 00:35:58,270
+boundedونثبت إنه T Continuous T is bounded عارفين
+
+478
+00:35:58,270 --> 00:36:00,910
+شو معناته؟ bounded norm للـ T X أزرار شوية اللي هو
+
+479
+00:36:00,910 --> 00:36:04,730
+C في norm ال X ده كل ال Xاتر الآن و بدنا ناخد X
+
+480
+00:36:04,730 --> 00:36:08,330
+note arbitrary X note بس بدنا نحكي عن واحدة محددة
+
+481
+00:36:08,330 --> 00:36:11,410
+يعني باجي باخد هكوم هالعناصر اللي في ال domain of
+
+482
+00:36:11,410 --> 00:36:15,660
+T باخد من X note arbitrary و ببدأ أحكي عنهاإذا
+
+483
+00:36:15,660 --> 00:36:17,960
+اللي بنطبق عليه hard book علي غيرها يعني مش مانهي
+
+484
+00:36:17,960 --> 00:36:24,100
+أنا باخدها عشوائي let X not be any fixed point in
+
+485
+00:36:24,100 --> 00:36:30,640
+domain of Tالان احنا مفترضين انها bounded او بدنا
+
+486
+00:36:30,640 --> 00:36:33,440
+نثبت انها continuous ايش كيف نثبت انه continuous؟
+
+487
+00:36:33,440 --> 00:36:37,700
+نثبت انه continuous انه اللي هو لكل y أكبر من 0
+
+488
+00:36:37,700 --> 00:36:41,700
+بدي لاجي delta أكبر من 0 such that لما ال X minus
+
+489
+00:36:41,700 --> 00:36:46,460
+X not يكون أصغر من Delta يعطيني ال TX نقص ال TX
+
+490
+00:36:46,460 --> 00:36:50,940
+not ايش ماله أصغر من Y هي اللي بدي اشتغل عليهاماشي
+
+491
+00:36:50,940 --> 00:36:55,820
+بدي أصلّه بدي أصلّه بالاستعانة بالاستعانة باللي هي
+
+492
+00:36:55,820 --> 00:37:04,120
+اللي عندي طيب خدوا الآن suppose that T is bounded
+
+493
+00:37:04,120 --> 00:37:07,580
+and let X not be any fixed point on D of T و let Y
+
+494
+00:37:07,580 --> 00:37:12,560
+أكبر من 0 be arbitrary given Y لأن بما أنه T is
+
+495
+00:37:12,560 --> 00:37:18,950
+linearإذا بقدر ألاقي Delta بتساوي E على norm of T
+
+496
+00:37:18,950 --> 00:37:22,470
+أكبر من 0 such that إذا أنا جاءت بحضر للي بدّيها،
+
+497
+00:37:22,470 --> 00:37:26,850
+بدّي ألاقي مين؟ Delta أنا بقول للمستقبل اللي
+
+498
+00:37:26,850 --> 00:37:31,110
+بدّيها، أنا بتدعي إنها Delta إيش هتساوي E على norm
+
+499
+00:37:31,110 --> 00:37:34,670
+of T، norm of T بين إيديا و الـ E انت عطيتني إيها
+
+500
+00:37:34,670 --> 00:37:37,170
+إذا صارت عندي الـ Delta بتساوي E على norm of T
+
+501
+00:37:37,170 --> 00:37:41,170
+أكبر من مين من 0 such that if X element in domain
+
+502
+00:37:41,170 --> 00:37:47,320
+of Tعند x-x0 أصغر من دلتا بدّى أثبت لك أن هذا يكون
+
+503
+00:37:47,320 --> 00:37:51,820
+أصغر من مين من إبسلون شوفوا الآن then norm of T x
+
+504
+00:37:51,820 --> 00:37:58,040
+نقص T x0 ايش بيساوي norm of T في x minus x0Linear
+
+505
+00:37:58,040 --> 00:38:02,200
+Linear أصغر أو سوى نورم الـ T في نورم من X minus X
+
+506
+00:38:02,200 --> 00:38:05,780
+naught هذا من وين جبته؟ من الـ boundedness للـ T
+
+507
+00:38:05,780 --> 00:38:08,820
+مش عارف معناته الـ bounded؟ طيب أصغر أو سوى نورم
+
+508
+00:38:08,820 --> 00:38:12,460
+الـ T في نورم هذا الآن نورم الـ X minus X naught
+
+509
+00:38:12,460 --> 00:38:16,300
+أنا إيش ماخده؟ أصغر من Delta اللي هي إيش بتسوى Y
+
+510
+00:38:16,300 --> 00:38:20,460
+على مين؟ على نورم الـ T اللي هي أصغر من نورم الـ T
+
+511
+00:38:20,460 --> 00:38:23,500
+في Deltaحاصل ضربه Delta Epsilon على نورم الـT
+
+512
+00:38:23,500 --> 00:38:26,440
+بتطلع يشمله Epsilon و هذا Therefore T is
+
+513
+00:38:26,440 --> 00:38:30,020
+continuous at X0 لكن X0 was arbitrarily زي ما قلنا
+
+514
+00:38:30,020 --> 00:38:36,440
+Then T is continuous on all domain of T سهل يلّا
+
+515
+00:38:36,440 --> 00:38:42,660
+لبعده الآن بدنا نفترض مين أنها continuous و نصل
+
+516
+00:38:42,660 --> 00:38:48,860
+لمين للboundedness بدا أثبتلكم بدا أستخدم هذا هذا
+
+517
+00:38:48,860 --> 00:38:55,140
+معناه اتنين ال continuityبستخدمه بطريقة ما على إن
+
+518
+00:38:55,140 --> 00:39:00,200
+أثبت الـ norm للـ T Y أصغر أو ساوي C في الـ norm
+
+519
+00:39:00,200 --> 00:39:06,540
+للـ Y لكل Y element in domain of T هذا إذا أثبتت
+
+520
+00:39:06,540 --> 00:39:09,420
+لكم there exists C أكبر من 0 such that هذا إذا
+
+521
+00:39:09,420 --> 00:39:11,640
+أثبتت هذا معناه أنك أثبتت انه bounded كيف بده
+
+522
+00:39:11,640 --> 00:39:15,940
+أثبته بالاستعانة باللي فوق ماشي إذا الأن بده أقول
+
+523
+00:39:18,650 --> 00:39:21,090
+Conversely suppose that أو assume that T is
+
+524
+00:39:21,090 --> 00:39:23,910
+continuous at an arbitrary point x0 element in
+
+525
+00:39:23,910 --> 00:39:27,090
+domain of T مدام continuous ده بنطبق تعريف ال
+
+526
+00:39:27,090 --> 00:39:30,310
+continuity بمعنى then for every أكبر من أكبر من
+
+527
+00:39:30,310 --> 00:39:30,910
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+528
+00:39:30,910 --> 00:39:30,990
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+529
+00:39:30,990 --> 00:39:31,150
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+530
+00:39:31,150 --> 00:39:31,430
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+531
+00:39:31,430 --> 00:39:32,470
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+532
+00:39:32,470 --> 00:39:33,450
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+533
+00:39:33,450 --> 00:39:44,390
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر
+
+534
+00:39:44,390 --> 00:39:47,630
+من أكبر
+
+535
+00:39:47,670 --> 00:39:50,590
+عشان هيك احنا لو استثننا الصفر مش فارقة معناه قبل
+
+536
+00:39:50,590 --> 00:39:54,430
+شوية اصلا استثنناها من norm وماحكيناش لأن ال
+
+537
+00:39:54,430 --> 00:39:59,070
+inequality دُغر بتشتغل في حالة الصفر الآن عشان
+
+538
+00:39:59,070 --> 00:40:03,450
+اثبت هذه بدي اخد الآن اي واحد دويل موجودة في ال
+
+539
+00:40:03,450 --> 00:40:07,770
+domain of T واشيل الصفر منها، ماشي؟ اذا الان let Y
+
+540
+00:40:07,770 --> 00:40:11,370
+لا تساوي صفر بي أنقل من تمين in domain of T بدي
+
+541
+00:40:11,370 --> 00:40:15,190
+اثبتلكم ان norm لتي Y عن norm لY أصغر من sum C
+
+542
+00:40:16,230 --> 00:40:21,230
+شوفوا صلوا على النبي عليه الصلاة والسلام and set
+
+543
+00:40:21,230 --> 00:40:26,170
+خد الآن X بتساوي X not هذول اللي فوق اللي فوق اللي
+
+544
+00:40:26,170 --> 00:40:29,830
+فوق اللي قبل وشوية بدي أقولكم هتتحققن انا بدي
+
+545
+00:40:29,830 --> 00:40:35,890
+أقولكم هذول هيحققن الفوق وخد X بتساوي X notزائد
+
+546
+00:40:35,890 --> 00:40:41,390
+delta y على 2 normal y ماشي then خد الآن norm ال x
+
+547
+00:40:41,390 --> 00:40:46,550
+minus x not ايش هيساوي delta في y على 2 normal y
+
+548
+00:40:46,550 --> 00:40:51,030
+norm صح اللي هو ايش ماله norm هذي هيروح مع norm
+
+549
+00:40:51,030 --> 00:40:54,090
+هذي بيصير ايش ماله اصغر من delta اللي هو delta على
+
+550
+00:40:54,090 --> 00:40:59,120
+2 اصغر من delta اذا ادملتلكم الآن هذاأصغر من دلتا
+
+551
+00:40:59,120 --> 00:41:03,120
+مدام أصغر من دلتا إذا يتحقق عليه الشرط هذا لإن
+
+552
+00:41:03,120 --> 00:41:06,580
+احنا مفترضين ال T is continuous إذا أكيد by two
+
+553
+00:41:06,580 --> 00:41:11,400
+هيكون عنده نورم ال T X ناطس T X ناطس أصغر من مين؟
+
+554
+00:41:11,400 --> 00:41:15,500
+من إبسلون since T is continuous ابدأ في حسابات هذه
+
+555
+00:41:15,500 --> 00:41:21,920
+هتوصلي للبدية ويساويTX-TX0 بيساوي T of X minus TX0
+
+556
+00:41:21,920 --> 00:41:25,720
+عوضلي على ال X minus X0 اللي هي اش بيساوي منها ال
+
+557
+00:41:25,720 --> 00:41:29,680
+X نقص X0 اللي هي Delta Y على 2 في ال normal Y T is
+
+558
+00:41:29,680 --> 00:41:32,680
+linear إذا بتطلع الدلتا بتطلع حد و بتطلع حد براها
+
+559
+00:41:32,680 --> 00:41:37,620
+بيصير عند دلتاعلى 2 في نورم الـY طالعين من برا
+
+560
+00:41:37,620 --> 00:41:42,400
+الـT ومن برا الـNorm هن حرات لإن هن إيه شمال هن
+
+561
+00:41:42,400 --> 00:41:46,140
+Scalars هدول باعتبار اللي هو بيظال مين اللي جوا
+
+562
+00:41:46,140 --> 00:41:51,200
+الـNorm نورم الـT of مين؟ of Y نورم الـT of Y صار
+
+563
+00:41:51,200 --> 00:41:56,820
+عندي الآن هذا المقدار هيه هيه أصغر من Epsilon يعني
+
+564
+00:41:56,820 --> 00:42:01,840
+بمعنى أخر نورم الـTY أصغر من هذا في هذا على هذا في
+
+565
+00:42:01,840 --> 00:42:08,390
+Epsilonصار عند نورم الـTy أصغر من 2 في إبسلون على
+
+566
+00:42:08,390 --> 00:42:11,690
+دلتا في النورم لميين للـY هذا كله سموه ميين الـC
+
+567
+00:42:11,690 --> 00:42:15,630
+فبصير نورم الـTy أصغر شويه نورم الـY و الـY was
+
+568
+00:42:15,630 --> 00:42:20,110
+arbitrary بـ element in domain of T و بسويش سفر
+
+569
+00:42:20,110 --> 00:42:25,910
+إذا صار عند T إيش ما لها is bounded طيب اللي بعد
+
+570
+00:42:25,910 --> 00:42:33,630
+ويلانفترض أن الـ T مستمر في موقع واحد نفترض أن الـ
+
+571
+00:42:33,630 --> 00:42:35,210
+T مستمر في موقع واحد
+
+572
+00:42:39,460 --> 00:42:43,260
+أنا كله هنا .. هنا في البرهان لما .. اطلع .. لما
+
+573
+00:42:43,260 --> 00:42:47,740
+جيت برهانك هنا انا استغلت اللي هو ال continuity لل
+
+574
+00:42:47,740 --> 00:42:52,620
+.. لل .. لل T وين عند نقطة و أثبتت أنه أشمالها T
+
+575
+00:42:52,620 --> 00:42:56,940
+is bounded اذا from this proof اطلع إلى فوق from
+
+576
+00:42:56,940 --> 00:43:03,000
+this proof from this proofالان from this proof
+
+577
+00:43:03,000 --> 00:43:06,080
+assume that T is continuous at single point اذا
+
+578
+00:43:06,080 --> 00:43:09,680
+from this proof then by the second part of the
+
+579
+00:43:09,680 --> 00:43:14,140
+proof above of A T is bounded و احنا اثبتنا انه
+
+580
+00:43:14,140 --> 00:43:17,320
+لما تكون T is bounded ايش مالها continuous اذا T
+
+581
+00:43:17,320 --> 00:43:19,600
+is continuous فعلا لما تكون continuous عند one
+
+582
+00:43:19,600 --> 00:43:23,640
+single pointفي بعض الناس طبعا بتثبتاش بيكون الكتب
+
+583
+00:43:23,640 --> 00:43:27,260
+عارضة كيف عارضة هادى بدون اللي هي ال .. ال .. ال
+
+584
+00:43:27,260 --> 00:43:29,480
+.. ال .. الboundedness اللي في الطريق يعني ممكن
+
+585
+00:43:29,480 --> 00:43:33,080
+تكون عارضة انه إذا كانت T Linear اثبت لما تكون T
+
+586
+00:43:33,080 --> 00:43:36,720
+continuous تكون على طول اشمالها as اللي هي
+
+587
+00:43:36,720 --> 00:43:39,820
+continuous عند single point and continuous عند
+
+588
+00:43:39,820 --> 00:43:43,520
+every point طبعا بيكون جابلها مثبت اللي هو T is
+
+589
+00:43:43,520 --> 00:43:46,600
+bounded لما تكون continuous is bounded و بشتغل هنا
+
+590
+00:43:46,600 --> 00:43:47,140
+مباشرة
+
+591
+00:43:50,190 --> 00:43:52,630
+أو بعيد البرهان اللي حكيناها قبل شوية عشان يثبتها،
+
+592
+00:43:52,630 --> 00:43:56,230
+فاهمين؟ بعيد البرهان لو كانت اللي هو في الشعار
+
+593
+00:43:56,230 --> 00:44:02,390
+الدلالأولى طيب، اللي بعد؟ Noteولا Corollary لسه
+
+594
+00:44:02,390 --> 00:44:06,270
+Corollary لت T من domain of T لعند Y بيبقى bounded
+
+595
+00:44:06,270 --> 00:44:09,230
+linear operator where domain of T جزء من مين؟ من X
+
+596
+00:44:09,230 --> 00:44:13,570
+and X وY are non-disbases then ايه؟ لما X قالت
+
+597
+00:44:13,570 --> 00:44:17,150
+تروح .. يعني بمعنى أخر T bounded linear operator T
+
+598
+00:44:17,150 --> 00:44:20,330
+bounded linear operator بقول إذا ما يليه التحقق؟
+
+599
+00:44:20,330 --> 00:44:24,970
+إيش هو؟ إن لما X قالت تروح لل Xحيث xn والـ x في
+
+600
+00:44:24,970 --> 00:44:28,610
+domain الـ T بيعطيني automatic T x بتروح ل .. T xn
+
+601
+00:44:28,610 --> 00:44:32,590
+بتروح لمين لـ Tx هذا ما هو تعريف الـ continuity صح
+
+602
+00:44:32,590 --> 00:44:35,650
+ولا لأ تعريف ال continuity إذن بما أنه bounded إذن
+
+603
+00:44:35,650 --> 00:44:38,210
+من النظرية اللي جابل بشوية is a continuous مدام
+
+604
+00:44:38,210 --> 00:44:42,430
+continuous إذن بيطلع إن لما xn تروح لل X لل X لل X
+
+605
+00:44:42,430 --> 00:44:45,030
+في domain ال T وال Xn في domain ال T أكيد ال T xn
+
+606
+00:44:45,030 --> 00:44:48,580
+بتروح ل T x by ده continuityالجزء الثاني ضلال ال
+
+607
+00:44:48,580 --> 00:44:52,480
+space N of T إيش ماله is closed خلّينا نثبت ال N
+
+608
+00:44:52,480 --> 00:44:57,080
+of T is closed كيف نثبت انها closed؟ بتاخدوا X في
+
+609
+00:44:57,080 --> 00:45:02,010
+ال N of T إيش ماله closureوبتثبتوا إن X مين موجودة
+
+610
+00:45:02,010 --> 00:45:07,730
+في الـN of T ماشي؟ طيب إيش معناة X في الـN of T
+
+611
+00:45:07,730 --> 00:45:13,670
+closure؟ إنه there exists Xn in N of T such that
+
+612
+00:45:13,670 --> 00:45:21,010
+Xn converge the mean للـX صح ولا لأ؟بط T X N
+
+613
+00:45:21,010 --> 00:45:26,310
+بتساوي سفر لكل N صح ولا لأ لأن من وين جايات هدوله
+
+614
+00:45:26,310 --> 00:45:29,790
+من ال .. من ال .. من ال .. ال non-less base مظبوط
+
+615
+00:45:29,790 --> 00:45:33,790
+أو اللي هو ال .. ال .. ال .. ال .. ال N of T ماشي
+
+616
+00:45:33,790 --> 00:45:41,250
+فمين؟ اذا طيب لكن انا عمالي بقول ان ال N .. T X N
+
+617
+00:45:41,250 --> 00:45:45,310
+بتروح للسفر اذا اكيد T X N نفسها converge دمين
+
+618
+00:45:45,310 --> 00:45:52,280
+للسفرمعايا و بال continuity الاصلية ال continuity
+
+619
+00:45:52,280 --> 00:45:55,740
+الاصلية مش continuous about it then continuous اذا
+
+620
+00:45:55,740 --> 00:46:01,200
+هيعطيني TXN و تروح لمين لل TX ان XN و X1 موجودة في
+
+621
+00:46:01,200 --> 00:46:06,010
+domain of T تبعيأه مدام T X N بتروح ل T X و T X N
+
+622
+00:46:06,010 --> 00:46:09,850
+لجأت تروح لل سفر و الوحيدة اللي هي هتكون ال limit
+
+623
+00:46:09,850 --> 00:46:14,710
+إذا T X إيش بتساوي إذا T X بتساوي سفر و ما معنى T
+
+624
+00:46:14,710 --> 00:46:18,370
+X بتساوي سفر يعني X element في ال N of T يعني بدأت
+
+625
+00:46:18,370 --> 00:46:20,830
+في ال X N of T closure وصبت ال X في ال N of T
+
+626
+00:46:20,830 --> 00:46:24,210
+معناه أصلا ال N of T closure جزئية من ال N of T و
+
+627
+00:46:24,210 --> 00:46:26,210
+بعرف ال N of T جزئية من ال N of T closure يعني ال
+
+628
+00:46:26,210 --> 00:46:28,970
+N of T closure بيساوي ال N of T معناه أن ال N of T
+
+629
+00:46:28,970 --> 00:46:34,870
+is a closed setاللي بعده Note for any bounded
+
+630
+00:46:34,870 --> 00:46:38,710
+linear operators أو operator for any bounded
+
+631
+00:46:38,710 --> 00:46:42,520
+linear operator مش operatorsلأ، بدّو أكتر .. آه
+
+632
+00:46:42,520 --> 00:46:46,140
+بدّو أكتر آسف For any bounded linear operators T
+
+633
+00:46:46,140 --> 00:46:49,560
+من X عند Y و S من عند Y لعند Z شكل بدو يعملين
+
+634
+00:46:49,560 --> 00:46:54,820
+composition أه؟ Where X .. Y و Z are known spaces,
+
+635
+00:46:55,020 --> 00:46:59,920
+we have نورم الـ T S أصغر أشهر نورم الـ T في نورم
+
+636
+00:46:59,920 --> 00:47:04,320
+الـ S and نورم الـ T N أصغر أشهر نورم الـ T أُس H
+
+637
+00:47:04,320 --> 00:47:09,540
+أُس N هذه induction من هذهوهذه تعملوا تعريف اللي
+
+638
+00:47:09,540 --> 00:47:12,860
+هو norm of Ts ايش norm of Ts بيساوي اللي هو
+
+639
+00:47:12,860 --> 00:47:16,520
+Supremum لكده وشتغلوا عليها هتلاقوها أزرع شوية هذه
+
+640
+00:47:16,520 --> 00:47:21,140
+اللي هو بيبقى ال exercise بسيط معاكم بسهل
+
+641
+00:47:21,140 --> 00:47:29,100
+ماتتقلقوش طيب theorem 2711 مفردات المادة كتير عشان
+
+642
+00:47:29,100 --> 00:47:35,090
+هي صعبة الواحد هيبره كل حاجة طيب theoremبرضه هذه
+
+643
+00:47:35,090 --> 00:47:38,410
+خلّيني أقول سيئة المركزية في ال section اللي
+
+644
+00:47:38,410 --> 00:47:41,390
+بتقوللي let T من domain of T لعند Y بيه a bounded
+
+645
+00:47:41,390 --> 00:47:45,790
+linear operator اه bounded linear operator D of T
+
+646
+00:47:45,790 --> 00:47:50,710
+ماله جزء من normed space اسمه X والـ Y ايش ماله
+
+647
+00:47:50,710 --> 00:47:56,310
+جالنه بنخ space اه complete normed space بيقوللي
+
+648
+00:47:56,310 --> 00:48:00,350
+مدام T جاية من اللي هو domain of T في normed space
+
+649
+00:48:00,350 --> 00:48:05,870
+لعند بنخ space لعند بنخ spacethen T has an
+
+650
+00:48:05,870 --> 00:48:11,470
+extension بقدر أعملك extension للـ T ومش بس بقدر
+
+651
+00:48:11,470 --> 00:48:14,350
+أعمل extension ال extension هيكون من مين؟ من
+
+652
+00:48:14,350 --> 00:48:20,970
+domain of T ماله closure لعند ال Y و هيكون T تلده
+
+653
+00:48:20,970 --> 00:48:25,970
+هيكون برضه bounded linear operator و norm هو norm
+
+654
+00:48:25,970 --> 00:48:34,370
+الأصلي norm هو هيكون norm ال T الأصليةيلّا خلّينا
+
+655
+00:48:34,370 --> 00:48:45,910
+نشوف البرهان لأن البرهان منيح وفيه فكرة يا
+
+656
+00:48:45,910 --> 00:48:53,350
+رب .. طيب .. نشوف إيش بقولالان لت X element من ال
+
+657
+00:48:53,350 --> 00:48:56,310
+domain of T مقفل مادة N في ال domain of T مقفل
+
+658
+00:48:56,310 --> 00:48:56,610
+مادة N في ال domain of T مقفل مادة N في ال domain
+
+659
+00:48:56,610 --> 00:48:57,030
+of T مقفل مادة N في ال domain of T مقفل مادة N في
+
+660
+00:48:57,030 --> 00:48:58,330
+ال domain of T مقفل مادة N في ال domain of T مقفل
+
+661
+00:48:58,330 --> 00:49:01,090
+مادة N في ال domain of T مقفل مادة N في ال domain
+
+662
+00:49:01,090 --> 00:49:11,320
+of T مقفل مادة N في ال domain of Tمعروف By using
+
+663
+00:49:11,320 --> 00:49:14,680
+the linearity and boundedness of T we have ناخد
+
+664
+00:49:14,680 --> 00:49:20,620
+مين اللي هو ايش اللي هو هذي نستخدم ان الـ T is
+
+665
+00:49:20,620 --> 00:49:24,360
+linear و bounded تشوفوا كده احسبولي انه انا انا
+
+666
+00:49:24,360 --> 00:49:25,600
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+667
+00:49:25,600 --> 00:49:31,530
+انا انا انا انا اناT XM ناقص T XM بساوي T XM ناقص
+
+668
+00:49:31,530 --> 00:49:41,390
+T XM بساوي T XM ناقص T XM ناقص T XM بساوي T XM
+
+669
+00:49:41,390 --> 00:49:42,770
+ناقص T XM ناقص T XM بساوي T XM ناقص T XM ناقص T XM
+
+670
+00:49:42,770 --> 00:49:43,310
+ناقص T XM ناقص T XM ناقص T XM ناقص T XM ناقص T XM
+
+671
+00:49:43,310 --> 00:49:46,250
+ناقص T XM ناقص T XM ناقص T XM ناقص T XM ناقص T XM
+
+672
+00:49:46,250 --> 00:49:47,810
+ناقص T XM ناقص T XM ناقص T XM ناقص T XM ناقص T XM
+
+673
+00:49:47,810 --> 00:49:48,590
+ناقص T XM ناقص T XM ناقص T XM ناقص T XM ناقصإذا
+
+674
+00:49:48,590 --> 00:49:52,490
+أنا أخدت الـ XN معاها اللي هو الـ Conversion of
+
+675
+00:49:52,490 --> 00:49:58,050
+the mean للـ X إذا مدام كوشي إذا هذه اللي هي هيكون
+
+676
+00:49:58,050 --> 00:50:01,770
+عنده أصغر من أي أبسلون في الدنيا من ضبلهم الأبسل
+
+677
+00:50:01,770 --> 00:50:05,610
+على نورميل T يعني بمعنى أخر هذا provided that
+
+678
+00:50:05,610 --> 00:50:08,760
+نورميل T لبش سفربهذا معناته صار ايش ماله أصغر من
+
+679
+00:50:08,760 --> 00:50:12,860
+إبسلون إذا صار برضه إيش ماله كوشي إذا صارت ال TXN
+
+680
+00:50:12,860 --> 00:50:17,000
+كوشي الآن لازم ال إيش ال TXN كوشي في مين؟ في ال Y
+
+681
+00:50:17,000 --> 00:50:22,400
+و ال Y complete إذا هذا إيش هتكون converge إذا
+
+682
+00:50:22,400 --> 00:50:27,180
+الآن TXN كوشي sequence because XN is but Y is
+
+683
+00:50:27,180 --> 00:50:31,920
+complete then TXN converge say thatT X N converts
+
+684
+00:50:31,920 --> 00:50:37,240
+the mean Y element in Y وشوفوا هل اللي عملناه اللي
+
+685
+00:50:37,240 --> 00:50:41,580
+سوناه عشان هو أساس البرهان الآن أساس تركيبة الـ T
+
+686
+00:50:41,580 --> 00:50:49,280
+Extension الـ T تلدة أخدت الآن X N راحت لمين؟ لل X
+
+687
+00:50:49,280 --> 00:50:53,480
+ال X من وين هذه؟ هذه هي أصلا اللي أشغل غرضي أن
+
+688
+00:50:53,480 --> 00:50:58,900
+أعمل T تلدة من domain of T closure لعند مين؟ لعند
+
+689
+00:50:58,900 --> 00:51:05,140
+ال Yالان extension معناته انا مفكر شو معناته
+
+690
+00:51:05,140 --> 00:51:10,520
+extension اصلا ان ال T دلده هتساوي T لكل X في ال
+
+691
+00:51:10,520 --> 00:51:15,890
+domain الأصليوالآن اللي بيظل بتعرفه مين اللي بيظل
+
+692
+00:51:15,890 --> 00:51:18,430
+اللي في الـ .. اللي في الـ closure اللي برا ماشي
+
+693
+00:51:18,430 --> 00:51:23,230
+الحال اللي مش موجود فيها دي وبدو يكون حسابي انه
+
+694
+00:51:23,230 --> 00:51:25,850
+اللي أنا عرفته اللي هو اللي .. اللي .. اللي في ال
+
+695
+00:51:25,850 --> 00:51:28,470
+domain T و ال closure لو التقت واحدة في ال domain
+
+696
+00:51:28,470 --> 00:51:32,190
+T و ال closure موجودة في نفسها يعني أحيان ممكن
+
+697
+00:51:32,190 --> 00:51:34,750
+يكون Demon if they close أصلا فيكون هي نفس الاشياء
+
+698
+00:51:34,750 --> 00:51:38,750
+فلازم يكون اللي هي الصورة under T و under T تلدة
+
+699
+00:51:38,750 --> 00:51:42,640
+للعناصر اللي موجودة في الأصل زي بعضوالجديد بدي
+
+700
+00:51:42,640 --> 00:51:46,720
+أعرفه بطريقة معينة فالآن أنا بدأت في الـ X و إيه
+
+701
+00:51:46,720 --> 00:51:53,480
+الموجودة في ال domain of T closure إيش عملت؟ اللي
+
+702
+00:51:53,480 --> 00:51:56,840
+جاية TXN بتروح لمين لل X؟ و فدولة موجودة وين؟ في
+
+703
+00:51:56,840 --> 00:51:59,080
+ال domain of T يعني في الأصل الموجودة و معرفة عند
+
+704
+00:51:59,080 --> 00:52:07,460
+T ماشي الآن لما نمشيت أثبتتلكم أن TXN صورة هدولة
+
+705
+00:52:07,460 --> 00:52:15,710
+راحت لمين؟Y وين موجودة في الـ Y كابتنال
+
+706
+00:52:19,690 --> 00:52:26,230
+اللي من خلاله بدأ أقول عرفلي T تلدة لل X اللي
+
+707
+00:52:26,230 --> 00:52:30,370
+بدأتها عشان أشتغل على هذه بساوة مين Y اللي وجيتها
+
+708
+00:52:30,370 --> 00:52:35,090
+هنا إذا Y هذه مين لما عرفت T تلدة X بساوة Y هي Y
+
+709
+00:52:35,090 --> 00:52:41,010
+اللي نتجت من لما XN راحت لل X وطلعت T XN راحت
+
+710
+00:52:41,010 --> 00:52:45,630
+لإيشي هو الإيشي هذا اللي بدي أسميه T مين T X واضح
+
+711
+00:52:45,630 --> 00:52:55,800
+هذا T تلدة لل Xطيب إذا الآن define T tilde by T
+
+712
+00:52:55,800 --> 00:52:58,940
+tilde X بسوء Y we show that T tilde is well
+
+713
+00:52:58,940 --> 00:53:04,220
+defined الآن T tilde بتنثبت أنها إيش مالها well
+
+714
+00:53:04,220 --> 00:53:09,240
+defined الآن well defined هو خايف إيش؟ خايف إنه
+
+715
+00:53:09,240 --> 00:53:15,600
+إنتوا لما أخدنا X في ال domain T closureأنا بقول
+
+716
+00:53:15,600 --> 00:53:20,900
+لجيت في عندي XN راحة ل X و لجيتها و حطيتها روحتوا
+
+717
+00:53:20,900 --> 00:53:24,040
+انتوا و جبتوا واحدة تانية في عندك ممكن infinite
+
+718
+00:53:24,040 --> 00:53:26,880
+number of sequences يروح إلى مين لنفس ال limit و
+
+719
+00:53:26,880 --> 00:53:31,960
+هدولة من .. زي ما بتعرفوا مثلا لو نحكي في ذاك نص و
+
+720
+00:53:31,960 --> 00:53:35,240
+تلت و ربع إلى أخر هدولة كلهم بروح إلى مين للسفر
+
+721
+00:53:35,240 --> 00:53:40,760
+صح؟فلجيته نص و ربع و تمن الاخر بروح برضه لمين لصفر
+
+722
+00:53:40,760 --> 00:53:45,380
+واحد على اتنين أُس ثلاثة أُس ثلاثان واحد على اتنين
+
+723
+00:53:45,380 --> 00:53:49,480
+أُس أربعان كلهم بروح لصفر فبخافوا كل واحد أخده
+
+724
+00:53:49,480 --> 00:53:52,240
+sequence بتختلف عن التانية حتى لو كلنا أخدنا
+
+725
+00:53:52,240 --> 00:53:55,440
+sequences باختلفنا عن التانية هنلاجيه ال .. ال ..
+
+726
+00:53:55,440 --> 00:54:02,600
+ال .. ال ..لن يؤثر على اللي هو تعريفنا لخوف إن X
+
+727
+00:54:02,600 --> 00:54:06,780
+أنه تروح لل X أنا ديبتها و أنتوا عندكم Z أن تروح
+
+728
+00:54:06,780 --> 00:54:10,580
+لمين لل X بقولك بالرغم إن هيك ما تجلجوش هيكون
+
+729
+00:54:10,580 --> 00:54:14,800
+التعريف نفس التعريف شوفوا كيف .. شوفوا كيفالان
+
+730
+00:54:14,800 --> 00:54:20,640
+suppose that xn هدأت تعريفك او تعريفك xn بتروح
+
+731
+00:54:20,640 --> 00:54:26,620
+لمين لل x وانا جبت zn راحت لمين لل x وبدأت سلسل
+
+732
+00:54:26,620 --> 00:54:31,340
+اذا الان انا
+
+733
+00:54:31,340 --> 00:54:36,440
+سلسلت وجبت تي xn راحت لمين ل y وانت جبت تي zn
+
+734
+00:54:36,440 --> 00:54:39,860
+وراحت لمين ل y شرطة هتكون y شرطة و y أشمالين نفس
+
+735
+00:54:39,860 --> 00:54:45,550
+الاشي الدليلthen الان خدوا VM VM هتروح لل X مين ال
+
+736
+00:54:45,550 --> 00:54:49,670
+VM هو عبارة عن X واحد Z واحد X اتنين Z اتنين X
+
+737
+00:54:49,670 --> 00:54:52,990
+تلاتة Z تلاتة واضح ان هذه الطيارة وين ناحية ال X
+
+738
+00:54:52,990 --> 00:54:56,090
+ماشي الحال اذا هذه راحت لل X طب ما كل ال
+
+739
+00:54:56,090 --> 00:55:01,550
+subsequence اللي انت صار عندي TVM برضه converts
+
+740
+00:55:02,960 --> 00:55:07,560
+بنفس الأشياء VM مش راحت لل X حسب اللي حكيناه قبل
+
+741
+00:55:07,560 --> 00:55:12,120
+شوية هلاقي الـ TVM مين هتروح لصورة معينة اللي هي
+
+742
+00:55:12,120 --> 00:55:16,520
+TVM converts ده الـ Y اللي بيقول عنها الآن الـ TVM
+
+743
+00:55:16,520 --> 00:55:21,060
+ماهيها and the two subsequences TX and TZ and
+
+744
+00:55:21,060 --> 00:55:25,680
+هدولة subsequences من مين؟ من TVM و هذه راحت ل
+
+745
+00:55:25,680 --> 00:55:30,000
+limit و هدولة converts حسب الحديث الأولاني إذا كله
+
+746
+00:55:30,000 --> 00:55:33,350
+اللي هيروح لمين؟لنفس الـ Limit إن ده معناته إنه
+
+747
+00:55:33,350 --> 00:55:37,610
+TXN و TZN إيش مابتكم خدوا Sequences بتروح لل X
+
+748
+00:55:37,610 --> 00:55:43,330
+هنصل في النهاية TXN تبعتي و TZN تبعتكم و TWN تبعت
+
+749
+00:55:43,330 --> 00:55:47,290
+أي واحد اللي هي في الأصل كانت كله نراحل لل X هيكون
+
+750
+00:55:47,290 --> 00:55:51,470
+نقله نفس الـ T نفس ال Y اللي بتطلع Limit للـ TXN
+
+751
+00:55:51,470 --> 00:55:55,170
+أو TZN أو TWN إذا .. إذا صار عندنا تعريف Now
+
+752
+00:55:55,170 --> 00:55:59,650
+Definedإذاً hence T تلدة is well-defined in domain
+
+753
+00:55:59,650 --> 00:56:03,570
+of T a closure اللي عم نضل ليش ما نثبت؟ بدنا نثبت
+
+754
+00:56:03,570 --> 00:56:10,550
+أنه اللي هو ال linearity و بدنا نثبت اللي هي ال
+
+755
+00:56:10,550 --> 00:56:13,370
+boundedness و نثبت في النهاية نورم هذا بسوء نورم
+
+756
+00:56:13,370 --> 00:56:14,410
+هذا شوفوا الآن
+
+757
+00:56:18,840 --> 00:56:24,320
+Hence T tilde is well defined لان let X and X
+
+758
+00:56:24,320 --> 00:56:31,140
+prime be any elements in domain of T closure عشان
+
+759
+00:56:31,140 --> 00:56:34,640
+أثبت ال linearity والألفة بيه any scalar then
+
+760
+00:56:34,640 --> 00:56:37,480
+there are sequences مدام X في domain of T إذا
+
+761
+00:56:37,480 --> 00:56:45,840
+بلاجي sequence XNلل X و XN' لل X' حيث معايا XN
+
+762
+00:56:45,840 --> 00:56:51,380
+بتروح لل X و XN' بتروح لمين لل X' as above بالظبط
+
+763
+00:56:51,380 --> 00:56:55,340
+القالية التعريف اللي عارفينها هيكون ال TXN بيروح
+
+764
+00:56:55,340 --> 00:57:01,780
+لمين ل some Y في ال Y و TXN' هيروح لمين ل Y' هذا
+
+765
+00:57:01,780 --> 00:57:07,050
+قالية التعريفإذاً هيكون T تلدة لل X اللي هي ال Y
+
+766
+00:57:07,050 --> 00:57:13,610
+اللي روحت لل X و T تلدة X برايم إيش هتكون ال Y
+
+767
+00:57:13,610 --> 00:57:20,190
+برايم هذه الآن since T is a linear then T of Alpha
+
+768
+00:57:20,190 --> 00:57:25,400
+X N زائد X N برايم إيش هتساوي؟الـ T العصرية الـ T
+
+769
+00:57:25,400 --> 00:57:28,180
+العصرية اللي أنا بشتغلها دي بساوة Alpha T X N زي
+
+770
+00:57:28,180 --> 00:57:32,320
+Alpha T X N Prime هدول حيروح لمين Alpha T X N زي T
+
+771
+00:57:32,320 --> 00:57:36,400
+X N Prime الـ T X N هتروح لمين للـ Y و T X N Prime
+
+772
+00:57:36,400 --> 00:57:39,820
+هتروح لمين للـ Y Prime إذا هذا كله راح لمين للـ
+
+773
+00:57:39,820 --> 00:57:45,200
+Alpha I زي Y Prime يعني بمعنى آخر لما Alpha X N زي
+
+774
+00:57:45,200 --> 00:57:50,620
+X M Prime راحت للـ Alpha X زي X Prime الـ T تبعته
+
+775
+00:57:50,620 --> 00:57:55,630
+راحت لهذهإذن هذه هي عبارة عن الـ T تلدة للي قلتن
+
+776
+00:57:55,630 --> 00:58:00,550
+حسب التعريف بمعنى but alpha xn زائد xn prime هذه
+
+777
+00:58:00,550 --> 00:58:04,110
+مش هي بتقدر تتعريف بتروح لل alpha x زايد x prime
+
+778
+00:58:04,110 --> 00:58:08,850
+then by the definition of T تلدة T of هذه اللي
+
+779
+00:58:08,850 --> 00:58:14,080
+راحاتي لها هذه بتساوي سور اللي هواللي راح اتيلها
+
+780
+00:58:14,080 --> 00:58:18,180
+صورة هادى مين اللي هي صورة هادى؟ راحت لمين؟ للـ α
+
+781
+00:58:18,180 --> 00:58:23,460
+y زائد y' إذن هادى بيصير T of α T تلدة of α x زائد
+
+782
+00:58:23,460 --> 00:58:27,420
+x' بيساوي α y زائد y' اللي هي α y اللي هي مين؟ هي
+
+783
+00:58:27,420 --> 00:58:33,040
+α T تلدة x والـ y' اللي هي T تلدة x' إذن فعلا طلعت
+
+784
+00:58:33,040 --> 00:58:37,600
+عندي T تلدة إيش ما لها is linear لذا مفتاح الحل هو
+
+785
+00:58:37,600 --> 00:58:42,720
+هذا هذا مفتاح الشغل كله إنه كيف أنا عرفت المفروض
+
+786
+00:58:42,720 --> 00:58:47,890
+فاهمينمش فاهمين عدوها هتلاقي الكلام واضح انا بشر
+
+787
+00:58:47,890 --> 00:58:57,390
+اصلا ما يكون الكلام مش واضح و بعيده بعيده
+
+788
+00:58:57,390 --> 00:59:02,770
+بطريقة تصير أوضح لكن بعتقد انه واضح الان
+
+789
+00:59:03,950 --> 00:59:08,150
+أثبتنا ان T is linear الان نثبت لكم ان T تلد اصلا
+
+790
+00:59:08,150 --> 00:59:12,310
+extension ايش معناه extension ان هي بتساوي الأصل
+
+791
+00:59:12,310 --> 00:59:16,920
+في الأصليعني T تلدة على ال domain of T هي نفس T و
+
+792
+00:59:16,920 --> 00:59:19,480
+لا بتبطئ ال extension عشواء معايا ده لتانية أصلا
+
+793
+00:59:19,480 --> 00:59:22,760
+أما مادام extension مفهومها أنها بدها تبقى على
+
+794
+00:59:22,760 --> 00:59:26,900
+الأصل زي ما هو و تزيد على زيادة بطريقة تلائم اللي
+
+795
+00:59:26,900 --> 00:59:30,320
+موجود أو تحقق هدف إذا كان بديه هدفانة الهدفانة أن
+
+796
+00:59:30,320 --> 00:59:33,540
+تكون T تلدة normal بيساوي normal T كل هذا حجبناه
+
+797
+00:59:33,540 --> 00:59:38,960
+مرة واحدة الان but T تلدة لل X أشهر بتساوي T X for
+
+798
+00:59:38,960 --> 00:59:44,620
+all X in every domain من جلك becauseالـ X عندى X
+
+799
+00:59:44,620 --> 00:59:48,440
+هي بتروح للـ X يعني الـ sequence X X X X بتروح
+
+800
+00:59:48,440 --> 00:59:52,100
+لمين للـ X هاي الـ sequence اللى عندى ماشي بتروح
+
+801
+00:59:52,100 --> 01:00:00,280
+لمين للـ X و الـ TX الـ TX هتروح لمين للـ TX ليش
+
+802
+01:00:00,280 --> 01:00:04,660
+لأن الـ X هادى من وين دي يعني من ال domain of T و
+
+803
+01:00:04,660 --> 01:00:09,420
+ال domain of TT continuous عنده أه إذا أكيد هيكون
+
+804
+01:00:09,420 --> 01:00:13,930
+مش boundedما دام باوندد يا جماعة هال gate فيه عندي
+
+805
+01:00:13,930 --> 01:00:18,310
+sequence of elements كله انثباتات X بيروح لمين لل
+
+806
+01:00:18,310 --> 01:00:25,760
+X و ال X وين موجودة في domain ال Tو domain الـ T،
+
+807
+01:00:25,760 --> 01:00:29,340
+T is continuous عنده مدام .. يعني بدل ما أقول Xn
+
+808
+01:00:29,340 --> 01:00:33,980
+بتروح للـ Xn للـ X الـ Xn هذه أشمع لل X واحد X الـ
+
+809
+01:00:33,980 --> 01:00:37,420
+X اتنين X الـ X ثلاثة X والـ X أربعة X والـ X خمسة
+
+810
+01:00:37,420 --> 01:00:41,940
+X يعني sequence of كل مين X X X هدورها بيروح لمين؟
+
+811
+01:00:41,940 --> 01:00:47,080
+للـ X ماشي الحال الآن أكيد مزامة الـ X موجودة في
+
+812
+01:00:47,080 --> 01:00:54,990
+domain of T هيكون TXn بيروح لمين؟ للـ TXهذه اللي
+
+813
+01:00:54,990 --> 01:01:00,150
+أنا بعرف الـ T تلدة بساوي هذا اللي طلع عندى اللي
+
+814
+01:01:00,150 --> 01:01:06,670
+كنت أسميها Y اللي هي T تلدة لل X هيساومين TX الـ N
+
+815
+01:01:06,670 --> 01:01:09,930
+TXN هي في الواقع Xات كلها يعني أه فعشانك بقول X
+
+816
+01:01:09,930 --> 01:01:14,310
+بتروح لل X إذا TX بتروح ل TX ومن ثم T تلدة اللي
+
+817
+01:01:14,310 --> 01:01:21,760
+بعرفها لل X هي TXN لما تروح لرقم هو اسمه TXهذا
+
+818
+01:01:21,760 --> 01:01:26,800
+بصوتين اذا اكيد اكيد اكيد so T تلده is a linear
+
+819
+01:01:26,800 --> 01:01:32,300
+extension of T وطلع فوق خلّينا ننهي القمر ان نثبت
+
+820
+01:01:32,300 --> 01:01:38,500
+انها bounded ومن ثم نثبت اللي هو norm T هو نفسه
+
+821
+01:01:38,500 --> 01:01:44,440
+norm T تلده وركزوا في ما نتحدث به طيب صلى على
+
+822
+01:01:44,440 --> 01:01:48,880
+النبعخدوا الآن IX في domain الـ T closure خلاص صار
+
+823
+01:01:48,880 --> 01:01:54,070
+domain هو هذا الـ T تلدThere is a sequence xn of
+
+824
+01:01:54,070 --> 01:01:57,830
+elements in D of T such that xn بتروح لمين للإكس
+
+825
+01:01:57,830 --> 01:02:02,650
+هذا اللي هو مفتاح الحلو ومفتاح التعريف xn بتروح
+
+826
+01:02:02,650 --> 01:02:06,670
+للإكس وزي ما عملنا فوق هيطلع T xn بتروح لمين للواي
+
+827
+01:02:06,670 --> 01:02:14,310
+و هتكون T تلدة للإكس هو مين الواي and T تلدة للإكس
+
+828
+01:02:14,310 --> 01:02:19,630
+هتكون يش من هي بتساوي Yالان شوف كيف بدي اصل ل T
+
+829
+01:02:19,630 --> 01:02:25,190
+تلده is bounded يعني بدي اثبتلكم ان T تلده T تلده
+
+830
+01:02:25,190 --> 01:02:35,290
+is bounded بمعنى بمعنى
+
+831
+01:02:35,290 --> 01:02:41,950
+بدي اثبت norm T تلده X أصغر لو سوى C في norm X
+
+832
+01:02:45,110 --> 01:02:48,570
+هو في الواقع حثبتلكم أن T تلدة لل X أصغر أشهر هو C
+
+833
+01:02:48,570 --> 01:02:55,690
+اللي هي نورم ال T في نورم ال X طيب تشوف صلوا على
+
+834
+01:02:55,690 --> 01:03:01,290
+النبي عليه الصلاة والسلام احسبولي نورم ال T Xأكيد
+
+835
+01:03:01,290 --> 01:03:04,890
+هيكون تـis bounded أصغر يساوي نورم الـT في نورم
+
+836
+01:03:04,890 --> 01:03:11,090
+الـMain الـXN for all mean N الـNorm الـT
+
+837
+01:03:11,090 --> 01:03:13,490
+continuous ليش معناه continuous بدخل الـlimit جوا
+
+838
+01:03:13,490 --> 01:03:17,190
+و بطلع برا زي ما بده ماشي هنا معناته أن هو نورم
+
+839
+01:03:17,190 --> 01:03:20,850
+الـT continuous letting N بتروح لـinfinity and
+
+840
+01:03:20,850 --> 01:03:25,650
+using the continuity of the norm to getالان خدوا
+
+841
+01:03:25,650 --> 01:03:30,910
+الان norm تل دل ال X من جهة أخرى ايش هيساوي؟ norm
+
+842
+01:03:30,910 --> 01:03:34,470
+ال Y مش عارفين ماحنا قولنا ال T تل د X مين هي؟
+
+843
+01:03:34,470 --> 01:03:38,090
+بيساوي .. خدوا norm هذي بيساوي norm هذي ماشي؟ Y
+
+844
+01:03:38,090 --> 01:03:45,010
+ساوي الان norm ال Y اللي هو عبارة عن limit ل norm
+
+845
+01:03:45,010 --> 01:03:50,390
+T X N مظبوط؟ ال T X N بيروح لمين؟الـ T X N بتروح
+
+846
+01:03:50,390 --> 01:03:54,710
+لمين للـ Y إذا الـ limit هذا بروح لمين لـ Normal Y
+
+847
+01:03:54,710 --> 01:04:04,650
+الـ Y بساوة T X N صح Normal Y بساوة norm هذا صح
+
+848
+01:04:04,650 --> 01:04:10,370
+إذا خدوا ال limit للجهتين بطلع Normal Y limit
+
+849
+01:04:10,370 --> 01:04:13,550
+بساوة
+
+850
+01:04:13,550 --> 01:04:21,800
+limit norm T X Nلأن ال limit بتنزل من جواه ال norm
+
+851
+01:04:21,800 --> 01:04:28,260
+لأن انا بعرف y بساوي limit ال T xn صح ولا لأ norm
+
+852
+01:04:28,260 --> 01:04:32,600
+هذه بساوي norm هذه طلعيني ال limit برا لإنها
+
+853
+01:04:32,600 --> 01:04:34,860
+continuous بيصير norm ال y بساوي limit norm ال T
+
+854
+01:04:34,860 --> 01:04:39,820
+xn إذا طلع عندي norm ال y automatic بساوي limit
+
+855
+01:04:39,820 --> 01:04:43,340
+norm ال T xn نيجي الآن norm ال T xn أصلا يساوي
+
+856
+01:04:43,340 --> 01:04:46,170
+norm ال T في norm ال x صح؟إذاً limit هذا أصغر شهر
+
+857
+01:04:46,170 --> 01:04:49,130
+و limit هذه إذاً صار عيدي limit هذا أصغر شهر و
+
+858
+01:04:49,130 --> 01:04:52,050
+limit هذه في هذه طب ما هي constant بالنسبة لل
+
+859
+01:04:52,050 --> 01:04:55,650
+limit اللي بتطلع برا بيصير limit norm ال xn limit
+
+860
+01:04:55,650 --> 01:04:59,570
+norm ال xn مع أن ما أقول ال xn بتروح لل x و ال
+
+861
+01:04:59,570 --> 01:05:03,410
+norm continuous إذاً limit norm ال xn هو عبارة عن
+
+862
+01:05:03,410 --> 01:05:08,290
+norm ال x إذاً صار عندي norm ال T في norm ال x
+
+863
+01:05:08,290 --> 01:05:15,660
+اللي حصلته norm ال T تلدة لل x انتبهنأصغر أو يساوي
+
+864
+01:05:15,660 --> 01:05:20,520
+نورم الـT في نورم الـX نورم الـT هو الـC إذا صارت
+
+865
+01:05:20,520 --> 01:05:25,340
+الـT تلدة is bounded ومش هيك ونورم الـT تلدة أصغر
+
+866
+01:05:25,340 --> 01:05:30,700
+يساوي مين؟ نورم الـT ليش؟ لأنه انا اثبتت نورمالـ T
+
+867
+01:05:30,700 --> 01:05:35,000
+تلدة X أصغر أو شويه نورم الـ T في نورم الـ X يعني
+
+868
+01:05:35,000 --> 01:05:37,300
+على نورم الـ X X لا تشويه شويه تلد أصغر أو شويه
+
+869
+01:05:37,300 --> 01:05:39,980
+هدى لكل X في دمية الـ T معدى الـ Zero خدوا الـ
+
+870
+01:05:39,980 --> 01:05:45,240
+Supremum بيصير أصغر أو شويه هذا معناته أنه هذا الـ
+
+871
+01:05:45,240 --> 01:05:49,220
+Supremum إيش بيساوي نورم الـ T تلدة صارت نورم الـ
+
+872
+01:05:49,220 --> 01:05:53,980
+T تلدة أصغر أو شويه نورم الـ T العكس سهل العكس سهل
+
+873
+01:05:53,980 --> 01:05:58,920
+و شريعhowever norm of T تلدة عارفين هو ايش بيساوي
+
+874
+01:05:58,920 --> 01:06:03,360
+احنا supremum ل norm of T تلدة X X في domain T
+
+875
+01:06:03,360 --> 01:06:06,600
+تبعها closure such that norm of X بيساوي واحد سهل
+
+876
+01:06:06,600 --> 01:06:08,300
+اللي لنا نشتغل على norm of X بيساوي واحد من زمنا
+
+877
+01:06:08,300 --> 01:06:13,650
+التكافئة في قادة الان هذه الست هذه الستأكبر من ال
+
+878
+01:06:13,650 --> 01:06:17,570
+6 اللي X فيه مالها في domain الـ T وحنا بنعرف في
+
+879
+01:06:17,570 --> 01:06:21,710
+domain الـ T norm الـ T X هو نفسه norm الـ T تلد X
+
+880
+01:06:21,710 --> 01:06:24,710
+لأنه على domain الـ T الـ T تلد و الـ T زي بعض مش
+
+881
+01:06:24,710 --> 01:06:29,810
+exception إذا هذه المجموعة جزئية من هذهأه، إذا
+
+882
+01:06:29,810 --> 01:06:32,790
+أكيد الـ Supremum على الكبير أكبر أو يساوي الـ
+
+883
+01:06:32,790 --> 01:06:36,090
+Supremum على الأزهر هذا الـ Supremum هو عبارة عن
+
+884
+01:06:36,090 --> 01:06:40,230
+Norm of T يعني بمعنى أخر أثبتنا Norm of T تلدة
+
+885
+01:06:40,230 --> 01:06:45,290
+أكبر أو يساوي Norm من الـ T ومن الأصل Norm of T
+
+886
+01:06:45,290 --> 01:06:47,750
+تلدة أزهر يساوي Norm of T همهالة أصلا الصعوبة في
+
+887
+01:06:47,750 --> 01:06:50,370
+الحل، هذا كسيلة بيطلع Norm of T تلدة هو بيساوي
+
+888
+01:06:50,370 --> 01:06:55,350
+Norm of T و هكذا بالانهيأ اللي هو الـ Section هذا
+
+889
+01:06:55,350 --> 01:06:56,670
+و إلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/KVXWicAzB2A_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/KVXWicAzB2A_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..24b35de70ef870e93d7017b02db88f02f1b73ecc
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/KVXWicAzB2A_raw.srt
@@ -0,0 +1,3568 @@
+1
+00:00:05,210 --> 00:00:07,970
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,970 --> 00:00:11,030
+والصلاة والسلام على سيد المرسلين سيدنا محمد عليه
+
+3
+00:00:11,030 --> 00:00:15,530
+والصحابي الأجمعين هذه هي المحاضرة رقم 13 مساق
+
+4
+00:00:15,530 --> 00:00:19,670
+تحليل اقتراني أو تحليل دالي طلاب طالبات الجامعة
+
+5
+00:00:19,670 --> 00:00:25,240
+الإسلامية ماجستير رياضيةوصلنا لعند الاتنين سبعة
+
+6
+00:00:25,240 --> 00:00:28,340
+اللي هو تحت عنوان bounded and continuous linear
+
+7
+00:00:28,340 --> 00:00:33,660
+operators لنتعرف على مفهوم اليوم مفهوم مهم وكمان
+
+8
+00:00:33,660 --> 00:00:38,660
+اللي هو بعض خواصه أو البعض النظريات اللي هتكون
+
+9
+00:00:38,660 --> 00:00:42,420
+ملازمانة على طول الفصل اللي هي بما يتعلق شو معنات
+
+10
+00:00:42,420 --> 00:00:46,770
+bounded linear operatorsالـ Bounded Linear
+
+11
+00:00:46,770 --> 00:00:50,110
+Operator احنا عرفناه المرة الماضية وعرفناه كمان في
+
+12
+00:00:50,110 --> 00:00:53,190
+الجبر الخطوة و بنعرفه بالاصل اللي هنعرفه شو معناه
+
+13
+00:00:53,190 --> 00:00:56,230
+Bounded Linear Operator؟ وإيش معناه الـ
+
+14
+00:00:56,230 --> 00:00:58,430
+Continuity؟ طبعا احنا الـ Continuity بنعرفها شو
+
+15
+00:00:58,430 --> 00:01:01,670
+معناه الـ Continuity؟ بنعرفها بدنا نربط شو علاقة
+
+16
+00:01:01,670 --> 00:01:04,830
+الـ Continuous Linear Operator بالـ Bounded Linear
+
+17
+00:01:04,830 --> 00:01:07,610
+Operator وخلينا نشوف هذا الكلام بنجاوب عليه من
+
+18
+00:01:07,610 --> 00:01:12,070
+خلال اللي هو حديثنا اليوم إن شاء اللهالـ
+
+19
+00:01:12,070 --> 00:01:15,330
+Definition الأول لو كان عندي X و Y normed spaces
+
+20
+00:01:15,330 --> 00:01:21,150
+التنين على نفس ال field التنين ياريال يتنين أشمال
+
+21
+00:01:21,150 --> 00:01:25,290
+وكمبليكس و المرة الفاترة قلنا ليش لأن let domain T
+
+22
+00:01:25,290 --> 00:01:29,010
+من domain of T لعند Y بيقى linear operator و ال
+
+23
+00:01:29,010 --> 00:01:33,390
+domain of T ده جزء من من اللي هو normed space X
+
+24
+00:01:33,390 --> 00:01:38,080
+طبعا X عليها نورمها و Y عليها نورمهاThe operator T
+
+25
+00:01:38,080 --> 00:01:41,480
+is said to be bounded منقول عنه bounded linear
+
+26
+00:01:41,480 --> 00:01:45,660
+operator هذا اعرفنا على مين؟ على linear operator
+
+27
+00:01:45,660 --> 00:01:50,920
+منقول عنه bounded if there is a number c such that
+
+28
+00:01:50,920 --> 00:01:56,200
+for all x element in domain of T norm TX أصغر
+
+29
+00:01:56,200 --> 00:02:03,380
+يساوي في مين؟ C في norm LX إذن الآن منقول عن Tمن
+
+30
+00:02:03,380 --> 00:02:08,560
+domain of T جزء من X طبعا لعند Y انه bounded انه
+
+31
+00:02:08,560 --> 00:02:13,900
+يتحقق TX normal طبعا هذا normal موجود في Y أصغر أو
+
+32
+00:02:13,900 --> 00:02:18,560
+ساوى C في norm ال X ال X طبعا هو الموجود في domain
+
+33
+00:02:18,560 --> 00:02:22,780
+of T أو ال norm الموجود على اللي هي ال Xاللي كان
+
+34
+00:02:22,780 --> 00:02:26,320
+هذا الكلام يكون صحيح لكل x و m موجودة في ال domain
+
+35
+00:02:26,320 --> 00:02:29,340
+of D إذا كان هذا صحيح معناته أنه على طول بنقول عن
+
+36
+00:02:29,340 --> 00:02:34,700
+ال T إيش ما لها is a bounded linear operator طبعا
+
+37
+00:02:34,700 --> 00:02:37,800
+هذا ال bounded linear operator بهذا التعريف والاسم
+
+38
+00:02:37,800 --> 00:02:41,760
+نفسه is standard كل الناس بتستخدمه وفي نفس الوقت
+
+39
+00:02:41,760 --> 00:02:46,170
+برضه ال bounded functionالـ bounded as a function
+
+40
+00:02:46,170 --> 00:02:51,050
+برضه standard إذا كانت T بعتبرها as a function من
+
+41
+00:02:51,050 --> 00:02:54,930
+domain of T أو من اللي هي لعند X بقول a bounded
+
+42
+00:02:54,930 --> 00:02:58,590
+function أو لعند Y بنقول a bounded function مقصود
+
+43
+00:02:58,590 --> 00:03:01,810
+فيها في كل ال functions سواء كان اللي هو عند A
+
+44
+00:03:01,810 --> 00:03:05,070
+اللي هي هذا known space أو vector space أو أو
+
+45
+00:03:05,070 --> 00:03:08,030
+الأخرين المهم يكون فيه topology بنقول عنه bounded
+
+46
+00:03:08,030 --> 00:03:13,470
+إذا كان T Xabsolute value او norm او اللي هو اصغر
+
+47
+00:03:13,470 --> 00:03:18,570
+او يساوي اللي هو c for every x element in main in
+
+48
+00:03:18,570 --> 00:03:23,310
+domain of D هذا معناته bounded as a function احنا
+
+49
+00:03:23,310 --> 00:03:27,830
+الآن بنا .. وهذا standardالناس بتستعمله وهذا ال
+
+50
+00:03:27,830 --> 00:03:31,290
+standard الناس بتستعمله الان احنا ال focusing
+
+51
+00:03:31,290 --> 00:03:35,850
+هنعمله على مين على ال bounded linear operator هذا
+
+52
+00:03:35,850 --> 00:03:39,810
+معناته ايش ماله is a bounded linear operator هذي
+
+53
+00:03:39,810 --> 00:03:42,690
+is a bounded as a function عشان ما يشيرش confusion
+
+54
+00:03:42,690 --> 00:03:49,190
+عند الناس او اللي هو اي التباس طيبنجي الآن نشوف
+
+55
+00:03:49,190 --> 00:03:52,710
+ايش الملاحظة اللي .. الملاحظات اللي بحكيها Notes
+
+56
+00:03:52,710 --> 00:03:56,590
+الملاحظة الأولى The smallest c such that the above
+
+57
+00:03:56,590 --> 00:04:00,750
+inequality holds for all and zero excellent in
+
+58
+00:04:00,750 --> 00:04:05,590
+domain of T is defined as norm of T ايش بيقول؟
+
+59
+00:04:05,590 --> 00:04:09,990
+بيقول انت مش بتقول bounded إذا لقينا c بحيث norm
+
+60
+00:04:09,990 --> 00:04:14,740
+of T X أصغر شوه مين؟ C في مين؟ في norm of Xالأن
+
+61
+00:04:14,740 --> 00:04:19,340
+أصغر واحدة في الـCs هذولة أصغر واحدة في الـCs اللي
+
+62
+00:04:19,340 --> 00:04:24,560
+هو بنسميه إيش منها نورمين الـT طب مين أصغر واحدة
+
+63
+00:04:24,560 --> 00:04:29,900
+في الـCs هذه؟ الآن معناته إن نورم الـTX على نورم
+
+64
+00:04:29,900 --> 00:04:33,240
+الـX provided that النورم لا يساوي سفر أصغر أو
+
+65
+00:04:33,240 --> 00:04:37,140
+يساوي C بدي أصغر واحدة في الـCs هذه هذول الـCs
+
+66
+00:04:37,140 --> 00:04:40,800
+كلهم upper bound لهذه الستأصغر واحدة فين؟ إيش
+
+67
+00:04:40,800 --> 00:04:44,260
+هتكون؟ The least upper bound، اللي هو مين؟ بمعنى
+
+68
+00:04:44,260 --> 00:04:51,500
+آخر الـ Supremum لـ Normal T X ع Normal X Such
+
+69
+00:04:51,500 --> 00:04:56,940
+that X element in domain of T ناقص مين؟ السفر هذا
+
+70
+00:04:56,940 --> 00:05:00,420
+اللي هو الـ Supremum اللي هيطلع عن مين هو؟ عبارة
+
+71
+00:05:00,420 --> 00:05:08,270
+عن مين؟ Normal Tالآن إذا كان domain الـ T بيساوي 0
+
+72
+00:05:08,270 --> 00:05:11,850
+يعني مافيش فيلة غير الـ 0 domain الـ T الـ 0 إذا
+
+73
+00:05:11,850 --> 00:05:15,170
+أي function بتعملها عليها تنجل الـ 0 لميلا الـ 0
+
+74
+00:05:15,170 --> 00:05:19,610
+عشان تكون linear إذا حيكون بنعرف في هذه الحالة
+
+75
+00:05:19,610 --> 00:05:23,610
+نورم الـ T إيش بيساوي بيساوي 0 أما أي linear
+
+76
+00:05:23,610 --> 00:05:28,470
+operator domainه لا يساوي 0 على طول norm الـ T
+
+77
+00:05:28,470 --> 00:05:33,250
+تبعته اللي هي ال operatorالنوم لمين لـ Operator
+
+78
+00:05:33,250 --> 00:05:38,510
+اللي هو بيساوي هذا الكلامهذا اللي عندي نورم الـ T
+
+79
+00:05:38,510 --> 00:05:43,210
+أنا مسميه نورم الـ T هو في الواقع هيحقق شروط
+
+80
+00:05:43,210 --> 00:05:47,850
+النورم كلها عشان هيك اسمه بنسميه نورم فهو فعلاً
+
+81
+00:05:47,850 --> 00:05:52,830
+هيعمل نورم نورم عالمين يعني الآن احنا و كإني جاعد
+
+82
+00:05:52,830 --> 00:05:56,590
+انا ما احنا كنا نعمل نورم نورم احنا عالمين احنا
+
+83
+00:05:56,590 --> 00:06:02,760
+ناخد X as a vector space و نعمل عليه مينnorm طب
+
+84
+00:06:02,760 --> 00:06:06,040
+هذا ال norm على مين؟ أنا و كإني بقول the
+
+85
+00:06:06,040 --> 00:06:12,540
+collection of all bounded linear operators بعرف
+
+86
+00:06:12,540 --> 00:06:15,960
+عليه ال norm المهم الآن طبعا هذا جايين الكلام الآن
+
+87
+00:06:15,960 --> 00:06:20,120
+هذا norm ال T بعرف واش بساوي بساوي المقدار هذا طيب
+
+88
+00:06:20,120 --> 00:06:23,220
+from
+
+89
+00:06:23,220 --> 00:06:27,800
+the definition above من التعريف above norm ال T X
+
+90
+00:06:30,910 --> 00:06:34,830
+أحنا بنقول أصغر أو يساوي C في ميان في normal X
+
+91
+00:06:34,830 --> 00:06:40,950
+نورم ال T واحدة منهم مش ال T the smallest one
+
+92
+00:06:40,950 --> 00:06:47,590
+هيكون عندي نورم ال T X أصغر أو يساوي نورم ال T في
+
+93
+00:06:47,590 --> 00:06:53,850
+ميانفى norm ال X ومن هنا كمان اللى هو norm ال T فى
+
+94
+00:06:53,850 --> 00:06:58,190
+X على norm ال X هيكون اللى هو طبيعى أصغر أو سوى
+
+95
+00:06:58,190 --> 00:07:01,930
+مين norm ال T فأدور بالطرفين فبطلع norm ال T X
+
+96
+00:07:01,930 --> 00:07:05,070
+أصغر أو سوى C اللى هو norm ال T فى norm ال X أي
+
+97
+00:07:05,070 --> 00:07:10,990
+سؤال؟ طيب الآن نيجينا اللمّة الأولى اطلع لفوق
+
+98
+00:07:10,990 --> 00:07:19,790
+بالله اللمّة الأولى إيش بتقول اللمّة؟لما بتقول
+
+99
+00:07:19,790 --> 00:07:24,450
+مرايالي انه
+
+100
+00:07:24,450 --> 00:07:29,750
+let T من domain of T لعند ال while اللي قلت قبل
+
+101
+00:07:29,750 --> 00:07:36,940
+شوية be bounded linear operatorثم نورم الـ T
+
+102
+00:07:36,940 --> 00:07:40,660
+بيساوي supremum لـ T X X element in domain و T
+
+103
+00:07:40,660 --> 00:07:45,500
+وخدت مين الآن على نورمك لـ X بس إيش اللي بيساوي؟
+
+104
+00:07:45,500 --> 00:07:52,360
+واحد، بتدعي .. بتدعي إن هذا هيعمل لي نورم و T
+
+105
+00:07:52,360 --> 00:07:56,720
+هيكون satisfied من واحد عند أربعة يعني و كإن بيقول
+
+106
+00:07:56,720 --> 00:08:04,310
+لي في هذه النظرية إن نورم الـ T بيساوي supremumلـ
+
+107
+00:08:04,310 --> 00:08:10,930
+Tx as a norm such that norm ال X بتسوي واحد و ال X
+
+108
+00:08:10,930 --> 00:08:19,810
+في domain ال T يكافئ ال supremum لnorm ال Tx على
+
+109
+00:08:19,810 --> 00:08:28,830
+norm ال X such that X element in domain of TX
+
+110
+00:08:28,830 --> 00:08:33,130
+element in domain of T وإثباته مش صعب لأن نثبت أنه
+
+111
+00:08:33,130 --> 00:08:36,610
+norm بده يحقق الأربع شروط والأربع شروط يعني اللي
+
+112
+00:08:36,610 --> 00:08:39,850
+هي سهلة يعني مافيش فيها إشكالية الآن إنه هذا
+
+113
+00:08:39,850 --> 00:08:47,030
+بيساوي هذا برضه اللي هو عنده لو أخدنا أي X في في
+
+114
+00:08:47,030 --> 00:08:51,610
+domain T هنلاقي اللي هو ال X ع نورمها موجود في
+
+115
+00:08:51,610 --> 00:08:55,480
+domain Tفلو سميتها y بيصير normal y هنا بيساوي
+
+116
+00:08:55,480 --> 00:08:58,280
+واحد و عليها بتشتغلوا فبتقولوا هذا اللي هو أصغر
+
+117
+00:08:58,280 --> 00:09:00,980
+يساوي هذا و هذا أصغر يساوي هذا و بطلع اللي هي
+
+118
+00:09:00,980 --> 00:09:04,060
+المساوية المهم exercise عشان هي كانت سهلة بقولكم
+
+119
+00:09:04,060 --> 00:09:11,770
+طيبالنهائي هو الـ Example الـ Examples لن تثبت أن
+
+120
+00:09:11,770 --> 00:09:17,250
+كلها مرتبطة لأن ما سيثبتهم قدام الـ Boundedness
+
+121
+00:09:17,250 --> 00:09:20,410
+سيغنون عن هؤلاء الذين يشعرون أن هؤلاء سهلات
+
+122
+00:09:20,410 --> 00:09:25,050
+بالنسبة له وسيكونون على طول بالثبتين الآن Zero
+
+123
+00:09:25,050 --> 00:09:29,940
+Operatorواحد من أمثلة اللي هو الـ Bounded Linear
+
+124
+00:09:29,940 --> 00:09:33,580
+Operator ايش الـ Zero Operator؟ الـ Zero Operator
+
+125
+00:09:33,580 --> 00:09:37,480
+زي Zero من X لعند Y on a normed space X is a
+
+126
+00:09:37,480 --> 00:09:41,320
+Bounded Linear Operator وإيش اللي هو الـ Zero
+
+127
+00:09:41,320 --> 00:09:44,620
+Operator؟ بياخد كل Element لـ 100 للصفراللي هو هذا
+
+128
+00:09:44,620 --> 00:09:49,560
+norm وإيش هيطلع عبارة عن سفر bounded أو linear ال
+
+129
+00:09:49,560 --> 00:09:52,640
+linear اللي احنا حكينا المرة الفاتة عن بعض الأمثلة
+
+130
+00:09:52,640 --> 00:09:56,680
+وهو اثباته انه linear سهل واثباته bounded برضه
+
+131
+00:09:56,680 --> 00:10:02,450
+مافيش فيه إشكاليةاللي بعده خلّيني أشوف المثال اللي
+
+132
+00:10:02,450 --> 00:10:07,070
+بعده let x اللي بنسميه differentiation operator
+
+133
+00:10:07,070 --> 00:10:10,230
+differentiation operator خلّيني أبرهنه و أريكم
+
+134
+00:10:10,230 --> 00:10:15,090
+أمور البرهان سهلا ان شاء الله البرهان بقصده اللي
+
+135
+00:10:15,090 --> 00:10:19,710
+هو برهان اللي هي أن ال operator اللي بنعرضه أنه
+
+136
+00:10:19,710 --> 00:10:22,330
+bounded هناخدكم عدة أمثلة الآن و نبرهنها
+
+137
+00:10:23,470 --> 00:10:27,310
+differentiation operator اللي هو let x be a norm
+
+138
+00:10:27,310 --> 00:10:30,670
+of the space of all polynomials أخدنا مين؟ اللي هو
+
+139
+00:10:30,670 --> 00:10:35,530
+space of all polynomials on الفترة 0 و 1 و ال norm
+
+140
+00:10:35,530 --> 00:10:38,490
+ال x إيش بناخده؟ اللي هو ال maximum اللي أخدناه
+
+141
+00:10:38,490 --> 00:10:41,330
+قبل هيك هاد عملنا norm of the space عمليا اللي هو
+
+142
+00:10:41,330 --> 00:10:44,530
+اللي بيساوي طبعا هذه أخدت أنا مين؟ هي norm of the
+
+143
+00:10:44,530 --> 00:10:48,050
+space of all polynomials إذا بتذكر و أثبتنا إن هذا
+
+144
+00:10:48,050 --> 00:10:52,030
+مش completeالان with norm ال X بيساوي ال maximum
+
+145
+00:10:52,030 --> 00:10:54,750
+ال absolute value X of T T element in J the
+
+146
+00:10:54,750 --> 00:10:58,150
+differential operator T من X لعندي X ده عارف
+
+147
+00:10:58,150 --> 00:11:02,190
+operator بياخد من X ل X ايش بيسوي بيجي اللي هو
+
+148
+00:11:02,190 --> 00:11:07,510
+بياخد اي element هنا الى تفاضله يعني بياخد اي T X
+
+149
+00:11:07,510 --> 00:11:10,790
+of T ال X of T هدي يشملها polynomial ايش بيساوي
+
+150
+00:11:10,790 --> 00:11:16,050
+صورتها X prime of Tis an unbounded linear operator
+
+151
+00:11:16,050 --> 00:11:19,650
+مثلًا على مين؟ على unbounded linear operator نحن
+
+152
+00:11:19,650 --> 00:11:22,750
+ناخده لكم برضه على bounded linear operator شوفوا
+
+153
+00:11:22,750 --> 00:11:25,850
+الآن كيف نثبت أنه unbounded linear operator ال
+
+154
+00:11:25,850 --> 00:11:31,630
+linearity سهلة لو أثبتوها لحالكم بتنفع عشان
+
+155
+00:11:31,630 --> 00:11:37,150
+أورجيكم أنه أنا فعلاً لما أقولكم سهلة هي سهلة خدوا
+
+156
+00:11:37,150 --> 00:11:40,330
+الآن for all x y element in x and all scalars
+
+157
+00:11:40,330 --> 00:11:44,200
+alpha بدأ أثبتلكم أنها linearأيش اللي هي T of α X
+
+158
+00:11:44,200 --> 00:11:48,480
+زي Y بدأت بتبت سواء α T X زي الـ T Y هذا مناط
+
+159
+00:11:48,480 --> 00:11:53,260
+اللينيه شوفوا الآن T of α X زي Y شو معناته هذه
+
+160
+00:11:53,260 --> 00:11:58,300
+بترسل إلى α X زي Y prime of مين لأن هذه عبارة عن
+
+161
+00:11:58,300 --> 00:12:00,820
+بلونوميا لو هذه بلونوميا لو Alpha مضروبة فيها
+
+162
+00:12:00,820 --> 00:12:05,480
+الاخره عبارة عن ال .. ال .. ال .. ال operator تبعي
+
+163
+00:12:05,480 --> 00:12:09,960
+وظيفته أنه يفاضل هيك هواللي هو صار عندى Alpha زياد
+
+164
+00:12:09,960 --> 00:12:14,320
+X وPrime T وانا بعرف ان الـ Linearity .. ال .. ال
+
+165
+00:12:14,320 --> 00:12:17,760
+.. التفاضل Linear اللي هي بمعنى آخر بيصير Alpha في
+
+166
+00:12:17,760 --> 00:12:22,020
+X Prime of T زياد Y Prime of V of T الأولى هي
+
+167
+00:12:22,020 --> 00:12:25,440
+عبارة عن Alpha T X والتانى عبارة عن T Y معناته T
+
+168
+00:12:25,440 --> 00:12:28,380
+is Linear إذا الموضوع سهل وما بدناش نظلنا .. اللي
+
+169
+00:12:28,380 --> 00:12:31,620
+هو .. نحكي فيه سرنا اللي هو تجاوزنا هذه المرحلة
+
+170
+00:12:31,620 --> 00:12:38,750
+احنا نيجي الآنهنثبت أنه اللي هو unbounded بدأ أثبت
+
+171
+00:12:38,750 --> 00:12:42,150
+لكم unbounded بدأ أجيلكم sequence احنا لازم نلاقي
+
+172
+00:12:42,150 --> 00:12:47,730
+إيش عشان نثبت bounded أنه نثبت أنه norm TX أصغر أو
+
+173
+00:12:47,730 --> 00:12:52,850
+سوء C في norm X لكل X موجودة في domain T بدأ
+
+174
+00:12:52,850 --> 00:12:57,170
+أجيلكم sequence أو جزء من هال Xات اللي هنا يستحيل
+
+175
+00:12:57,170 --> 00:13:01,490
+ينطبق عليها مستحيل يجيلها C تنفع لهم كلهم أو نلاقي
+
+176
+00:13:01,490 --> 00:13:06,250
+C اللي هو بتنفعأو نجيه لـ C مهما كانت كبيرة تشوفوا
+
+177
+00:13:06,250 --> 00:13:12,710
+كيف الأمر بسيط let XN of T ايش بتساوي؟ T أوسان
+
+178
+00:13:12,710 --> 00:13:17,290
+بولونوميا مظهوطة لا لا بولونوميا البسيطة كمانwhere
+
+179
+00:13:17,290 --> 00:13:21,350
+n element in N ثم دور بالـ Xn إيش هيساوي حسب اللي
+
+180
+00:13:21,350 --> 00:13:25,150
+إحنا عارفينه اللي هو maximum لل Xn of T من ال Xn
+
+181
+00:13:25,150 --> 00:13:29,070
+of T اللي هي T أس N يعني بدي maximum لل T أس N لل
+
+182
+00:13:29,070 --> 00:13:32,790
+T اللي هو الموجودة في الـ J والـ J إيش هي ماخدينها
+
+183
+00:13:32,790 --> 00:13:38,330
+01 إذا ال maximum لل T أس N لكل T هناالـ maximum
+
+184
+00:13:38,330 --> 00:13:46,730
+بيساوي واحد إذا ال norm لكل ال Xn بيساوي واحد إذا
+
+185
+00:13:46,730 --> 00:13:51,350
+ال norm هذه لكل ال Xn لجته بيساوي واحد
+
+186
+00:13:54,070 --> 00:13:59,450
+الان شوفوا تي اكس ان تي اكس ان ايش هو normal بساوي
+
+187
+00:13:59,450 --> 00:14:03,290
+ال maximum لأ لأنه برضه في وين برمي وين من
+
+188
+00:14:03,290 --> 00:14:08,430
+polynomial ل polynomial لنفس ال space اللي هو صورة
+
+189
+00:14:08,430 --> 00:14:10,850
+تي اكس ان اللي هي ان في تي اكس ان نقص واحد مش
+
+190
+00:14:10,850 --> 00:14:16,320
+دقتهاالان norm ال maximum له هذا المقدار اللي هو
+
+191
+00:14:16,320 --> 00:14:21,500
+عندك ال T المقصة نقص واحد في T limited J واحد اللي
+
+192
+00:14:21,500 --> 00:14:25,240
+هو maximum لها وفي عندك N إيش بدي يطلع بسوءًا إذا
+
+193
+00:14:25,240 --> 00:14:31,660
+طلع عندي norm T X N بسوءًا معناته إن norm T X N
+
+194
+00:14:31,660 --> 00:14:36,260
+على X N إيش بساوي بسوءًا لا يمكن بأي حال من
+
+195
+00:14:36,260 --> 00:14:42,380
+الأحوال إن اللي جيلنا C بحيث أنه يكون normالـ T X
+
+196
+00:14:42,380 --> 00:14:47,740
+N على Normal X N يكون أصغر أوي سوى C لكل أنوية
+
+197
+00:14:47,740 --> 00:14:54,200
+موجودة في الـ N أو لكل X N موجودة في الـ Space مين
+
+198
+00:14:54,200 --> 00:14:59,160
+مش ممكن لأن الـ N إيش هنا عندي هذا طلع إيش بتساوي
+
+199
+00:14:59,160 --> 00:15:03,860
+بساوة N فش C تكون أكبر من الـ N زي اللي في الدنيا
+
+200
+00:15:03,860 --> 00:15:07,360
+لأ لإن أحنا بنعرف أصلا The set of all natural
+
+201
+00:15:07,360 --> 00:15:13,670
+numbers is unboundedفهذا اللي هو بناء عليه لا يمكن
+
+202
+00:15:13,670 --> 00:15:17,790
+إيجاد such C إذا therefore T is not bounded إذا
+
+203
+00:15:17,790 --> 00:15:24,350
+هذا مثال على Unbounded Linear Operator اطلع لفوق
+
+204
+00:15:24,350 --> 00:15:29,450
+الآن Integral Operator لناخد T برضه من ال
+
+205
+00:15:29,450 --> 00:15:31,990
+continuous functions لل continuous functions كلها
+
+206
+00:15:33,970 --> 00:15:38,070
+be defined by T X of T بساوية ال integration من
+
+207
+00:15:38,070 --> 00:15:42,910
+صفر لعين لواحد K of T وTau X of Tau D من D Tau
+
+208
+00:15:42,910 --> 00:15:45,970
+where K اللي هي هذه is a continuous is a given
+
+209
+00:15:45,970 --> 00:15:47,870
+continuous function يعني اللي كنا نسميه kernel
+
+210
+00:15:47,870 --> 00:15:51,590
+زمان في المعادلة التكملية أو المعادلة التفاضلية
+
+211
+00:15:51,590 --> 00:15:58,000
+هذا الآن عندي اللي هي دالة متصلةاللي هي داية متصلة
+
+212
+00:15:58,000 --> 00:16:03,080
+معينة K الان صورة X of T هي عبارة عن ال
+
+213
+00:16:03,080 --> 00:16:06,380
+integration من صفر إلى واحد للدالة اللي أنا أخدتها
+
+214
+00:16:06,380 --> 00:16:11,060
+اللي نسميها kernel مضروبة في مين في ال X اللي هي
+
+215
+00:16:11,060 --> 00:16:15,560
+اللي بدأت أكملها of Tau دي مين Tau يعني هي دي
+
+216
+00:16:15,560 --> 00:16:18,320
+function of two variables وانا ماعطيكم إنه دي
+
+217
+00:16:18,320 --> 00:16:22,950
+continuous functionماشي الحال continuous على اللي
+
+218
+00:16:22,950 --> 00:16:25,550
+هي طبعا هدى واضح انها function of two variables
+
+219
+00:16:25,550 --> 00:16:29,810
+continuous على الـG cross G معايا عشان اضمن انه
+
+220
+00:16:29,810 --> 00:16:32,450
+هدى متصلة و هدى متصلة اذا الـTin-Tin متصلات
+
+221
+00:16:32,450 --> 00:16:35,350
+بالنسبة لتاو اللي بده كامل إليها معناته التكامل
+
+222
+00:16:35,350 --> 00:16:40,530
+المضمون انه ايش ماله موجود طيب اذا صارت هدى T X of
+
+223
+00:16:40,530 --> 00:16:46,250
+T بسوء كده اللي هو فعلا اشي اللي هو معرف تعريفا
+
+224
+00:16:46,250 --> 00:16:51,540
+تماماwhich is called the kernel on D of T مش مشكلة
+
+225
+00:16:51,540 --> 00:16:55,500
+هذي then T is a bounded linear operator ليها مثال
+
+226
+00:16:55,500 --> 00:16:59,940
+عالمين a bounded linear operator اطلع على فوق اطلع
+
+227
+00:16:59,940 --> 00:17:04,940
+على فوق الان نيجي نشوف طبعا احنا ال C01 اتفاجنا ال
+
+228
+00:17:04,940 --> 00:17:10,400
+C01 عبارة عن ال space ال norms space ال continuous
+
+229
+00:17:10,400 --> 00:17:13,480
+functions مين ال normal اللي عليه ال maximum ماشي
+
+230
+00:17:13,480 --> 00:17:16,180
+ال normal اللي عليه ال maximum وهذا ال space
+
+231
+00:17:16,180 --> 00:17:22,500
+completeبالمناسبة اه طيبfor all x,y elements in C0
+
+232
+00:17:22,500 --> 00:17:22,980
+,1
+
+233
+00:17:50,230 --> 00:17:53,270
+الـ Scale of Multiplication و الـ Additivity اللي
+
+234
+00:17:53,270 --> 00:17:56,490
+هو الـ Integration بتوزع عليها و يساوي هذه اللي هي
+
+235
+00:17:56,490 --> 00:18:02,410
+TX و التانية TY إذا صارت اللي هو T is Linear الآن
+
+236
+00:18:02,410 --> 00:18:05,830
+بتثبتلكم أنه اللي هو ال .. ال .. ال .. ال operator
+
+237
+00:18:05,830 --> 00:18:11,990
+اللي عندنا اللي هو TX TX بساوي ال Integration من
+
+238
+00:18:11,990 --> 00:18:19,070
+صفر اللي عنده واحد K T و Tau X of TauD τاو انها
+
+239
+00:18:19,070 --> 00:18:24,470
+ايش معناها is bounded يعني بمعنى اخر نورم ال TX
+
+240
+00:18:24,470 --> 00:18:30,350
+على نورم ال X أصغر يساوي some C انشوف ايش هي ال C
+
+241
+00:18:30,350 --> 00:18:35,110
+اللي بحكي عنها صلى على النبي عليه الصلاة والسلام
+
+242
+00:18:35,110 --> 00:18:41,160
+نيجي الأن أول إشيعندي اللي هو الـ Kernel الـ
+
+243
+00:18:41,160 --> 00:18:47,000
+Kernel اللي هو الـ K of K الـ K هذه is continuous
+
+244
+00:18:47,000 --> 00:18:50,720
+على closed bounded square G اللي اتفاجنا على انه
+
+245
+00:18:50,720 --> 00:18:54,120
+معرفين على G cross G و G اللي هو عبارة عن اللي هي
+
+246
+00:18:54,120 --> 00:18:57,320
+closed interval و G cross G بيصير bounded closed
+
+247
+00:18:57,320 --> 00:19:02,350
+اللي هي إياش squareإذن بمعنى أخر continuous على
+
+248
+00:19:02,350 --> 00:19:07,470
+closed bounded region إذن أكيد هتكون اللي هي ال K
+
+249
+00:19:07,470 --> 00:19:12,390
+نفسها bounded نظرية دي اللي بدكم then K is bounded
+
+250
+00:19:12,390 --> 00:19:16,310
+ماشي الحال as a function that is there is C أكبر
+
+251
+00:19:16,310 --> 00:19:19,530
+من صفر such that ال absolute value لل K of T وTau
+
+252
+00:19:19,530 --> 00:19:23,190
+أصغر أو ساوى مين أصغر أو ساوى C على كل المنطقة
+
+253
+00:19:23,190 --> 00:19:26,610
+المعرفة عليها لإنها continuous على closed bounded
+
+254
+00:19:26,610 --> 00:19:32,680
+regionfurthermore ال absolute value لل X of T اللي
+
+255
+00:19:32,680 --> 00:19:35,980
+هي أكيد واحدة منهن أصغر أو شاو ال maximum عليهم
+
+256
+00:19:35,980 --> 00:19:40,300
+كلهن عالميا عند ال T معينة X of T عند T معينة أصغر
+
+257
+00:19:40,300 --> 00:19:43,440
+أو شاو ال maximum يعني بمعنى أخر ال X of T أكيد
+
+258
+00:19:43,440 --> 00:19:49,950
+أصغر أو شاو من نورمها يعني الآن X of TX of T هذي
+
+259
+00:19:49,950 --> 00:19:53,530
+أصغر أو يساوي Normal X لأن Normal X هو ال maximum
+
+260
+00:19:53,530 --> 00:19:59,410
+لكل هذولة معناه أن Normal X أكبر يساوي X of T لكل
+
+261
+00:19:59,410 --> 00:20:04,950
+T في الفترة 0 و 1 اللي بشتغل عليها إذا خذوا
+
+262
+00:20:04,950 --> 00:20:08,690
+المعلومتين المعلومة باتجاه ال kernel و المعلومة
+
+263
+00:20:08,690 --> 00:20:13,900
+باتجاه X of T هنسوا الآنالـ .. الـ norm لـ T of
+
+264
+00:20:13,900 --> 00:20:17,300
+Xاش بيساوي الـ TX ما هي بترمي وين برضه في ال
+
+265
+00:20:17,300 --> 00:20:20,580
+continuous إذن هيطلع عبارة عن .. طبعا هذه function
+
+266
+00:20:20,580 --> 00:20:25,680
+of V هتطلع of T تاوة هتطلع اللي هي عدد .. هت ..
+
+267
+00:20:25,680 --> 00:20:28,640
+هتروح .. إذن هتبقى لها function في مين بس؟ في T
+
+268
+00:20:28,640 --> 00:20:33,300
+إذن الآن norm الـ TX أو الـ TX بيساوي هذا norm هو
+
+269
+00:20:33,300 --> 00:20:37,640
+ال maximum للقيمة هذه على الـ T اللي وين ما لها
+
+270
+00:20:37,640 --> 00:20:41,930
+الـ Ts اللي موجودة في الـ Jاللي هي أكيد أصغر أو
+
+271
+00:20:41,930 --> 00:20:45,550
+يساوي بما أن هذا absolute value أصغر أو يساوي ال
+
+272
+00:20:45,550 --> 00:20:49,010
+integration لل absolute value صح؟ أصغر أو يساوي ال
+
+273
+00:20:49,010 --> 00:20:51,130
+integration ال absolute value في ال absolute value
+
+274
+00:20:51,130 --> 00:20:56,150
+الآن هذه من فوق أثبتت أنها أشمالها أصغر أو يساوي C
+
+275
+00:20:56,150 --> 00:21:00,710
+وهذه أصغر أو يساوي 100 اللي هو اللي هو النور،
+
+276
+00:21:00,710 --> 00:21:05,570
+مظبوط؟معايا هايها ال X و T أصغر أو أصغر منين ال
+
+277
+00:21:05,570 --> 00:21:09,830
+norm إذا بشيل هذه بحط مكانها ال C وهذه بشيلها بحط
+
+278
+00:21:09,830 --> 00:21:13,910
+مكانها اللي هو ال norm فبصير ال integration اللي
+
+279
+00:21:13,910 --> 00:21:17,310
+هو هذا أصغر أو أصغر منين ال integration C في نورم
+
+280
+00:21:17,310 --> 00:21:21,430
+ال X بطلع برا برضه لأنه عدد من Zero ل واحد دي Tau
+
+281
+00:21:21,430 --> 00:21:25,050
+ومن Zero ل واحد دي Tau إيش قيمته واحد إلا إذا بصير
+
+282
+00:21:25,050 --> 00:21:30,090
+C في نورم ال X يعني بمعنى آخر أثبتت الآن أن نورم
+
+283
+00:21:30,090 --> 00:21:37,080
+ال TXأصغر أو سوى C في نور مين ال X لكل X وين
+
+284
+00:21:37,080 --> 00:21:41,400
+موجودة في domain T وهذا يعني أن T is bounded أي
+
+285
+00:21:41,400 --> 00:21:49,180
+سؤال المفروض أن الكلام بدأ يحلو يعني نيجي الآن
+
+286
+00:21:49,180 --> 00:21:59,620
+نشوف اللي هو نعرف functionمن Rn لعند Rm بالاستعانة
+
+287
+00:21:59,620 --> 00:22:03,180
+.. وهذا مثال موجود في الجبر الخاطي بالاستعانة ..
+
+288
+00:22:03,180 --> 00:22:07,000
+بالاستعانة بالـ matrix اللي بيحول ال element من
+
+289
+00:22:07,000 --> 00:22:11,720
+هنا إلى element وين في الـ Rmالنورم اللي على
+
+290
+00:22:11,720 --> 00:22:15,520
+القرار نعرفينه اللي هو الجدر التربيعي x1 تربيع زاد
+
+291
+00:22:15,520 --> 00:22:20,920
+x2 تربيع زاد xn تربيع لأن عناصرها إيش هذه؟ x1, x2,
+
+292
+00:22:21,020 --> 00:22:26,840
+x3 و xn هذه عناصرها x1, x2, x3 و xm إذا نورمها هذا
+
+293
+00:22:26,840 --> 00:22:31,580
+هو الجدر التربيعي ل x1 تربيع زاد x2 تربيع زاد xn
+
+294
+00:22:31,580 --> 00:22:34,970
+تربيع وهذه كانت نورمها مشابهاللي هم بيقولي لو
+
+295
+00:22:34,970 --> 00:22:38,110
+أخدنا Matrix هذا الـ Matrix الـ Real Matrix اللي
+
+296
+00:22:38,110 --> 00:22:42,390
+هو أداة تعريف ال .. ال .. ال .. ال function اللي
+
+297
+00:22:42,390 --> 00:22:45,490
+عندي أو ال operator اللي عنده أخدت A بتساوي Alpha
+
+298
+00:22:45,490 --> 00:22:50,990
+J K ب M by N Matrix M by N عشان يناسب مين اللي هو
+
+299
+00:22:50,990 --> 00:22:55,270
+في حالة الضرب اللي هو ال Rn و ال Rm و ينجلي من Rn
+
+300
+00:22:55,270 --> 00:23:02,660
+لمين لعند RmDefined by TXاش بساوي FX الـ X من وين
+
+301
+00:23:02,660 --> 00:23:06,940
+عبارة عن element اللي هو XI واحد و XI اتنين و XI N
+
+302
+00:23:06,940 --> 00:23:11,600
+ماشي الحل الان بقولك إذا T is a bounded linear
+
+303
+00:23:11,600 --> 00:23:14,640
+operator إذا الـ linear و A شماله abounded خلّينا
+
+304
+00:23:14,640 --> 00:23:21,290
+نشوفلكل x و y element in Rn and all scalars α T of
+
+305
+00:23:21,290 --> 00:23:25,430
+α x زائد y ايش بيساوي؟ بيساوي هذا ولا طبعا هذا
+
+306
+00:23:25,430 --> 00:23:28,790
+اللي هو عبارة عن element في Rn وهذا element في Rn
+
+307
+00:23:28,790 --> 00:23:32,290
+هذا ال A matrix اشمله M by N matrix خلّينا نجوه
+
+308
+00:23:32,290 --> 00:23:39,990
+عشان ال A عبارة عن ألف واحد واحد لما نقصل Mby N
+
+309
+00:23:39,990 --> 00:23:45,550
+أكم عمود N من الأعمدة لعند Alpha 1 N مظبوط و بمشي
+
+310
+00:23:45,550 --> 00:23:52,490
+من هنا Alpha M 1 لعند Alpha M N هاي ال matrix اللي
+
+311
+00:23:52,490 --> 00:23:58,530
+عندى مش الحال الآن هذا ال matrix بدي أضربه في اللي
+
+312
+00:23:58,530 --> 00:24:06,110
+هو مين عندى T من R Nلعند RM بسمحولي بس أكتب على
+
+313
+00:24:06,110 --> 00:24:08,970
+صورة أعمدة اللي هي ال RN اللي هي اللي في ال RN
+
+314
+00:24:08,970 --> 00:24:14,810
+اللي هو عبارة عن Xi 1 لعند Xi N بدها ترمي وين؟ في
+
+315
+00:24:14,810 --> 00:24:21,910
+جامعة 1 لمين؟ لجامعة M ماشي؟ شوفوا الآن T
+
+316
+00:24:25,140 --> 00:24:31,940
+T of هذه الـ X التي هي XI واحد لعند XI N ما هي
+
+317
+00:24:31,940 --> 00:24:37,400
+ساوي الماتريكس هذا مضروب في XI واحد لعند XI N
+
+318
+00:24:37,400 --> 00:24:43,810
+معاياعملية الضرب هذا هيجيب ال element كله وبعدين
+
+319
+00:24:43,810 --> 00:24:46,210
+هذا هيجيب ال element لما أصل للأخر بيجيب ال
+
+320
+00:24:46,210 --> 00:24:49,930
+element أما كم element هنجيب M من ال elements هذا
+
+321
+00:24:49,930 --> 00:24:53,710
+هيجيب واحد هذا اتنين العديش لما أصل عند ال M إذا
+
+322
+00:24:53,710 --> 00:25:01,230
+هيطلع عندي عبارة عن جامعة واحد عند جامعةإذا فعلاً
+
+323
+00:25:01,230 --> 00:25:04,710
+هذا اللي هو بيعمل ليه linear operator من A بيعمل
+
+324
+00:25:04,710 --> 00:25:08,390
+ليه operator من RN لعند RM Linear اه Linear ليش
+
+325
+00:25:08,390 --> 00:25:11,930
+Linear لأن لو أخدت T of Alpha X زائد Y تنسوش أن
+
+326
+00:25:11,930 --> 00:25:16,130
+هذا Matrix وهذا Matrix كلهم Matrixالأن إيش هيساوي
+
+327
+00:25:16,130 --> 00:25:21,410
+حسب القانون A matrix في هدولة Alpha scalar ماشي
+
+328
+00:25:21,410 --> 00:25:24,570
+الحال في ضرب ال matrices ال alpha ال scalar بتطلع
+
+329
+00:25:24,570 --> 00:25:27,190
+برا عن المشترك بتظهر اللي هو A في X و بقى دي A في
+
+330
+00:25:27,190 --> 00:25:32,030
+Y اللي هو عبارة عن AX اللي هو ال TX وال AY ال TY
+
+331
+00:25:32,030 --> 00:25:36,580
+إذا صارت عبارة عن linear operator طيبلأن .. ال ..
+
+332
+00:25:36,580 --> 00:25:41,060
+ضال عليا أستخدم مين الآن؟ أثبت مين؟ أثبت أنه is
+
+333
+00:25:41,060 --> 00:25:44,920
+bounded بدي أستخدم في .. في أثبات ال boundedness
+
+334
+00:25:44,920 --> 00:25:48,320
+الكوششوارزينكواليتي مذاكرين الكوششوارزينكواليتي ال
+
+335
+00:25:48,320 --> 00:25:53,340
+summation xi i gamma i أصغر أو ساوي ال summation
+
+336
+00:25:53,340 --> 00:25:59,520
+xi i تربيع الكل أص نص في ال summation gamma i
+
+337
+00:25:59,520 --> 00:26:03,850
+تربيع الكل أشماله أص نصليه استخدمها؟ خلّيني نشوف
+
+338
+00:26:03,850 --> 00:26:06,670
+إيش اللي .. إيش .. إيش اللي بدي أعمله الموضوع
+
+339
+00:26:06,670 --> 00:26:10,990
+حسابات الآن وحسابات سهلة إن شاء الله خدوا الآن زي
+
+340
+00:26:10,990 --> 00:26:14,650
+ما قلنا خدوا أي X موجودة في ال domain الـR of T هي
+
+341
+00:26:14,650 --> 00:26:19,450
+كولوم Matrix أخدته Xi واحد and Xi N وحسبوه لنورم
+
+342
+00:26:19,450 --> 00:26:22,390
+الـTX اللي هو تربيع عشان اللي هو تسهيل عملية
+
+343
+00:26:22,390 --> 00:26:26,870
+الحسابات أخدت التربيع بساوي نورم الـX الكلمين
+
+344
+00:26:26,870 --> 00:26:32,270
+تربيع لأن الـTX مش بساوي A في X تربيعالان ax هي ال
+
+345
+00:26:32,270 --> 00:26:36,310
+a وهي ال x نضربهم نضرب اللي هو السطر الأول في
+
+346
+00:26:36,310 --> 00:26:40,430
+العمود الأول بطلع summation للضرب هذا اه اللي هو
+
+347
+00:26:40,430 --> 00:26:44,570
+بطلع ال .. اطلع لفوق شوية لفوق شوية اه بس خلي بس
+
+348
+00:26:44,570 --> 00:26:48,570
+اظهر هنا بطلع ال summation الأول summation اللي هو
+
+349
+00:26:48,570 --> 00:26:52,170
+السطر الأول في العمود الأولفي العمود نفسه هاي ال
+
+350
+00:26:52,170 --> 00:26:55,870
+entry الأول الان ال summation هذا العمود التاني في
+
+351
+00:26:55,870 --> 00:26:59,210
+السطر التاني في العمود اللي عندى هاي و بطلع لما
+
+352
+00:26:59,210 --> 00:27:03,950
+أصل لأخر واحد اللي هو بيجيب هذا طيب هذول الآن
+
+353
+00:27:03,950 --> 00:27:08,230
+عبارة عن Gamma 1 و Gamma 2 و Gamma 3 و Gamma M ايش
+
+354
+00:27:08,230 --> 00:27:11,870
+form هنا بشغل في الأرقام الآن اللي هو تربيح هذا و
+
+355
+00:27:11,870 --> 00:27:15,470
+تربيح هذا و تربيح هذا و كل انتحت مين الجدر و بجمحل
+
+356
+00:27:15,470 --> 00:27:19,920
+صح بجمحل و أخد انتحت الجدر معايا كيف؟بصير الآن
+
+357
+00:27:19,920 --> 00:27:24,000
+عبارة عن summation مجموح هذا اللي هو لكل واحد
+
+358
+00:27:24,000 --> 00:27:30,200
+تربيع آسف اه هنا اللي هي هذا تربيع اه و هذا تربيع
+
+359
+00:27:30,200 --> 00:27:33,700
+و هذا تربيع و هذا تربيع و بعدين ماله بجمحها و الكل
+
+360
+00:27:33,700 --> 00:27:38,140
+تحت الجذر من المناخ التربيع فاهمين اه؟اللي هو هذا
+
+361
+00:27:38,140 --> 00:27:41,800
+أصغر أو ساوي بالـ Schwarz inequality بدي أطبّقها
+
+362
+00:27:41,800 --> 00:27:44,620
+على اللي جوا على هذه الـSchwarz inequality هذه
+
+363
+00:27:44,620 --> 00:27:49,700
+تربيع أص نص تربيع أص نص وهذه تربيع أص نص والباقي
+
+364
+00:27:49,700 --> 00:27:54,580
+فوق أيضا أيش ماله تربية معايا واضح هذا أصغر أو
+
+365
+00:27:54,580 --> 00:27:58,420
+ساوي الآن لو جينا شوفنا هذه هذه بتمثل مين يا جماعة
+
+366
+00:27:58,420 --> 00:28:02,970
+اللي جواNormal X صح ولا لأ وهي فيه تربيع بتطلع
+
+367
+00:28:02,970 --> 00:28:06,770
+Normal X ماله تربيع بيظل ال summation لل summation
+
+368
+00:28:06,770 --> 00:28:10,450
+لأن هذا ثابت بيصير بيطلع برا فبيصير Normal X تربيع
+
+369
+00:28:10,450 --> 00:28:14,530
+في ال summation اللي عند double summation هذا في
+
+370
+00:28:14,530 --> 00:28:18,850
+النهاية عدد لأن هذا من هو هذا جاي من ال matrix
+
+371
+00:28:18,850 --> 00:28:22,150
+اللي أنا استخدمته في تعريف الدالة يعني إيش محدد
+
+372
+00:28:22,150 --> 00:28:26,110
+يعني هيكون عبارة عن إيش قيمة عددية إذا صار عندي
+
+373
+00:28:26,110 --> 00:28:31,670
+Normal TXتربيع أصغر أو شويه Normal X تربيع في مين؟
+
+374
+00:28:31,670 --> 00:28:36,850
+في some constant C يلا
+
+375
+00:28:36,850 --> 00:28:40,470
+اللي بعده اطلع لفوق اطلع لفوق فبصير عندي Normal T
+
+376
+00:28:40,470 --> 00:28:43,370
+X تربيع أصغر أو شويه اللي هو C تربيع في Normal X
+
+377
+00:28:43,370 --> 00:28:45,710
+حيث و C تربيع بالساوية ال summation اللي قلنا عنه
+
+378
+00:28:45,710 --> 00:28:51,070
+إذن و هذا يعني T is bounded إذن عبارة عن bounded
+
+379
+00:28:51,070 --> 00:28:54,850
+linear operator اللي أثبتناه نأتي إلى نظرية
+
+380
+00:28:57,850 --> 00:29:03,610
+لو انتوا لاحظته بس قبل احكيها النظرية theorem if
+
+381
+00:29:03,610 --> 00:29:06,850
+and only if this base X is finite dimensional then
+
+382
+00:29:06,850 --> 00:29:10,970
+every linear operator on X أشماله is bounded كلام
+
+383
+00:29:10,970 --> 00:29:17,270
+خطيرإنه أي Linear Operator في الدنيا على finite
+
+384
+00:29:17,270 --> 00:29:20,970
+dimensional space هيطلع bounded linear EIH
+
+385
+00:29:20,970 --> 00:29:24,930
+Operator يعني اللي جاب البشوية هدولة تبع الـRN وRK
+
+386
+00:29:24,930 --> 00:29:28,110
+خلاص ما هو bounded linear operator على .. linear
+
+387
+00:29:28,110 --> 00:29:31,230
+operator على اللي هو finite dimensional space لأن
+
+388
+00:29:31,230 --> 00:29:34,230
+automatic هيكون إيش ماله؟ bounded linear operator
+
+389
+00:29:35,250 --> 00:29:39,590
+بدنا نبرهنها لان لو اتيت و لاحظته يمكن برهنها بيجي
+
+390
+00:29:39,590 --> 00:29:42,770
+تلت نظريات جابلها دي او نظريتين على الـ finite
+
+391
+00:29:42,770 --> 00:29:47,670
+dimensional و فيهم كلهم يمكن نروح لبرهان واحدة
+
+392
+00:29:47,670 --> 00:29:52,430
+كلهم استخدمنا فرضنا ال bases و استخدمنا اللمّة
+
+393
+00:29:52,430 --> 00:29:56,230
+اللي احنا تبعت اللي هي summation أكبر أو يساوي
+
+394
+00:29:56,230 --> 00:30:00,250
+اللي هو C في اللي هو اللي هي كتلة ال scalars،
+
+395
+00:30:00,250 --> 00:30:06,640
+مظبوط؟ عساس انه يعني لتتكارب البرهانطيب، الآن
+
+396
+00:30:06,640 --> 00:30:09,360
+خلّينا نفترض أن الـ dimension للـ space اللي عنده
+
+397
+00:30:09,360 --> 00:30:14,240
+X يش بيساوي N ونفترض ال basis تبعته E1 وE2 وEN بيه
+
+398
+00:30:14,240 --> 00:30:18,200
+a basis for X then every X element in X has a
+
+399
+00:30:18,200 --> 00:30:20,500
+unique representation عارفينه هذا الكلام من الجبر
+
+400
+00:30:20,500 --> 00:30:25,940
+الخطي اللي هي بغسط أي X في الـ X عشانه basis بنكد
+
+401
+00:30:25,940 --> 00:30:29,040
+و أسوء as a linear combination من العناصر هدولة
+
+402
+00:30:29,040 --> 00:30:34,340
+ووحيد و اللي بيبطل basisالفا واحد اي واحد زي الفا
+
+403
+00:30:34,340 --> 00:30:37,400
+اتنين اي اتنين زي الفا ان اياش اي ان هاد ال X
+
+404
+00:30:37,400 --> 00:30:41,120
+where الفا واحد و الفا اتنين are mean scalar by
+
+405
+00:30:41,120 --> 00:30:44,160
+linearity of T لأن هو مفترض اياش ماله linear و بدك
+
+406
+00:30:44,160 --> 00:30:48,940
+تثبت انه اياش bounded شوفوا كيف نورم ال TX ايش
+
+407
+00:30:48,940 --> 00:30:55,100
+هيساوي اللي هو ال summation لل alpha I TEI اكيد
+
+408
+00:30:55,770 --> 00:31:01,630
+Txاش بيساوي .. Txاش بيساوي اللي هو T لهذا إذا
+
+409
+00:31:01,630 --> 00:31:04,690
+Alpha واحد تي واحد زاد Alpha اتنين تي اتنين زاد
+
+410
+00:31:04,690 --> 00:31:08,690
+Alpha N تي N اللي هو هذا بحطه جوا تمين norm الان
+
+411
+00:31:08,690 --> 00:31:13,960
+أنا شغلي وين الان هذا normalإذا أصغر أوي و ساوي
+
+412
+00:31:13,960 --> 00:31:17,760
+اللي هو ال .. ال .. ال .. ال .. ال .. ال triangle
+
+413
+00:31:17,760 --> 00:31:21,380
+inequality اللي هو norm ال .. ال .. ال .. الأول
+
+414
+00:31:21,380 --> 00:31:24,820
+زاد التاني زاد التالت زاد مية norm هنا أصغر أوي و
+
+415
+00:31:24,820 --> 00:31:26,700
+ساوي نورم الأول زاد نورم التاني و زاد نورم الأخر
+
+416
+00:31:26,700 --> 00:31:30,440
+هذا اللي استخدمته إذا ال norm للمجموع أصغر أوي
+
+417
+00:31:30,440 --> 00:31:34,590
+مجموع لل normالآن الـ α I اللي هي scalar فبتدخل و
+
+418
+00:31:34,590 --> 00:31:37,750
+بتخرج من برا النورم بإيش ما لها ب absolute value
+
+419
+00:31:37,750 --> 00:31:41,630
+فاهمين اللي بحكيه؟ summation في نورمين اللي بيظل
+
+420
+00:31:41,630 --> 00:31:46,720
+نورمين الـ T E Iإذا الـ T I أكم واحدة هنا معروف أن
+
+421
+00:31:46,720 --> 00:31:50,380
+طبعا الـ E 1 و E 2 و E N بحكي عن إشي محدد اللي
+
+422
+00:31:50,380 --> 00:31:53,660
+وعددهن N من العناصر إذا أكيد فيه أكبر واحدة فيهم
+
+423
+00:31:53,660 --> 00:31:57,540
+أكيد لأن هدول أعداد مودبة أكبر ساو سيفر خدوا ال
+
+424
+00:31:57,540 --> 00:32:02,580
+maximum الهن هدولة فبصير هذا المقدار أصغر أو يساوي
+
+425
+00:32:02,580 --> 00:32:05,740
+ال maximum الهن في ال main في ال summation اللي
+
+426
+00:32:05,740 --> 00:32:10,560
+عندي اطلعي لفوق الان من لمة اتنين اربعة واحد اللي
+
+427
+00:32:10,560 --> 00:32:14,430
+وعدتكم فيهابدي اتخلص من هذولة بدي اتخلص من هذه
+
+428
+00:32:14,430 --> 00:32:19,060
+انزلينبدا تخلص منها الـ scalars اللي موجودة و تبدأ
+
+429
+00:32:19,060 --> 00:32:26,100
+تبدأ تبدأ تبدأ تبدأ تبدأ
+
+430
+00:32:26,100 --> 00:32:28,600
+تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ
+
+431
+00:32:28,600 --> 00:32:31,920
+تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ
+
+432
+00:32:31,920 --> 00:32:31,920
+تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ
+
+433
+00:32:31,920 --> 00:32:31,920
+تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ
+
+434
+00:32:31,920 --> 00:32:31,920
+تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ
+
+435
+00:32:31,920 --> 00:32:31,940
+تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ
+
+436
+00:32:31,940 --> 00:32:44,340
+تبدأ تبدأ
+
+437
+00:32:44,340 --> 00:32:50,360
+تماشي هذه اللي ما الان بتربط هذه مع الاولى صار هذا
+
+438
+00:32:50,360 --> 00:32:55,140
+ال summation اصغر او يساوي normal x على ال c انزل
+
+439
+00:32:55,140 --> 00:32:59,060
+لتحت .. انزل لتحت بدي اللي هو اخد .. اخد خلص من
+
+440
+00:32:59,060 --> 00:33:02,760
+هذه بيصير اصغر او يساوي هذا في normal x على مين؟
+
+441
+00:33:02,760 --> 00:33:07,000
+على ال c اطلع لفوق قدر من واحد و اللي عندي هذه
+
+442
+00:33:07,000 --> 00:33:11,020
+بقدر اقول normal T x اصغر يساوي واحد على c في ال
+
+443
+00:33:11,020 --> 00:33:17,040
+maximum هذا في normal x هذا كله على بعضثابت لأن
+
+444
+00:33:17,040 --> 00:33:20,880
+هذا عبارة عن قيمة عددية و 1 على C قيمة عددية إذا
+
+445
+00:33:20,880 --> 00:33:24,680
+نورم الـ TX أصغر يساوي some number M في نورم الـ X
+
+446
+00:33:24,680 --> 00:33:28,520
+إذا صار عنده و الـ M طبعا هذه المشمولة هي هذه M
+
+447
+00:33:28,520 --> 00:33:32,800
+مشمولة تغيروا هذا M كم تهلل الفعل بساوي 1 على C في
+
+448
+00:33:32,800 --> 00:33:39,060
+ال maximum للنورم hence T أشمالها is bounded يلّا
+
+449
+00:33:39,060 --> 00:33:43,440
+لبعده نيجي
+
+450
+00:33:43,440 --> 00:33:44,180
+نشوف
+
+451
+00:33:49,850 --> 00:33:57,170
+Theorem 279 إعلان كبير إعلان بقولكم باختصارلما
+
+452
+00:33:57,170 --> 00:33:59,690
+يكون عندنا linear operator لما يكون عندنا linear
+
+453
+00:33:59,690 --> 00:34:04,190
+operator هتلاقوا مفهوم ال boundedness هو نفس مفهوم
+
+454
+00:34:04,190 --> 00:34:08,250
+ال continuity هو نفس مفهوم ال continuity عند نقطة
+
+455
+00:34:08,250 --> 00:34:12,390
+يعني لو كان عندك linear operator و كانت continuous
+
+456
+00:34:12,390 --> 00:34:16,250
+عند نقطة توكل على الله continuous على كل مين على
+
+457
+00:34:16,250 --> 00:34:19,770
+كل ال domain و هيكون bounded و لو كان bounded
+
+458
+00:34:19,770 --> 00:34:21,850
+هيكون continuous عند كل ال domain و هيكون
+
+459
+00:34:21,850 --> 00:34:25,090
+continuous عند مين عند كل نقطة كلام خوى .. خوى جدا
+
+460
+00:34:25,950 --> 00:34:29,230
+ومريح let T من domain of T لعند Y بيقالينا
+
+461
+00:34:29,230 --> 00:34:32,310
+operator where domain of T subset من X and X and Y
+
+462
+00:34:32,310 --> 00:34:36,450
+are normed spaces then T is continuous if and only
+
+463
+00:34:36,450 --> 00:34:40,530
+if T is bounded هاي واحدة اتنين إذا كانت T
+
+464
+00:34:40,530 --> 00:34:45,030
+continuous عند بس نقطة هتلاقيها نقلها continuous
+
+465
+00:34:45,030 --> 00:34:51,730
+على كل ال domain يلا نشوف بدنا نبرهن ال theorem
+
+466
+00:34:51,730 --> 00:34:57,310
+ناخد اتجاه الأول اتجاه التاني و بعدين ناخد Bطيب
+
+467
+00:34:57,310 --> 00:35:07,370
+سلّع على النبي عليه الصلاة والسلام شوفوا
+
+468
+00:35:07,370 --> 00:35:13,610
+خلّينا نشوف اللي بحكيهاالان بس بدنا نشيل هال سفر
+
+469
+00:35:13,610 --> 00:35:16,430
+من عندنا عشان لو بدنا نجسم على سفر كده نجسم على T
+
+470
+00:35:16,430 --> 00:35:20,750
+مايكون مرتاحين نفش نجسم على سفر الـ 4T بيساوي سفر
+
+471
+00:35:20,750 --> 00:35:23,110
+ال .. ال .. ال .. ال .. ال .. ال linear operator
+
+472
+00:35:23,110 --> 00:35:25,850
+اللي هو ال zero linear operator هذا linear و
+
+473
+00:35:25,850 --> 00:35:28,530
+bounded و كل الدنيا حلوة فيه و كنتوا حلوة فيهfor T
+
+474
+00:35:28,530 --> 00:35:33,130
+بيساوى 0 the statement is trivial لأن لت لا تساوي
+
+475
+00:35:33,130 --> 00:35:38,370
+0 نفترض انه مش هو ال zero operator ماشي الان مدام
+
+476
+00:35:38,370 --> 00:35:41,470
+مش هو ال zero operator اذا اكيد ال norm لت اشماله
+
+477
+00:35:41,470 --> 00:35:45,910
+مش سفر ماشي الحال طيب لان اصلا من تعريف ال norm ال
+
+478
+00:35:45,910 --> 00:35:48,190
+norm ت بيساوى سفر if and only if ت اللي جوه بيساوي
+
+479
+00:35:48,190 --> 00:35:53,250
+سفر طيب اذا ال norm ت لا يساوي سفر لان نفترض ت is
+
+480
+00:35:53,250 --> 00:35:58,270
+boundedونثبت إنه T Continuous T is bounded عارفين
+
+481
+00:35:58,270 --> 00:36:00,910
+شو معناته؟ bounded norm للـ T X أزرار شوية اللي هو
+
+482
+00:36:00,910 --> 00:36:04,730
+C في norm ال X ده كل ال Xاتر الآن و بدنا ناخد X
+
+483
+00:36:04,730 --> 00:36:08,330
+note arbitrary X note بس بدنا نحكي عن واحدة محددة
+
+484
+00:36:08,330 --> 00:36:11,410
+يعني باجي باخد هكوم هالعناصر اللي في ال domain of
+
+485
+00:36:11,410 --> 00:36:15,660
+T باخد من X note arbitrary و ببدأ أحكي عنهاإذا
+
+486
+00:36:15,660 --> 00:36:17,960
+اللي بنطبق عليه hard book علي غيرها يعني مش مانهي
+
+487
+00:36:17,960 --> 00:36:24,100
+أنا باخدها عشوائي let X not be any fixed point in
+
+488
+00:36:24,100 --> 00:36:30,640
+domain of Tالان احنا مفترضين انها bounded او بدنا
+
+489
+00:36:30,640 --> 00:36:33,440
+نثبت انها continuous ايش كيف نثبت انه continuous؟
+
+490
+00:36:33,440 --> 00:36:37,700
+نثبت انه continuous انه اللي هو لكل y أكبر من 0
+
+491
+00:36:37,700 --> 00:36:41,700
+بدي لاجي delta أكبر من 0 such that لما ال X minus
+
+492
+00:36:41,700 --> 00:36:46,460
+X not يكون أصغر من Delta يعطيني ال TX نقص ال TX
+
+493
+00:36:46,460 --> 00:36:50,940
+not ايش ماله أصغر من Y هي اللي بدي اشتغل عليهاماشي
+
+494
+00:36:50,940 --> 00:36:55,820
+بدي أصلّه بدي أصلّه بالاستعانة بالاستعانة باللي هي
+
+495
+00:36:55,820 --> 00:37:04,120
+اللي عندي طيب خدوا الآن suppose that T is bounded
+
+496
+00:37:04,120 --> 00:37:07,580
+and let X not be any fixed point on D of T و let Y
+
+497
+00:37:07,580 --> 00:37:12,560
+أكبر من 0 be arbitrary given Y لأن بما أنه T is
+
+498
+00:37:12,560 --> 00:37:18,950
+linearإذا بقدر ألاقي Delta بتساوي E على norm of T
+
+499
+00:37:18,950 --> 00:37:22,470
+أكبر من 0 such that إذا أنا جاءت بحضر للي بدّيها،
+
+500
+00:37:22,470 --> 00:37:26,850
+بدّي ألاقي مين؟ Delta أنا بقول للمستقبل اللي
+
+501
+00:37:26,850 --> 00:37:31,110
+بدّيها، أنا بتدعي إنها Delta إيش هتساوي E على norm
+
+502
+00:37:31,110 --> 00:37:34,670
+of T، norm of T بين إيديا و الـ E انت عطيتني إيها
+
+503
+00:37:34,670 --> 00:37:37,170
+إذا صارت عندي الـ Delta بتساوي E على norm of T
+
+504
+00:37:37,170 --> 00:37:41,170
+أكبر من مين من 0 such that if X element in domain
+
+505
+00:37:41,170 --> 00:37:47,320
+of Tعند x-x0 أصغر من دلتا بدّى أثبت لك أن هذا يكون
+
+506
+00:37:47,320 --> 00:37:51,820
+أصغر من مين من إبسلون شوفوا الآن then norm of T x
+
+507
+00:37:51,820 --> 00:37:58,040
+نقص T x0 ايش بيساوي norm of T في x minus x0Linear
+
+508
+00:37:58,040 --> 00:38:02,200
+Linear أصغر أو سوى نورم الـ T في نورم من X minus X
+
+509
+00:38:02,200 --> 00:38:05,780
+naught هذا من وين جبته؟ من الـ boundedness للـ T
+
+510
+00:38:05,780 --> 00:38:08,820
+مش عارف معناته الـ bounded؟ طيب أصغر أو سوى نورم
+
+511
+00:38:08,820 --> 00:38:12,460
+الـ T في نورم هذا الآن نورم الـ X minus X naught
+
+512
+00:38:12,460 --> 00:38:16,300
+أنا إيش ماخده؟ أصغر من Delta اللي هي إيش بتسوى Y
+
+513
+00:38:16,300 --> 00:38:20,460
+على مين؟ على نورم الـ T اللي هي أصغر من نورم الـ T
+
+514
+00:38:20,460 --> 00:38:23,500
+في Deltaحاصل ضربه Delta Epsilon على نورم الـT
+
+515
+00:38:23,500 --> 00:38:26,440
+بتطلع يشمله Epsilon و هذا Therefore T is
+
+516
+00:38:26,440 --> 00:38:30,020
+continuous at X0 لكن X0 was arbitrarily زي ما قلنا
+
+517
+00:38:30,020 --> 00:38:36,440
+Then T is continuous on all domain of T سهل يلّا
+
+518
+00:38:36,440 --> 00:38:42,660
+لبعده الآن بدنا نفترض مين أنها continuous و نصل
+
+519
+00:38:42,660 --> 00:38:48,860
+لمين للboundedness بدا أثبتلكم بدا أستخدم هذا هذا
+
+520
+00:38:48,860 --> 00:38:55,140
+معناه اتنين ال continuityبستخدمه بطريقة ما على إن
+
+521
+00:38:55,140 --> 00:39:00,200
+أثبت الـ norm للـ T Y أصغر أو ساوي C في الـ norm
+
+522
+00:39:00,200 --> 00:39:06,540
+للـ Y لكل Y element in domain of T هذا إذا أثبتت
+
+523
+00:39:06,540 --> 00:39:09,420
+لكم there exists C أكبر من 0 such that هذا إذا
+
+524
+00:39:09,420 --> 00:39:11,640
+أثبتت هذا معناه أنك أثبتت انه bounded كيف بده
+
+525
+00:39:11,640 --> 00:39:15,940
+أثبته بالاستعانة باللي فوق ماشي إذا الأن بده أقول
+
+526
+00:39:18,650 --> 00:39:21,090
+Conversely suppose that أو assume that T is
+
+527
+00:39:21,090 --> 00:39:23,910
+continuous at an arbitrary point x0 element in
+
+528
+00:39:23,910 --> 00:39:27,090
+domain of T مدام continuous ده بنطبق تعريف ال
+
+529
+00:39:27,090 --> 00:39:30,310
+continuity بمعنى then for every أكبر من أكبر من
+
+530
+00:39:30,310 --> 00:39:30,910
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+531
+00:39:30,910 --> 00:39:30,990
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+532
+00:39:30,990 --> 00:39:31,150
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+533
+00:39:31,150 --> 00:39:31,430
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+534
+00:39:31,430 --> 00:39:32,470
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+535
+00:39:32,470 --> 00:39:33,450
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+536
+00:39:33,450 --> 00:39:44,390
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر
+
+537
+00:39:44,390 --> 00:39:47,630
+من أكبر
+
+538
+00:39:47,670 --> 00:39:50,590
+عشان هيك احنا لو استثننا الصفر مش فارقة معناه قبل
+
+539
+00:39:50,590 --> 00:39:54,430
+شوية اصلا استثنناها من norm وماحكيناش لأن ال
+
+540
+00:39:54,430 --> 00:39:59,070
+inequality دُغر بتشتغل في حالة الصفر الآن عشان
+
+541
+00:39:59,070 --> 00:40:03,450
+اثبت هذه بدي اخد الآن اي واحد دويل موجودة في ال
+
+542
+00:40:03,450 --> 00:40:07,770
+domain of T واشيل الصفر منها، ماشي؟ اذا الان let Y
+
+543
+00:40:07,770 --> 00:40:11,370
+لا تساوي صفر بي أنقل من تمين in domain of T بدي
+
+544
+00:40:11,370 --> 00:40:15,190
+اثبتلكم ان norm لتي Y عن norm لY أصغر من sum C
+
+545
+00:40:16,230 --> 00:40:21,230
+شوفوا صلوا على النبي عليه الصلاة والسلام and set
+
+546
+00:40:21,230 --> 00:40:26,170
+خد الآن X بتساوي X not هذول اللي فوق اللي فوق اللي
+
+547
+00:40:26,170 --> 00:40:29,830
+فوق اللي قبل وشوية بدي أقولكم هتتحققن انا بدي
+
+548
+00:40:29,830 --> 00:40:35,890
+أقولكم هذول هيحققن الفوق وخد X بتساوي X notزائد
+
+549
+00:40:35,890 --> 00:40:41,390
+delta y على 2 normal y ماشي then خد الآن norm ال x
+
+550
+00:40:41,390 --> 00:40:46,550
+minus x not ايش هيساوي delta في y على 2 normal y
+
+551
+00:40:46,550 --> 00:40:51,030
+norm صح اللي هو ايش ماله norm هذي هيروح مع norm
+
+552
+00:40:51,030 --> 00:40:54,090
+هذي بيصير ايش ماله اصغر من delta اللي هو delta على
+
+553
+00:40:54,090 --> 00:40:59,120
+2 اصغر من delta اذا ادملتلكم الآن هذاأصغر من دلتا
+
+554
+00:40:59,120 --> 00:41:03,120
+مدام أصغر من دلتا إذا يتحقق عليه الشرط هذا لإن
+
+555
+00:41:03,120 --> 00:41:06,580
+احنا مفترضين ال T is continuous إذا أكيد by two
+
+556
+00:41:06,580 --> 00:41:11,400
+هيكون عنده نورم ال T X ناطس T X ناطس أصغر من مين؟
+
+557
+00:41:11,400 --> 00:41:15,500
+من إبسلون since T is continuous ابدأ في حسابات هذه
+
+558
+00:41:15,500 --> 00:41:21,920
+هتوصلي للبدية ويساويTX-TX0 بيساوي T of X minus TX0
+
+559
+00:41:21,920 --> 00:41:25,720
+عوضلي على ال X minus X0 اللي هي اش بيساوي منها ال
+
+560
+00:41:25,720 --> 00:41:29,680
+X نقص X0 اللي هي Delta Y على 2 في ال normal Y T is
+
+561
+00:41:29,680 --> 00:41:32,680
+linear إذا بتطلع الدلتا بتطلع حد و بتطلع حد براها
+
+562
+00:41:32,680 --> 00:41:37,620
+بيصير عند دلتاعلى 2 في نورم الـY طالعين من برا
+
+563
+00:41:37,620 --> 00:41:42,400
+الـT ومن برا الـNorm هن حرات لإن هن إيه شمال هن
+
+564
+00:41:42,400 --> 00:41:46,140
+Scalars هدول باعتبار اللي هو بيظال مين اللي جوا
+
+565
+00:41:46,140 --> 00:41:51,200
+الـNorm نورم الـT of مين؟ of Y نورم الـT of Y صار
+
+566
+00:41:51,200 --> 00:41:56,820
+عندي الآن هذا المقدار هيه هيه أصغر من Epsilon يعني
+
+567
+00:41:56,820 --> 00:42:01,840
+بمعنى أخر نورم الـTY أصغر من هذا في هذا على هذا في
+
+568
+00:42:01,840 --> 00:42:08,390
+Epsilonصار عند نورم الـTy أصغر من 2 في إبسلون على
+
+569
+00:42:08,390 --> 00:42:11,690
+دلتا في النورم لميين للـY هذا كله سموه ميين الـC
+
+570
+00:42:11,690 --> 00:42:15,630
+فبصير نورم الـTy أصغر شويه نورم الـY و الـY was
+
+571
+00:42:15,630 --> 00:42:20,110
+arbitrary بـ element in domain of T و بسويش سفر
+
+572
+00:42:20,110 --> 00:42:25,910
+إذا صار عند T إيش ما لها is bounded طيب اللي بعد
+
+573
+00:42:25,910 --> 00:42:33,630
+ويلانفترض أن الـ T مستمر في موقع واحد نفترض أن الـ
+
+574
+00:42:33,630 --> 00:42:35,210
+T مستمر في موقع واحد
+
+575
+00:42:39,460 --> 00:42:43,260
+أنا كله هنا .. هنا في البرهان لما .. اطلع .. لما
+
+576
+00:42:43,260 --> 00:42:47,740
+جيت برهانك هنا انا استغلت اللي هو ال continuity لل
+
+577
+00:42:47,740 --> 00:42:52,620
+.. لل .. لل T وين عند نقطة و أثبتت أنه أشمالها T
+
+578
+00:42:52,620 --> 00:42:56,940
+is bounded اذا from this proof اطلع إلى فوق from
+
+579
+00:42:56,940 --> 00:43:03,000
+this proof from this proofالان from this proof
+
+580
+00:43:03,000 --> 00:43:06,080
+assume that T is continuous at single point اذا
+
+581
+00:43:06,080 --> 00:43:09,680
+from this proof then by the second part of the
+
+582
+00:43:09,680 --> 00:43:14,140
+proof above of A T is bounded و احنا اثبتنا انه
+
+583
+00:43:14,140 --> 00:43:17,320
+لما تكون T is bounded ايش مالها continuous اذا T
+
+584
+00:43:17,320 --> 00:43:19,600
+is continuous فعلا لما تكون continuous عند one
+
+585
+00:43:19,600 --> 00:43:23,640
+single pointفي بعض الناس طبعا بتثبتاش بيكون الكتب
+
+586
+00:43:23,640 --> 00:43:27,260
+عارضة كيف عارضة هادى بدون اللي هي ال .. ال .. ال
+
+587
+00:43:27,260 --> 00:43:29,480
+.. ال .. الboundedness اللي في الطريق يعني ممكن
+
+588
+00:43:29,480 --> 00:43:33,080
+تكون عارضة انه إذا كانت T Linear اثبت لما تكون T
+
+589
+00:43:33,080 --> 00:43:36,720
+continuous تكون على طول اشمالها as اللي هي
+
+590
+00:43:36,720 --> 00:43:39,820
+continuous عند single point and continuous عند
+
+591
+00:43:39,820 --> 00:43:43,520
+every point طبعا بيكون جابلها مثبت اللي هو T is
+
+592
+00:43:43,520 --> 00:43:46,600
+bounded لما تكون continuous is bounded و بشتغل هنا
+
+593
+00:43:46,600 --> 00:43:47,140
+مباشرة
+
+594
+00:43:50,190 --> 00:43:52,630
+أو بعيد البرهان اللي حكيناها قبل شوية عشان يثبتها،
+
+595
+00:43:52,630 --> 00:43:56,230
+فاهمين؟ بعيد البرهان لو كانت اللي هو في الشعار
+
+596
+00:43:56,230 --> 00:44:02,390
+الدلالأولى طيب، اللي بعد؟ Noteولا Corollary لسه
+
+597
+00:44:02,390 --> 00:44:06,270
+Corollary لت T من domain of T لعند Y بيبقى bounded
+
+598
+00:44:06,270 --> 00:44:09,230
+linear operator where domain of T جزء من مين؟ من X
+
+599
+00:44:09,230 --> 00:44:13,570
+and X وY are non-disbases then ايه؟ لما X قالت
+
+600
+00:44:13,570 --> 00:44:17,150
+تروح .. يعني بمعنى أخر T bounded linear operator T
+
+601
+00:44:17,150 --> 00:44:20,330
+bounded linear operator بقول إذا ما يليه التحقق؟
+
+602
+00:44:20,330 --> 00:44:24,970
+إيش هو؟ إن لما X قالت تروح لل Xحيث xn والـ x في
+
+603
+00:44:24,970 --> 00:44:28,610
+domain الـ T بيعطيني automatic T x بتروح ل .. T xn
+
+604
+00:44:28,610 --> 00:44:32,590
+بتروح لمين لـ Tx هذا ما هو تعريف الـ continuity صح
+
+605
+00:44:32,590 --> 00:44:35,650
+ولا لأ تعريف ال continuity إذن بما أنه bounded إذن
+
+606
+00:44:35,650 --> 00:44:38,210
+من النظرية اللي جابل بشوية is a continuous مدام
+
+607
+00:44:38,210 --> 00:44:42,430
+continuous إذن بيطلع إن لما xn تروح لل X لل X لل X
+
+608
+00:44:42,430 --> 00:44:45,030
+في domain ال T وال Xn في domain ال T أكيد ال T xn
+
+609
+00:44:45,030 --> 00:44:48,580
+بتروح ل T x by ده continuityالجزء الثاني ضلال ال
+
+610
+00:44:48,580 --> 00:44:52,480
+space N of T إيش ماله is closed خلّينا نثبت ال N
+
+611
+00:44:52,480 --> 00:44:57,080
+of T is closed كيف نثبت انها closed؟ بتاخدوا X في
+
+612
+00:44:57,080 --> 00:45:02,010
+ال N of T إيش ماله closureوبتثبتوا إن X مين موجودة
+
+613
+00:45:02,010 --> 00:45:07,730
+في الـN of T ماشي؟ طيب إيش معناة X في الـN of T
+
+614
+00:45:07,730 --> 00:45:13,670
+closure؟ إنه there exists Xn in N of T such that
+
+615
+00:45:13,670 --> 00:45:21,010
+Xn converge the mean للـX صح ولا لأ؟بط T X N
+
+616
+00:45:21,010 --> 00:45:26,310
+بتساوي سفر لكل N صح ولا لأ لأن من وين جايات هدوله
+
+617
+00:45:26,310 --> 00:45:29,790
+من ال .. من ال .. من ال .. ال non-less base مظبوط
+
+618
+00:45:29,790 --> 00:45:33,790
+أو اللي هو ال .. ال .. ال .. ال .. ال N of T ماشي
+
+619
+00:45:33,790 --> 00:45:41,250
+فمين؟ اذا طيب لكن انا عمالي بقول ان ال N .. T X N
+
+620
+00:45:41,250 --> 00:45:45,310
+بتروح للسفر اذا اكيد T X N نفسها converge دمين
+
+621
+00:45:45,310 --> 00:45:52,280
+للسفرمعايا و بال continuity الاصلية ال continuity
+
+622
+00:45:52,280 --> 00:45:55,740
+الاصلية مش continuous about it then continuous اذا
+
+623
+00:45:55,740 --> 00:46:01,200
+هيعطيني TXN و تروح لمين لل TX ان XN و X1 موجودة في
+
+624
+00:46:01,200 --> 00:46:06,010
+domain of T تبعيأه مدام T X N بتروح ل T X و T X N
+
+625
+00:46:06,010 --> 00:46:09,850
+لجأت تروح لل سفر و الوحيدة اللي هي هتكون ال limit
+
+626
+00:46:09,850 --> 00:46:14,710
+إذا T X إيش بتساوي إذا T X بتساوي سفر و ما معنى T
+
+627
+00:46:14,710 --> 00:46:18,370
+X بتساوي سفر يعني X element في ال N of T يعني بدأت
+
+628
+00:46:18,370 --> 00:46:20,830
+في ال X N of T closure وصبت ال X في ال N of T
+
+629
+00:46:20,830 --> 00:46:24,210
+معناه أصلا ال N of T closure جزئية من ال N of T و
+
+630
+00:46:24,210 --> 00:46:26,210
+بعرف ال N of T جزئية من ال N of T closure يعني ال
+
+631
+00:46:26,210 --> 00:46:28,970
+N of T closure بيساوي ال N of T معناه أن ال N of T
+
+632
+00:46:28,970 --> 00:46:34,870
+is a closed setاللي بعده Note for any bounded
+
+633
+00:46:34,870 --> 00:46:38,710
+linear operators أو operator for any bounded
+
+634
+00:46:38,710 --> 00:46:42,520
+linear operator مش operatorsلأ، بدّو أكتر .. آه
+
+635
+00:46:42,520 --> 00:46:46,140
+بدّو أكتر آسف For any bounded linear operators T
+
+636
+00:46:46,140 --> 00:46:49,560
+من X عند Y و S من عند Y لعند Z شكل بدو يعملين
+
+637
+00:46:49,560 --> 00:46:54,820
+composition أه؟ Where X .. Y و Z are known spaces,
+
+638
+00:46:55,020 --> 00:46:59,920
+we have نورم الـ T S أصغر أشهر نورم الـ T في نورم
+
+639
+00:46:59,920 --> 00:47:04,320
+الـ S and نورم الـ T N أصغر أشهر نورم الـ T أُس H
+
+640
+00:47:04,320 --> 00:47:09,540
+أُس N هذه induction من هذهوهذه تعملوا تعريف اللي
+
+641
+00:47:09,540 --> 00:47:12,860
+هو norm of Ts ايش norm of Ts بيساوي اللي هو
+
+642
+00:47:12,860 --> 00:47:16,520
+Supremum لكده وشتغلوا عليها هتلاقوها أزرع شوية هذه
+
+643
+00:47:16,520 --> 00:47:21,140
+اللي هو بيبقى ال exercise بسيط معاكم بسهل
+
+644
+00:47:21,140 --> 00:47:29,100
+ماتتقلقوش طيب theorem 2711 مفردات المادة كتير عشان
+
+645
+00:47:29,100 --> 00:47:35,090
+هي صعبة الواحد هيبره كل حاجة طيب theoremبرضه هذه
+
+646
+00:47:35,090 --> 00:47:38,410
+خلّيني أقول سيئة المركزية في ال section اللي
+
+647
+00:47:38,410 --> 00:47:41,390
+بتقوللي let T من domain of T لعند Y بيه a bounded
+
+648
+00:47:41,390 --> 00:47:45,790
+linear operator اه bounded linear operator D of T
+
+649
+00:47:45,790 --> 00:47:50,710
+ماله جزء من normed space اسمه X والـ Y ايش ماله
+
+650
+00:47:50,710 --> 00:47:56,310
+جالنه بنخ space اه complete normed space بيقوللي
+
+651
+00:47:56,310 --> 00:48:00,350
+مدام T جاية من اللي هو domain of T في normed space
+
+652
+00:48:00,350 --> 00:48:05,870
+لعند بنخ space لعند بنخ spacethen T has an
+
+653
+00:48:05,870 --> 00:48:11,470
+extension بقدر أعملك extension للـ T ومش بس بقدر
+
+654
+00:48:11,470 --> 00:48:14,350
+أعمل extension ال extension هيكون من مين؟ من
+
+655
+00:48:14,350 --> 00:48:20,970
+domain of T ماله closure لعند ال Y و هيكون T تلده
+
+656
+00:48:20,970 --> 00:48:25,970
+هيكون برضه bounded linear operator و norm هو norm
+
+657
+00:48:25,970 --> 00:48:34,370
+الأصلي norm هو هيكون norm ال T الأصليةيلّا خلّينا
+
+658
+00:48:34,370 --> 00:48:45,910
+نشوف البرهان لأن البرهان منيح وفيه فكرة يا
+
+659
+00:48:45,910 --> 00:48:53,350
+رب .. طيب .. نشوف إيش بقولالان لت X element من ال
+
+660
+00:48:53,350 --> 00:48:56,310
+domain of T مقفل مادة N في ال domain of T مقفل
+
+661
+00:48:56,310 --> 00:48:56,610
+مادة N في ال domain of T مقفل مادة N في ال domain
+
+662
+00:48:56,610 --> 00:48:57,030
+of T مقفل مادة N في ال domain of T مقفل مادة N في
+
+663
+00:48:57,030 --> 00:48:58,330
+ال domain of T مقفل مادة N في ال domain of T مقفل
+
+664
+00:48:58,330 --> 00:49:01,090
+مادة N في ال domain of T مقفل مادة N في ال domain
+
+665
+00:49:01,090 --> 00:49:11,320
+of T مقفل مادة N في ال domain of Tمعروف By using
+
+666
+00:49:11,320 --> 00:49:14,680
+the linearity and boundedness of T we have ناخد
+
+667
+00:49:14,680 --> 00:49:20,620
+مين اللي هو ايش اللي هو هذي نستخدم ان الـ T is
+
+668
+00:49:20,620 --> 00:49:24,360
+linear و bounded تشوفوا كده احسبولي انه انا انا
+
+669
+00:49:24,360 --> 00:49:25,600
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+670
+00:49:25,600 --> 00:49:31,530
+انا انا انا انا اناT XM ناقص T XM بساوي T XM ناقص
+
+671
+00:49:31,530 --> 00:49:41,390
+T XM بساوي T XM ناقص T XM ناقص T XM بساوي T XM
+
+672
+00:49:41,390 --> 00:49:42,770
+ناقص T XM ناقص T XM بساوي T XM ناقص T XM ناقص T XM
+
+673
+00:49:42,770 --> 00:49:43,310
+ناقص T XM ناقص T XM ناقص T XM ناقص T XM ناقص T XM
+
+674
+00:49:43,310 --> 00:49:46,250
+ناقص T XM ناقص T XM ناقص T XM ناقص T XM ناقص T XM
+
+675
+00:49:46,250 --> 00:49:47,810
+ناقص T XM ناقص T XM ناقص T XM ناقص T XM ناقص T XM
+
+676
+00:49:47,810 --> 00:49:48,590
+ناقص T XM ناقص T XM ناقص T XM ناقص T XM ناقصإذا
+
+677
+00:49:48,590 --> 00:49:52,490
+أنا أخدت الـ XN معاها اللي هو الـ Conversion of
+
+678
+00:49:52,490 --> 00:49:58,050
+the mean للـ X إذا مدام كوشي إذا هذه اللي هي هيكون
+
+679
+00:49:58,050 --> 00:50:01,770
+عنده أصغر من أي أبسلون في الدنيا من ضبلهم الأبسل
+
+680
+00:50:01,770 --> 00:50:05,610
+على نورميل T يعني بمعنى أخر هذا provided that
+
+681
+00:50:05,610 --> 00:50:08,760
+نورميل T لبش سفربهذا معناته صار ايش ماله أصغر من
+
+682
+00:50:08,760 --> 00:50:12,860
+إبسلون إذا صار برضه إيش ماله كوشي إذا صارت ال TXN
+
+683
+00:50:12,860 --> 00:50:17,000
+كوشي الآن لازم ال إيش ال TXN كوشي في مين؟ في ال Y
+
+684
+00:50:17,000 --> 00:50:22,400
+و ال Y complete إذا هذا إيش هتكون converge إذا
+
+685
+00:50:22,400 --> 00:50:27,180
+الآن TXN كوشي sequence because XN is but Y is
+
+686
+00:50:27,180 --> 00:50:31,920
+complete then TXN converge say thatT X N converts
+
+687
+00:50:31,920 --> 00:50:37,240
+the mean Y element in Y وشوفوا هل اللي عملناه اللي
+
+688
+00:50:37,240 --> 00:50:41,580
+سوناه عشان هو أساس البرهان الآن أساس تركيبة الـ T
+
+689
+00:50:41,580 --> 00:50:49,280
+Extension الـ T تلدة أخدت الآن X N راحت لمين؟ لل X
+
+690
+00:50:49,280 --> 00:50:53,480
+ال X من وين هذه؟ هذه هي أصلا اللي أشغل غرضي أن
+
+691
+00:50:53,480 --> 00:50:58,900
+أعمل T تلدة من domain of T closure لعند مين؟ لعند
+
+692
+00:50:58,900 --> 00:51:05,140
+ال Yالان extension معناته انا مفكر شو معناته
+
+693
+00:51:05,140 --> 00:51:10,520
+extension اصلا ان ال T دلده هتساوي T لكل X في ال
+
+694
+00:51:10,520 --> 00:51:15,890
+domain الأصليوالآن اللي بيظل بتعرفه مين اللي بيظل
+
+695
+00:51:15,890 --> 00:51:18,430
+اللي في الـ .. اللي في الـ closure اللي برا ماشي
+
+696
+00:51:18,430 --> 00:51:23,230
+الحال اللي مش موجود فيها دي وبدو يكون حسابي انه
+
+697
+00:51:23,230 --> 00:51:25,850
+اللي أنا عرفته اللي هو اللي .. اللي .. اللي في ال
+
+698
+00:51:25,850 --> 00:51:28,470
+domain T و ال closure لو التقت واحدة في ال domain
+
+699
+00:51:28,470 --> 00:51:32,190
+T و ال closure موجودة في نفسها يعني أحيان ممكن
+
+700
+00:51:32,190 --> 00:51:34,750
+يكون Demon if they close أصلا فيكون هي نفس الاشياء
+
+701
+00:51:34,750 --> 00:51:38,750
+فلازم يكون اللي هي الصورة under T و under T تلدة
+
+702
+00:51:38,750 --> 00:51:42,640
+للعناصر اللي موجودة في الأصل زي بعضوالجديد بدي
+
+703
+00:51:42,640 --> 00:51:46,720
+أعرفه بطريقة معينة فالآن أنا بدأت في الـ X و إيه
+
+704
+00:51:46,720 --> 00:51:53,480
+الموجودة في ال domain of T closure إيش عملت؟ اللي
+
+705
+00:51:53,480 --> 00:51:56,840
+جاية TXN بتروح لمين لل X؟ و فدولة موجودة وين؟ في
+
+706
+00:51:56,840 --> 00:51:59,080
+ال domain of T يعني في الأصل الموجودة و معرفة عند
+
+707
+00:51:59,080 --> 00:52:07,460
+T ماشي الآن لما نمشيت أثبتتلكم أن TXN صورة هدولة
+
+708
+00:52:07,460 --> 00:52:15,710
+راحت لمين؟Y وين موجودة في الـ Y كابتنال
+
+709
+00:52:19,690 --> 00:52:26,230
+اللي من خلاله بدأ أقول عرفلي T تلدة لل X اللي
+
+710
+00:52:26,230 --> 00:52:30,370
+بدأتها عشان أشتغل على هذه بساوة مين Y اللي وجيتها
+
+711
+00:52:30,370 --> 00:52:35,090
+هنا إذا Y هذه مين لما عرفت T تلدة X بساوة Y هي Y
+
+712
+00:52:35,090 --> 00:52:41,010
+اللي نتجت من لما XN راحت لل X وطلعت T XN راحت
+
+713
+00:52:41,010 --> 00:52:45,630
+لإيشي هو الإيشي هذا اللي بدي أسميه T مين T X واضح
+
+714
+00:52:45,630 --> 00:52:55,800
+هذا T تلدة لل Xطيب إذا الآن define T tilde by T
+
+715
+00:52:55,800 --> 00:52:58,940
+tilde X بسوء Y we show that T tilde is well
+
+716
+00:52:58,940 --> 00:53:04,220
+defined الآن T tilde بتنثبت أنها إيش مالها well
+
+717
+00:53:04,220 --> 00:53:09,240
+defined الآن well defined هو خايف إيش؟ خايف إنه
+
+718
+00:53:09,240 --> 00:53:15,600
+إنتوا لما أخدنا X في ال domain T closureأنا بقول
+
+719
+00:53:15,600 --> 00:53:20,900
+لجيت في عندي XN راحة ل X و لجيتها و حطيتها روحتوا
+
+720
+00:53:20,900 --> 00:53:24,040
+انتوا و جبتوا واحدة تانية في عندك ممكن infinite
+
+721
+00:53:24,040 --> 00:53:26,880
+number of sequences يروح إلى مين لنفس ال limit و
+
+722
+00:53:26,880 --> 00:53:31,960
+هدولة من .. زي ما بتعرفوا مثلا لو نحكي في ذاك نص و
+
+723
+00:53:31,960 --> 00:53:35,240
+تلت و ربع إلى أخر هدولة كلهم بروح إلى مين للسفر
+
+724
+00:53:35,240 --> 00:53:40,760
+صح؟فلجيته نص و ربع و تمن الاخر بروح برضه لمين لصفر
+
+725
+00:53:40,760 --> 00:53:45,380
+واحد على اتنين أُس ثلاثة أُس ثلاثان واحد على اتنين
+
+726
+00:53:45,380 --> 00:53:49,480
+أُس أربعان كلهم بروح لصفر فبخافوا كل واحد أخده
+
+727
+00:53:49,480 --> 00:53:52,240
+sequence بتختلف عن التانية حتى لو كلنا أخدنا
+
+728
+00:53:52,240 --> 00:53:55,440
+sequences باختلفنا عن التانية هنلاجيه ال .. ال ..
+
+729
+00:53:55,440 --> 00:54:02,600
+ال .. ال ..لن يؤثر على اللي هو تعريفنا لخوف إن X
+
+730
+00:54:02,600 --> 00:54:06,780
+أنه تروح لل X أنا ديبتها و أنتوا عندكم Z أن تروح
+
+731
+00:54:06,780 --> 00:54:10,580
+لمين لل X بقولك بالرغم إن هيك ما تجلجوش هيكون
+
+732
+00:54:10,580 --> 00:54:14,800
+التعريف نفس التعريف شوفوا كيف .. شوفوا كيفالان
+
+733
+00:54:14,800 --> 00:54:20,640
+suppose that xn هدأت تعريفك او تعريفك xn بتروح
+
+734
+00:54:20,640 --> 00:54:26,620
+لمين لل x وانا جبت zn راحت لمين لل x وبدأت سلسل
+
+735
+00:54:26,620 --> 00:54:31,340
+اذا الان انا
+
+736
+00:54:31,340 --> 00:54:36,440
+سلسلت وجبت تي xn راحت لمين ل y وانت جبت تي zn
+
+737
+00:54:36,440 --> 00:54:39,860
+وراحت لمين ل y شرطة هتكون y شرطة و y أشمالين نفس
+
+738
+00:54:39,860 --> 00:54:45,550
+الاشي الدليلthen الان خدوا VM VM هتروح لل X مين ال
+
+739
+00:54:45,550 --> 00:54:49,670
+VM هو عبارة عن X واحد Z واحد X اتنين Z اتنين X
+
+740
+00:54:49,670 --> 00:54:52,990
+تلاتة Z تلاتة واضح ان هذه الطيارة وين ناحية ال X
+
+741
+00:54:52,990 --> 00:54:56,090
+ماشي الحال اذا هذه راحت لل X طب ما كل ال
+
+742
+00:54:56,090 --> 00:55:01,550
+subsequence اللي انت صار عندي TVM برضه converts
+
+743
+00:55:02,960 --> 00:55:07,560
+بنفس الأشياء VM مش راحت لل X حسب اللي حكيناه قبل
+
+744
+00:55:07,560 --> 00:55:12,120
+شوية هلاقي الـ TVM مين هتروح لصورة معينة اللي هي
+
+745
+00:55:12,120 --> 00:55:16,520
+TVM converts ده الـ Y اللي بيقول عنها الآن الـ TVM
+
+746
+00:55:16,520 --> 00:55:21,060
+ماهيها and the two subsequences TX and TZ and
+
+747
+00:55:21,060 --> 00:55:25,680
+هدولة subsequences من مين؟ من TVM و هذه راحت ل
+
+748
+00:55:25,680 --> 00:55:30,000
+limit و هدولة converts حسب الحديث الأولاني إذا كله
+
+749
+00:55:30,000 --> 00:55:33,350
+اللي هيروح لمين؟لنفس الـ Limit إن ده معناته إنه
+
+750
+00:55:33,350 --> 00:55:37,610
+TXN و TZN إيش مابتكم خدوا Sequences بتروح لل X
+
+751
+00:55:37,610 --> 00:55:43,330
+هنصل في النهاية TXN تبعتي و TZN تبعتكم و TWN تبعت
+
+752
+00:55:43,330 --> 00:55:47,290
+أي واحد اللي هي في الأصل كانت كله نراحل لل X هيكون
+
+753
+00:55:47,290 --> 00:55:51,470
+نقله نفس الـ T نفس ال Y اللي بتطلع Limit للـ TXN
+
+754
+00:55:51,470 --> 00:55:55,170
+أو TZN أو TWN إذا .. إذا صار عندنا تعريف Now
+
+755
+00:55:55,170 --> 00:55:59,650
+Definedإذاً hence T تلدة is well-defined in domain
+
+756
+00:55:59,650 --> 00:56:03,570
+of T a closure اللي عم نضل ليش ما نثبت؟ بدنا نثبت
+
+757
+00:56:03,570 --> 00:56:10,550
+أنه اللي هو ال linearity و بدنا نثبت اللي هي ال
+
+758
+00:56:10,550 --> 00:56:13,370
+boundedness و نثبت في النهاية نورم هذا بسوء نورم
+
+759
+00:56:13,370 --> 00:56:14,410
+هذا شوفوا الآن
+
+760
+00:56:18,840 --> 00:56:24,320
+Hence T tilde is well defined لان let X and X
+
+761
+00:56:24,320 --> 00:56:31,140
+prime be any elements in domain of T closure عشان
+
+762
+00:56:31,140 --> 00:56:34,640
+أثبت ال linearity والألفة بيه any scalar then
+
+763
+00:56:34,640 --> 00:56:37,480
+there are sequences مدام X في domain of T إذا
+
+764
+00:56:37,480 --> 00:56:45,840
+بلاجي sequence XNلل X و XN' لل X' حيث معايا XN
+
+765
+00:56:45,840 --> 00:56:51,380
+بتروح لل X و XN' بتروح لمين لل X' as above بالظبط
+
+766
+00:56:51,380 --> 00:56:55,340
+القالية التعريف اللي عارفينها هيكون ال TXN بيروح
+
+767
+00:56:55,340 --> 00:57:01,780
+لمين ل some Y في ال Y و TXN' هيروح لمين ل Y' هذا
+
+768
+00:57:01,780 --> 00:57:07,050
+قالية التعريفإذاً هيكون T تلدة لل X اللي هي ال Y
+
+769
+00:57:07,050 --> 00:57:13,610
+اللي روحت لل X و T تلدة X برايم إيش هتكون ال Y
+
+770
+00:57:13,610 --> 00:57:20,190
+برايم هذه الآن since T is a linear then T of Alpha
+
+771
+00:57:20,190 --> 00:57:25,400
+X N زائد X N برايم إيش هتساوي؟الـ T العصرية الـ T
+
+772
+00:57:25,400 --> 00:57:28,180
+العصرية اللي أنا بشتغلها دي بساوة Alpha T X N زي
+
+773
+00:57:28,180 --> 00:57:32,320
+Alpha T X N Prime هدول حيروح لمين Alpha T X N زي T
+
+774
+00:57:32,320 --> 00:57:36,400
+X N Prime الـ T X N هتروح لمين للـ Y و T X N Prime
+
+775
+00:57:36,400 --> 00:57:39,820
+هتروح لمين للـ Y Prime إذا هذا كله راح لمين للـ
+
+776
+00:57:39,820 --> 00:57:45,200
+Alpha I زي Y Prime يعني بمعنى آخر لما Alpha X N زي
+
+777
+00:57:45,200 --> 00:57:50,620
+X M Prime راحت للـ Alpha X زي X Prime الـ T تبعته
+
+778
+00:57:50,620 --> 00:57:55,630
+راحت لهذهإذن هذه هي عبارة عن الـ T تلدة للي قلتن
+
+779
+00:57:55,630 --> 00:58:00,550
+حسب التعريف بمعنى but alpha xn زائد xn prime هذه
+
+780
+00:58:00,550 --> 00:58:04,110
+مش هي بتقدر تتعريف بتروح لل alpha x زايد x prime
+
+781
+00:58:04,110 --> 00:58:08,850
+then by the definition of T تلدة T of هذه اللي
+
+782
+00:58:08,850 --> 00:58:14,080
+راحاتي لها هذه بتساوي سور اللي هواللي راح اتيلها
+
+783
+00:58:14,080 --> 00:58:18,180
+صورة هادى مين اللي هي صورة هادى؟ راحت لمين؟ للـ α
+
+784
+00:58:18,180 --> 00:58:23,460
+y زائد y' إذن هادى بيصير T of α T تلدة of α x زائد
+
+785
+00:58:23,460 --> 00:58:27,420
+x' بيساوي α y زائد y' اللي هي α y اللي هي مين؟ هي
+
+786
+00:58:27,420 --> 00:58:33,040
+α T تلدة x والـ y' اللي هي T تلدة x' إذن فعلا طلعت
+
+787
+00:58:33,040 --> 00:58:37,600
+عندي T تلدة إيش ما لها is linear لذا مفتاح الحل هو
+
+788
+00:58:37,600 --> 00:58:42,720
+هذا هذا مفتاح الشغل كله إنه كيف أنا عرفت المفروض
+
+789
+00:58:42,720 --> 00:58:47,890
+فاهمينمش فاهمين عدوها هتلاقي الكلام واضح انا بشر
+
+790
+00:58:47,890 --> 00:58:57,390
+اصلا ما يكون الكلام مش واضح و بعيده بعيده
+
+791
+00:58:57,390 --> 00:59:02,770
+بطريقة تصير أوضح لكن بعتقد انه واضح الان
+
+792
+00:59:03,950 --> 00:59:08,150
+أثبتنا ان T is linear الان نثبت لكم ان T تلد اصلا
+
+793
+00:59:08,150 --> 00:59:12,310
+extension ايش معناه extension ان هي بتساوي الأصل
+
+794
+00:59:12,310 --> 00:59:16,920
+في الأصليعني T تلدة على ال domain of T هي نفس T و
+
+795
+00:59:16,920 --> 00:59:19,480
+لا بتبطئ ال extension عشواء معايا ده لتانية أصلا
+
+796
+00:59:19,480 --> 00:59:22,760
+أما مادام extension مفهومها أنها بدها تبقى على
+
+797
+00:59:22,760 --> 00:59:26,900
+الأصل زي ما هو و تزيد على زيادة بطريقة تلائم اللي
+
+798
+00:59:26,900 --> 00:59:30,320
+موجود أو تحقق هدف إذا كان بديه هدفانة الهدفانة أن
+
+799
+00:59:30,320 --> 00:59:33,540
+تكون T تلدة normal بيساوي normal T كل هذا حجبناه
+
+800
+00:59:33,540 --> 00:59:38,960
+مرة واحدة الان but T تلدة لل X أشهر بتساوي T X for
+
+801
+00:59:38,960 --> 00:59:44,620
+all X in every domain من جلك becauseالـ X عندى X
+
+802
+00:59:44,620 --> 00:59:48,440
+هي بتروح للـ X يعني الـ sequence X X X X بتروح
+
+803
+00:59:48,440 --> 00:59:52,100
+لمين للـ X هاي الـ sequence اللى عندى ماشي بتروح
+
+804
+00:59:52,100 --> 01:00:00,280
+لمين للـ X و الـ TX الـ TX هتروح لمين للـ TX ليش
+
+805
+01:00:00,280 --> 01:00:04,660
+لأن الـ X هادى من وين دي يعني من ال domain of T و
+
+806
+01:00:04,660 --> 01:00:09,420
+ال domain of TT continuous عنده أه إذا أكيد هيكون
+
+807
+01:00:09,420 --> 01:00:13,930
+مش boundedما دام باوندد يا جماعة هال gate فيه عندي
+
+808
+01:00:13,930 --> 01:00:18,310
+sequence of elements كله انثباتات X بيروح لمين لل
+
+809
+01:00:18,310 --> 01:00:25,760
+X و ال X وين موجودة في domain ال Tو domain الـ T،
+
+810
+01:00:25,760 --> 01:00:29,340
+T is continuous عنده مدام .. يعني بدل ما أقول Xn
+
+811
+01:00:29,340 --> 01:00:33,980
+بتروح للـ Xn للـ X الـ Xn هذه أشمع لل X واحد X الـ
+
+812
+01:00:33,980 --> 01:00:37,420
+X اتنين X الـ X ثلاثة X والـ X أربعة X والـ X خمسة
+
+813
+01:00:37,420 --> 01:00:41,940
+X يعني sequence of كل مين X X X هدورها بيروح لمين؟
+
+814
+01:00:41,940 --> 01:00:47,080
+للـ X ماشي الحال الآن أكيد مزامة الـ X موجودة في
+
+815
+01:00:47,080 --> 01:00:54,990
+domain of T هيكون TXn بيروح لمين؟ للـ TXهذه اللي
+
+816
+01:00:54,990 --> 01:01:00,150
+أنا بعرف الـ T تلدة بساوي هذا اللي طلع عندى اللي
+
+817
+01:01:00,150 --> 01:01:06,670
+كنت أسميها Y اللي هي T تلدة لل X هيساومين TX الـ N
+
+818
+01:01:06,670 --> 01:01:09,930
+TXN هي في الواقع Xات كلها يعني أه فعشانك بقول X
+
+819
+01:01:09,930 --> 01:01:14,310
+بتروح لل X إذا TX بتروح ل TX ومن ثم T تلدة اللي
+
+820
+01:01:14,310 --> 01:01:21,760
+بعرفها لل X هي TXN لما تروح لرقم هو اسمه TXهذا
+
+821
+01:01:21,760 --> 01:01:26,800
+بصوتين اذا اكيد اكيد اكيد so T تلده is a linear
+
+822
+01:01:26,800 --> 01:01:32,300
+extension of T وطلع فوق خلّينا ننهي القمر ان نثبت
+
+823
+01:01:32,300 --> 01:01:38,500
+انها bounded ومن ثم نثبت اللي هو norm T هو نفسه
+
+824
+01:01:38,500 --> 01:01:44,440
+norm T تلده وركزوا في ما نتحدث به طيب صلى على
+
+825
+01:01:44,440 --> 01:01:48,880
+النبعخدوا الآن IX في domain الـ T closure خلاص صار
+
+826
+01:01:48,880 --> 01:01:54,070
+domain هو هذا الـ T تلدThere is a sequence xn of
+
+827
+01:01:54,070 --> 01:01:57,830
+elements in D of T such that xn بتروح لمين للإكس
+
+828
+01:01:57,830 --> 01:02:02,650
+هذا اللي هو مفتاح الحلو ومفتاح التعريف xn بتروح
+
+829
+01:02:02,650 --> 01:02:06,670
+للإكس وزي ما عملنا فوق هيطلع T xn بتروح لمين للواي
+
+830
+01:02:06,670 --> 01:02:14,310
+و هتكون T تلدة للإكس هو مين الواي and T تلدة للإكس
+
+831
+01:02:14,310 --> 01:02:19,630
+هتكون يش من هي بتساوي Yالان شوف كيف بدي اصل ل T
+
+832
+01:02:19,630 --> 01:02:25,190
+تلده is bounded يعني بدي اثبتلكم ان T تلده T تلده
+
+833
+01:02:25,190 --> 01:02:35,290
+is bounded بمعنى بمعنى
+
+834
+01:02:35,290 --> 01:02:41,950
+بدي اثبت norm T تلده X أصغر لو سوى C في norm X
+
+835
+01:02:45,110 --> 01:02:48,570
+هو في الواقع حثبتلكم أن T تلدة لل X أصغر أشهر هو C
+
+836
+01:02:48,570 --> 01:02:55,690
+اللي هي نورم ال T في نورم ال X طيب تشوف صلوا على
+
+837
+01:02:55,690 --> 01:03:01,290
+النبي عليه الصلاة والسلام احسبولي نورم ال T Xأكيد
+
+838
+01:03:01,290 --> 01:03:04,890
+هيكون تـis bounded أصغر يساوي نورم الـT في نورم
+
+839
+01:03:04,890 --> 01:03:11,090
+الـMain الـXN for all mean N الـNorm الـT
+
+840
+01:03:11,090 --> 01:03:13,490
+continuous ليش معناه continuous بدخل الـlimit جوا
+
+841
+01:03:13,490 --> 01:03:17,190
+و بطلع برا زي ما بده ماشي هنا معناته أن هو نورم
+
+842
+01:03:17,190 --> 01:03:20,850
+الـT continuous letting N بتروح لـinfinity and
+
+843
+01:03:20,850 --> 01:03:25,650
+using the continuity of the norm to getالان خدوا
+
+844
+01:03:25,650 --> 01:03:30,910
+الان norm تل دل ال X من جهة أخرى ايش هيساوي؟ norm
+
+845
+01:03:30,910 --> 01:03:34,470
+ال Y مش عارفين ماحنا قولنا ال T تل د X مين هي؟
+
+846
+01:03:34,470 --> 01:03:38,090
+بيساوي .. خدوا norm هذي بيساوي norm هذي ماشي؟ Y
+
+847
+01:03:38,090 --> 01:03:45,010
+ساوي الان norm ال Y اللي هو عبارة عن limit ل norm
+
+848
+01:03:45,010 --> 01:03:50,390
+T X N مظبوط؟ ال T X N بيروح لمين؟الـ T X N بتروح
+
+849
+01:03:50,390 --> 01:03:54,710
+لمين للـ Y إذا الـ limit هذا بروح لمين لـ Normal Y
+
+850
+01:03:54,710 --> 01:04:04,650
+الـ Y بساوة T X N صح Normal Y بساوة norm هذا صح
+
+851
+01:04:04,650 --> 01:04:10,370
+إذا خدوا ال limit للجهتين بطلع Normal Y limit
+
+852
+01:04:10,370 --> 01:04:13,550
+بساوة
+
+853
+01:04:13,550 --> 01:04:21,800
+limit norm T X Nلأن ال limit بتنزل من جواه ال norm
+
+854
+01:04:21,800 --> 01:04:28,260
+لأن انا بعرف y بساوي limit ال T xn صح ولا لأ norm
+
+855
+01:04:28,260 --> 01:04:32,600
+هذه بساوي norm هذه طلعيني ال limit برا لإنها
+
+856
+01:04:32,600 --> 01:04:34,860
+continuous بيصير norm ال y بساوي limit norm ال T
+
+857
+01:04:34,860 --> 01:04:39,820
+xn إذا طلع عندي norm ال y automatic بساوي limit
+
+858
+01:04:39,820 --> 01:04:43,340
+norm ال T xn نيجي الآن norm ال T xn أصلا يساوي
+
+859
+01:04:43,340 --> 01:04:46,170
+norm ال T في norm ال x صح؟إذاً limit هذا أصغر شهر
+
+860
+01:04:46,170 --> 01:04:49,130
+و limit هذه إذاً صار عيدي limit هذا أصغر شهر و
+
+861
+01:04:49,130 --> 01:04:52,050
+limit هذه في هذه طب ما هي constant بالنسبة لل
+
+862
+01:04:52,050 --> 01:04:55,650
+limit اللي بتطلع برا بيصير limit norm ال xn limit
+
+863
+01:04:55,650 --> 01:04:59,570
+norm ال xn مع أن ما أقول ال xn بتروح لل x و ال
+
+864
+01:04:59,570 --> 01:05:03,410
+norm continuous إذاً limit norm ال xn هو عبارة عن
+
+865
+01:05:03,410 --> 01:05:08,290
+norm ال x إذاً صار عندي norm ال T في norm ال x
+
+866
+01:05:08,290 --> 01:05:15,660
+اللي حصلته norm ال T تلدة لل x انتبهنأصغر أو يساوي
+
+867
+01:05:15,660 --> 01:05:20,520
+نورم الـT في نورم الـX نورم الـT هو الـC إذا صارت
+
+868
+01:05:20,520 --> 01:05:25,340
+الـT تلدة is bounded ومش هيك ونورم الـT تلدة أصغر
+
+869
+01:05:25,340 --> 01:05:30,700
+يساوي مين؟ نورم الـT ليش؟ لأنه انا اثبتت نورمالـ T
+
+870
+01:05:30,700 --> 01:05:35,000
+تلدة X أصغر أو شويه نورم الـ T في نورم الـ X يعني
+
+871
+01:05:35,000 --> 01:05:37,300
+على نورم الـ X X لا تشويه شويه تلد أصغر أو شويه
+
+872
+01:05:37,300 --> 01:05:39,980
+هدى لكل X في دمية الـ T معدى الـ Zero خدوا الـ
+
+873
+01:05:39,980 --> 01:05:45,240
+Supremum بيصير أصغر أو شويه هذا معناته أنه هذا الـ
+
+874
+01:05:45,240 --> 01:05:49,220
+Supremum إيش بيساوي نورم الـ T تلدة صارت نورم الـ
+
+875
+01:05:49,220 --> 01:05:53,980
+T تلدة أصغر أو شويه نورم الـ T العكس سهل العكس سهل
+
+876
+01:05:53,980 --> 01:05:58,920
+و شريعhowever norm of T تلدة عارفين هو ايش بيساوي
+
+877
+01:05:58,920 --> 01:06:03,360
+احنا supremum ل norm of T تلدة X X في domain T
+
+878
+01:06:03,360 --> 01:06:06,600
+تبعها closure such that norm of X بيساوي واحد سهل
+
+879
+01:06:06,600 --> 01:06:08,300
+اللي لنا نشتغل على norm of X بيساوي واحد من زمنا
+
+880
+01:06:08,300 --> 01:06:13,650
+التكافئة في قادة الان هذه الست هذه الستأكبر من ال
+
+881
+01:06:13,650 --> 01:06:17,570
+6 اللي X فيه مالها في domain الـ T وحنا بنعرف في
+
+882
+01:06:17,570 --> 01:06:21,710
+domain الـ T norm الـ T X هو نفسه norm الـ T تلد X
+
+883
+01:06:21,710 --> 01:06:24,710
+لأنه على domain الـ T الـ T تلد و الـ T زي بعض مش
+
+884
+01:06:24,710 --> 01:06:29,810
+exception إذا هذه المجموعة جزئية من هذهأه، إذا
+
+885
+01:06:29,810 --> 01:06:32,790
+أكيد الـ Supremum على الكبير أكبر أو يساوي الـ
+
+886
+01:06:32,790 --> 01:06:36,090
+Supremum على الأزهر هذا الـ Supremum هو عبارة عن
+
+887
+01:06:36,090 --> 01:06:40,230
+Norm of T يعني بمعنى أخر أثبتنا Norm of T تلدة
+
+888
+01:06:40,230 --> 01:06:45,290
+أكبر أو يساوي Norm من الـ T ومن الأصل Norm of T
+
+889
+01:06:45,290 --> 01:06:47,750
+تلدة أزهر يساوي Norm of T همهالة أصلا الصعوبة في
+
+890
+01:06:47,750 --> 01:06:50,370
+الحل، هذا كسيلة بيطلع Norm of T تلدة هو بيساوي
+
+891
+01:06:50,370 --> 01:06:55,350
+Norm of T و هكذا بالانهيأ اللي هو الـ Section هذا
+
+892
+01:06:55,350 --> 01:06:56,670
+و إلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/OMe_05RbxKs_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/OMe_05RbxKs_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e729e6dc232501c531674a6e5db773b7fce6bbd2
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/OMe_05RbxKs_postprocess.srt
@@ -0,0 +1,1056 @@
+1
+00:00:05,110 --> 00:00:07,730
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,730 --> 00:00:10,530
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,530 --> 00:00:18,050
+آله وصحبه أجمعين المحاضرة هي محاضرة رقم 14 مساق
+
+4
+00:00:18,050 --> 00:00:21,210
+تحليل اقتراني أو تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:21,210 --> 00:00:26,430
+الإسلامية ماجستيريا رياضيةوصلنا لعند اتنين تمانية
+
+6
+00:00:26,430 --> 00:00:32,590
+اللي هو تحت عنوان linear functionals حكينا المرة
+
+7
+00:00:32,590 --> 00:00:36,730
+الماضية عن ال bounded linear operators الآن ده
+
+8
+00:00:36,730 --> 00:00:39,370
+نحكي عن حالة خاصة من ال bounded linear operators
+
+9
+00:00:39,370 --> 00:00:42,290
+اللي هي حاجة اسمها linear functionals هي عبارة عن
+
+10
+00:00:42,290 --> 00:00:45,570
+bounded linear operators بس بترمي في field في ال
+
+11
+00:00:45,570 --> 00:00:51,130
+field او في scalars انشوف كدهdefinition a linear
+
+12
+00:00:51,130 --> 00:00:56,930
+functional is a linear operator عادى with domain
+
+13
+00:00:56,930 --> 00:01:02,030
+in a vector space and range when in the scalar
+
+14
+00:01:02,030 --> 00:01:05,210
+field of the vector space هذا ك linear operator من
+
+15
+00:01:05,210 --> 00:01:07,970
+دون ما نحكي عن ال bounded اللي هو اللي عندما نحكي
+
+16
+00:01:07,970 --> 00:01:10,850
+عن ال boundedness على طول بنحط vector spaces أو
+
+17
+00:01:10,850 --> 00:01:14,650
+بنحط norms أو بنحط topologiesdefinition a bounded
+
+18
+00:01:14,650 --> 00:01:17,690
+linear functional الان بدنا نحكي عن bounded linear
+
+19
+00:01:17,690 --> 00:01:21,510
+functional is a bounded linear operator with
+
+20
+00:01:21,510 --> 00:01:27,570
+domain in a normed space عادي and range وين بس in
+
+21
+00:01:27,570 --> 00:01:32,030
+the scalar field لnormed space اللي إيش اللي في ال
+
+22
+00:01:32,030 --> 00:01:35,730
+domain ماشي الحالة إذا يعني من normed space إلى ال
+
+23
+00:01:35,730 --> 00:01:39,690
+scalar field تبعه هذا اللي بنسميه bounded linear
+
+24
+00:01:39,690 --> 00:01:43,610
+functional يعني أعطينا اسم خاصفي النهاية اللي هو
+
+25
+00:01:43,610 --> 00:01:46,830
+الـ scalar ما هو عليه نور في حالة الـ R الـ
+
+26
+00:01:46,830 --> 00:01:49,930
+absolute value وفي حالة الـ C ما هو المدلس اللي هو
+
+27
+00:01:49,930 --> 00:01:54,690
+يعني اللي احنا بنتعامل معاه دائما نيجي لأول نظرية
+
+28
+00:01:54,690 --> 00:01:59,310
+النظرية الأولى a linear functional يعني كل linear
+
+29
+00:01:59,310 --> 00:02:02,730
+functional is a linear operator وكل bounded linear
+
+30
+00:02:02,730 --> 00:02:06,070
+functional is a bounded linear operator يعني اللي
+
+31
+00:02:06,070 --> 00:02:08,710
+انطبق على ال bounded linear operators هنطبق عالميا
+
+32
+00:02:08,710 --> 00:02:11,090
+على ال bounded linear functionals
+
+33
+00:02:13,450 --> 00:02:16,670
+النظرية 283 بتقول الـ a linear functional F with
+
+34
+00:02:16,670 --> 00:02:20,150
+domain T in a normed space is continuous if and
+
+35
+00:02:20,150 --> 00:02:24,090
+only if it is H-bound، ذات الحق إنها قبل شوية، هي
+
+36
+00:02:24,090 --> 00:02:26,830
+نفس النظرية بس اللي هي بنأكدها على حالة الـ linear
+
+37
+00:02:26,830 --> 00:02:30,600
+functionalالان examples بناخد أمثلة على اللي هو
+
+38
+00:02:30,600 --> 00:02:33,040
+bounded linear functionals أو على ال linear
+
+39
+00:02:33,040 --> 00:02:36,680
+functionals أو بدنا ناخد على اللي هو functionals
+
+40
+00:02:36,680 --> 00:02:40,520
+ما تكونش إيش اللي هو linear أحيانا الان the norm
+
+41
+00:02:40,520 --> 00:02:44,460
+ال norm اللي إحنا بنعرفه برمى من ال X لعند مين
+
+42
+00:02:44,460 --> 00:02:47,340
+لعند ال R بياخد أي norm في أي element من ال X
+
+43
+00:02:47,340 --> 00:02:50,760
+وبياخدله ال norm بطلع أيش ما له R positive اتحاد
+
+44
+00:02:50,760 --> 00:02:56,580
+ال zeroon a normed space X is a functional صح لكن
+
+45
+00:02:56,580 --> 00:03:00,960
+ايش ماله انه X which is not linear مش linear لأنه
+
+46
+00:03:00,960 --> 00:03:07,720
+بنعرف احنا اللي هو norm norm norm الـ Alpha X زائد
+
+47
+00:03:07,720 --> 00:03:12,380
+Beta أو Y زائد Y ليس شرطا هذا أصغر أو ساوي
+
+48
+00:03:12,380 --> 00:03:16,020
+absolute value لل X في norm ال X زائد norm ال Y
+
+49
+00:03:16,340 --> 00:03:23,120
+ولكن المساواة ليس شرطا أن تحدث عشان هيك اشماله is
+
+50
+00:03:23,120 --> 00:03:27,880
+not linear طيب الان نجي لـ Dot product ال dot
+
+51
+00:03:27,880 --> 00:03:31,380
+product العادل اللي احنا بنعرفه let A بتساوي الف
+
+52
+00:03:31,380 --> 00:03:34,740
+واحد الف اتنين الف تلاتة لعند B I fix element in R
+
+53
+00:03:34,740 --> 00:03:39,940
+تكعيب define F من R تكعيب لعند R byF of X ايش
+
+54
+00:03:39,940 --> 00:03:44,340
+بتساوي؟ X ضد الـA، ماشي الحال؟ الـ dot product
+
+55
+00:03:44,340 --> 00:03:47,220
+العادى اللي هو بياخد ال vector في الـR تكييب و
+
+56
+00:03:47,220 --> 00:03:49,880
+بضربه في ال vector لكن بطلع قيمة ال dot product
+
+57
+00:03:49,880 --> 00:03:54,060
+يشمله scalar اللي هو بطلع في الـR فهذا مثال على
+
+58
+00:03:54,060 --> 00:03:58,820
+linear functional which is bounded then F is a
+
+59
+00:03:58,820 --> 00:04:03,640
+bounded linear functional ومش هيك كمان normal F
+
+60
+00:04:03,640 --> 00:04:09,430
+هيساوي مين؟ normal Aخلّينا نشوف الآن اللي هي نبرهن
+
+61
+00:04:09,430 --> 00:04:15,550
+البرهان for all x y element in x and all scalars α
+
+62
+00:04:15,550 --> 00:04:21,330
+احسب للآن f of α x زائد y ايش حسب القانون؟ طبعا
+
+63
+00:04:21,330 --> 00:04:27,170
+الـ A عبارة عن جيبنا A متجه معين وهو أداة التعريف
+
+64
+00:04:27,770 --> 00:04:31,990
+بضرب الـ X فيه ماشي بيصير Alpha X زائد Y Dot من
+
+65
+00:04:31,990 --> 00:04:34,870
+الـ A وعارفين أننا الـ dot و ال product بيتوزع من
+
+66
+00:04:34,870 --> 00:04:39,090
+الخلق و للـ C بيساوي Alpha في X Dot A زائد Y في
+
+67
+00:04:39,090 --> 00:04:44,050
+منه Dot A هذه بيصير Alpha F of X زائد F of Y وهذا
+
+68
+00:04:44,050 --> 00:04:47,470
+يعني أن F أشماله is a linear functional لإنها
+
+69
+00:04:47,470 --> 00:04:52,290
+بترمي في الـ R زي ما قلناالأقل بدأ تبتلكم إنها إيه
+
+70
+00:04:52,290 --> 00:04:55,490
+شمالها إنها bounded انتبهوا لهذه بس بدأ في شغل
+
+71
+00:04:55,490 --> 00:04:58,830
+بنصلحها هن Hence, F is linear زي ما قولنا وفرقاني
+
+72
+00:04:58,830 --> 00:05:00,990
+X بتساوي كساية واحد وكساية اتنين وكساية تلاتة
+
+73
+00:05:00,990 --> 00:05:05,110
+عناصر مين اللي هرتكعين حسبون ال absolute value لل
+
+74
+00:05:05,110 --> 00:05:07,990
+F of X ال absolute value لل F of X F of X إيش
+
+75
+00:05:07,990 --> 00:05:13,270
+بتساوي X ضد مين انتبهوا هن بس عشان في هنا بس شغلة
+
+76
+00:05:13,270 --> 00:05:17,190
+بنعملها ال absolute value لل F of X بساوي ال
+
+77
+00:05:17,190 --> 00:05:21,810
+absolute value لل X ضد مين ال إيه؟معاها؟ لو فرضنا
+
+78
+00:05:21,810 --> 00:05:28,930
+الـ A هي عبارة عن Alpha 1 Alpha 2 Alpha 3 معاها؟ و
+
+79
+00:05:28,930 --> 00:05:34,470
+X زي ما فرضناها عبارة عن XI 1 XI 2 XI 3 dot
+
+80
+00:05:34,470 --> 00:05:38,350
+product بساوة اللي هو ال dot product لا mean ال
+
+81
+00:05:38,350 --> 00:05:44,070
+absolute value لاالـ Dot Alpha 1 X I 1 Alpha 1 X I
+
+82
+00:05:44,070 --> 00:05:50,090
+1 زاد Alpha 2 X I 2 زاد Alpha 3 X I 2 3 يعني بمعنى
+
+83
+00:05:50,090 --> 00:05:52,650
+آخر هو عبارة عن بلغة الـ summation اللي عملها
+
+84
+00:05:52,650 --> 00:05:55,870
+عبارة عن الـ absolute value للـ summation Alpha I
+
+85
+00:05:55,870 --> 00:06:01,230
+X I I معايا يا جماعة I من واحد لمين لتلتة انتبهوا
+
+86
+00:06:01,230 --> 00:06:04,870
+الآن هذا أصغر أو يساوي عشان تصلحوا اللي مكتوب هنا
+
+87
+00:06:04,870 --> 00:06:07,510
+أصغر أو يساوي ال summation لل absolute value Alpha
+
+88
+00:06:07,510 --> 00:06:12,580
+Iفي الـ absolute value of xi I I من عند واحد لمين
+
+89
+00:06:12,580 --> 00:06:18,220
+لتلاتة وهذه بالكوششوارز in quality أصغر أو يساوي
+
+90
+00:06:18,220 --> 00:06:24,360
+ال summation لل alpha I تربيع أص نص في ال
+
+91
+00:06:24,360 --> 00:06:30,800
+summation لل xi I تربيع أص إياش أص نص، مظبوط؟
+
+92
+00:06:30,800 --> 00:06:37,090
+معايا؟ هذه مين هي؟ نور من الـAلأن وين وين قاعد انا
+
+93
+00:06:37,090 --> 00:06:41,910
+في الـ R تكعيب وهذا نور مين؟ نور من الـ X إذا صار
+
+94
+00:06:41,910 --> 00:06:45,910
+عندي الآن absolute value ل F of X أصغر أو ساوي هذا
+
+95
+00:06:45,910 --> 00:06:50,870
+المقدار بمعنى صار عندي ال absolute value ل F of X
+
+96
+00:06:51,540 --> 00:06:56,740
+أصغر أو يساوي C في نورم الـ X الـ C إيش بيساوي
+
+97
+00:06:56,740 --> 00:07:02,140
+نورم الـ A معايا؟ الآن لاحظوا .. لاحظوا .. خليني
+
+98
+00:07:02,140 --> 00:07:06,680
+أكملكم هنا لاحظوا الـ absolute value of F of X على
+
+99
+00:07:06,680 --> 00:07:14,120
+نورم الـ X اللي هو أصغر أو يساوي نورمين الـ Aلأ
+
+100
+00:07:14,120 --> 00:07:18,460
+الأدات التعريف الان الان هذه صارت upper bound لهذا
+
+101
+00:07:18,460 --> 00:07:21,840
+هذا X لاتشهر شفر طبعا خدوا ال supremum عليها بيصير
+
+102
+00:07:21,840 --> 00:07:25,840
+اللي هو ال supremum هو عبارة عن normal F أصغر أو
+
+103
+00:07:25,840 --> 00:07:31,040
+شو مين normal A واضح؟ إذا طلع عندي الان normal F
+
+104
+00:07:31,040 --> 00:07:34,400
+أصغر أو شو مين normal A بدي أجيب اللي هو العكس
+
+105
+00:07:34,400 --> 00:07:37,880
+normal A أصغر أو شو مين normal F هذا الأسلوب اللي
+
+106
+00:07:37,880 --> 00:07:43,390
+بدي أجيبه الآن هو سلوب اختيار نقطةنقطة مناسبة تجيب
+
+107
+00:07:43,390 --> 00:07:46,750
+ليها هتلاقوها في هذا المثال وفي المثال اللي بعده
+
+108
+00:07:46,750 --> 00:07:49,210
+وإلى آخره نفس الأسلوب انتبهوا الآن عندي
+
+109
+00:07:52,110 --> 00:07:54,950
+صارت عندي نورم ال F أصغر تساوي نورم ال A however
+
+110
+00:07:54,950 --> 00:07:58,590
+نورم ال F بتساوي زي ما قلنا ال suprem of absolute
+
+111
+00:07:58,590 --> 00:08:01,430
+value of F of X على نورم ال X X element in X و X
+
+112
+00:08:01,430 --> 00:08:06,470
+تساوي سفر الآن اللي بدي أجيب أنا اللي هو ال
+
+113
+00:08:06,470 --> 00:08:09,190
+absolute value of F of X أنا بعرفها عبارة عن X dot
+
+114
+00:08:09,190 --> 00:08:15,760
+mean ال A ماشيهذه هذه absolute value of x dot a و
+
+115
+00:08:15,760 --> 00:08:18,940
+normal x هي normal x بدي اختار اللي هو انا قيمة
+
+116
+00:08:18,940 --> 00:08:23,080
+معينة عشان اللي هي احصل بس ال a لو اخدت ال
+
+117
+00:08:23,080 --> 00:08:27,780
+absolute value هذا اكيد ال supremum اكبر او يساوي
+
+118
+00:08:27,780 --> 00:08:32,490
+عند اي قيمة من القيمممضمنها عند مين؟ عند الـ A إذا
+
+119
+00:08:32,490 --> 00:08:35,090
+أكبر أوي يسوى absolute value of F of A على norm
+
+120
+00:08:35,090 --> 00:08:37,750
+الـ A absolute value of F of A إيش هو؟ نعرفه
+
+121
+00:08:37,750 --> 00:08:41,170
+مسبقًا A Dot A A Dot A هو عبارة عن norm الـ A
+
+122
+00:08:41,170 --> 00:08:45,190
+تربية absolute value له على norm الـ A بطلع norm
+
+123
+00:08:45,190 --> 00:08:49,050
+الـ A إذا حصلت norm الـ F أكبر أوي يسوى norm الـ A
+
+124
+00:08:49,050 --> 00:08:54,870
+باختياري للنقطة المعينة اللي هي الـ A عسى أحصل عن
+
+125
+00:08:54,870 --> 00:08:58,130
+quality هذه وصار عند norm الـ F من التلتين بسوى
+
+126
+00:08:58,130 --> 00:09:05,560
+norm الـ Aاللي بعده يالاخلصنا الدبطة البردكتية
+
+127
+00:09:05,560 --> 00:09:12,240
+ديفينيت انتيجرال الان اللي جاب في السؤال اللي جابه
+
+128
+00:09:12,240 --> 00:09:16,980
+كنا نرمي .. حطينا kernel جوه ال integration عشان
+
+129
+00:09:16,980 --> 00:09:20,080
+يطلع function في T ضال function of two variables
+
+130
+00:09:20,080 --> 00:09:23,800
+واحدة بنكملها والتانية بتبقى حرة هي اللي بتخليني
+
+131
+00:09:23,800 --> 00:09:26,680
+.. بضل اللي ناتج continuous function برمي في ال
+
+132
+00:09:26,680 --> 00:09:28,700
+continuous فصار من norm of this space ل norm of
+
+133
+00:09:28,700 --> 00:09:33,100
+this space هنا الآن لأ بدي أحسب Aبدي أحسب اللي أخد
+
+134
+00:09:33,100 --> 00:09:36,400
+الـ J من A إلى الـ B و الـ F من C من A و B إلى R
+
+135
+00:09:36,400 --> 00:09:40,080
+دي defined by what؟ by F of X هي اللي هنا في الـ
+
+136
+00:09:40,080 --> 00:09:42,300
+continuous functions بيساوي ال integration ال
+
+137
+00:09:42,300 --> 00:09:45,120
+integration من A إلى B لل X of T DT يعني ماضلش إيش
+
+138
+00:09:45,120 --> 00:09:48,760
+هتضل الرقم الرقم اللي هيطلع من هنا اللي هو ال
+
+139
+00:09:48,760 --> 00:09:53,290
+field اللي هو ال vector space اللي عنديthen F is a
+
+140
+00:09:53,290 --> 00:09:56,890
+bounded linear functional with norm ال F هيطلع
+
+141
+00:09:56,890 --> 00:10:02,930
+لمين طول الفترة المذكورة ماشي شوفوا هل مثل المحلق
+
+142
+00:10:03,570 --> 00:10:06,090
+الأن F is linear functional مافيش دا أنا أعيد حالي
+
+143
+00:10:06,090 --> 00:10:08,390
+F is linear ماعملناها قبل شويه ال integration is
+
+144
+00:10:08,390 --> 00:10:13,110
+linear ف why إلكم أعملناها اللي الآن بدأ أثبت main
+
+145
+00:10:13,110 --> 00:10:15,770
+اللي هو ال boundedness و أثبت norm ال F بساوي
+
+146
+00:10:15,770 --> 00:10:18,890
+normal B minus A اللي هو norm ال F أصغر بساوي B
+
+147
+00:10:18,890 --> 00:10:21,630
+minus A بنثبتها و بعدين بنختار نقطة معينة و بنثبت
+
+148
+00:10:21,630 --> 00:10:28,080
+كده و هتلاقوا الأساليب متشابهة نشوف كيفfor any x
+
+149
+00:10:28,080 --> 00:10:31,420
+element in c0,1 يعني continuous function على فترة
+
+150
+00:10:31,420 --> 00:10:35,080
+0,1 we have حسبول ال absolute value ل f of x ال
+
+151
+00:10:35,080 --> 00:10:37,820
+absolute value ل f of x لأنه ماكتبش norm لأن f of
+
+152
+00:10:37,820 --> 00:10:40,420
+x بترمي في ال R فإيش ال norm هو عبارة عن absolute
+
+153
+00:10:40,420 --> 00:10:43,900
+value absolute value ل f of x بيساوي ال absolute
+
+154
+00:10:43,900 --> 00:10:47,640
+value لل integration من a و b هذا أصغر أو يساوي من
+
+155
+00:10:47,640 --> 00:10:50,160
+صحيحة ال integration ال integration لل absolute
+
+156
+00:10:50,160 --> 00:10:54,110
+value صح؟واللي جوا اللي هو X of T أكيد أصغر أو
+
+157
+00:10:54,110 --> 00:10:58,030
+يساوي ال maximum على كل ال T، ماشي؟ إذا أصغر أو
+
+158
+00:10:58,030 --> 00:11:00,850
+يساوي B minus A في ال maximum ل X of T T element
+
+159
+00:11:00,850 --> 00:11:06,180
+in Jمفهوم، أه؟ إذا صار عندى الآن B minus A مضروب
+
+160
+00:11:06,180 --> 00:11:09,680
+في مين؟ هذا عبارة عن الـ Norm Normal X صار عنده
+
+161
+00:11:09,680 --> 00:11:12,340
+Absolute Value of X أصغر أو سوى B minus A في
+
+162
+00:11:12,340 --> 00:11:16,380
+Normal X بمعنى أخر صارت F bounded ومش هيك و
+
+163
+00:11:16,380 --> 00:11:20,440
+Absolute Value of X على Normal X أصغر أو سوى B
+
+164
+00:11:20,440 --> 00:11:23,840
+minus A صارت الـ B minus A يتبع عن Upper Bound لـ
+
+165
+00:11:23,840 --> 00:11:27,260
+Absolute Value of X على Normal X إذا صار Supremum
+
+166
+00:11:27,260 --> 00:11:29,720
+اللي هو الـ Upper Bound أصغر أو سوى B minus A اللي
+
+167
+00:11:29,720 --> 00:11:32,440
+هي Upper Boundيعني norm of f أخر شو بيه minus a
+
+168
+00:11:32,440 --> 00:11:35,700
+قلته هذا قبلين عيده
+
+169
+00:11:39,850 --> 00:11:43,870
+Conversely أكبر اوي ساوي اختيار نقطة تخدمني ماشي
+
+170
+00:11:43,870 --> 00:11:46,990
+الحال النقطة اللي بتجيبلي هذه واحد واضح ان انا
+
+171
+00:11:46,990 --> 00:11:49,970
+بتاخدها ايه اش مالها واحد عشان اعمل انت اللي هو
+
+172
+00:11:49,970 --> 00:11:53,070
+تكامل يطلع عقل دي بي مانس واحد و تنحل أموري ده
+
+173
+00:11:53,070 --> 00:11:55,670
+نشوف كيف ايش اللي بقوله Now choose X not
+
+174
+00:11:55,670 --> 00:12:00,070
+independent of C,A,B وخد X not of T ايش بتساوي ال
+
+175
+00:12:00,070 --> 00:12:02,670
+constant function واحد وده متصل اما احنا عارفين
+
+176
+00:12:03,230 --> 00:12:07,490
+الان norm ال F أكبر أو يساوي اللي هو ال absolute
+
+177
+00:12:07,490 --> 00:12:10,730
+value علي هذه عند نقطة معينة النقطة المعينة أخد
+
+178
+00:12:10,730 --> 00:12:14,010
+تميين اللي هي واحد الان absolute value ل F of X
+
+179
+00:12:14,010 --> 00:12:18,550
+بساوي اللي هي بساوي هذه نورمها واحد لأن قيمتها
+
+180
+00:12:18,550 --> 00:12:22,270
+واحد النورم على الفترة من A من A ل B minus B هيطلع
+
+181
+00:12:22,270 --> 00:12:27,550
+ايش بساوي integration فاهمين أه؟طيب، الآن بيصير
+
+182
+00:12:27,550 --> 00:12:30,690
+عندي الـ Absolute Value of .. لأ الـ X0 هذه عبارة
+
+183
+00:12:30,690 --> 00:12:34,170
+عن نقطة في الـ Continuous Function قيمتها ..
+
+184
+00:12:34,170 --> 00:12:37,610
+نورمها هو الـ Maximum لقيمة الدالة، ما هي ثابتة،
+
+185
+00:12:37,610 --> 00:12:39,790
+الـ Maximum اللي هو واحد، ماعنديش فراش اللقاء في
+
+186
+00:12:39,790 --> 00:12:42,970
+الـ Integration فبيصير عندي نورم الـ F أكبر أو شوه
+
+187
+00:12:42,970 --> 00:12:45,870
+هذا القيمة، والـ H دي واحد، بيصير بس اللي فوقه F
+
+188
+00:12:45,870 --> 00:12:48,370
+of X0 ماعرف الـ F of X0 هي عبارة عن الـ
+
+189
+00:12:48,370 --> 00:12:52,670
+Integration من LBDTabsolute value لها اللي هو هذه
+
+190
+00:12:52,670 --> 00:12:56,690
+اللي عبارة عن نفسها لان دي موجب اصلا بي ماينوس ايه
+
+191
+00:12:56,690 --> 00:13:00,590
+اذا صار عندي norm of بيساوي اكبره بيساوي اصلا
+
+192
+00:13:00,590 --> 00:13:14,210
+بيساوي اذا في مساوية اللي بعدها نيجي الان ناخد
+
+193
+00:13:14,210 --> 00:13:20,110
+اللي هيF من continuous function لR بس هنسويها
+
+194
+00:13:20,110 --> 00:13:26,790
+بتساوي قيمة الدالة اللي بدرسلها عند نقطة معينةيعني
+
+195
+00:13:26,790 --> 00:13:30,510
+الآن في عندي F باسم C و A و B اللي هو continuous
+
+196
+00:13:30,510 --> 00:13:33,950
+function let F من C و A و B اللي عند الار بي
+
+197
+00:13:33,950 --> 00:13:39,990
+defined by إيش عرفتها؟ F of X بتساوي X عن T note
+
+198
+00:13:39,990 --> 00:13:43,010
+أنا ماخد T note أدى التعريف T note معينة خمسة ستة
+
+199
+00:13:43,010 --> 00:13:46,930
+سبعة نص ربع في الفترة من A و B بحسب قيمة الدالة
+
+200
+00:13:46,930 --> 00:13:51,190
+عند هذا ال T noteوبتكون هي صورة مين ال X under F
+
+201
+00:13:51,190 --> 00:13:55,290
+فبتكون F of X بيساوي X of مين of T not صارت عبارة
+
+202
+00:13:55,290 --> 00:13:59,750
+عن هذه لأن ال X من وين جاية من A و B continuous
+
+203
+00:13:59,750 --> 00:14:02,950
+function من A و B بترمي في ال R فقيمتها أشمالها
+
+204
+00:14:02,950 --> 00:14:06,930
+عبارة عن عدد حقيقي ف X عند أي نقطة اللي هو بيساوي
+
+205
+00:14:06,930 --> 00:14:10,970
+اللي هو عدد حقيقي إذا صارت F of X ترمي وين في ال R
+
+206
+00:14:10,970 --> 00:14:14,570
+طيب F of X بيساوي X of T not where T not is
+
+207
+00:14:14,570 --> 00:14:20,580
+affixedpoint in J اللي هي A وB then F is a bounded
+
+208
+00:14:20,580 --> 00:14:24,160
+linear functional ونورم ال F أيش بيساوي؟ بيساوي
+
+209
+00:14:24,160 --> 00:14:27,620
+واحد، هيكون ال bounded linear functional ونورمه
+
+210
+00:14:27,620 --> 00:14:32,460
+هيساوي مين؟ بس الواحد يشوفه كده، بسهل الامرF is a
+
+211
+00:14:32,460 --> 00:14:35,400
+linear functional اللي هي سهلة لإنه اصلا هي عبارة
+
+212
+00:14:35,400 --> 00:14:39,760
+عن F of Alpha X زائد Beta Y أو زائد Y بيساوي أيش
+
+213
+00:14:39,760 --> 00:14:43,840
+قيمتها Alpha X زائد Y عند الـT Note ويساوي Alpha
+
+214
+00:14:43,840 --> 00:14:47,600
+of X عند الـT Note زائد Y عند الـT Note وبيصير
+
+215
+00:14:47,600 --> 00:14:51,180
+Alpha في F زائد اللي هي FY إذا اللي لينيارات، إذا
+
+216
+00:14:51,180 --> 00:14:54,640
+الموضوع اللي لينيارات سهل طيب إذا Y تبعت اللي
+
+217
+00:14:54,640 --> 00:14:59,100
+لينيارات سهلة وهيني حكيتها نيجي نحكي عن ال
+
+218
+00:14:59,100 --> 00:15:04,010
+boundednessfor any x element in C01 خدلي ال
+
+219
+00:15:04,010 --> 00:15:07,910
+absolute value لمن؟ لل F of X ال absolute value ل
+
+220
+00:15:07,910 --> 00:15:10,630
+F of X احسبه عبارة عن بساوي ال absolute value
+
+221
+00:15:10,630 --> 00:15:16,890
+لقيمتها ايش قيمتها؟ X of T0 X of T0 اكيد اكيد اكيد
+
+222
+00:15:16,890 --> 00:15:21,760
+قيمة ده اللي عند واحدة من هنا T0إن إذا أكيد أصغر
+
+223
+00:15:21,760 --> 00:15:25,620
+أو يساوي ال maximum على كل الفترة عن T نقطة و T
+
+224
+00:15:25,620 --> 00:15:30,400
+واحد و كل ال T الموجودة في الجيب اللي هو بمثل مين
+
+225
+00:15:30,400 --> 00:15:33,140
+Normal X إذا صارت عبارة عن ال absolute value of F
+
+226
+00:15:33,140 --> 00:15:37,400
+of X أصغر أو يساوي Normal X ومنه ال absolute value
+
+227
+00:15:37,400 --> 00:15:41,220
+of F of X على Normal X لو X لا تساوي سفر أو Normal
+
+228
+00:15:41,220 --> 00:15:44,860
+لا تساوي سفر أصغر أو يساوي واحد ال supremum صار
+
+229
+00:15:44,860 --> 00:15:48,880
+أصغر اللي هو أو يساوي واحدمعايا إذا صار عندي
+
+230
+00:15:48,880 --> 00:15:53,780
+Normal F أصغر أو يساوي واحد كده الفكرة مكررة الآن
+
+231
+00:15:53,780 --> 00:15:58,080
+طب الآن بدنا نجيب اللي هو الأكبر يساوي ونختاره عند
+
+232
+00:15:58,080 --> 00:16:02,340
+نقطة معينة Now choose X note في C, V وB with X
+
+233
+00:16:02,340 --> 00:16:06,520
+note أش بتساوي واحد هيك الحدث بقول أصلا عشان أحصل
+
+234
+00:16:06,520 --> 00:16:10,950
+على الواحد ال absolute value ل F of Xأكبر أو يساوي
+
+235
+00:16:10,950 --> 00:16:14,470
+F عند قيمة معينة absolute value على نورم القيمة
+
+236
+00:16:14,470 --> 00:16:17,530
+اللي أخدتها القيمة اللي أخدتها مانا أخدها واحد
+
+237
+00:16:17,530 --> 00:16:21,870
+فنورمها بتساوي واحد واللي فوق أصلا قيمتها absolute
+
+238
+00:16:21,870 --> 00:16:26,330
+F of X هي عبارة عن قيمة X of T naught وفي الأصل ما
+
+239
+00:16:26,330 --> 00:16:30,030
+هي أصلا معرفهاش بتساوي واحدإذا صار عنده norm لـ F
+
+240
+00:16:30,030 --> 00:16:30,930
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+241
+00:16:30,930 --> 00:16:31,730
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+242
+00:16:31,730 --> 00:16:34,730
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+243
+00:16:34,730 --> 00:16:36,290
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+244
+00:16:36,290 --> 00:16:41,850
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+245
+00:16:41,850 --> 00:16:44,650
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+246
+00:16:44,650 --> 00:16:46,650
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+247
+00:16:46,650 --> 00:16:52,830
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+248
+00:16:52,830 --> 00:16:57,960
+أكbe a fixed point in L2 من L2 اللي هو summation
+
+249
+00:16:57,960 --> 00:17:02,660
+كذا norm هال summation المدرستربيع الكل أص نص بدل
+
+250
+00:17:02,660 --> 00:17:05,340
+من I من عند واحد لخمسة أو I من واحد لاتنين I لعند
+
+251
+00:17:05,340 --> 00:17:09,020
+واحد لما لا نهاية يعني مش هيختلف بروحانه عن مين عن
+
+252
+00:17:09,020 --> 00:17:13,160
+الشغلات اللي أثبتناها بالنسبة لـR تكعيب وR تربيع
+
+253
+00:17:13,160 --> 00:17:18,260
+وRم الاخرين let αI be الا بعض الشغلات بسيطة let αI
+
+254
+00:17:18,260 --> 00:17:21,660
+be a fixed point in التربيع and F من التربيع اللي
+
+255
+00:17:21,660 --> 00:17:27,030
+عنده R تربيع be defined byF of X أيش بتساوي صميم
+
+256
+00:17:27,030 --> 00:17:31,190
+XI I Alpha I I من واحد لعند مين لعند infinity for
+
+257
+00:17:31,190 --> 00:17:34,130
+all X elementين قالتوا بالظبط بالظبط بالظبط زي
+
+258
+00:17:34,130 --> 00:17:38,610
+المثال اللي قبله شوية F of X بيساوي X Dot Aالـ X
+
+259
+00:17:38,610 --> 00:17:42,010
+ضد الـ إيش؟ إيش كانت؟ XI واحد Gamma واحد زيدي XI
+
+260
+00:17:42,010 --> 00:17:44,790
+اتنين Gamma اتنين زيدي XI تلاتة Gamma تلاتة الآن
+
+261
+00:17:44,790 --> 00:17:47,970
+إيش ماله هذا؟ من واحد إلى وين إلى الأعلى نهاية إذا
+
+262
+00:17:47,970 --> 00:17:52,130
+الـ linearity و ال boundedness بالظبط زيها then F
+
+263
+00:17:52,130 --> 00:17:56,330
+is bounded linear functional عشان هيك لفت to the
+
+264
+00:17:56,330 --> 00:17:59,430
+reader مبارك الله فيكم و إلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/OMe_05RbxKs_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/OMe_05RbxKs_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..2e5ab15adb950fb3caed837fe5de2356077f9df8
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/OMe_05RbxKs_raw.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RstVGUoRP6o.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RstVGUoRP6o.srt
new file mode 100644
index 0000000000000000000000000000000000000000..de55c649aa71ccbcb858c052dd4033de68b4c538
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RstVGUoRP6o.srt
@@ -0,0 +1,2757 @@
+1
+00:00:05,360 --> 00:00:08,000
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,000 --> 00:00:11,400
+والصلاة والسلام علي سيد المرسلين هذه المحاضرة
+
+3
+00:00:11,400 --> 00:00:18,880
+الثانية في مساق تحليل اقتراني أو تحليل دالي لطلب
+
+4
+00:00:18,880 --> 00:00:26,620
+طلبات الماجستير الجامعة الإسلامية بغزة حكينا المرة
+
+5
+00:00:26,620 --> 00:00:30,580
+الماضية بدأنا في المحاضرة الأولى حكينا عن ال
+
+6
+00:00:30,580 --> 00:00:34,930
+metric space اليوم إن شاء الله هنحكي عن اللي هو
+
+7
+00:00:34,930 --> 00:00:39,550
+examples on metric space وهو 1، 2 تحت عنوان further
+
+8
+00:00:39,550 --> 00:00:43,890
+examples on metric space خليني بس عشان نذكركم بشيء
+
+9
+00:00:43,890 --> 00:00:46,990
+اللي حكيناه المرة الماضية عشان تكون الأمور يعني
+
+10
+00:00:46,990 --> 00:00:51,770
+مترابطة وفي عندنا اللي هو تواصل بالحديث اللي المرة
+
+11
+00:00:51,770 --> 00:00:55,500
+الماضية المرة الماضية مراجعة سريعة اللي حكيته المرة
+
+12
+00:00:55,500 --> 00:00:58,940
+الماضية قلت أنا شو تعريف الـ metric space  إيش الـ
+
+13
+00:00:58,940 --> 00:01:03,500
+metric space بنعرفه بنيجي بناخد X و بعدين بنعرف
+
+14
+00:01:03,500 --> 00:01:08,060
+عليه دالة D هذه الـ D اللي هي دالة على من مش على
+
+15
+00:01:08,060 --> 00:01:12,200
+الـ X نفسها الـ D هذه عبارة دالة على X cross X يعني
+
+16
+00:01:12,200 --> 00:01:18,180
+D هتاخد من X cross X و ترمي بالضبط في R positive
+
+17
+00:01:18,180 --> 00:01:23,260
+اتحاد الـ zero بنقول عن هذه D عبارة عن دالة مسافة أو
+
+18
+00:01:23,260 --> 00:01:27,700
+metric إذا حققت الشروط التالية الشرط الأول أنها
+
+19
+00:01:27,700 --> 00:01:31,380
+تكون non-negative طبيعي المسافة حتى في R أكيد non
+
+20
+00:01:31,380 --> 00:01:35,520
+-negative أصلا مستحيلها تكون سالبة D(X,Y) بتساوي صفر إذا
+
+21
+00:01:35,520 --> 00:01:39,660
+فقط إذا X بتساوي Y يعني النقطتين اللي بيكون
+
+22
+00:01:39,660 --> 00:01:44,720
+مسافتهم عن بعض بتساوي صفر هي بس النقطة X نفسها
+
+23
+00:01:45,210 --> 00:01:48,470
+الشغل الثالث هو أن المسافة بين X و Y هي نفس
+
+24
+00:01:48,470 --> 00:01:51,490
+المسافة بين Y و X يعني اللي هو الـ Symmetry
+
+25
+00:01:51,490 --> 00:01:55,290
+الشغل الرابع هو أن هي الـ Triangle Inequality D(X
+
+26
+00:01:55,290 --> 00:01:59,950
+و Y) أصغر أو يساوي D(X و Z) + D(Z و Y) فصلنا
+
+27
+00:01:59,950 --> 00:02:04,930
+المرة الماضية عن هذا اللي هو التعريف الآن أخذنا
+
+28
+00:02:04,930 --> 00:02:11,170
+برضه اللي هو أمثلة على هذا اللي هو أخذنا أمثلة على
+
+29
+00:02:11,170 --> 00:02:14,590
+الـ Metric اللي هو على الـ R إيش الـ Metric على الـ R
+
+30
+00:02:14,590 --> 00:02:17,990
+اللي هو absolute value of X minus Y على R تربيع
+
+31
+00:02:17,990 --> 00:02:22,830
+هي الآن وبعدين وقفنا عند حاجة اسمها سمينا الـ الـ
+
+32
+00:02:22,830 --> 00:02:26,170
+infinity هذه من الـ spaces المهمة عندنا الـ الـ
+
+33
+00:02:26,170 --> 00:02:29,270
+infinity شو الـ l infinity اذكركم فيه اللي حكينا
+
+34
+00:02:29,270 --> 00:02:33,700
+المرة الماضية هي عبارة عن عناصر و sequences يعني
+
+35
+00:02:33,700 --> 00:02:38,040
+الـ L infinity اللي هو عبارة عن space of sequences
+
+36
+00:02:38,040 --> 00:02:41,680
+طب أي sequences يكون الـ sequence bounded يعني the
+
+37
+00:02:41,680 --> 00:02:46,760
+set of all x_i مثلا اللي هي sequence of numbers
+
+38
+00:02:46,760 --> 00:02:51,750
+سواء complex number أو real number بحيث إنه اللي هو
+
+39
+00:02:51,750 --> 00:02:56,550
+الـ x_i تكون أصغر أو يساوي من يساوي some constant
+
+40
+00:02:56,550 --> 00:03:00,510
+C ماشي الـ .. الـ .. الـ .. الـ bounded sequences
+
+41
+00:03:00,510 --> 00:03:03,390
+حطيناها في من في الـ l infinity وبناء عليه
+
+42
+00:03:03,390 --> 00:03:08,570
+عرفنا الـ metric عليها عرفنا الدالة كانت الدالة D(x,y)
+
+43
+00:03:08,570 --> 00:03:14,250
+بتساوي الـ supremum للـ absolute value x_i ناقص y_i
+
+44
+00:03:14,250 --> 00:03:22,120
+i over i من هي هذه الـ x_i؟ x بتساوي x_i و y
+
+45
+00:03:22,120 --> 00:03:25,060
+بتساوي y_i هذا كله كان حكيناه المرة الماضية
+
+46
+00:03:25,060 --> 00:03:30,840
+وقلنا هذه هتعمل لنا metric على الـ l infinity يعني
+
+47
+00:03:30,840 --> 00:03:33,760
+هتحقق الشروط الأربعة وبالمناسبة زي ما قلنا المرة
+
+48
+00:03:33,760 --> 00:03:38,420
+الماضية إن شروط الـ metric الأولى هي التلاتة
+
+49
+00:03:38,420 --> 00:03:42,260
+automatic سهلة والكل بعرف إجابتها بظل الشرط الأخير
+
+50
+00:03:42,260 --> 00:03:46,080
+هو اللي شوية بده شغل عموما أمثلة المرة الماضية زي
+
+51
+00:03:46,080 --> 00:03:51,720
+ما قلنا كانت أمثلة سهلة ومباشرة وعرفنا برضه اللي هو
+
+52
+00:03:51,720 --> 00:03:54,960
+الـ function space اللي هو الـ space of all
+
+53
+00:03:54,960 --> 00:03:59,640
+continuous functions على closed bounded interval
+
+54
+00:03:59,640 --> 00:04:03,160
+وعرفنا الـ metric برضه بنفس الأسلوب المسافة بين أي
+
+55
+00:04:03,160 --> 00:04:08,260
+نقطتين دالتين هدول v(x,y) موجودة في C[a,b] بس الـ
+
+56
+00:04:08,260 --> 00:04:13,390
+maximum لـ  اللي حصل طرح الدالتين على من على الفترة
+
+57
+00:04:13,390 --> 00:04:17,390
+اللي بنحكي فيها هذا برضه عمل له metric وشوفنا كيف
+
+58
+00:04:17,390 --> 00:04:22,490
+عمل metric وبررنا أنه عمل metric وبصير الـC[a,b]
+
+59
+00:04:22,490 --> 00:04:28,300
+مع هذه الـD المعرفة بتصير metric space بتحقق
+
+60
+00:04:28,300 --> 00:04:31,140
+الشروط هذا ما حكيناه المرة الماضية واللي ناسي
+
+61
+00:04:31,140 --> 00:04:34,620
+شيء ممكن يرجع للمحاضرة ما هي مسجلة وجينا على
+
+62
+00:04:34,620 --> 00:04:38,960
+metric آخر سميناها discrete metric space اللي هو
+
+63
+00:04:38,960 --> 00:04:44,960
+الـ D(X و Y) عرفناها بتساوي صفر إذا كانت الـ X هي Y و
+
+64
+00:04:44,960 --> 00:04:48,400
+بتساوي واحد إذا كانت الـ X لا تساوي Y و أبرهنّا برضه إن
+
+65
+00:04:48,400 --> 00:04:52,100
+هذا بيعمل metric فسميناها الـ X و D is a metric a
+
+66
+00:04:52,100 --> 00:04:56,460
+discrete metric space الآن يا جماعة أخذنا exercises
+
+67
+00:04:56,460 --> 00:05:01,700
+وقلنا هدول exercises بتحلوهن وقلنا اللي هو عندي
+
+68
+00:05:01,700 --> 00:05:06,100
+أنا بكتب لكم homeworks اللي هي من الكتاب هدول
+
+69
+00:05:06,100 --> 00:05:09,540
+الأسئلة أرقام الأسئلة وفي homework أسئلة من
+
+70
+00:05:09,540 --> 00:05:12,200
+الكتاب هذول الـ homework أسئلة هم اللي بتكون
+
+71
+00:05:12,200 --> 00:05:16,440
+الواجبات بتكون الواجبات يعني أربعة وخمسة وثمانية
+
+72
+00:05:16,440 --> 00:05:19,980
+وعشرة وواحد واثنين هدول اللي هن هذا بتكون الـ
+
+73
+00:05:19,980 --> 00:05:23,120
+homework الأول وزي ما حكينا المرة الماضية في خطة
+
+74
+00:05:23,120 --> 00:05:28,420
+المساق إنه بدنا نحاول نعطيكم امتحانين ونعطيكم
+
+75
+00:05:28,420 --> 00:05:31,700
+اللي هو الـ homework وممكن نعطيكم ثلاث امتحانات
+
+76
+00:05:31,700 --> 00:05:35,820
+ونحسب لكم أحسن اثنين وعليهم أربعين في المئة
+
+77
+00:05:35,820 --> 00:05:38,400
+لاختبارين وعشرة في المئة على الـ homework والخمسين في المئة
+
+78
+00:05:38,400 --> 00:05:41,360
+بتكون على الـ final وموضوع الهدك إن شاء الله
+
+79
+00:05:41,360 --> 00:05:45,870
+بنتفق عليه نيجي لموضوعنا اليوم نبدأ في محاضرتنا
+
+80
+00:05:45,870 --> 00:05:49,830
+اليوم إن شاء الله بفصل تفصيل اللي بدنا نحكيه لأن
+
+81
+00:05:49,830 --> 00:05:55,050
+further examples of metric spaces اللي هو يعني في
+
+82
+00:05:55,050 --> 00:05:59,410
+عندي أمثلة أخرى غير الأمثلة اللي حكيناها المرة
+
+83
+00:05:59,410 --> 00:06:05,920
+الماضية أول مثال بدي أحكي عنه اللي هو مثال آخر على
+
+84
+00:06:05,920 --> 00:06:11,020
+الـ sequences spaces هتلاقونا احنا بنركز على اللي هو
+
+85
+00:06:11,020 --> 00:06:15,840
+الفراغات اللي عناصرها sequences اللي جايين بشوية
+
+86
+00:06:15,840 --> 00:06:18,520
+الـ l infinity كانت اللي هي sequences تبعت l
+
+87
+00:06:18,520 --> 00:06:21,990
+infinity اللي هي الـ bounded sequences الآن بتاخد
+
+88
+00:06:21,990 --> 00:06:28,470
+الـ s small هذه  be the space of all sequences طبعا
+
+89
+00:06:28,470 --> 00:06:31,930
+اللي باخدها complex numbers أو الـ real numbers
+
+90
+00:06:31,930 --> 00:06:35,990
+خليني أحكي عن الـ complex إذا s هذه small هي
+
+91
+00:06:35,990 --> 00:06:42,490
+عبارة عن the set of all sequences of numbers الـ
+
+92
+00:06:42,490 --> 00:06:47,970
+sequence اللي فيها لو أخذنا x و y في الـ s الـ x
+
+93
+00:06:47,970 --> 00:06:51,390
+هتكون sequence يعني لو جينا رمزنا لها الـ x بتساوي
+
+94
+00:06:51,390 --> 00:06:55,750
+x_i يعني x بتساوي x_1، x_2، x_3، x_4، إلى مدى النهاية ونفس الشيء y لو سميناها مثلا
+
+95
+00:06:55,750 --> 00:06:59,610
+بتساوي y_i أو اللي بدكم إياه يعني y_1،
+
+96
+00:06:59,610 --> 00:07:02,610
+y_2، y_3، إلى مدى النهاية الآن بدي أعرف
+
+97
+00:07:02,610 --> 00:07:06,580
+هذا تنسوش أن هدول any sequences لا converge مش
+
+98
+00:07:06,580 --> 00:07:10,740
+converge bounded مش bounded أي شيء عشان هيك بدي
+
+99
+00:07:10,740 --> 00:07:14,860
+أختار metric لأن أختار صيغة لـ metric أنها تكون
+
+100
+00:07:14,860 --> 00:07:19,980
+معقولة وبتلم كل الـ sequences هذه تكون صحيحة لكل
+
+101
+00:07:19,980 --> 00:07:24,560
+الـ sequences اللي بتنطلع علينا شوفوا اللي باخدها
+
+102
+00:07:24,560 --> 00:07:28,200
+بقول لك خدوا d(x,y) عرفنا كالتالي d(x,y) بتساوي الـ summation
+
+103
+00:07:28,200 --> 00:07:32,960
+للـ x_i ناقص y_i على 1 زائد x_i ناقص y_i
+
+104
+00:07:33,800 --> 00:07:45,460
+ما قالش هيكوا بس لإنه لو حتى زي هيكوا بس الـ series
+
+105
+00:07:45,460 --> 00:07:51,220
+هذه اللي هي y_i من عند 1 لعند infinity حدش
+
+106
+00:07:51,220 --> 00:07:55,420
+بيدمن لكوا أنها تكون converge يعني حدش بضمن لكم يكون
+
+107
+00:07:55,420 --> 00:07:59,300
+هذا إيش ماله عبارة عن عدد و d(x,y) ده اللي هو metric
+
+108
+00:08:04,120 --> 00:08:08,580
+يعني metric في الآخر بتطلع لإيش عدد الآن ضربوا
+
+109
+00:08:08,580 --> 00:08:14,960
+عشان هيك في واحد على اثنين أس i في هذا الحلق ضمن لكم أن
+
+110
+00:08:14,960 --> 00:08:19,640
+الـ series converge ليش لأنه بالـ Comparison Test لو
+
+111
+00:08:19,640 --> 00:08:23,860
+دي نطلعنا أو الجزء الصميشي من واحد على اثنين أس i هذه الـC
+
+112
+00:08:23,860 --> 00:08:27,420
+series بنعرف إنها converge، بظبط؟ أساسها نص اللي
+
+113
+00:08:27,420 --> 00:08:30,020
+هو geometric series أساسها نص أتوفتك اللي هو
+
+114
+00:08:30,020 --> 00:08:34,360
+converge، لاحظوا إن هذا المقدار اللي هو الـNth
+
+115
+00:08:34,360 --> 00:08:39,880
+term هذا اللي جوا اللي مضروب واحد على اثنين أس i الـ x_i ناقص
+
+116
+00:08:39,880 --> 00:08:47,400
+y_i على 1 زائد x_i ناقص y_i هذا الأن أكيد
+
+117
+00:08:47,400 --> 00:08:53,120
+أكيد أكيد أصغر أو يساوي واحد على اثنين أس إيش أس i
+
+118
+00:08:53,120 --> 00:08:57,440
+مظبوط ولا لأ لما نضربه هدف مينوحدة لاثنين لأن هذا
+
+119
+00:08:57,440 --> 00:09:01,280
+المقدار أصغر أو يساوي واحد لأن اللي تحت أكبر من
+
+120
+00:09:01,280 --> 00:09:06,160
+من اللي فوق فاهمين؟ إذا ما دامت هذه الـ series
+
+121
+00:09:06,160 --> 00:09:09,300
+الـ Nth term تبعها أكبر أو يساوي هذا والـ series
+
+122
+00:09:09,300 --> 00:09:12,860
+هذه converge إذا automatically هذه converge إذا الأول
+
+123
+00:09:12,860 --> 00:09:17,360
+حاجة اللي هو شغله اللي هو لحتى الآن بالنسبة للي
+
+124
+00:09:17,360 --> 00:09:22,270
+عرفوا في الطريق الصحيح الآن بيقول لي define اللي هو
+
+125
+00:09:22,270 --> 00:09:25,610
+هذا for أنا x بتساوي كده وأنا y بتساوي كده
+
+126
+00:09:25,610 --> 00:09:31,270
+in s show that s وd إيش مالها is a metric space
+
+127
+00:09:31,270 --> 00:09:37,270
+الآن الشروط الشروط الأولى التلاتة الأولى سهلة بتمر
+
+128
+00:09:37,270 --> 00:09:43,300
+عليها على السريع الشرط الأول أن هذا المقدار
+
+129
+00:09:43,300 --> 00:09:47,100
+absolute value أو مدرس إذا أكبر أو يساوي صفر وهذا أكبر
+
+130
+00:09:47,100 --> 00:09:49,820
+أو يساوي صفر وهذا أكبر أو يساوي صفر إذا أكيد هذا أكبر أو يساوي
+
+131
+00:09:49,820 --> 00:09:52,860
+صفر إذا السلسلة الشمالية هتكون أكبر أو يساوي صفر
+
+132
+00:09:52,860 --> 00:09:57,420
+إذا الشرط الأول متحقق إذا هذا أكبر أو يساوي صفر
+
+133
+00:09:57,420 --> 00:10:02,800
+الشرط الأول تحقق نزل للشرط الثاني الشرط الثاني هذا
+
+134
+00:10:02,800 --> 00:10:07,200
+بتساوي صفر إذا و فقط إذا هذا المقدار بيساوي صفر إذا
+
+135
+00:10:07,200 --> 00:10:10,920
+و فقط إذا اللي هو دوله هذا non negative وهذا non
+
+136
+00:10:10,920 --> 00:10:15,240
+negative لازم هذا بيكون صفر إذا و فقط إذا اللي هو
+
+137
+00:10:15,240 --> 00:10:18,840
+كل اللي في هذا مجموع اللي هو ساوي صفر وهذا لا
+
+138
+00:10:18,840 --> 00:10:23,920
+يساوي صفر لما بيساوي صفر الـ x_i ناقص الـ y_i
+
+139
+00:10:23,920 --> 00:10:29,040
+بتساوي صفر مثل عساله سهل هذا
+
+
+
+141
+00:10:29,040 --> 00:10:33,100
+and only F(X) يشملها بساوي Gamma(X) و هذا الكلام
+
+142
+00:10:33,100 --> 00:10:37,300
+لكل X  إيش معناه F(X) بساوي Gamma(X) لكله X
+
+143
+00:10:37,300 --> 00:10:42,340
+معناته S(X) بساوي R وايضا هذا الشرط مرضي إيش معناه
+
+144
+00:10:42,340 --> 00:10:46,290
+شرط سهل وسريع، الشرط الأخير اللي هو الـ symmetry
+
+145
+00:10:46,290 --> 00:10:50,550
+اللي هو المسافة بين X و Y هي نفسها بين Y و X بيصير
+
+146
+00:10:50,550 --> 00:10:53,370
+جمع على نقص إقصائي، ما هي absolute value أو modulus
+
+147
+00:10:53,370 --> 00:10:57,550
+ده متساويتاه، واضح؟ إذا الشرط الثاني كما .. ثالث
+
+148
+00:10:57,550 --> 00:11:02,210
+متحقق، ضال عندنا الشرط الثالث، الشرط الثالث، بس
+
+149
+00:11:02,210 --> 00:11:07,770
+عشان نحققه اسمحولي بس ناخد دالة مساعدة auxiliary
+
+150
+00:11:07,770 --> 00:11:12,980
+function وبدنا نشوف هذه الدالة، الدالة هنستقيها من
+
+151
+00:11:12,980 --> 00:11:17,800
+اللي عندي هذه الآن، هذه وهذه نفس الشيء، فبدي أخد
+
+152
+00:11:17,800 --> 00:11:22,940
+دالة اسميها F of T، طبعا هذه بتيجي مع الخبرة، سوى T
+
+153
+00:11:22,940 --> 00:11:29,520
+على واحد زائد T، هذه الدالة الآن، لو أخدتلها الـ
+
+154
+00:11:29,520 --> 00:11:33,020
+derivative هتطلع الـ derivative إليها واحد على واحد
+
+155
+00:11:33,020 --> 00:11:37,760
+زائد T لكل شيء شمالها تربيع، ماشي الحال، إذا واضح أن
+
+156
+00:11:37,760 --> 00:11:43,190
+الـ F prime of T أكبر أو يساوي إيش؟ صفر حتى
+
+157
+00:11:43,190 --> 00:11:46,210
+strictly أكبر من صفر، إذا الـ function .. ال ..
+
+158
+00:11:46,210 --> 00:11:50,710
+الدالة إيش مالها؟ increasing function، واضح، إذا
+
+159
+00:11:50,710 --> 00:11:55,010
+الدالة increasing، إذا الآن بدي أخزن المعلومة عندي
+
+160
+00:11:55,010 --> 00:12:01,350
+f of t is increasing، طيب شوفوا إيش بدي أستفيد من
+
+161
+00:12:01,350 --> 00:12:10,120
+هذه، أنا الآن بدي أثبت اللي هو D(X, Y) أظهر يسموه D(X 
+
+162
+00:12:10,120 --> 00:12:16,040
+و Z زائد DZ, Y) هي ترينجلين كواليتيه، شوفوا كيفه، خدوا 
+
+163
+00:12:16,040 --> 00:12:23,500
+الآن X سموها Xi(X) و Y سموها Gamma(X) وخد Z أي شيء
+
+164
+00:12:23,500 --> 00:12:26,780
+يسميه .. اللي هي أي سيكوينسيز في الاس وسميها Beta
+
+165
+00:12:26,780 --> 00:12:33,800
+(X)، ماشي؟ لاحظوا التالي الآن لو أجينا أخدنا الـ Xi(X)
+
+166
+00:12:33,800 --> 00:12:40,470
+ناقص Gamma(X)، طبعا أنا بدور حوالين الـ mean، حوالين
+
+167
+00:12:40,470 --> 00:12:44,230
+المسافة بين X و Y هنا بدور حواليها، إذا بدي أربطها
+
+168
+00:12:44,230 --> 00:12:48,950
+بين المسافة بين X و Z و Y و Z، إذا أصغر أو يساوي X
+
+169
+00:12:48,950 --> 00:12:53,430
+(X)، أكيد هدخل الـ mean اللي هي طبعة الـ Z زائد
+
+170
+00:12:53,430 --> 00:12:57,370
+Beta(X) ناقص Gamma(X)، هذه بالـ Triangling Quality
+
+171
+00:12:57,370 --> 00:13:00,610
+العادية اللي بنعرفها، اللي هي Triangling Quality of
+
+172
+00:13:00,610 --> 00:13:04,470
+Numbers، معايا؟ طيب صليوا على النبي عليه الصلاة
+
+173
+00:13:04,470 --> 00:13:11,940
+والسلام، الـ L عندي اللي هو هذه أصغر أو يساوي هذه و
+
+174
+00:13:11,940 --> 00:13:14,220
+الـ function اللي عندي increasing، مظبوط ولا لا، اطلع
+
+175
+00:13:14,220 --> 00:13:19,140
+لفوق شوية، خلّيني نكون مع اللي مكتوب، صارت عندي هذه
+
+176
+00:13:19,140 --> 00:13:23,360
+أصغر أو يساوي هذه، و الـ function increasing، إذا F
+
+177
+00:13:23,360 --> 00:13:29,140
+لهذه أصغر أو يساوي F لهذه، إذا F لهذه أصغر أو يساوي F
+
+178
+00:13:29,140 --> 00:13:33,600
+لهذه، because the function is increasing، إيش F لهذه
+
+179
+00:13:33,600 --> 00:13:41,170
+هي Xi(X) ناقص Gamma(X)، هذا الـ T، لأن على واحد زي Xi(X)
+
+180
+00:13:41,170 --> 00:13:47,130
+ناقص Gamma(X)، أصغر أو يساوي F هذه كلها، اللي هي Xi(X)
+
+181
+00:13:47,130 --> 00:13:53,570
+هذه كلها الـ T صارت، ناقص Beta(X)، زي Beta(X) ناقص Gamma
+
+182
+00:13:53,570 --> 00:14:00,310
+(X)، طبعا كله مدخلة على واحد زي Xi(X) ناقص Beta(X) زي
+
+183
+00:14:00,310 --> 00:14:08,160
+Beta(X) ناقص مين؟ Gamma(X)، بدينا نجرب على اللي هي
+
+184
+00:14:08,160 --> 00:14:12,260
+المسافة بين x و y، هاي المسافة بين x و y، احنا
+
+185
+00:14:12,260 --> 00:14:17,580
+معرفينها اللي فوق اه؟ معرفين هي اه؟ بدينا نجرب بس
+
+186
+00:14:17,580 --> 00:14:21,740
+هنا لسه بعادي شوية، فخلينا نفصل هذه لحال و هذه لحال
+
+187
+00:14:21,740 --> 00:14:26,940
+عشان نفصل تبعات الـ z لحال و الـ x و الـ y و الـ z
+
+188
+00:14:26,940 --> 00:14:29,580
+لحال، إذا هذه بتساوي بالظبط
+
+189
+00:14:32,230 --> 00:14:39,390
+ناقص Beta(X) على 1 زائد Xi(X) ناقص Beta(X) زائد Beta(X)
+
+190
+00:14:39,390 --> 00:14:46,240
+ناقص Gamma(X)، صح؟ اللي بعمله، زائد التانية Beta(X) ناقص
+
+191
+00:14:46,240 --> 00:14:51,640
+Gamma(X) على واحد زائد Psi(X) ناقص Beta(X)، بنجلهم
+
+192
+00:14:51,640 --> 00:14:56,740
+نفسي زائد Beta(X) ناقص Gamma(X)، بس اللي عملته فصلتن
+
+193
+00:14:56,740 --> 00:15:03,200
+عن بعض، ماشي الحال، الآن هذه نفسها هيها، أصغر أو
+
+194
+00:15:03,200 --> 00:15:11,640
+يساوي، صح؟ اه، يعني بتصغر المقام فتكبر هذا وهذا نفس
+
+195
+00:15:11,640 --> 00:15:18,680
+الشيء، ماشي، واضح؟ اللي عملته الآن، إيش بده يسوي عشان
+
+196
+00:15:18,680 --> 00:15:22,180
+أصل اللي في ذاك مضياج، اضرب في هذا 1/2
+
+197
+00:15:22,180 --> 00:15:25,280
+(X) وهذا في 1/2 (X)، عارفين ليش
+
+198
+00:15:34,970 --> 00:15:40,470
+هذا أصغر شويه Alpha(X) ناقص Beta(X) و Beta(X) ناقص Gamma
+
+199
+00:15:40,470 --> 00:15:48,030
+(X)، هي ليش اللي دلت اللي مسحناها Beta(X) ناقص Gamma(X)
+
+200
+00:15:48,030 --> 00:15:51,810
+ماشي الحال، واضحة الفكرة اه، هذا في 1/2 (X)
+
+201
+00:15:51,810 --> 00:15:57,530
+هنا صار هذا أصغر شويه هذا، الآن بأخذ الـ summation
+
+202
+00:15:57,530 --> 00:16:01,460
+ماله إلى ما لا نهاية، وضامن إن الـ summation كله بتوزع
+
+203
+00:16:01,460 --> 00:16:06,780
+ليش؟ لأن الـ series هنا converts و الـ series هنا
+
+204
+00:16:06,780 --> 00:16:10,420
+converts، واضح؟ إذا صار الـ summation على هذه (X) من
+
+205
+00:16:10,420 --> 00:16:13,880
+واحد إلى ما لا نهاية، أصغر أو يساوي الـ summation على
+
+206
+00:16:13,880 --> 00:16:16,880
+هذه (X) من واحد إلى ما لا نهاية، زائد الـ summation على
+
+207
+00:16:16,880 --> 00:16:20,340
+الأخيرة (X) من واحد إلى ما لا نهاية، هذه مين هي يا
+
+208
+00:16:20,340 --> 00:16:26,140
+جماعة؟ هذه عبارة عن D(x,y)
+
+209
+00:16:27,220 --> 00:16:35,420
+و هذه مين هي؟ بين الـ X و الـ Z، دي X و Z ذات، هذه بين
+
+210
+00:16:35,420 --> 00:16:43,840
+مين؟ بين Y و Z ذات، دي Z و Y أو Y و مين؟ و Z، مظبوط
+
+211
+00:16:43,840 --> 00:16:51,100
+هيك؟ و بيكون أثبتنا إنه عبارة عن اللي هو metric، أي
+
+212
+00:16:51,100 --> 00:17:00,240
+سؤال؟ طيب، إذا صار عندي الـ S مع هذا الـ metric is a
+
+213
+00:17:00,240 --> 00:17:05,080
+metric space، بتعمل إيه شمالها؟ metric space، نيجي
+
+214
+00:17:05,080 --> 00:17:09,720
+الآن ناخد space شبيه بالـ space اللي حكينا عنه قبل
+
+215
+00:17:09,720 --> 00:17:12,800
+شوية، اللي هو الـ L infinity، هداك كان في حالة الـ
+
+216
+00:17:12,800 --> 00:17:15,420
+sequences، الـ L infinity bounded sequences، هلا في
+
+217
+00:17:15,420 --> 00:17:18,860
+حالة الدوال، يعني بتاخد اللي هو the space of all
+
+218
+00:17:18,860 --> 00:17:22,660
+bounded functions على اللي هي الـ 6
+
+219
+00:17:26,720 --> 00:17:31,740
+طيب يا جماعة، شوفوا، بدأ
+
+220
+00:17:31,740 --> 00:17:38,880
+أحكي الآن عن space آخر، اللي هو space of functions
+
+221
+00:17:38,880 --> 00:17:42,160
+المرة الماضية حكينا عن space of continuous
+
+222
+00:17:42,160 --> 00:17:46,540
+functions، فسمي continuous functions على closed
+
+223
+00:17:46,540 --> 00:17:49,580
+bounded interval، وعرفنا الـ metric في حينه، الـ
+
+224
+00:17:49,580 --> 00:17:54,800
+maximum، تجرأنا وعرفنا الـ maximum لأنه احنا عارفين
+
+225
+00:17:54,800 --> 00:17:57,240
+الـ continuous function على closed bounded interval
+
+226
+00:17:57,240 --> 00:18:00,500
+أكيد attain its maximum و minimum في الـ interval
+
+227
+00:18:00,500 --> 00:18:05,580
+عشان ذلك عرفنا الـ maximum، بس اليوم إنا بأخذ الـ
+
+228
+00:18:05,580 --> 00:18:09,600
+space of bounded functions، يعني عناصر الـ space
+
+229
+00:18:09,600 --> 00:18:13,100
+اللي عندي هي عبارة عن دوال محدودة bounded
+
+230
+00:18:13,100 --> 00:18:18,300
+functions، الـ bounded function ليس شرطا أنه ألاقي
+
+231
+00:18:18,300 --> 00:18:20,900
+الـ maximum و الـ minimum له، وين الـ absolute maximum
+
+232
+00:18:20,900 --> 00:18:26,120
+و الـ absolute minimum وين؟ على اللي هي للست اللي
+
+233
+00:18:26,120 --> 00:18:31,160
+عندي، عشان هيك بتعرفهاش، بيساوي الـ supremum الـ
+
+234
+00:18:31,160 --> 00:18:35,060
+supremum مضمون أنه موجود لأنها bounded، عشان إيه
+
+235
+00:18:35,060 --> 00:18:38,080
+بتقول الآن، let B of A be the set of all bounded
+
+236
+00:18:38,080 --> 00:18:43,060
+functions defined on a set A، define الـ metric الآن،
+
+237
+00:18:43,060 --> 00:18:48,120
+المسافة بين اللي هو أي دالتين في الـ B of A بتساوي
+
+238
+00:18:48,120 --> 00:18:51,740
+الـ supremum للـ X of T ناقص Y of T over اللي هو T
+
+239
+00:18:51,740 --> 00:18:56,570
+over A، هذا الآن بعرف الـ metric بالظبط .. بالظبط
+
+240
+00:18:56,570 --> 00:19:01,570
+البرهان مشابه بل typical للبرهان تبع الـ L
+
+241
+00:19:01,570 --> 00:19:04,830
+infinity وحكيناها المرة الماضية وشرحناها بالتفصيل
+
+242
+00:19:04,830 --> 00:19:11,050
+اللي نسيه برجعله مافي مشكلة خالص، طيب نيجي الآن لـ
+
+243
+00:19:11,050 --> 00:19:19,050
+.. اللي هو بدي الآن امهد للوصول
+
+244
+00:19:20,070 --> 00:19:26,830
+الـ Space الأول
+
+245
+00:19:26,830 --> 00:19:33,010
+الـ Infinity، الـ Space of Sequences بس هذه Bounded
+
+246
+00:19:33,010 --> 00:19:38,550
+Sequences، وحكينا عن Space ثاني S اللي هو Space of
+
+247
+00:19:38,550 --> 00:19:43,310
+Sequences in General، هذا عرفناه Metric يناسبه وهذا
+
+248
+00:19:43,310 --> 00:19:48,450
+عرفناه Metric يناسبه، بعدين أجينا، طبعا هذا كل
+
+249
+00:19:48,450 --> 00:19:52,510
+الكلام فيه له مستقبل وفيه تبعات في المستقبل له
+
+250
+00:19:52,510 --> 00:19:57,270
+الآن، و جينا عرفنا اللي هو space of sequences و
+
+251
+00:19:57,270 --> 00:20:03,550
+جينا عرفنا اللي هو space آخر اللي هو .. اللي هو C
+
+252
+00:20:03,550 --> 00:20:07,610
+of A و B، space of continuous functions على closed
+
+253
+00:20:07,610 --> 00:20:11,750
+bounded interval، ودينا بـ metric تبعه ودينا عرفنا
+
+254
+00:20:11,750 --> 00:20:17,610
+قبل بشوية space B of A، space of bounded functions
+
+255
+00:20:17,610 --> 00:20:22,830
+على الـ A وعرفنا الـ metric تبعه، الآن واضح تودهنا
+
+256
+00:20:22,830 --> 00:20:28,330
+أننا حديثنا في معظم الأنفلة اللي عندنا على main
+
+257
+00:20:28,330 --> 00:20:31,950
+على space of functions وعلى space of main of
+
+258
+00:20:31,950 --> 00:20:37,510
+sequences، وهذا له أهمية كبيرة في نفس الـ functional
+
+259
+00:20:37,510 --> 00:20:42,370
+analysis وحتى تطبيقاتها في الأمور الحياتية الآن،
+
+260
+00:20:42,370 --> 00:20:48,530
+بدي أعرف أدخل لـ space جديد اسمه الـ B spaces، الـ B
+
+261
+00:20:48,530 --> 00:20:53,290
+Spaces، و B عندي هذه بديها أكبر أو يساوي إيش؟ واحد،
+
+262
+00:20:53,290 --> 00:20:58,510
+طيب الـ الـ الـ B Spaces، إيش الـ الـ B هدا؟ هو عبارة عن
+
+263
+00:20:58,510 --> 00:21:02,310
+Space of Sequences، طيب إيش .. إيش شروط اللي على الـ
+
+264
+00:21:02,310 --> 00:21:05,630
+.. ال .. ال Sequences هدا عشان تكون جوة الـ الـ B؟
+
+265
+00:21:05,630 --> 00:21:12,680
+بقول إنك Psi(X) هذه الـ Sequence في الـ الـ B إذا بتحقق
+
+266
+00:21:12,680 --> 00:21:19,460
+مالي أن الـ summation للـ Xi(X) أس p(X) من واحد
+
+267
+00:21:19,460 --> 00:21:24,840
+إلى ما لا نهاية تكون converge، كل الـ sequences اللي
+
+268
+00:21:24,840 --> 00:21:29,920
+في الدنيا اللي Xi(X) لها بتكون في الـ B، إذا تحقق
+
+269
+00:21:29,920 --> 00:21:37,260
+Xi(X) أس p summation is finite، هذا بنسميه الـ B
+
+270
+00:21:37,260 --> 00:21:44,430
+space، بدّي الآن أروح باتجاه تعريف metric عليه، بدي
+
+271
+00:21:44,430 --> 00:21:48,310
+أعرف metric على الـ space هذا، لو قلت هي X بتساوي
+
+272
+00:21:48,310 --> 00:21:54,860
+Psi(X) و Y بتساوي Gamma(X) element in lB، المتريك اللي
+
+273
+00:21:54,860 --> 00:22:00,060
+بتعرفه هتلاقوني عرفته بعد شوية، D(X,Y) بساوي summation
+
+274
+00:22:00,060 --> 00:22:07,840
+للـ Xi(X) ناقص Gamma(X) أس p، عشان أضبن أنه موجود
+
+275
+00:22:07,840 --> 00:22:12,440
+هال هذا finite، و هذا إلها Gamma(X) finite، بس هذا
+
+276
+00:22:12,440 --> 00:22:18,740
+لسه بده شغل و الكل أس واحد عدبيهذا، بعد شوية
+
+277
+00:22:18,740 --> 00:22:24,120
+هتلاقونا وصلنا أنه هذا هيعمل ليه metric على الـ B
+
+278
+00:22:24,120 --> 00:22:28,180
+على الـ B، يعني هيصير الـ B مع هذا الـ metric
+
+279
+00:22:28,180 --> 00:22:33,480
+المعرف اسمه الـ B metric space، وهذا من الفراغات
+
+280
+00:22:33,480 --> 00:22:38,890
+المهمة جدا اللي هو وفيه اللي هو مقابل هنشوف اللي هو 
+
+281
+00:22:38,890 --> 00:22:44,150
+مقابل في الـ space of functions برضه اسمه الـ B بس
+
+282
+00:22:44,150 --> 00:22:48,890
+بيسميه الـ B function وفي حينه أنا بقى بنحكيلكم عنه
+
+283
+00:22:48,890 --> 00:22:55,750
+بالتفصيل ممكن الآن عشان نوصل لهذا أنه metric أنا
+
+284
+00:22:55,750 --> 00:23:02,160
+بلزمني تلت شغلات بالزمن أول شيء الآن اللي هو
+
+285
+00:23:02,160 --> 00:23:08,780
+متباينة أبرهن متباينة مساعدة، المتباينة المساعدة هذه 
+
+286
+00:23:08,780 --> 00:23:14,080
+بدي استخدمها في إثبات حاجة اسمها holder inequality
+
+287
+00:23:15,240 --> 00:23:19,840
+الـ Holder Inequality هذه بتستخدمها لإثبات حاجة
+
+288
+00:23:19,840 --> 00:23:24,620
+اسمها Minkowski Inequality اللي هي هتكون سبب في
+
+289
+00:23:24,620 --> 00:23:28,420
+إثبات الـ Triangle Inequality هذه، لهذا وبهيك بيكون
+
+290
+00:23:28,420 --> 00:23:33,320
+اجتملت الصورة وخلصناها وعملنا اللي بدنا إياه بخصوص
+
+291
+00:23:33,320 --> 00:23:39,560
+اللي هو مين الـ metric space اللي أمامنا، طيب شوفوا
+
+292
+00:23:41,150 --> 00:23:45,990
+الدالة المساعدة، المتباينة المساعدة هذه، المتباينة
+
+293
+00:23:45,990 --> 00:23:51,050
+المساعدة بعد شوية طبعا هتعرفوا ليش هذه أخدناها
+
+294
+00:23:51,050 --> 00:23:53,730
+عشان نستفيد منها في أيش كمان؟
+
+295
+00:23:59,230 --> 00:24:04,430
+في احنا بنعرف في المدارس كنتوا تقولوا المرافق
+
+296
+00:24:04,430 --> 00:24:09,170
+العدد والمرافق هو في سبب للمرافقة، المرافقة أنه
+
+297
+00:24:09,170 --> 00:24:12,730
+يعملوا فرق بين مربعين، أو المرافقة اللي هو في حالة
+
+298
+00:24:12,730 --> 00:24:16,750
+الـ .. الـ .. الـ .. العدد والكنج تبعه الآخرين الآن
+
+299
+00:24:16,750 --> 00:24:21,940
+هنا مرافقة برضه بنقول إن بي وكي مرافقات لبعضهم تحت
+
+300
+00:24:21,940 --> 00:24:28,180
+العلاقة 1 على B زائد 1 على Q ايش بيساوي هذا اللي
+
+301
+00:24:28,180 --> 00:24:32,500
+بنسميه بي وQ conjugate لبعض with respect to this
+
+302
+00:24:32,500 --> 00:24:36,220
+relation، ماشي الحال إذا الآن احنا في عالمنا هذا
+
+303
+00:24:36,220 --> 00:24:38,880
+لما نقول بي وQ بنقصد واحد على بي زائد واحد على
+
+304
+00:24:38,880 --> 00:24:44,000
+كيو بيساوي واحد، وبي وكيو اشمالهن أكبر أو يساوي
+
+305
+00:24:44,000 --> 00:24:48,960
+واحد، طيب نيجي نشوف اللي هو الـ auxiliary inequality
+
+306
+00:24:52,520 --> 00:24:56,480
+اللي هنجيب بس لو سمحت أنا سيبني من الواحد أنا
+
+307
+00:24:56,480 --> 00:25:00,980
+بتاخد بي أش مالها strictly أكبر من اش من واحد
+
+308
+00:25:00,980 --> 00:25:03,900
+بتناشي اللي هو حالة اللي هي مين بي بتساوي واحد
+
+309
+00:25:03,900 --> 00:25:08,980
+لإنها هيعملني مشكلة في العلاقة هذه فخليني ما أبعدش
+
+310
+00:25:08,980 --> 00:25:11,740
+واحد، يلاقوني بشتغل على الـ بي أكبر من واحد لكن عشان
+
+311
+00:25:11,740 --> 00:25:14,600
+العلاقة هذه الـ conjugation بتاخد الـ بي أش مالها
+
+312
+00:25:14,600 --> 00:25:20,300
+strictly أكبر من واحد، طيب بقول لي هتلاقي دائما لأي
+
+313
+00:25:20,300 --> 00:25:27,180
+Alpha و Beta ألفا وبيتا non negative numbers دائما
+
+314
+00:25:27,180 --> 00:25:31,400
+دائما هتلاقي الالفا في بيتا، طبعا الـ non negative
+
+315
+00:25:31,400 --> 00:25:34,960
+numbers أنا مبسوط فيها بس سرية لإن هو ما ينفعش أقول
+
+316
+00:25:34,960 --> 00:25:37,760
+complex لإنه ما فيش order في الـ complex ما أنتو
+
+317
+00:25:37,760 --> 00:25:41,940
+عارفين إذا الفا في بيتا هتكون أصغر أو ساوي Alpha
+
+318
+00:25:41,940 --> 00:25:47,040
+to the B على B زي بيتا to the Q على مين على Q إذا
+
+319
+00:25:47,040 --> 00:25:52,900
+بدي أُثبت الآن الفا في بيتا أصغر أو ساوي الفا تدا بي
+
+320
+00:25:52,900 --> 00:26:01,180
+على بي زائد بيتا تدا كيو على مين على كيو، القلب، بدي 
+
+321
+00:26:01,180 --> 00:26:07,120
+أستقي من هذه اللي هو اللي هو دالة أسية بتعرفوا
+
+322
+00:26:07,120 --> 00:26:10,780
+أنتوا الدالة الأسية اللي هي لو أجينا أخدنا هذه T
+
+323
+00:26:10,780 --> 00:26:16,280
+وهذه U وأخدنا U بتساوي T أس بي minus واحد مثلا
+
+324
+00:26:16,280 --> 00:26:18,960
+على سبيل المثال هذه الدالة لازم تعرفوا ايش أخدت
+
+325
+00:26:18,960 --> 00:26:20,800
+هذه الدالة
+
+326
+00:26:22,300 --> 00:26:28,120
+هي اللي هو عندي الدالة هذه وكانت هذه عندي Alpha و
+
+327
+00:26:28,120 --> 00:26:34,720
+كانت هذه عندي مثلا مين Beta الآن Alpha في Beta هي
+
+328
+00:26:34,720 --> 00:26:41,900
+Alpha في Beta مظبوط؟
+
+329
+00:26:41,900 --> 00:26:51,870
+هذه عبارة عن مساحة المستطيل هذا مظبوط؟ طيب الآن لو
+
+330
+00:26:51,870 --> 00:26:57,090
+جيت على المساحة تحت المنحنى هذا، المساحة تحت
+
+331
+00:26:57,090 --> 00:27:02,410
+المنحنى هذا هيها هيها ماشي هذه المساحة تحت المنحنى
+
+332
+00:27:02,410 --> 00:27:10,510
+هذا هيها صحيح ولا لأ؟ هذه إيش بتمثل؟ بتمثل الـ
+
+333
+00:27:10,510 --> 00:27:17,890
+integration T-1 dt من أين إلى أين؟ من صفر إلى
+
+334
+00:27:17,890 --> 00:27:23,210
+ألفا صح أم لا؟ طيب من صفر إلى ألفا لو جينا تطلعنا
+
+335
+00:27:23,210 --> 00:27:29,290
+من جهة أخرى، من جهة أخرى
+
+336
+00:27:29,290 --> 00:27:34,610
+لأ اللي هو المساحة تحت المنحنى هذا هيها اللي
+
+337
+00:27:34,610 --> 00:27:39,710
+بالأخضر هذه المساحة تحت المنحنى هذا هيها هيها هي
+
+338
+00:27:39,710 --> 00:27:46,200
+دول الأخضر هذه المساحة اللي هي بدا تصير اللي هو T
+
+339
+00:27:46,200 --> 00:27:50,520
+أس U أس 1 على B-1 صح بيصير الـ integration بتبعها
+
+340
+00:27:50,520 --> 00:27:55,540
+زائد الـ integration فاني كيف لإنه بتتغير هذا بيصير
+
+341
+00:27:55,540 --> 00:27:58,060
+اللي هو الـ independent variable وهذا الـ dependent
+
+342
+00:27:58,060 --> 00:28:06,900
+variable بيصير T الـ U أس B أس 1 على B-1 اللي هو
+
+343
+00:28:06,900 --> 00:28:13,010
+من وين لوين بيصير من 0 لـ 100 لـ Beta طبعا الرسم هذه
+
+344
+00:28:13,010 --> 00:28:18,270
+الآن واضح.. واضح أن المساحة هذه زاد المساحة هذه
+
+345
+00:28:18,270 --> 00:28:23,070
+.. هذه.. هي.. هي اللي بالأحمر هنا أكيد أكبر أو
+
+346
+00:28:23,070 --> 00:28:28,200
+يساوي الألف في مين في بيتها، لأن هذه زيادة، هذه
+
+347
+00:28:28,200 --> 00:28:32,920
+الجزء زيادة عن اللي هي مساحة المربع، المساطيل،
+
+348
+00:28:32,920 --> 00:28:38,280
+مظبوط؟ الآن قد تكون الشغل مختلفة شوية، قد يكون
+
+349
+00:28:38,280 --> 00:28:43,000
+اللي هو بدل هيك، بدل بالشكل هذا، تكون الرسمة،
+
+350
+00:28:43,000 --> 00:28:50,200
+ماعليش أغير شيء بسيط، الرسمة تكون هاي Alpha هنا هي
+
+351
+00:28:50,200 --> 00:28:53,700
+Alpha وهي Beta فبتكون ليه مساحة الـ Alpha في Beta
+
+352
+00:28:53,700 --> 00:29:00,040
+ويصير المساحة تحت المنحنى هذه زاد هذه فبتكون هذه
+
+353
+00:29:00,040 --> 00:29:03,520
+الزيادة يعني تكون زيادة هنا أو تكون زيادة من هنا
+
+354
+00:29:03,520 --> 00:29:06,900
+فاهمين ليش اللي بقوله؟ فبالآن أي إن كانتوا لو
+
+355
+00:29:06,900 --> 00:29:09,380
+التقين الـ Alpha من الرتم مع بعض بيصير اللي هو إيه
+
+356
+00:29:09,380 --> 00:29:13,780
+في ماله مسواهم معايا، فالآن صار الـ integration هذا الـ
+
+357
+00:29:13,780 --> 00:29:16,900
+alpha في beta أصغر شوية، الـ integration هذا زاد الـ
+
+358
+00:29:16,900 --> 00:29:20,060
+integration هذا، بدنا نحسب الـ integration هذا الـ
+
+359
+00:29:20,060 --> 00:29:23,760
+integration هذا إيش بده يكون قيمته؟ كلكم أكيد بعرف
+
+360
+00:29:23,760 --> 00:29:31,060
+اللي هو عبارة عن Tu أس بي على بي من صفر لعند alpha
+
+361
+00:29:31,060 --> 00:29:38,180
+زاد الآن هذا يقصد الـ Du هذا يقصد واحد على بي ماينس
+
+362
+00:29:38,180 --> 00:29:44,310
+واحد، لو جينا على جهة واحد على بي زائد واحد على كيو
+
+363
+00:29:44,310 --> 00:29:48,370
+ايش بيساوي؟ بيساوي واحد يعني وحدنا المقامات فبيصير
+
+364
+00:29:48,370 --> 00:29:53,190
+بي في كيو، وأنا بي زائد كيو بيساوي واحد يعني عند بي
+
+365
+00:29:53,190 --> 00:29:57,190
+زائد كيو بيساوي بي في كيو خليه في الذاكرة لو جيتوا
+
+366
+00:29:57,190 --> 00:30:00,930
+حسبتوا بي ماينس واحد في كيو ماينس واحد بيساوي
+
+367
+00:30:00,930 --> 00:30:09,600
+اضربوهم في بعض بيصير بي في كيو ناقص بي ناقص كيو زائد
+
+368
+00:30:09,600 --> 00:30:14,760
+واحد، صح؟ هذول مع بعض، هذول مع بعض، لو نقول إن أنا
+
+369
+00:30:14,760 --> 00:30:18,500
+بيصير إني أشتفر، زائد واحد دلوقتي ايش بيساوي؟ إذا
+
+370
+00:30:18,500 --> 00:30:21,920
+يعني الآن P minus واحد في Q minus واحد ايش بيساوي؟
+
+371
+00:30:21,920 --> 00:30:27,680
+يعني واحد على P minus واحد هي مين؟ Q ناقص واحد،
+
+372
+00:30:27,680 --> 00:30:34,990
+ماشي؟ فبيصير زائد، فهذه Q ناقص واحد، وصلتم ماشي الحال
+
+373
+00:30:34,990 --> 00:30:38,730
+فالآن بيصير Q U أس Q ماينس واحد اللي هي عبارة عن
+
+374
+00:30:38,730 --> 00:30:46,930
+U أس Q على Q من صفر لمين لـ Beta ويساوي هذا بتصير
+
+375
+00:30:46,930 --> 00:30:54,550
+T يعني بتصير Alpha أس B على B زائد Beta أس Q على
+
+376
+00:30:54,550 --> 00:30:58,930
+Q هذا أكبر يساوي مين Alpha في Beta فبتكون الـ
+
+377
+00:30:58,930 --> 00:31:04,700
+auxiliary اللي هو inequality تم ضمنها ماشي إذا
+
+378
+00:31:04,700 --> 00:31:09,800
+خلينا الآن نحطها عندنا عشان نستخدمها، أنا برهنتها إن
+
+379
+00:31:09,800 --> 00:31:13,900
+هي مش أصلا هي يعني مش هي مجال اهتمامي لكن أنا
+
+380
+00:31:13,900 --> 00:31:17,320
+برهنتها عشان نستخدمها بعد شوية في شغلة مجال
+
+381
+00:31:17,320 --> 00:31:23,930
+اهتمامي Alpha في Beta أزرع يساوي قولوا معايا Alpha
+
+382
+00:31:23,930 --> 00:31:30,070
+أس بي على بي زائد Beta أس Q على Q هذا خليه في
+
+383
+00:31:30,070 --> 00:31:32,830
+الذاكرة هذا الـ auxiliary inequality اللي أمامي
+
+384
+00:31:32,830 --> 00:31:37,810
+الآن بدي أجي لللي هي الهدف الثاني اللي هيوصلني
+
+385
+00:31:37,810 --> 00:31:42,450
+لهدفي اللي هو حاجة اسمها اللي هي holder inequality
+
+386
+00:31:42,450 --> 00:31:46,960
+بس جيب لي الـ holder inequality الـ.. كتبته أنا هذا
+
+387
+00:31:46,960 --> 00:31:51,000
+الـ LP كتبته، قول قولته قبل شوية will denote the
+
+388
+00:31:51,000 --> 00:31:54,360
+set of all sequences of number xi I number xi I
+
+389
+00:31:54,360 --> 00:31:57,520
+such that الـ summation هذا is finite where P
+
+390
+00:31:57,520 --> 00:32:02,520
+أشماله أكبر أو يساوي واحد الآن
+
+391
+00:32:03,750 --> 00:32:09,330
+الـ Holder Inequality خليني أركزوا معايا لأن
+
+392
+00:32:09,330 --> 00:32:14,130
+الرموز هي اللي بت.. شوية بت.. فيها عفاشة لكن إن
+
+393
+00:32:14,130 --> 00:32:20,390
+شاء الله بنفهمها، ما بديش أكتب كثير هلأ لإنه حنطول
+
+394
+00:32:20,390 --> 00:32:26,370
+خليني نشرع على اللي موجود، شوف
+
+395
+00:32:26,370 --> 00:32:31,060
+ايش بتقول الـ Holder Inequality بتقول ايه لنا؟ لو
+
+396
+00:32:31,060 --> 00:32:33,720
+كانت الـ P والـ Q زي قبل شوية يعني واحد على P زائد
+
+397
+00:32:33,720 --> 00:32:38,220
+واحد على Q بسوء واحد وكان عند XI I و I الموجودة في
+
+398
+00:32:38,220 --> 00:32:42,540
+القلب P والجامعة I و I الموجودة في القلب Q إذا ما
+
+399
+00:32:42,540 --> 00:32:46,660
+يلي يتحقق ايش هو ما يلي؟ summation of absolute
+
+400
+00:32:46,660 --> 00:32:52,420
+value XI I في جامعة I أصغر أو ساوي XI K أس P كله
+
+401
+00:32:52,420 --> 00:32:56,770
+واحد على P في الـ Summation Gamma M .. اللي بتكون
+
+402
+00:32:56,770 --> 00:33:01,250
+بيسموها K أس Q أس واحد مين على Q هذه اللي بيسميها
+
+403
+00:33:01,250 --> 00:33:03,590
+Holder Inequality يعني الـ Summation ..
+
+404
+00:33:03,590 --> 00:33:14,690
+Summation لـ Xi I Gamma I أزرع أو ساوي Summation
+
+405
+00:33:14,690 --> 00:33:22,230
+Xi I أس B أس واحد على B في الـ Summation Gamma I
+
+406
+00:33:22,910 --> 00:33:29,190
+أس Q بس واحد على مين الـ Q، لحظة لو هذه .. لو هذه
+
+407
+00:33:29,190 --> 00:33:35,890
+XII في الـ LB بضمن إنه هذي Converse هيك تعريفها و
+
+408
+00:33:35,890 --> 00:33:40,070
+Gamma M هذي مدام أنت في الـ LQ هذي برضه تكون إيه
+
+409
+00:33:40,070 --> 00:33:43,430
+أشماله Converse إذا الدنيا ده مقام نيحة هيك بيصير
+
+410
+00:33:43,430 --> 00:33:46,130
+هذا Converse أكبر شوية هذي ده أكيد أشماله هذا
+
+411
+00:33:46,130 --> 00:33:53,430
+Converse واضح؟ طيب الآن بدو بس شغلة هيك بدو
+
+412
+00:33:53,430 --> 00:34:00,910
+يستخدمها كجسر بدو يسمي اللي هو طبعا بس بشايلكم
+
+413
+00:34:00,910 --> 00:34:06,030
+شغلة عشان بدو يكسم على الصماش فبدو يشيها سفر فجالك
+
+414
+00:34:06,030 --> 00:34:10,390
+حالة إن XII والجامعة I صفرتين هذه صفر أو هذه
+
+415
+00:34:10,390 --> 00:34:15,770
+صفر هذا trivial case لو لو كانت كsequences يعني Xi
+
+416
+00:34:15,770 --> 00:34:21,790
+I 00000 أو Gamma I 000 هيكون اللي هو حاصل الضرب
+
+417
+00:34:21,790 --> 00:34:25,170
+هذا صفر ومن ثم هذا هيكون أكبر أو شهر هذا وتموتك
+
+418
+00:34:25,170 --> 00:34:30,110
+بل بساومي تلان صفر الآن شيلنا هذه الحالة سرنا
+
+419
+00:34:30,110 --> 00:34:35,830
+أخدنا الآن إن Xi I و Gamma I تتمتئن among zero
+
+420
+00:34:35,830 --> 00:34:39,670
+sequences يعني في على الأقل term في كل واحدة مش
+
+421
+00:34:39,670 --> 00:34:47,190
+سفر ماشي طيب اسمعوا psi I تلده هذا الجسر اللي بدأ
+
+422
+00:34:47,190 --> 00:34:52,450
+عبره من خلاله بساوي psi I على القيمة هذه ماشي ايش 
+
+423
+00:34:52,450 --> 00:34:58,930
+القيمة هذه اللي هو هذا ال summation اه اه واضح
+
+424
+00:34:58,930 --> 00:35:04,130
+واخدت الـ  جامعة I بساوي الـ جامعة I تلده بساوي جامعة I
+
+425
+00:35:04,130 --> 00:35:11,660
+على ال summation هذا ماشي واضح؟ الآن لو اجينا ضربنا
+
+426
+00:35:11,660 --> 00:35:17,940
+Xi I في Gamma I ماشي الحال حسب ال auxiliary
+
+427
+00:35:17,940 --> 00:35:23,480
+inequality هيها هيها هيها يعني بتاخد ال Alpha إيش
+
+428
+00:35:23,480 --> 00:35:30,040
+بتساوي Xi I تلده و ال Beta إيش بتساوي Gamma I تلده
+
+429
+00:35:30,040 --> 00:35:34,600
+هتساوي هذه أس بي على بي و هذه أس بي Q على مين؟ على
+
+430
+00:35:34,600 --> 00:35:41,390
+Q إذا صارت بالأماميالآن لما أخدته هيك خد ال
+
+431
+00:35:41,390 --> 00:35:46,650
+summation اللي هو للجهتين من I1 I شماله إلى يمينه
+
+432
+00:35:46,650 --> 00:35:50,150
+نهاية معايا؟ خد ال summation هنا و ال summation
+
+433
+00:35:50,150 --> 00:35:54,570
+هنا أخدنا ال summation و هي ال summation و هي ال
+
+434
+00:35:54,570 --> 00:36:00,270
+main ال summation ماشي الحال طبعا هذا هتلاقوه مضمون
+
+435
+00:36:00,270 --> 00:36:03,870
+ال summation اللي هو finite تبعا لإن هذا الأصل
+
+436
+00:36:03,870 --> 00:36:07,190
+finite و اللي تحت ما هو عبارة عن يا شعن عدد بتاخد
+
+437
+00:36:07,190 --> 00:36:12,630
+اعمل مشترك طيب .. الآن ما يساوي .. الآن نشوف هذا
+
+438
+00:36:12,630 --> 00:36:16,610
+إيش بده يطلع عنها اللي هو xi i في ال summation هنا
+
+439
+00:36:16,610 --> 00:36:23,330
+خدوا هذا و أس بي أس بيبعدين خدوله ال summation
+
+440
+00:36:23,330 --> 00:36:28,610
+مكان هذا معايا الان هذا بيصير رقم الواحدة والتانية
+
+441
+00:36:28,610 --> 00:36:35,810
+زيها الان xi i تلده بيساوي xi i على اللي هو خليني
+
+442
+00:36:35,810 --> 00:36:40,350
+أسمي هذا مثلا scene أو خليني أكتب ليه ليش
+
+443
+00:36:40,350 --> 00:36:47,690
+summation xi i أُس بي وكل أس واحد عالميا على بي
+
+444
+00:36:47,690 --> 00:36:51,670
+معايا إلا أن رفعولي يا أس بي هذا خدولي مدرس يرفعوا
+
+445
+00:36:51,670 --> 00:36:55,870
+أس بي خمدولي مدرس يرفعوا أس بي بتروح هذا ال بي صح
+
+446
+00:36:55,870 --> 00:37:01,050
+هذا رقم هذا رقم بين دايا خدولي ال summation I من
+
+447
+00:37:01,050 --> 00:37:04,530
+عند واحد إلى ما لنهاية خدولي ال summation I من عند
+
+448
+00:37:04,530 --> 00:37:07,750
+واحد إلى ما لنهاية عامل مشترك بطلع لأنه عدد فبصير
+
+449
+00:37:07,750 --> 00:37:12,450
+هذا اللي فوق هو اللي تحت إذا مش هيساوي واحد صح ولا
+
+450
+00:37:12,450 --> 00:37:17,550
+لأ فبصير عندي هذا المقدار واحد وهذا زيه بالظبط
+
+451
+00:37:17,550 --> 00:37:21,550
+واحد فبصير عبارة عن واحد عربي زي آدم واحد عربي
+
+452
+00:37:21,550 --> 00:37:22,190
+واحد عربي واحد عربي واحد عربي واحد عربي واحد عربي
+
+453
+00:37:22,190 --> 00:37:22,550
+واحد عربي واحد عربي واحد عربي واحد عربي واحد عربي
+
+454
+00:37:22,550 --> 00:37:23,810
+واحد عربي واحد عربي واحد عربي واحد عربي واحد عربي
+
+455
+00:37:23,810 --> 00:37:27,870
+واحد عربي واحد عربي واحد عربي واحد عربي واحد عربي
+
+456
+00:37:27,870 --> 00:37:28,910
+واحد عربي واحد عربي واحد عربي واحد عربي واحد عربي
+
+457
+00:37:28,910 --> 00:37:29,880
+واحد عربي واحد عربي واحد عربي واحد عربي الـ
+
+458
+00:37:29,880 --> 00:37:37,700
+Summation للـ Xi I Gamma I تلدة I من واحد إلى ما
+
+459
+00:37:37,700 --> 00:37:43,300
+لنهاية أصغر أو يساوي واحد على B زائد واحد على Q
+
+460
+00:37:43,300 --> 00:37:47,200
+اللي هو إيش بتساوي أكتبها واحد وخلاص ما فيش داعي أن
+
+461
+00:37:47,200 --> 00:37:55,200
+أتكرر ماشي الحالة الآن بدي أعوض الآن هذه قيمتها Xi
+
+462
+00:37:55,200 --> 00:38:03,750
+I في Gamma I اللي هي صارت عندي اللي هو automatic
+
+463
+00:38:03,750 --> 00:38:10,750
+منها لما عوض مكانها هذه و هذه، مظبوط؟ بيصير هذه في
+
+464
+00:38:10,750 --> 00:38:16,830
+هذه و هدول تحت بعض، ماشي الحال معايا؟ طيب خلينا
+
+465
+00:38:16,830 --> 00:38:24,150
+نشوف ال summation ل XI I تلدة في جامعة I تلدة I من
+
+466
+00:38:24,150 --> 00:38:30,400
+واحد إلى وين إلى ما إلى النهاية إيش بتساوي اللي هو
+
+467
+00:38:30,400 --> 00:38:37,400
+ال summation معايا ايه هذولة هذولة طلع عليها xi i
+
+468
+00:38:37,400 --> 00:38:44,640
+gamma i مظبوط على اللي هو مين هذولة عاوز مش شركة
+
+469
+00:38:44,640 --> 00:38:53,380
+بتطلع التانية اه اللي هو ال summation لل xi i SB S1
+
+470
+00:38:53,380 --> 00:38:58,540
+على B في الـ summation Gamma I SQ S1 على Q صح ولا
+
+471
+00:38:58,540 --> 00:39:03,880
+لا؟ ماشي، هذا كله إيش ماله؟ قلنا عنه أصغر أو يساوي
+
+472
+00:39:03,880 --> 00:39:10,540
+واحد خلاص، أدر بهذا في هذا، بطلع ال summation Xi I
+
+473
+00:39:10,540 --> 00:39:17,840
+Gamma I أصغر أو يساوي هذا المقدر و هو المطلوب،
+
+474
+00:39:17,840 --> 00:39:24,490
+واضح؟ إيش يا روحي؟ بعيد زي ذلك هل جيت احنا هذا
+
+475
+00:39:24,490 --> 00:39:28,570
+عوضنا طاولة طلعت هذا صار هذا ما هو احنا ما نقوله من
+
+476
+00:39:28,570 --> 00:39:31,230
+فوق ان هذا اصغر اصغر و واحد اذا صار هذا المقدر
+
+477
+00:39:31,230 --> 00:39:34,530
+اصغر اصغر واحد اضربه طرفين في وسطين بطلع اللي هو
+
+478
+00:39:34,530 --> 00:39:40,110
+ال inequality اللي بدنا اياها يلا اللي بعده نيجي
+
+479
+00:39:40,110 --> 00:39:47,450
+الان اللي هو بس ملاحظة لو كانت بي بتساوي كيو بتساوي
+
+480
+00:39:47,450 --> 00:39:53,770
+اثنين بتطلع عندي XII I من واحد ده ماله نهاية باعود
+
+481
+00:39:53,770 --> 00:39:59,270
+بس عن اتنين اصغره ساوي XIK اص نص جامعة اص اتنين
+
+482
+00:39:59,270 --> 00:40:02,970
+اص مين اص نص هذا ال space محترم هذا ال space
+
+483
+00:40:02,970 --> 00:40:07,790
+هنفردله كلام كتير اللي هو بنسميه ال space العناصره
+
+484
+00:40:07,790 --> 00:40:11,950
+اللي هو في ال L2 اسمه ال L2 هذا اسمه Hilbert
+
+485
+00:40:11,950 --> 00:40:15,910
+Sequence Space هذا هنحكي عنه بالتفصيل جدا ان شاء
+
+486
+00:40:15,910 --> 00:40:22,470
+الله الان هو في الواقع تعميم .. تعميم هذا .. تعميم
+
+487
+00:40:22,470 --> 00:40:27,790
+للمترك تبعنا تبع زمان لما كنا ناخد ال .. لو أخدنا
+
+488
+00:40:27,790 --> 00:40:34,490
+في ال .. في ال R2 X بالساوي XI واحد و Psi 2 و Y
+
+489
+00:40:34,490 --> 00:40:38,470
+بتساوي Gamma 1 و Gamma 2 إيش كنا ناخد ال metric في
+
+490
+00:40:38,470 --> 00:40:45,330
+الزمان الجدر التربيعي يعني نقص نص Psi 1 ناقص Gamma
+
+491
+00:40:45,330 --> 00:40:50,230
+1 تربيع زائد Psi 2 ناقص Gamma 2 كل إيش ماله تربيع
+
+492
+00:40:50,740 --> 00:40:54,580
+فهذا في الواقع تعميم إلى ما لا نهاية مش عدد اللي
+
+493
+00:40:54,580 --> 00:40:58,780
+هي اثنين لما لا و أيضا تعميم هذا على الار تربيع
+
+494
+00:40:58,780 --> 00:41:01,680
+بنسميه metric عالمين على الار تربيع وهذا مثلا على
+
+495
+00:41:01,680 --> 00:41:04,800
+ال metric على الار تربيع على الار and in general
+
+496
+00:41:06,700 --> 00:41:12,940
+الـ Rn بيكون الـ Dxy بساوة الـ summation للـ Xi I
+
+497
+00:41:12,940 --> 00:41:18,840
+ناقص Gamma I لكل تربيع I من عند 1 لعند N لكل
+
+498
+00:41:18,840 --> 00:41:31,240
+اسمانه أس نص فالـ Rn و كأنه special case لـ L2 بس
+
+499
+00:41:31,240 --> 00:41:36,050
+العماصر من عند N زايد 1 و طالع كل مسفرواضح يعني
+
+500
+00:41:36,050 --> 00:41:39,170
+بتقدر نعملها ك sequence تصير اكساية واحد اكساية
+
+501
+00:41:39,170 --> 00:41:41,790
+اثنين عندك ساعة و بعدين سفر سفر سفر ماشي الحال
+
+502
+00:41:41,790 --> 00:41:46,250
+اطلع اللي بعده يعني لو أثبتنا ان ال LB metric
+
+503
+00:41:46,250 --> 00:41:50,190
+space بيكون أثبتنا ال RN تبعنا تبع زمان و ال R
+
+504
+00:41:50,190 --> 00:41:53,990
+تربيع كله من هذه ال metric spaces يلا اللي بعده
+
+505
+00:41:53,990 --> 00:42:00,250
+طيب مينكوسكي inequality ماشي الحال ال
+
+506
+00:42:00,250 --> 00:42:06,010
+auxiliary هذه الآن استخدمناها في إثبات مين اللي هو
+
+507
+00:42:06,010 --> 00:42:09,310
+الـHolder in Quality اللي هو Absolute Value أو
+
+508
+00:42:09,310 --> 00:42:14,310
+Modulus XII Gamma I أصغر أو ساوي Summation XII أُس
+
+509
+00:42:14,310 --> 00:42:19,870
+B أُس واحد على B في الـSummation للـGamma I أُس Q
+
+510
+00:42:19,870 --> 00:42:24,890
+أُس واحد على Q هذه الآن هتلزمنا في إثبات اللي هو
+
+511
+00:42:24,890 --> 00:42:31,680
+مين الـ Minkowski Inquality اللي هي الأساس في إثبات
+
+512
+00:42:31,680 --> 00:42:35,960
+الـ Triangular Inquality دخل الواحد كمان لأنه
+
+513
+00:42:35,960 --> 00:42:40,020
+بيقولك إذا كانت B أكبر من واحد وكان Xi I وGamma I
+
+514
+00:42:40,020 --> 00:42:45,080
+وين موجودة؟ في القلب، إذا ال summation للXi I زائد
+
+515
+00:42:45,080 --> 00:42:49,540
+Gamma I أس B أس واحد على B أصغر من ال summation Xi
+
+516
+00:42:49,540 --> 00:42:54,080
+K أس B أس واحد على B زائد ال summation Gamma B أس 2
+
+517
+00:42:54,080 --> 00:42:58,440
+أس واحد على B الآن حالة الـ B بيساوي واحد هي حالتنا
+
+518
+00:42:58,440 --> 00:43:01,440
+تبعت زمان الـ Triangling Quality لإنه بتصير
+
+519
+00:43:01,440 --> 00:43:06,480
+شمالها Xi I زائد Gamma I و بس أصغر من الصممشن
+
+520
+00:43:06,480 --> 00:43:11,100
+Xi K زائد الصممشن من Gamma N وهذه هي من ال
+
+521
+00:43:11,100 --> 00:43:16,560
+Triangling Quality العادية، ماشي؟ طيب إذا الآن
+
+522
+00:43:16,560 --> 00:43:19,800
+بدنا نبدأ نشتغل على الـ B أكبر من واحد اللي
+
+523
+00:43:19,800 --> 00:43:27,900
+نظريتنا هذه هي الها صحيحة، ماشي؟ ليجي الآن تطلعوا
+
+524
+00:43:27,900 --> 00:43:34,900
+لها الفكرة اللي بده يشتغل فيها ويطبق الـholding
+
+525
+00:43:34,900 --> 00:43:41,360
+quality عليها شوفوا هاي هدفه هو، باشي، بعدين بياخد
+
+526
+00:43:41,360 --> 00:43:44,900
+الـsummation، بعدين، من الحاجين اللي هانجلك خدوا B
+
+527
+00:43:44,900 --> 00:43:48,180
+أكبر من واحد وخد A fixed I يعني بنحكي عن I
+
+528
+00:43:48,180 --> 00:43:54,330
+arbitrarily لكن يشمله I محدد شوفوا Xi I زي Gamma I
+
+529
+00:43:54,330 --> 00:44:00,350
+أُس B بتساوي، بتدفرطها جزئين جزء أُس واحد وجزء أُس
+
+530
+00:44:00,350 --> 00:44:04,650
+B ناقص واحد، ماشي الحال؟ لأن حاصل ضرب هدولة
+
+531
+00:44:04,650 --> 00:44:09,850
+الاثنين شكله بياخد واحدة هذه وواحدة هذه ويشتغل على
+
+532
+00:44:09,850 --> 00:44:15,720
+مين؟ على المنكوسكي طيب، الآن أصغر أو يساوي؟XII
+
+533
+00:44:15,720 --> 00:44:19,460
+زائد gamma I في المقدار هذا وهي الجزء الأول وهي
+
+534
+00:44:19,460 --> 00:44:23,240
+الجزء مين الثاني وقال ال code اللي هو ال summation
+
+535
+00:44:23,240 --> 00:44:27,770
+من عند واحد لعند مين لعند النهاية تلاقيه حسب ال
+
+536
+00:44:27,770 --> 00:44:29,770
+equality اللي هنا أصغر أو سوى ال summation على
+
+537
+00:44:29,770 --> 00:44:33,890
+الجهتين هسير ال summation لهذا أصغر أو سوى ال
+
+538
+00:44:33,890 --> 00:44:37,410
+summation لهذا زائد ال summation للثاني أصغر أو
+
+539
+00:44:37,410 --> 00:44:41,710
+سوى ال summation xi i في ال summation هذا أُس b-1
+
+540
+00:44:41,710 --> 00:44:45,390
+زائد ال summation للثاني أُس b-1 وسميها دي إيش
+
+541
+00:44:45,390 --> 00:44:49,970
+واحد، خليني أكتب هنا عشان هتروح من عندنا الآن ال
+
+542
+00:44:49,970 --> 00:44:57,060
+summation لل xi i زائد gamma i أُس بي أصغر أو ساوي
+
+543
+00:44:57,060 --> 00:45:01,860
+طبعا أخد I من واحدة من عند النهاية لأنه لسه مش ضامن من
+
+544
+00:45:01,860 --> 00:45:04,880
+واحد إلى ما لا نهاية يكون converge ولا لأ عشان هيك
+
+545
+00:45:04,880 --> 00:45:10,120
+في الآخر حتلاقي أخدها لما يصير الأمر ناضج أنه كل
+
+546
+00:45:10,120 --> 00:45:13,580
+اللي معناه converge فبشتغل عليها اللي هي إلى ما لا
+
+547
+00:45:13,580 --> 00:45:22,500
+نهاية أصغر أو ساوي summation xi I في xi i زائد
+
+548
+00:45:22,500 --> 00:45:27,500
+gamma i أس بي ماينس واحد هذه الأولانة زائد
+
+549
+00:45:27,500 --> 00:45:35,780
+summation gamma i في xi i زائد gamma i أس بي ماينس
+
+550
+00:45:35,780 --> 00:45:39,920
+واحد مظبوط؟
+
+551
+00:45:39,920 --> 00:45:46,240
+طيب الآن هذه سموها واحد و أطلع لفوق واستخدموا الآن
+
+552
+00:45:46,240 --> 00:45:51,080
+ال holding quality بدي أستخدمها للأولى أولاتانية
+
+553
+00:45:51,080 --> 00:45:55,300
+خلينا نستخدم الأولى و نعوض و بعدين بنشتغل الأولى
+
+554
+00:45:55,300 --> 00:46:02,320
+هي هذه و كأنها اللي هي هذه و هذه و كأنها مين جامعة
+
+555
+00:46:02,320 --> 00:46:06,760
+فبيصير أصغر أو ساوي على هذه بدي أطبّق الأولى Exile
+
+556
+00:46:06,760 --> 00:46:11,480
+is بيوس واحد على بيه ماشي الحال هديك على اي من
+
+557
+00:46:11,480 --> 00:46:15,660
+واحد المالانهاية و غيره و تقولولي fine I تانية اه
+
+558
+00:46:15,660 --> 00:46:17,820
+ما هي اللي بتطبق على مالانهاية بتطبق عليها تبعد
+
+559
+00:46:17,820 --> 00:46:23,450
+تبرهن كل الناس فار البجيات ماشي فبتصير
+
+560
+00:46:23,450 --> 00:46:26,930
+أس بي أس واحد على بي والتانية بتصير هذه أس بي 
+
+561
+00:46:26,930 --> 00:46:31,190
+ماينص واحد الكل أس كيو أس واحد على مين على كيو
+
+562
+00:46:31,190 --> 00:46:35,690
+مظبوط طبقت مين الـ Holder inequality اللي هي اللي
+
+563
+00:46:35,690 --> 00:46:40,330
+هنا هي هذه أس كيو أس واحد على كيو هي أس كيو أس 
+
+564
+00:46:40,330 --> 00:46:43,910
+واحد على كيو على هذه طبقت اللي هي الأولى هذه بتنزل
+
+565
+00:46:43,910 --> 00:46:47,130
+زي ما هي والتانية بيصير بي ماينص واحد في مين في
+
+566
+00:46:47,130 --> 00:46:51,810
+كيو الان اللي هي الـ .. الـ .. الـ .. الـ ..  و هذه أس
+
+567
+00:46:51,810 --> 00:46:56,870
+مين؟ أس واحد على Q، أه؟ الان B minus واحد في Q
+
+568
+00:46:56,870 --> 00:47:02,990
+بتساوي اللي هو مين؟ بتساوي اللي هي B، أه؟ في ده .. 
+
+569
+00:47:02,990 --> 00:47:07,270
+في ده أنا أعملها؟ كده؟
+
+570
+00:47:07,270 --> 00:47:11,610
+أه، مظبوط؟
+
+571
+00:47:11,610 --> 00:47:17,380
+أعملها ولا خلاص؟ كلهم جايات من مين؟ من 1 على B زائد
+
+572
+00:47:17,380 --> 00:47:23,800
+1 على Q بساوي 1 ماشي الحال طيب الأنصار عندي XI K
+
+573
+00:47:23,800 --> 00:47:30,780
+أس B أس 1 على B وهذه أس B أس 1 على مين؟ على Q واضح
+
+574
+00:47:30,780 --> 00:47:35,500
+اللي بحكيه؟ طيب التانية similarly بنفس الأسلوب
+
+575
+00:47:35,500 --> 00:47:41,320
+Gamma I في XI هذا عملناها مين يا جماعة؟ هذه هي
+
+576
+00:47:41,320 --> 00:47:48,930
+أصغر أو يساوي هذه هذه التانية بالظبط زيها بس بدل 
+
+577
+00:47:48,930 --> 00:47:53,410
+لـ XI I بتاخد 100 Gram I ماشي الحال إذا خلّيني 
+
+578
+00:47:53,410 --> 00:48:01,430
+أسجلها هادي هان أصغر أو يساوي summation XI K أُس B
+
+579
+00:48:01,430 --> 00:48:11,610
+أُس 1 على B في summation XI M زائد Gram M أُس B
+
+580
+00:48:11,610 --> 00:48:13,290
+أُس 1 على 100
+
+581
+00:48:16,590 --> 00:48:22,830
+واضح أه طيب التانية نفس الشيء بس بدل هذه بده احط 
+
+582
+00:48:22,830 --> 00:48:27,510
+هذه ماشي فبصير هذه و هذه زي بعض هذه زي الأولى و
+
+583
+00:48:27,510 --> 00:48:32,810
+هذه زائد زائد summation بدل هذه مين هيكون Gamma K
+
+584
+00:48:32,810 --> 00:48:41,320
+أس بي أس واحد على بي في الـ summation نفسه نفسه
+
+585
+00:48:41,320 --> 00:48:45,280
+ناخده مين على المشترك بيصير هذا ويساوي الـ
+
+586
+00:48:45,280 --> 00:48:49,400
+summation اللي عامل المشترك هذا هذا مضروب في مين 
+
+587
+00:48:49,400 --> 00:48:53,960
+في الـ summation Gamma K أس بي زائد الـ summation
+
+588
+00:48:53,960 --> 00:49:04,700
+اكسايكل ونفعله هذي Gamma K أس واحد على بي أس بي أس
+
+589
+00:49:04,700 --> 00:49:10,150
+مين واحد على كيو صح اطلع على فوق نشوف ده عشان نقول
+
+590
+00:49:10,150 --> 00:49:23,850
+خربطنا مافي حاجة substitute
+
+591
+00:49:23,850 --> 00:49:28,210
+of the two inequalities in main in واحد فبصير اللي
+
+592
+00:49:28,210 --> 00:49:30,250
+هو إن شاء الله مانكون خربطناش في الحسابات
+
+593
+00:49:37,050 --> 00:49:47,950
+أه واحد على Q ولا .. خلّيني أرجع لها هذه
+
+594
+00:49:47,950 --> 00:49:54,610
+واحد على B وهذه اللي هي التانية واحد على B أظن 
+
+595
+00:49:54,610 --> 00:49:57,750
+واحد على B خلّيني أرجع لها دقيقة .. دقيقة .. دقيقة
+
+596
+00:49:57,750 --> 00:50:00,170
+.. دقيقة .. دقيقة .. دقيقة .. دقيقة .. دقيقة ..
+
+597
+00:50:00,170 --> 00:50:00,730
+.. دقيقة .. دقيقة .. دقيقة .. دقيقة .. دقيقة ..
+
+598
+00:50:00,730 --> 00:50:00,770
+.. دقيقة .. دقيقة .. دقيقة .. دقيقة .. دقيقة ..
+
+599
+00:50:00,770 --> 00:50:00,850
+دقيقة .. دقيقة
+
+600
+00:50:05,230 --> 00:50:21,290
+بـ -1 في Q أس واحد على Q لأ
+
+601
+00:50:21,290 --> 00:50:28,110
+تبقى تلعاب المشترك التنتين واحد على Q واحد على بي
+
+602
+00:50:28,110 --> 00:50:34,350
+واحد على بي واحد على بي مظبوط إن هذه الواحد على بي و
+
+603
+00:50:34,350 --> 00:50:44,810
+هذه يشبهلها واحد على بي طيب شوف الـ .. تبهوا لوين
+
+604
+00:50:44,810 --> 00:50:52,250
+احنا وصلنا .. خليني أمسح حاجة، ميمش؟ بصير عند الـ
+
+605
+00:50:52,250 --> 00:50:55,690
+.. and summation
+
+606
+00:50:56,990 --> 00:51:02,850
+Summation هذا شايفينه هذا هذا هذا أصغر أو يساوي
+
+607
+00:51:02,850 --> 00:51:05,950
+اللي هو هذا الـ summation و هذا الـ summation زائد
+
+608
+00:51:05,950 --> 00:51:10,850
+هذا و قلنا هنا خد عامل مشترك اللي هو هذا شايفينه
+
+609
+00:51:10,850 --> 00:51:16,450
+هاي هاي هذا عامل مشترك دل هذا و دل هذا فطلعنا هذا 
+
+610
+00:51:16,450 --> 00:51:20,630
+العامل المشترك هاي و هان و هذول الجمع هاي هان ماشي
+
+611
+00:51:20,630 --> 00:51:24,950
+الحالة الان لاحظوا على هذا و هذا
+
+612
+00:51:27,950 --> 00:51:32,510
+نفس الشيء بس هذا أس واحد على Q و هذا أس واحد فلما 
+
+613
+00:51:32,510 --> 00:51:35,730
+أجسم عليها بيصير اللي هو اللي على الطرف هنا أس
+
+614
+00:51:35,730 --> 00:51:40,920
+واحد ماينص واحد على Q واضحة فبصير عنده الآن الـ
+
+615
+00:51:40,920 --> 00:51:44,740
+summation هذا اللي حكيته عن نقص واحد ناقص مين واحد
+
+616
+00:51:44,740 --> 00:51:48,620
+على Q اللي هو أصغر أو يساوي هذا بيظل زي ما هو وهذا
+
+617
+00:51:48,620 --> 00:51:53,660
+بيظل زي ما هو قبل N واحد ناقص واحد على Q هو واحد
+
+618
+00:51:53,660 --> 00:51:59,000
+على P مصدود واحد على P واحد على P فبصير عنده الآن
+
+619
+00:51:59,000 --> 00:52:04,480
+هذا صار عبارة عن واحد على بيه معليش ده شو جودني
+
+620
+00:52:04,480 --> 00:52:08,140
+بتبقى كتير واحد على مين على بيه الان صار هذا
+
+621
+00:52:08,140 --> 00:52:10,940
+المقدار واحد على بيه و هذا واحد على بيه و هذا واحد
+
+622
+00:52:10,940 --> 00:52:15,360
+على بيه و الـ submissions اتوزع زي اللي انا اصلا
+
+623
+00:52:15,360 --> 00:52:23,340
+بروح بدياها الان انا مرتاح هاخد الان مالة تروح
+
+624
+00:52:23,340 --> 00:52:27,020
+لمالة نهاية ليش مرتاح لإنه ضامن هذا converge زي
+
+625
+00:52:27,020 --> 00:52:29,860
+إنه هذا في القلبي وضامن هذا converge زي إنه في
+
+626
+00:52:29,860 --> 00:52:35,300
+القلبي فبصير عندي هذا من واحد إلى مالة نهاية بالهو
+
+627
+00:52:35,300 --> 00:52:39,840
+اللي أنا بديه أزرع يساوي هذا أس واحد على بيه زائد
+
+628
+00:52:39,840 --> 00:52:42,420
+هذا أس واحد على بيه وكامن واحد إلى مالة نهاية
+
+629
+00:52:42,420 --> 00:52:47,800
+وبكون حصلت عالميا على الـ Minkowski in quad واضح
+
+630
+00:52:49,660 --> 00:52:54,420
+طيب، صلى على النبي أسوأ السنة الآن أصلنا للثمرة 
+
+631
+00:52:54,420 --> 00:52:58,160
+اللي بتنيها اللي هو الـ sequence space اللي هو مين
+
+632
+00:52:58,160 --> 00:53:04,100
+الـ LB space قلنا الآن consider the asset LB of 
+
+633
+00:53:04,100 --> 00:53:08,160
+all sequences of numbers XI I such that الـ
+
+634
+00:53:08,160 --> 00:53:11,380
+summation هذا يكون أشماله converts أو is finite
+
+635
+00:53:11,380 --> 00:53:15,880
+هذه الـ sequences اللي بالخاصية هذه هي اللي بتعمل 
+
+636
+00:53:15,880 --> 00:53:22,660
+للـ LB الـ B تحت الـ D اللي في الأول أنا عرفته اللي
+
+637
+00:53:22,660 --> 00:53:26,760
+هو هيه .. هيه عندي D X Y بساوية summation X I I
+
+638
+00:53:26,760 --> 00:53:31,100
+نقص جمعي أس بي قص واحد على B هيعملني metric على الـ
+
+639
+00:53:31,100 --> 00:53:37,610
+B فبصير الـ B عبارة عن metric space الان هي المث
+
+640
+00:53:37,610 --> 00:53:43,010
+هذا اللي بنثبته بحقق الخصية الأولى واحد اثنين ثلاثة
+
+641
+00:53:43,010 --> 00:53:46,130
+أربعة الخصية الأولى automatic أكبر بساوية صفر هين
+
+642
+00:53:46,130 --> 00:53:50,450
+اللي هو بساوية صفر F وان دول F هذي بتساوي هذي يعني
+
+643
+00:53:50,450 --> 00:53:56,480
+X بتساوي Y باللي هو الـ x و y هي نفسها y و x تبع
+
+644
+00:53:56,480 --> 00:53:59,500
+الهادي الآن الخاصية الأخيرة الاثنين in quality
+
+645
+00:53:59,500 --> 00:54:03,520
+جاهزين لها ليش جاهزين لها من الـ min cost ك in
+
+646
+00:54:03,520 --> 00:54:07,960
+quality شوفوا كيف احنا جاهزين منها هتلاقوا الأمر
+
+647
+00:54:07,960 --> 00:54:13,490
+automatic بطلع خدوا اي x بساوي psi i و Y بيساوي 
+
+648
+00:54:13,490 --> 00:54:16,830
+Gamma I و Z بيساوي Beta I كل هي اللي موجودات في
+
+649
+00:54:16,830 --> 00:54:22,070
+القلبي خد المسافة X Y بين X Y اللي احنا عرفنا الـ
+
+650
+00:54:22,070 --> 00:54:27,070
+metric على أساسها اللي هو بيساوي هذه قطعا اللي هو 
+
+651
+00:54:27,810 --> 00:54:32,270
+اللي جوا بس بدي .. بعد إذن كن بدي اكتبها بضاطيف
+
+652
+00:54:32,270 --> 00:54:36,750
+Beta I واش ونقص Beta I بصير أصغر أو يساوي
+
+653
+00:54:36,750 --> 00:54:40,350
+واستخدمين الـ Triangling الـ Quality العادية اللي
+
+654
+00:54:40,350 --> 00:54:44,990
+هو XI I نقص Beta I زي الـ Beta I نقص من XI I وخلّي
+
+655
+00:54:44,990 --> 00:54:49,610
+.. يعني اشتغل هذه أصغر أو يساوي هذه وهذه B وهذه B
+
+656
+00:54:49,610 --> 00:54:54,220
+واحدة على B واحدة على B فاهمين؟ طيب، الآن هذا بيصير
+
+657
+00:54:54,220 --> 00:54:57,760
+عندي حسب الـ Minkowski inequality اللي قبل بشوية هذا
+
+658
+00:54:57,760 --> 00:55:02,900
+لحاله و هذا لحاله هذا بيصير أس بي سواحد على بي و
+
+659
+00:55:02,900 --> 00:55:07,820
+هذا بيصير أس كيو سواحد على كيو فاهمين؟ هذا اللي هو 
+
+660
+00:55:07,820 --> 00:55:14,800
+استخدام الـ Minkowski اللي مسحتها مباشرة يعني هذا بيمثل
+
+661
+00:55:14,800 --> 00:55:18,660
+في الـ Minkowski اللي قبل شوية XII و هذا بيمثل Gamma I
+
+662
+00:55:19,950 --> 00:55:26,370
+فطبقتها فطلعت هذه زائد هذه هذه اللي هي DXY DX و Z
+
+663
+00:55:26,370 --> 00:55:30,810
+هي طبعت الـ XY الـ Z و هذي DY و Z و هيك بيكون عندنا
+
+664
+00:55:30,810 --> 00:55:35,610
+أثبتنا أن هذا عبارة عن مين عن metric space في حالة
+
+665
+00:55:35,610 --> 00:55:40,030
+الـ B بالساوة اثنين قولنا هذا metric محترم بنعتبره
+
+666
+00:55:40,490 --> 00:55:44,430
+اللي هو اسمه الـ Hilbert space الـ Hilbert sequence
+
+667
+00:55:44,430 --> 00:55:49,350
+space الـ Hilbert 
+
+668
+00:55:49,350 --> 00:55:50,170
+sequence space الـ Hilbert sequence space الـ Hilbert
+
+669
+00:55:50,170 --> 00:55:51,050
+sequence space الـ Hilbert sequence space الـ Hilbert
+
+670
+00:55:51,050 --> 00:55:51,110
+sequence space الـ Hilbert sequence space الـ Hilbert
+
+671
+00:55:51,110 --> 00:55:53,090
+sequence space الـ Hilbert sequence space الـ Hilbert
+
+672
+00:55:53,090 --> 00:55:55,810
+sequence space الـ Hilbert sequence space اللي هو
+
+673
+00:55:55,810 --> 00:55:59,390
+العناصر اللي هي X,Y,I,Y الـ R تكعيب اتبعنا اللي هو
+
+674
+00:55:59,390 --> 00:56:02,410
+الـ Ordered Pair اللي هو هذا الـ DXY اللي هو الجذر
+
+675
+00:56:02,410 --> 00:56:06,410
+التربيعي اللي حكيته قبل وشوية حالة خاصة منه والـ R
+
+676
+00:56:06,410 --> 00:56:13,170
+تكعيب اللي بنفس الأسلوب بنعرفه حالة خاصة لأرضه
+
+677
+00:56:13,170 --> 00:56:18,130
+منين من الـ L2 Space وكل هنا بنكون أثبتناه
+
+678
+00:56:18,130 --> 00:56:22,310
+الـ Metric Space مادام أثبتنا مين اللي هو الـ B in
+
+679
+00:56:22,310 --> 00:56:25,830
+general is a metric space لأنه بنعتبر الباقي اللي
+
+680
+00:56:25,830 --> 00:56:30,930
+هو إيش اللي هي أصفار والـ RN برضه زي ما قلت قبل 
+
+681
+00:56:30,930 --> 00:56:35,070
+شوية نفس الأسلوب في حالة الـ CN الـ CN برضه نفس
+
+682
+00:56:35,070 --> 00:56:38,050
+الشيء بس باخد بدل التربية إيش باخد للمدرس عشان
+
+683
+00:56:38,050 --> 00:56:43,350
+يصير إن أعداد يطلع قيمة لأن عشان يطلع DXY عبارة عن 
+
+684
+00:56:43,350 --> 00:56:48,310
+عدد فباخد المدرس فبكون هذا عبارة عن الـ CN و بيكون
+
+685
+00:56:48,310 --> 00:56:52,750
+كل الحالات خاصة من اللي حكيته قبل بشوية و بيكون
+
+686
+00:56:52,750 --> 00:56:58,310
+معكم exercise الآن هذا اللي عندي بالإضافة ده
+
+687
+00:56:58,310 --> 00:57:03,150
+ثمانية و عشرة هدول لكم السيرمونيان و هدولة اللي هو 
+
+688
+00:57:03,150 --> 00:57:07,790
+حلون و فيها العمون الحلون الموجودة عندي اللي
+
+689
+00:57:07,790 --> 00:57:12,270
+ماعرفش حاجة بنعطيها إن شاء الله و برك الله فيكم و
+
+690
+00:57:12,270 --> 00:57:13,110
+الله يعطيكم العافية 
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RstVGUoRP6o_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RstVGUoRP6o_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f52c5558533562a2cb8c2458aa832006986b9916
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RstVGUoRP6o_raw.srt
@@ -0,0 +1,2784 @@
+1
+00:00:05,360 --> 00:00:08,000
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,000 --> 00:00:11,400
+والصلاة والسلام علي سيد المرسلين هذه المحاضرة
+
+3
+00:00:11,400 --> 00:00:18,880
+الثانية في مساق تحليل اقتراني او تحليل دالي لطلب
+
+4
+00:00:18,880 --> 00:00:26,620
+طلبات الماجستير الجامعة الإسلامية بغزا حكينا المرة
+
+5
+00:00:26,620 --> 00:00:30,580
+الماضية بدأنا في المحاضرة الأولى حكينا عن ال
+
+6
+00:00:30,580 --> 00:00:34,930
+metric spaceاليوم إن شاء الله هنحكي عن اللي هو
+
+7
+00:00:34,930 --> 00:00:39,550
+examples on metric space وهو 1،2 تحت عنوان further
+
+8
+00:00:39,550 --> 00:00:43,890
+examples on metric space خليني بس عشان نذكركم باشي
+
+9
+00:00:43,890 --> 00:00:46,990
+اللي حكيناه المرة الماضية عشان تكون الأمور يعني
+
+10
+00:00:46,990 --> 00:00:51,770
+مترابطة وفي عندنا اللي هو تواصل بالحديث اللي المرة
+
+11
+00:00:51,770 --> 00:00:55,500
+الماضيةالمرة الماضية مروش سريعة اللي حكيته المرة
+
+12
+00:00:55,500 --> 00:00:58,940
+الماضية قولت انا شو تعريف ال metric space ايش ال
+
+13
+00:00:58,940 --> 00:01:03,500
+metric space بنعرفه بنيجي بناخد 6x و بعدين بنعرف
+
+14
+00:01:03,500 --> 00:01:08,060
+عليه دالة D هذه ال D اللي هي دالة على مين مش على
+
+15
+00:01:08,060 --> 00:01:12,200
+ال X نفسها ال D هذه عبارة دالة على X cross X يعني
+
+16
+00:01:12,200 --> 00:01:18,180
+D هتاخد من X cross X و ترمي بالظبط في R positive
+
+17
+00:01:18,180 --> 00:01:23,260
+اتحاد ال zeroبنقول عن هذه D عبارة عن دالة مسافة أو
+
+18
+00:01:23,260 --> 00:01:27,700
+metric إذا حققت الشروط التالية الشرط الأول أنها
+
+19
+00:01:27,700 --> 00:01:31,380
+تكون non-negative طبيعي المسافة حتى في R أكيد non
+
+20
+00:01:31,380 --> 00:01:35,520
+-negative أصلا مستقامها اتنين DX وY بتساوي سفر إذا
+
+21
+00:01:35,520 --> 00:01:39,660
+فقط إذا X ياش بتساوي Y يعني النقطتين اللي بيكون
+
+22
+00:01:39,660 --> 00:01:44,720
+مسافتهم عن بعض بتساوي سفر هي بس النقطة ياش نفسها
+
+23
+00:01:45,210 --> 00:01:48,470
+الشغل الثالث هو أن المسافة بين X و Y هي نفس
+
+24
+00:01:48,470 --> 00:01:51,490
+المسافة بين Y و X يعني اللي هو الـ Dissimetry
+
+25
+00:01:51,490 --> 00:01:55,290
+الشغل الثالث هو أن هي الـ Triangling Equality D X
+
+26
+00:01:55,290 --> 00:01:59,950
+و Y أصغر يساوي D X و Z زي ادمين D Z و Y فصلنا
+
+27
+00:01:59,950 --> 00:02:04,930
+المرة الماضية عن هذا اللي هو التعريف الآن أخدنا
+
+28
+00:02:04,930 --> 00:02:11,170
+برضه اللي هو أمثلة على هذا اللي هو أخدنا أمثلة على
+
+29
+00:02:11,170 --> 00:02:14,590
+الـ Matrixاللي هو ع ال R ايش ال mythical ع ال R
+
+30
+00:02:14,590 --> 00:02:17,990
+اللي هو absolute value of X minus Y على R تربيع
+
+31
+00:02:17,990 --> 00:02:22,830
+هيه الان و بعدين وقفنا عند حاجة اسمها سمينا ال ال
+
+32
+00:02:22,830 --> 00:02:26,170
+infinity هذه من ال spaces المهمة عندنا ال ال
+
+33
+00:02:26,170 --> 00:02:29,270
+infinity شو ال ال infinity اذكركم فيه اللي حكينا
+
+34
+00:02:29,270 --> 00:02:33,700
+المرة الماضية هي عضارة عن عناصر و sequencesيعني
+
+35
+00:02:33,700 --> 00:02:38,040
+الـ L infinity اللي هو عبارة عن space of sequences
+
+36
+00:02:38,040 --> 00:02:41,680
+طب أي sequences يكون ال sequence bounded يعني the
+
+37
+00:02:41,680 --> 00:02:46,760
+set of all xii مثلا اللي هي sequence of numbers
+
+38
+00:02:46,760 --> 00:02:51,750
+سواء complex number او real number ابحثإنه اللي هو
+
+39
+00:02:51,750 --> 00:02:56,550
+الـ XiI تكون أصغر أو يساوي مين يساوي sub constant
+
+40
+00:02:56,550 --> 00:03:00,510
+C ماشي ال .. ال .. ال .. ال boundary sequences
+
+41
+00:03:00,510 --> 00:03:03,390
+حطيناها في مين في القلة الانفينيتي وبناء عليه
+
+42
+00:03:03,390 --> 00:03:08,570
+عرفنا ال metric عليها عرفنا الدالة كانت الدالة Dxy
+
+43
+00:03:08,570 --> 00:03:14,250
+بتساوي ال supremum لل absolute value XiI نقص Gamma
+
+44
+00:03:14,250 --> 00:03:22,120
+I I over Iمن هي هذه الـ Xi I؟ X بتساوي Xi I وY
+
+45
+00:03:22,120 --> 00:03:25,060
+بتساوي Gamma I هذا كله كان حكيناه المرة الماضية
+
+46
+00:03:25,060 --> 00:03:30,840
+وقلنا هذه هتعملنا metric عالميين ال infinity يعني
+
+47
+00:03:30,840 --> 00:03:33,760
+هتحقق الشروط الأربعة وبالمناسبة زي ما قلنا المرة
+
+48
+00:03:33,760 --> 00:03:38,420
+الماضيةإن شروط الـ metric الأولى هي التلاتة
+
+49
+00:03:38,420 --> 00:03:42,260
+automatic سهلات والكل بعرف إجابة بظل الشرط الأخير
+
+50
+00:03:42,260 --> 00:03:46,080
+هو اللي شوية بده شغل عموما أمثلة المرة الماضية زي
+
+51
+00:03:46,080 --> 00:03:51,720
+ما قلنا كانت أمثلة سهلة ومباشرةوعرفنا برضه اللي هو
+
+52
+00:03:51,720 --> 00:03:54,960
+الـ function space اللي هو الـ space of all
+
+53
+00:03:54,960 --> 00:03:59,640
+continuous functions على closed bounded interval
+
+54
+00:03:59,640 --> 00:04:03,160
+وعرفنا ال metric برضه بنفس الأسلوب المسافة بين أي
+
+55
+00:04:03,160 --> 00:04:08,260
+نقطين دالتين هدولة Vxy موجودة في CAB بسوء ال
+
+56
+00:04:08,260 --> 00:04:13,390
+maximumلأ اللي حصل طرح الدالتين على مين على الفترة
+
+57
+00:04:13,390 --> 00:04:17,390
+اللي بنحكي فيها هذا برضه عمل ليه metric وشوفنا كيف
+
+58
+00:04:17,390 --> 00:04:22,490
+عمل metric وبررنا انه عمل metric وبصير الـC of A
+
+59
+00:04:22,490 --> 00:04:28,300
+وB مع هذه الـD المعرفة بتصير metric spaceبتحقق
+
+60
+00:04:28,300 --> 00:04:31,140
+الشروطة هذا ما حكيناه المرة الماضية و اللي ناسي
+
+61
+00:04:31,140 --> 00:04:34,620
+اشي ممكن يرجع للمحاضرة ما هي مسجلة و جينا على
+
+62
+00:04:34,620 --> 00:04:38,960
+metric آخر سمناها discrete metric space اللي هو
+
+63
+00:04:38,960 --> 00:04:44,960
+الـD X و Y عرفناها بتساوي سفر إذا كانت ال X هي Y و
+
+64
+00:04:44,960 --> 00:04:48,400
+بيساوي واحد إذا كانت ال X تساوي Y و أبرهنا برضه إن
+
+65
+00:04:48,400 --> 00:04:52,100
+هذا بيعمل metric فسمناها ال X و D is a metric a
+
+66
+00:04:52,100 --> 00:04:56,460
+discrete metric spaceالان يا جماعة أخدنا exercises
+
+67
+00:04:56,460 --> 00:05:01,700
+و قلنا هدولة exercises بتحلوهن و قلنا اللي هو عندي
+
+68
+00:05:01,700 --> 00:05:06,100
+أنا بكتبلكم homeworks اللي هي من الكتاب هدولة
+
+69
+00:05:06,100 --> 00:05:09,540
+الأسئلة أرقام الأسئلة و في homework أسطار من
+
+70
+00:05:09,540 --> 00:05:12,200
+الكتاب هذول ال homework أسطار هم اللي بتكون
+
+71
+00:05:12,200 --> 00:05:16,440
+السلمونيةبتكون السلموني يعني أربعة وخمسة و تمانية
+
+72
+00:05:16,440 --> 00:05:19,980
+و عشرة و واحد و اتنين هدولة اللي هان هذا بتكون ال
+
+73
+00:05:19,980 --> 00:05:23,120
+homework الأول و زي ما حكينا المرة الماضية في خطة
+
+74
+00:05:23,120 --> 00:05:28,420
+المساق انه بدنا نحاول نعطيكم امتحانين و نعطيكوا
+
+75
+00:05:28,420 --> 00:05:31,700
+اللي هو ال هو homework و ممكن نعطيكوا تلت امتحانات
+
+76
+00:05:31,700 --> 00:05:35,820
+و نحصل بلكم أحسن اتنين و عليهم اربعين فمية
+
+77
+00:05:35,820 --> 00:05:38,400
+لامتحانين و عشرة فمية ع ال homework و الخمسين فمية
+
+78
+00:05:38,400 --> 00:05:41,360
+بتكون عالمين ع ال final و موضوع الهدك ان شاء الله
+
+79
+00:05:41,360 --> 00:05:45,870
+بنتفج عليهنيجي لان موضوعنا اليوم نبدأ في محاضرتنا
+
+80
+00:05:45,870 --> 00:05:49,830
+اليوم ان شاء الله بفصل تفصيل اللي بدنا نحكيه لان
+
+81
+00:05:49,830 --> 00:05:55,050
+further examples of metric S bases اللي هو يعني في
+
+82
+00:05:55,050 --> 00:05:59,410
+عندي أمثلة أخرى غير الأمثلة اللي حكيناها المرة
+
+83
+00:05:59,410 --> 00:06:05,920
+الماضية أول مثال بدي أحكي عنهاللي هو مثال آخر على
+
+84
+00:06:05,920 --> 00:06:11,020
+الـ Sequences Base هتلاقونا احنا بنركز على اللي هو
+
+85
+00:06:11,020 --> 00:06:15,840
+الفراغات اللي عناصرها Sequences اللي جابل بشوية
+
+86
+00:06:15,840 --> 00:06:18,520
+الـ L Infinity كانت اللي هي Sequences تبعت L
+
+87
+00:06:18,520 --> 00:06:21,990
+Infinity اللي هي الـ Bounded Sequencesالآن بتاخد
+
+88
+00:06:21,990 --> 00:06:28,470
+الـ S small هذه بـ The space of all sequences طبعا
+
+89
+00:06:28,470 --> 00:06:31,930
+اللي باخده Complex numbers هو الـ Real numbers
+
+90
+00:06:31,930 --> 00:06:35,990
+خلّيني أحكي عن الـ Complex إذا S هذه small هي
+
+91
+00:06:35,990 --> 00:06:42,490
+عبارة عن The set of all sequences of numbersالـ
+
+92
+00:06:42,490 --> 00:06:47,970
+Sequence اللي فيها لو أخدنا X وY في الـ S الـ X
+
+93
+00:06:47,970 --> 00:06:51,390
+هتكون Sequence يعني لو جينا رمزنا لها الـ X بتساوي
+
+94
+00:06:51,390 --> 00:06:55,750
+قصاي I يعني X بتساوي قصاي 1، قصاي 2، قصاي 3، قصاي
+
+95
+00:06:55,750 --> 00:06:59,610
+4، إلى مدى النهاية ونفس الاشي Y لو سمناها مثلا
+
+96
+00:06:59,610 --> 00:07:02,610
+بتساوي Gamma I أو اللي بدكم إياه يعني Gamma 1،
+
+97
+00:07:02,610 --> 00:07:06,580
+Gamma 2، Gamma 3، إلى مدى النهايةالان بدّى اعرف
+
+98
+00:07:06,580 --> 00:07:10,740
+هذا تنسوش ان هدولة any sequences converges مش
+
+99
+00:07:10,740 --> 00:07:14,860
+converges bounded مش bounded اي اشي عشان هيك بدّى
+
+100
+00:07:14,860 --> 00:07:19,980
+اختار metric لان اختار صيغة ل metric انها تكون
+
+101
+00:07:19,980 --> 00:07:24,560
+معجولة و بتلم كل ال sequences هذه تكون صحيحة لكل
+
+102
+00:07:24,560 --> 00:07:28,200
+ال sequences اللي بتنطرع علينا شوفوا اللي باخدها
+
+103
+00:07:28,200 --> 00:07:32,960
+بقولك خدوا DXY عرفة كالتالي DXY بساوة ال summation
+
+104
+00:07:33,800 --> 00:07:45,460
+للـ Xi I ناقص Gamma I على 1 زاد Xi I ناقص Gamma I
+
+105
+00:07:45,460 --> 00:07:51,220
+ماقالش هيكوا بس لإنه لو حتى زي هيكوا بس ال series
+
+106
+00:07:51,220 --> 00:07:55,420
+هذه اللي هي Gamma I من عند 1 لعند infinity حدش
+
+107
+00:07:55,420 --> 00:07:59,300
+بدمنلكوا انها تكون convergeيعني حدش بضمنكم يكون
+
+108
+00:07:59,300 --> 00:08:04,120
+هذا إيش مالو عبارة عن عدد وDxy ده اللي هو metric
+
+109
+00:08:04,120 --> 00:08:08,580
+يعني metric في الآخر بتطلع لإيش عدد الآن ضربوا
+
+110
+00:08:08,580 --> 00:08:14,960
+عشان هيك في واحد على اتنين I في هذا الحلق ضمنكم ان
+
+111
+00:08:14,960 --> 00:08:19,640
+ال series converge ليشلأنه بالـ Comparison Test لو
+
+112
+00:08:19,640 --> 00:08:23,860
+دي نطلعنا أو الحجز الصميشي من 1 على 2I هذه الـC
+
+113
+00:08:23,860 --> 00:08:27,420
+السيريز بنعرف إنها Converse، بظبط؟ أساسها نص اللي
+
+114
+00:08:27,420 --> 00:08:30,020
+هو Geometric Series أساسها نص أتوفتك اللي هو
+
+115
+00:08:30,020 --> 00:08:34,360
+Converse، لاحظوا إن هذا المقدار اللي هو الـNth
+
+116
+00:08:34,360 --> 00:08:39,880
+term هذا اللي جوا اللي مضروف 1 على 2I الـXi I ناقص
+
+117
+00:08:39,880 --> 00:08:47,400
+Γامع I على 1 زاد Xi I ناقص غامع Iهذا الأن أكيد
+
+118
+00:08:47,400 --> 00:08:53,120
+أكيد أكيد أظهر أو يساوي واحد على اتنين أس إيش أس I
+
+119
+00:08:53,120 --> 00:08:57,440
+مظبوط ولا لأ لما نضربه هدف مينوحدة لاتنين لأن هذا
+
+120
+00:08:57,440 --> 00:09:01,280
+المقدار أصغر أو يساوي واحد لأن اللي تحت أكبر من
+
+121
+00:09:01,280 --> 00:09:06,160
+مين؟ من اللي فوق فاهمين؟ إذا ما دامت هذه ال series
+
+122
+00:09:06,160 --> 00:09:09,300
+ال length term تبعها أكبر أو يساوي هذا و ال series
+
+123
+00:09:09,300 --> 00:09:12,860
+هذي converge إذا اكتوماتيك هذي converge إذا الأول
+
+124
+00:09:12,860 --> 00:09:17,360
+حاجة اللي هو شغله اللي هو لحتى الآن بالنسبة للي
+
+125
+00:09:17,360 --> 00:09:22,270
+عرفوا في الطريق الصحيحالان بيقوللي define اللي هو
+
+126
+00:09:22,270 --> 00:09:25,610
+هذا for انا x بالساوية كده وانا ضايع بالساوية كده
+
+127
+00:09:25,610 --> 00:09:31,270
+in S show that S وD ايش مالها is a metric space
+
+128
+00:09:31,270 --> 00:09:37,270
+الان الشروط الشروط الأولى التلاتة الأولى سهلة بتمر
+
+129
+00:09:37,270 --> 00:09:43,300
+عليها على السريعالشرط الأول ان هذا المقدار
+
+130
+00:09:43,300 --> 00:09:47,100
+absolute value او مدرس اذا اكبر ساوة سفر وهذا اكبر
+
+131
+00:09:47,100 --> 00:09:49,820
+ساوة سفر وهذا اكبر ساوة سفر اذا اكيد هذا اكبر ساوة
+
+132
+00:09:49,820 --> 00:09:52,860
+سفر اذا السلسلة الشمالية هتكون اكبر او ساوة سفر
+
+133
+00:09:52,860 --> 00:09:57,420
+اذا الشرط الأول متحقق اذا هذا اكبر او ساوة سفر
+
+134
+00:09:57,420 --> 00:10:02,800
+الشرط الأول تحقق نزل الشرط التاني الشرط الثاني هذا
+
+135
+00:10:02,800 --> 00:10:07,200
+بساوة سفرإذا و فقط إذا هذا المقدار بيساوي صفر إذا
+
+136
+00:10:07,200 --> 00:10:10,920
+و فقط إذا اللي هو دوله هذا non negative و هذا non
+
+137
+00:10:10,920 --> 00:10:15,240
+negative لازم هذا بيكون صفر إذا و فقط إذا اللي هو
+
+138
+00:10:15,240 --> 00:10:18,840
+كل اللي في هذا أجمع اللي هو ساوي صفر و هذا لا
+
+139
+00:10:18,840 --> 00:10:23,920
+يساوي صفر لما بيساوي صفر ال F الدول ال F اللي هو
+
+140
+00:10:23,920 --> 00:10:29,040
+Xi I Magus Gamma I بيساوي صفر مثل عساله سهل هذاF
+
+141
+00:10:29,040 --> 00:10:33,100
+and only F XI I يشملها بساوي Gamma I و هذا الكلام
+
+142
+00:10:33,100 --> 00:10:37,300
+لكل مين I إيش معناه XI I بساوي Gamma I لكله I
+
+143
+00:10:37,300 --> 00:10:42,340
+معناته S X بساوي R وايضا هذا الشرط مرضو إيش معانو
+
+144
+00:10:42,340 --> 00:10:46,290
+شرط سهل وسريعالشرط الأخير اللي هو الـ symmetry
+
+145
+00:10:46,290 --> 00:10:50,550
+اللي هو المسافة بين X و Y هي هذه بين Y و X بيصير
+
+146
+00:10:50,550 --> 00:10:53,370
+جمع على نقص إقصائي ما هي absolute value او modulus
+
+147
+00:10:53,370 --> 00:10:57,550
+ده متساويته، واضح؟ إذا الشرط الثاني كما .. ثالث
+
+148
+00:10:57,550 --> 00:11:02,210
+متحقق، ضال عندنا الشرط الثالث الشرط الثالث، بس
+
+149
+00:11:02,210 --> 00:11:07,770
+عشان نحققه اسمحولي بس ناخد دالة مساعدة auxiliary
+
+150
+00:11:07,770 --> 00:11:12,980
+function وبدنا نشوف هذه الدالة، الدالة هنستقيهامن
+
+151
+00:11:12,980 --> 00:11:17,800
+اللي عندى هذه الان هذه وهذه نفس الاشي فبدي اخد
+
+152
+00:11:17,800 --> 00:11:22,940
+دالة اسميها F of T طبعا هذه بتيجي مع الخبرة سوى T
+
+153
+00:11:22,940 --> 00:11:29,520
+على واحد زائد T هذه الدالة الان لو أخدتلها ال
+
+154
+00:11:29,520 --> 00:11:33,020
+derivative هتطلع ال derivative إليها واحد على واحد
+
+155
+00:11:33,020 --> 00:11:37,760
+زائد T لكل إيه شمالها تربيع ماشي الحال إذا واضح أن
+
+156
+00:11:37,760 --> 00:11:43,190
+ال F prime of Tأكبر أو يساوي إيه إيش؟ سفر حتى
+
+157
+00:11:43,190 --> 00:11:46,210
+strictly أكبر من سفر إذا ال function .. ال ..
+
+158
+00:11:46,210 --> 00:11:50,710
+الدالة إيش ما لها increasing function واضح إذا
+
+159
+00:11:50,710 --> 00:11:55,010
+الدالة increasing إذا الآن بدي أخزن المعلومة عندي
+
+160
+00:11:55,010 --> 00:12:01,350
+f of t is increasing طيب شوفوا إيش بدي أستفيد من
+
+161
+00:12:01,350 --> 00:12:10,120
+هذه أنا الآن بدي أثبت اللي هوDX وY أظهر يسموه DX
+
+162
+00:12:10,120 --> 00:12:16,040
+وZ زائد DZ وY هي ترينجلين كواليتيه شوفوا كيفه خدوا
+
+163
+00:12:16,040 --> 00:12:23,500
+الان X سموها Xi I وY سموها Gamma I وخد Z أي شيء
+
+164
+00:12:23,500 --> 00:12:26,780
+يسميه .. اللي هي أي سيكوينسيز في الاس وسميها Beta
+
+165
+00:12:26,780 --> 00:12:33,800
+I ماشي؟ لاحظوا التالي الآن لو أجينا أخدنا الXi I
+
+166
+00:12:33,800 --> 00:12:40,470
+ناقص Gamma Iطبعا أنا بدور حوالين الـ mean حوالين
+
+167
+00:12:40,470 --> 00:12:44,230
+المسافة بين X و Y هنا بدور حواليها إذا بدي أربطها
+
+168
+00:12:44,230 --> 00:12:48,950
+بين المسافة بين X و Z و Y و Z إذا أصغر أو يساوي X
+
+169
+00:12:48,950 --> 00:12:53,430
+I I أكيد هدخل الـ mean اللي هي طبعة الـ Z زائد
+
+170
+00:12:53,430 --> 00:12:57,370
+Beta I ناجس Gamma I هذه بالـ Triangling Quality
+
+171
+00:12:57,370 --> 00:13:00,610
+العادية اللي بنعرفها اللي هي Triangling Quality of
+
+172
+00:13:00,610 --> 00:13:04,470
+Numbers معايا؟ طيب صليوا على النبي عليه الصلاة
+
+173
+00:13:04,470 --> 00:13:11,940
+والسلامالـ L عندى اللى هو هذه أصغر أو ساوى هذه و
+
+174
+00:13:11,940 --> 00:13:14,220
+ال function اللى عندى increasing مظبوط ولا لا اطلع
+
+175
+00:13:14,220 --> 00:13:19,140
+لفوق شوية خلّيني نكون مع اللى مكتوب صارت عندى هذه
+
+176
+00:13:19,140 --> 00:13:23,360
+أصغر أو ساوى هذه و ال function increasing اذا F
+
+177
+00:13:23,360 --> 00:13:29,140
+لهذه أصغر أو ساوى F لهذه اذا F لهذه أصغر أو ساوى F
+
+178
+00:13:29,140 --> 00:13:33,600
+لهذه because the function is increasing ايش F لهذه
+
+179
+00:13:33,600 --> 00:13:41,170
+هي XIنقص Gamma I هذا ال T لان على واحد زي KSI I
+
+180
+00:13:41,170 --> 00:13:47,130
+نقص Gamma I أصغر أوي ساوي F هذه كلها اللي هي KSI I
+
+181
+00:13:47,130 --> 00:13:53,570
+هذه كلها ال T صارت نقص Beta I زي Beta I نقص Gamma
+
+182
+00:13:53,570 --> 00:14:00,310
+I طبعا كله مدلس على واحد زي KSI I نقص Beta I زي
+
+183
+00:14:00,310 --> 00:14:08,160
+Beta I نقص مين Gamma Iبدينا نجرب على اللي هي
+
+184
+00:14:08,160 --> 00:14:12,260
+المسافة بين x و y هاي المسافة بين x و y احنا
+
+185
+00:14:12,260 --> 00:14:17,580
+معرفينها اللي فوق اه؟ معرفين هي اه؟ بدينا نجرب بس
+
+186
+00:14:17,580 --> 00:14:21,740
+هنا لسه بعادى شوية فخلينا نفصل هذه لحال و هذه لحال
+
+187
+00:14:21,740 --> 00:14:26,940
+عشان نفصل تبعات ال z لحال و ال x و ال y و ال z
+
+188
+00:14:26,940 --> 00:14:29,580
+لحال اذا هذه بتساوي بالظبط
+
+189
+00:14:32,230 --> 00:14:39,390
+نقص Beta I على 1 زائد Xi I نقص Beta I زائد Beta I
+
+190
+00:14:39,390 --> 00:14:46,240
+نقص Gamma I صح اللي بعمله زائد التانية Beta Iناجس
+
+191
+00:14:46,240 --> 00:14:51,640
+Gamma I على واحد زائد Psi I ناجس Beta I بنجلهم
+
+192
+00:14:51,640 --> 00:14:56,740
+نفسي زائد Beta I ناجس Gamma I بس اللي عملته فصلتن
+
+193
+00:14:56,740 --> 00:15:03,200
+عن بعض ماشي الحال الان هذه نفسها هيها أصغر أو
+
+194
+00:15:03,200 --> 00:15:11,640
+يساوي صح اه يعني بتزغر المقام فتكبر هذا و هذا نفس
+
+195
+00:15:11,640 --> 00:15:18,680
+الاشي ماشيواضح اللي عملته الان ايش بده اسوي عشان
+
+196
+00:15:18,680 --> 00:15:22,180
+اصل اللي في ذاك مضياجي اضرب في هذا واحد على اتنين
+
+197
+00:15:22,180 --> 00:15:25,280
+I وهذا في واحد على اتنين I عارفين ليش
+
+198
+00:15:34,970 --> 00:15:40,470
+هذا أصغر شوء Alpha I نقص Beta I و Beta I نقص Gamma
+
+199
+00:15:40,470 --> 00:15:48,030
+I هي ليش اللي دلت اللي مسحناها Beta I نقص Gamma I
+
+200
+00:15:48,030 --> 00:15:51,810
+ماشي الحال واضحة الفكرة أه هذا في واحد على اتنين I
+
+201
+00:15:51,810 --> 00:15:57,530
+هانيو صار هذا أصغر شوء هذا الان باخد ال summation
+
+202
+00:15:57,530 --> 00:16:01,460
+مالهإلى ما لنهاية وضامن إن ال summation كله بتوزع
+
+203
+00:16:01,460 --> 00:16:06,780
+ليش لإن ال series هنا converts و ال series هنا
+
+204
+00:16:06,780 --> 00:16:10,420
+converts واضح إذا صار ال summation على هذه I من
+
+205
+00:16:10,420 --> 00:16:13,880
+واحد إلى ما لنهاية أصغر أو سوى ال summation على
+
+206
+00:16:13,880 --> 00:16:16,880
+هذه I من واحد إلى ما لنهاية زاد ال summation على
+
+207
+00:16:16,880 --> 00:16:20,340
+الأخيرة I من واحد إلى ما لنهاية هذه مين هي يا
+
+208
+00:16:20,340 --> 00:16:26,140
+جماعة هذه عبارة عن Dxy
+
+209
+00:16:27,220 --> 00:16:35,420
+و هد مين هي بين ال X و ال Z دي X و Z ذات هد بين
+
+210
+00:16:35,420 --> 00:16:43,840
+مين؟ بين Y و Z ذات دي Z و Y أو Y و مين؟ و Z مظبوط
+
+211
+00:16:43,840 --> 00:16:51,100
+هيك؟ و بيكون أثبتنا إنه عبارة عن اللي هو metric أي
+
+212
+00:16:51,100 --> 00:17:00,240
+سؤال؟ طيبإذا صار عندي الـ S مع هذا الـ metric is a
+
+213
+00:17:00,240 --> 00:17:05,080
+metric space بتعمل إيه أشماله؟ metric space نيجي
+
+214
+00:17:05,080 --> 00:17:09,720
+الآن ناخد space شبيه بالـ space اللي حكينا عنه قبل
+
+215
+00:17:09,720 --> 00:17:12,800
+شوية اللي هو الـ L infinity هداك كان في حالة الـ
+
+216
+00:17:12,800 --> 00:17:15,420
+sequences الـ L infinity bounded sequences هلا في
+
+217
+00:17:15,420 --> 00:17:18,860
+حالة الدول يعني بتاخد اللي هو the space of all
+
+218
+00:17:18,860 --> 00:17:22,660
+bounded functions على اللي هي الـ 6
+
+219
+00:17:26,720 --> 00:17:31,740
+طيب يا جماعة شوفوا بدأ
+
+220
+00:17:31,740 --> 00:17:38,880
+أحكي الآن عن space آخر اللي هو space of functions
+
+221
+00:17:38,880 --> 00:17:42,160
+المرة الماضية حكينا عن space of continuous
+
+222
+00:17:42,160 --> 00:17:46,540
+functions فسمي continuous functions على closed
+
+223
+00:17:46,540 --> 00:17:49,580
+bounded interval وعرفنا ال metric في حينه ال
+
+224
+00:17:49,580 --> 00:17:54,800
+maximumتجرأنا وعرفنا ال maximum لإنه احنا عارفين
+
+225
+00:17:54,800 --> 00:17:57,240
+ال continuous function على closed bounded interval
+
+226
+00:17:57,240 --> 00:18:00,500
+أكيد attain its maximum و minimum في ال interval
+
+227
+00:18:00,500 --> 00:18:05,580
+عشان ذلك عرفنا ال maximum بس اليوم انابتاخد ال
+
+228
+00:18:05,580 --> 00:18:09,600
+space of bounded functions يعني عناصر ال space
+
+229
+00:18:09,600 --> 00:18:13,100
+اللي عندي هي عبارة عن دوال محدودة bounded
+
+230
+00:18:13,100 --> 00:18:18,300
+functions ال bounded function ليس شرطا أنه ألاقي
+
+231
+00:18:18,300 --> 00:18:20,900
+ال maximum و ال minimum له وين ال absolute maximum
+
+232
+00:18:20,900 --> 00:18:26,120
+و ال absolute minimum وين على اللي هي للست اللي
+
+233
+00:18:26,120 --> 00:18:31,160
+عندي عشان هيكبتعرفهاش بيساوي الـ supermom الـ
+
+234
+00:18:31,160 --> 00:18:35,060
+supermom مضمون انه موجود لأنها bounded عشان ايه
+
+235
+00:18:35,060 --> 00:18:38,080
+بتقول الان let B of A be the set of all bounded
+
+236
+00:18:38,080 --> 00:18:43,060
+functions defined on a set A define ال metric الان
+
+237
+00:18:43,060 --> 00:18:48,120
+المسافة بين اللي هو أي دالتين في ال B of A بتساوي
+
+238
+00:18:48,120 --> 00:18:51,740
+ال supermom لل X of T نقص Y of T over اللي هو T
+
+239
+00:18:51,740 --> 00:18:56,570
+over Aهذا الآن بعرف الـ metric بالظبط .. بالظبط
+
+240
+00:18:56,570 --> 00:19:01,570
+البرهان مشابه بل typical للبرهان تبع الـ L
+
+241
+00:19:01,570 --> 00:19:04,830
+infinity وحاكناها المرة الماضية وشرحناها بالتفصيل
+
+242
+00:19:04,830 --> 00:19:11,050
+اللي نسيه برجعله مافي مشكلة خالص طيب نيجي الآن ل
+
+243
+00:19:11,050 --> 00:19:19,050
+.. اللي هو بدي الآن امهد للوصول
+
+244
+00:19:20,070 --> 00:19:26,830
+الـ Space الـ الأول
+
+245
+00:19:26,830 --> 00:19:33,010
+الـ Infinity الـ Space of Sequences بس هذه Bounded
+
+246
+00:19:33,010 --> 00:19:38,550
+Sequences وحكينا عن Space تاني S اللي هو Space of
+
+247
+00:19:38,550 --> 00:19:43,310
+Sequences in General هذا عرفناه Metric يناسبه وهذا
+
+248
+00:19:43,310 --> 00:19:48,450
+عرفناه Metric يناسبه بعدين أجيناطبعاً هذا كل
+
+249
+00:19:48,450 --> 00:19:52,510
+الكلام فيه إله مستقبل وفيه تبعات في المستقبل إله
+
+250
+00:19:52,510 --> 00:19:57,270
+الآن و جينا عرفنا اللي هو space of sequences و
+
+251
+00:19:57,270 --> 00:20:03,550
+جينا عرفنا اللي هو space آخر اللي هو .. اللي هو C
+
+252
+00:20:03,550 --> 00:20:07,610
+of A و B space of continuous functions على closed
+
+253
+00:20:07,610 --> 00:20:11,750
+bounded intervalودينا بـ metric تبعه ودينا عرفنا
+
+254
+00:20:11,750 --> 00:20:17,610
+قبل بشوية space B of A space of bounded functions
+
+255
+00:20:17,610 --> 00:20:22,830
+على الـ A وعرفنا ال metric تبعهالان واضح تودهنا
+
+256
+00:20:22,830 --> 00:20:28,330
+أننا حديثنا في معظم الأنفلة اللي عندنا على main
+
+257
+00:20:28,330 --> 00:20:31,950
+على space of functions وعلى space of main of
+
+258
+00:20:31,950 --> 00:20:37,510
+sequences وهذا له همية كبيرة في نفس ال functional
+
+259
+00:20:37,510 --> 00:20:42,370
+analysis وحتى تطبيقاتها في الأمور الحياتية الآن
+
+260
+00:20:42,370 --> 00:20:48,530
+بدي أعرف أدخل ل space جديد اسمه ال B spacesالـ B
+
+261
+00:20:48,530 --> 00:20:53,290
+Spaces و B عندي هذه بديها أكبر أو يساوي إيش؟ واحد
+
+262
+00:20:53,290 --> 00:20:58,510
+طيب ال ال ال B Spaces إيش ال ال B هدا؟ هو عبارة عن
+
+263
+00:20:58,510 --> 00:21:02,310
+Space of Sequences طيب إيش .. إيش شروط اللي على ال
+
+264
+00:21:02,310 --> 00:21:05,630
+.. ال .. ال Sequences هدا عشان تكون جوة ال ال B؟
+
+265
+00:21:05,630 --> 00:21:12,680
+بقول إنك Psi I هذه ال Sequence في ال ال Bإذا بتحقق
+
+266
+00:21:12,680 --> 00:21:19,460
+مالي أن الـ summation للـ Xi I أُس بي I من واحد
+
+267
+00:21:19,460 --> 00:21:24,840
+إلى ملا نهاية تكون converge كل الـ sequences اللي
+
+268
+00:21:24,840 --> 00:21:29,920
+في الدنيا اللي Xi I لها بتكون في القلبي إذا تحقق
+
+269
+00:21:29,920 --> 00:21:37,260
+Xi I أُس بي summation is finite هذا بنسميه الـ B
+
+270
+00:21:37,260 --> 00:21:44,430
+spaceبدّي الآن أروح باتجاه تعريف metric عليه بدي
+
+271
+00:21:44,430 --> 00:21:48,310
+أعرف metric على ال space هذا لو قلت هي X بتساوي
+
+272
+00:21:48,310 --> 00:21:54,860
+Psi I و Y بتساوي Gamma I element in LBالمتريك اللي
+
+273
+00:21:54,860 --> 00:22:00,060
+بتعرفه هتلاقوني عرفته بعد شوية DXY بساوي summation
+
+274
+00:22:00,060 --> 00:22:07,840
+لل XI I ناقص Gamma I أس بيه عشان أضبن أنه موجود
+
+275
+00:22:07,840 --> 00:22:12,440
+هال هذا finite و هذا إلها Gamma I finite بس هذا
+
+276
+00:22:12,440 --> 00:22:18,740
+لسه بده شغل و الكل أس واحد عدبيهذا بعد شوية
+
+277
+00:22:18,740 --> 00:22:24,120
+هتلاقونا وصلنا انه هذا هيعمل ليه metric على الـB
+
+278
+00:22:24,120 --> 00:22:28,180
+على القلبي يعني هيصير القلبي مع هذا ال metric
+
+279
+00:22:28,180 --> 00:22:33,480
+المعرف اسمه الـB metric space وهذا من الفراغات
+
+280
+00:22:33,480 --> 00:22:38,890
+المهمة جدااللي هو وفيه اللي هو مقابل حنشوف اللي هو
+
+281
+00:22:38,890 --> 00:22:44,150
+مقابل في ال space of functions برضه اسمه ال B بس
+
+282
+00:22:44,150 --> 00:22:48,890
+بيسميه ال B function وفي حينه انا بقى بنحكيلكم عنه
+
+283
+00:22:48,890 --> 00:22:55,750
+بالتفصيل ممكن الآن عشان نوصل لهذا انه metric انا
+
+284
+00:22:55,750 --> 00:23:02,160
+بلزمني تلت شغلاتبالزمن أول إشي الآن اللي هو
+
+285
+00:23:02,160 --> 00:23:08,780
+متباينة أبرهن متباينة مساعدة المتباينة مساعدة هذه
+
+286
+00:23:08,780 --> 00:23:14,080
+بدي استخدمها في إثبات حاجة اسمها holder inequality
+
+287
+00:23:15,240 --> 00:23:19,840
+الـ Holder Inquality هذه بتستخدمها لإثبات حاجة
+
+288
+00:23:19,840 --> 00:23:24,620
+اسمها Minkowski Inquality اللي هي هتكون سبب في
+
+289
+00:23:24,620 --> 00:23:28,420
+إثبات الـ Triangle Inquality هذه لهذا وبهيك بيكون
+
+290
+00:23:28,420 --> 00:23:33,320
+اجتملت الصورة وخلصناها وعملنا اللي بدناها بخصوص
+
+291
+00:23:33,320 --> 00:23:39,560
+اللي هو مين ال metric space اللي أمامنا طيب شوفوا
+
+292
+00:23:41,150 --> 00:23:45,990
+الدلة المساعدة المتبينة المساعدة هذه المتبينة
+
+293
+00:23:45,990 --> 00:23:51,050
+المساعدة بعد شوية طبعا هتعرفوا ليش هذه أخدناها
+
+294
+00:23:51,050 --> 00:23:53,730
+عشان نستفدمها في أيش كمان
+
+295
+00:23:59,230 --> 00:24:04,430
+في احنا بنعرف في المدارس كنتوا تقولوا المرافق
+
+296
+00:24:04,430 --> 00:24:09,170
+العدد و المرافق هو في سبب للمرافقة المرافقة انه
+
+297
+00:24:09,170 --> 00:24:12,730
+يعملوا فرق بين مربعين او المرافقة اللي هو في حالة
+
+298
+00:24:12,730 --> 00:24:16,750
+ال .. ال .. ال .. العدد و الكنج تبعه الاخرين الان
+
+299
+00:24:16,750 --> 00:24:21,940
+هنا مرافقة برضه بنقول ان بي و كي مرافقات لبعضهمتحت
+
+300
+00:24:21,940 --> 00:24:28,180
+العلاقة 1 على b زائد 1 على q ايش بيساوي هذا اللي
+
+301
+00:24:28,180 --> 00:24:32,500
+بنسميه بي و q conjugate لبعض with respect to this
+
+302
+00:24:32,500 --> 00:24:36,220
+relation ماشي الحال اذا الان احنا في عالمنا هذا
+
+303
+00:24:36,220 --> 00:24:38,880
+لما نقول بي و q بنقصد واحد على بي زائد واحد على
+
+304
+00:24:38,880 --> 00:24:44,000
+كيو بيساوي واحد و بي و كيو اشمالهن اكبر او يساوي
+
+305
+00:24:44,000 --> 00:24:48,960
+واحد طيب نيجي نشوف اللي هو ال auxiliary inequality
+
+306
+00:24:52,520 --> 00:24:56,480
+اللي هنجلب بس لو سمحت أنا سيبني من الواحد أنا
+
+307
+00:24:56,480 --> 00:25:00,980
+بتاخد ب أش مالها strictly أكبر من أش من واحد
+
+308
+00:25:00,980 --> 00:25:03,900
+بتناشي اللي هو حالة اللي هي مين ب بتساوي واحد
+
+309
+00:25:03,900 --> 00:25:08,980
+لإنها هيعملني مشكلة في العلاقة هذه فخليني ما بعدش
+
+310
+00:25:08,980 --> 00:25:11,740
+واحد يلاقوني بشتغل على ال ب أكبر سوا واحد لكن عشان
+
+311
+00:25:11,740 --> 00:25:14,600
+العلاقة هذه ال conjugation بتاخد ال ب أش مالها
+
+312
+00:25:14,600 --> 00:25:20,300
+strictly أكبر من واحد طيب بقوللي هتلاقي دايما لأي
+
+313
+00:25:20,300 --> 00:25:27,180
+Alpha و Betaالفة و بيتا non negative numbers دائما
+
+314
+00:25:27,180 --> 00:25:31,400
+دائما هتلاقي الالفة في بيتا طبعا ال non negative
+
+315
+00:25:31,400 --> 00:25:34,960
+numbers أنا مبسوط فيها بس سرية لإن هو مابنفعش اقول
+
+316
+00:25:34,960 --> 00:25:37,760
+complex لإنه مافيش order في ال complex ماانتوا
+
+317
+00:25:37,760 --> 00:25:41,940
+عارفين إذا الفة في بيتا هتكون أصغر أو ساوي Alpha
+
+318
+00:25:41,940 --> 00:25:47,040
+to the B على B زي بيتا to the Q على مين على Q إذا
+
+319
+00:25:47,040 --> 00:25:52,900
+بدي أثبت الآن الفة في بيتا أصغر أو ساويالف تدا بي
+
+320
+00:25:52,900 --> 00:26:01,180
+على بي زايد بيتا تدا كيو على مين على كيو القلب بدي
+
+321
+00:26:01,180 --> 00:26:07,120
+أستقي من هذه اللي هو اللي هو دالة أُسية بتعرفوا
+
+322
+00:26:07,120 --> 00:26:10,780
+أنتوا الدالة الأُسية اللي هي لو أجينا أخدنا هذه T
+
+323
+00:26:10,780 --> 00:26:16,280
+و هذه U و أخدنا U بتساوي T أُس بي minus واحد مثلا
+
+324
+00:26:16,280 --> 00:26:18,960
+على سبيل المثال هذه الدالة لازم تعرفوا إيش أخدت
+
+325
+00:26:18,960 --> 00:26:20,800
+هذه الدالة
+
+326
+00:26:22,300 --> 00:26:28,120
+هي اللي هو عندي الدالة هذه و كانت هذه عندي Alpha و
+
+327
+00:26:28,120 --> 00:26:34,720
+كانت هذه عندي مثلا مين Beta الآن Alpha في Beta هي
+
+328
+00:26:34,720 --> 00:26:41,900
+Alpha في Beta مظبوط؟
+
+329
+00:26:41,900 --> 00:26:51,870
+هذه عبارة عن مساحة المستطيل هذا مظبوط؟ طيب الآنلو
+
+330
+00:26:51,870 --> 00:26:57,090
+جيت على المساحة تحت المنحنى هذا المساحة تحت
+
+331
+00:26:57,090 --> 00:27:02,410
+المنحنى هذا هيها هيها ماشي هذه المساحة تحت المنحنى
+
+332
+00:27:02,410 --> 00:27:10,510
+هذا هيها صحيح ولا لأ؟ هذه إيش بتمثل؟ بتمثل ال
+
+333
+00:27:10,510 --> 00:27:17,890
+integration التي-1 dt من أين إلى أين؟ من صفر إلى
+
+334
+00:27:17,890 --> 00:27:23,210
+ألفة صح أم لا؟ طيب من صفر إلى ألفة لو جينا تطلعنا
+
+335
+00:27:23,210 --> 00:27:29,290
+من جهة أخرى من جهة أخرى
+
+336
+00:27:29,290 --> 00:27:34,610
+لأ اللي هو المساحة تحت المنحنة هذا هيها اللي
+
+337
+00:27:34,610 --> 00:27:39,710
+بالأخضر هذه المساحة تحت المنحنة هذا هيها هيها هي
+
+338
+00:27:39,710 --> 00:27:46,200
+دول الأخضرهذه المساحة اللي هي بدا تصير اللي هو T
+
+339
+00:27:46,200 --> 00:27:50,520
+أُس U أُس 1 على B-1 صح بيصير ال integration بتبعها
+
+340
+00:27:50,520 --> 00:27:55,540
+زائد ال integration فاني كيف لإنه بتتغير هذا بيصير
+
+341
+00:27:55,540 --> 00:27:58,060
+اللي هو ال independent variable و هذا ال dependent
+
+342
+00:27:58,060 --> 00:28:06,900
+variable بيصير T ال U أُس B أُس 1 على B-1 اللي هو
+
+343
+00:28:06,900 --> 00:28:13,010
+من وين لوين بيصير من 0 ل 100 ل Betaطبعا الرسم هذه
+
+344
+00:28:13,010 --> 00:28:18,270
+الان واضح .. واضح ان المساحة هذه زاد المساحة هذه
+
+345
+00:28:18,270 --> 00:28:23,070
+.. هذه .. هي .. هي اللي بالأحمر هنا أكيد أكبر أو
+
+346
+00:28:23,070 --> 00:28:28,200
+يساوي الألف في مينفي بيتها، لأن هذه زيادة، هذه
+
+347
+00:28:28,200 --> 00:28:32,920
+الجزء زيادة عن اللي هي مساحة المرب، المساطيل،
+
+348
+00:28:32,920 --> 00:28:38,280
+مظبوط؟ الآن قد تكون الشغل مختلفة شوية، قد يكون
+
+349
+00:28:38,280 --> 00:28:43,000
+اللي هو بدل هيك، بدل بالشكل هذا، تكون الرسمة،
+
+350
+00:28:43,000 --> 00:28:50,200
+ماعليش أغير إشي بسيط، الرسمة تكون هاي Alpha Hanهي
+
+351
+00:28:50,200 --> 00:28:53,700
+Alpha وهي Beta فبتكون ليه مساحة الـ Alpha في Beta
+
+352
+00:28:53,700 --> 00:29:00,040
+و بيصير المساحة تحت المنحنة هذه زاد هذه فبتكون هذه
+
+353
+00:29:00,040 --> 00:29:03,520
+الزيادة يعني تكون زيادة هنا أو تكون زيادة من هنا
+
+354
+00:29:03,520 --> 00:29:06,900
+فاهميه ليش اللي بقوله فبالآن أي إن كانتوا لو
+
+355
+00:29:06,900 --> 00:29:09,380
+التقين ال Alpha من الرتم مع بعض بيصير اللي هو إيه
+
+356
+00:29:09,380 --> 00:29:13,780
+في ماله مسواهمعايا فالان صار ال integration هذا ال
+
+357
+00:29:13,780 --> 00:29:16,900
+alpha في beta أصغر شويه ال integration هذا زاد ال
+
+358
+00:29:16,900 --> 00:29:20,060
+integration هذا بدنا نحسب ال integration هذا ال
+
+359
+00:29:20,060 --> 00:29:23,760
+integration هذا إيش بده يكون قيمته؟ كلكم أكيد بعرف
+
+360
+00:29:23,760 --> 00:29:31,060
+اللي هو عبارة عن Tu س بي على بي من سفر لعند alpha
+
+361
+00:29:31,060 --> 00:29:38,180
+زاد الآن هذا يقص ال Du هذا يقص واحد على بي ماينس
+
+362
+00:29:38,180 --> 00:29:44,310
+واحدلو جينا على جهة واحد على بي زائد واحد على كيو
+
+363
+00:29:44,310 --> 00:29:48,370
+ايش بيساوي؟ بيساوي واحد يعني وحدنا المقامات فبصير
+
+364
+00:29:48,370 --> 00:29:53,190
+بي في كيو وانا بي زائد كيو بيساوي واحد يعني عند بي
+
+365
+00:29:53,190 --> 00:29:57,190
+زائد كيو بيساوي بي في كيو خليه في الذاكرة لو جيتوا
+
+366
+00:29:57,190 --> 00:30:00,930
+حسبتوا بي ماينس واحد في كيو ماينس واحد بيساوي
+
+367
+00:30:00,930 --> 00:30:09,600
+اضربوهم في بعض بصير بي في كيو ناقص بي ناقص كيوزائد
+
+368
+00:30:09,600 --> 00:30:14,760
+واحد، صح؟ هذول مع بعض، هذول مع بعض، لو نقول إن أنا
+
+369
+00:30:14,760 --> 00:30:18,500
+بصير إني أشتفر، زائد واحد دلوقتي إيش بيساوي؟ إذا
+
+370
+00:30:18,500 --> 00:30:21,920
+يعني الآن P minus واحد في Q minus واحد إيش بيساوي؟
+
+371
+00:30:21,920 --> 00:30:27,680
+يعني واحد على P minus واحد هي مين؟ Q ناقص واحد،
+
+372
+00:30:27,680 --> 00:30:34,990
+ماشي؟ فبصير زائد، فهذه Q ناقص واحد، وصلتماشي الحال
+
+373
+00:30:34,990 --> 00:30:38,730
+فالان بيصير Q U أُس Q ماينس واحد اللي هي عبارة عن
+
+374
+00:30:38,730 --> 00:30:46,930
+U أُس Q على Q من صفر لمين لـ Beta ويساوي هذا بتصير
+
+375
+00:30:46,930 --> 00:30:54,550
+T يعني بتصير Alpha أُس B على B زائد Beta أُس Q على
+
+376
+00:30:54,550 --> 00:30:58,930
+Q هذا أكبر يساوي مين Alpha في Beta فبتكون ال
+
+377
+00:30:58,930 --> 00:31:04,700
+auxiliary اللي هو inequality تم ضمنهاماشي اذا
+
+378
+00:31:04,700 --> 00:31:09,800
+خلّينا الان نحطها عنا عشان تستخدمها انا برهنتها ان
+
+379
+00:31:09,800 --> 00:31:13,900
+هي مش اصلا هي يعني مش هي مجال اهتمامي لكن انا
+
+380
+00:31:13,900 --> 00:31:17,320
+برهنتها عشان تستخدمها بعد شوية في شغلة مجال
+
+381
+00:31:17,320 --> 00:31:23,930
+اهتمامي Alpha في Beta أزرع يساويقولوا معايا Alpha
+
+382
+00:31:23,930 --> 00:31:30,070
+أس بي على بي زائد Beta SQ على Q هذا خلّيها في
+
+383
+00:31:30,070 --> 00:31:32,830
+الذاكرة هذا ال auxiliary inequality اللي أمامي
+
+384
+00:31:32,830 --> 00:31:37,810
+الآن بدي أجي لاللي هي الهدف الثاني اللي هيوصلني
+
+385
+00:31:37,810 --> 00:31:42,450
+لهدفي اللي هو حاجة اسمها اللي هي holder inequality
+
+386
+00:31:42,450 --> 00:31:46,960
+بس جيبلي me holder inequalityالـ .. كتبته أنا هذا
+
+387
+00:31:46,960 --> 00:31:51,000
+الـ L P كتبته قول قولته قبل شوية will denote the
+
+388
+00:31:51,000 --> 00:31:54,360
+set of all sequences of number xi I number xi I
+
+389
+00:31:54,360 --> 00:31:57,520
+such that ال summation هذا is finite where P
+
+390
+00:31:57,520 --> 00:32:02,520
+أشمالها أكبر أو يساوي واحد الآن
+
+391
+00:32:03,750 --> 00:32:09,330
+الـ Holder Inquality خلّيني أركزوا معايا لأن
+
+392
+00:32:09,330 --> 00:32:14,130
+الرموز هي اللي بت .. شوية بت .. فيها عفاشة لكن ان
+
+393
+00:32:14,130 --> 00:32:20,390
+شاء الله بنفهمها مابديش أكتب كتير هلأ لإنه حنطول
+
+394
+00:32:20,390 --> 00:32:26,370
+خلّيني نشرع على اللي موجود شوف
+
+395
+00:32:26,370 --> 00:32:31,060
+إيش بتقول الـHolder Inquality بتقول إيه لنا؟لو
+
+396
+00:32:31,060 --> 00:32:33,720
+كانت الـ P و الـ Q زي قبل شوية يعني واحد على P زاد
+
+397
+00:32:33,720 --> 00:32:38,220
+واحد على Q بسوء واحد وكان عند XI I و I الموجودة في
+
+398
+00:32:38,220 --> 00:32:42,540
+القلب P و الجامعة I و I الموجودة في القلب Q إذا ما
+
+399
+00:32:42,540 --> 00:32:46,660
+يلي يتحقق إيش هو ما يلي؟ summation of absolute
+
+400
+00:32:46,660 --> 00:32:52,420
+value XI I في جامعة I أصغر أو ساوية XI K أُس P كله
+
+401
+00:32:52,420 --> 00:32:56,770
+واحد على Pفي الـ Summation Gamma M .. اللي بتكون
+
+402
+00:32:56,770 --> 00:33:01,250
+بيسموها K أس Q أس واحد مين على Q هذه اللي بيسميها
+
+403
+00:33:01,250 --> 00:33:03,590
+Whole Dark Inquality يعني الـ Summation ..
+
+404
+00:33:03,590 --> 00:33:14,690
+Summation لـ Xi I Gamma I أزرع أو ساوي Summation
+
+405
+00:33:14,690 --> 00:33:22,230
+Xi I أس B أس واحد على B في الـ Summation Gamma I
+
+406
+00:33:22,910 --> 00:33:29,190
+قصة Q بس واحد على مين الـ Q لحظة لو هذه .. لو هذه
+
+407
+00:33:29,190 --> 00:33:35,890
+XII في الـ LB بضمن إنه هذي Converse هيك تعريفها و
+
+408
+00:33:35,890 --> 00:33:40,070
+Gamma M هذي مدام انت في الـ LQ هذي برضه تكون إيه
+
+409
+00:33:40,070 --> 00:33:43,430
+شمالها Converse إذا الدنيا ده مقام نيحة هيك بيصير
+
+410
+00:33:43,430 --> 00:33:46,130
+هذا Converse أكبر شوة هذي ده أكيد أشماله هذا
+
+411
+00:33:46,130 --> 00:33:53,430
+Converse واضح؟ طيبالان بدو بس شغلة هيكا بدو
+
+412
+00:33:53,430 --> 00:34:00,910
+يستخدمها كجسر بدو يسمي اللي هو طبعا بس بشايلكم
+
+413
+00:34:00,910 --> 00:34:06,030
+شغلة عشان بدو يكسم على الصماش فبدو يشيها سفر فجالك
+
+414
+00:34:06,030 --> 00:34:10,390
+حالة ان XII والجامعة I سفارت انتين هذه سفر او هذه
+
+415
+00:34:10,390 --> 00:34:15,770
+سفر هذا trivial caseلو لو كانت كsequences يعني Xi
+
+416
+00:34:15,770 --> 00:34:21,790
+I 00000 أو Gamma I 000 هيكون اللي هو حاصل الضرب
+
+417
+00:34:21,790 --> 00:34:25,170
+هذا سفر ومن ثم هذا هيكون أكبر أو شهر هذا و تموتك
+
+418
+00:34:25,170 --> 00:34:30,110
+بل بساومي تلان سفر الآن شيلنا هذه الحالة سرنا
+
+419
+00:34:30,110 --> 00:34:35,830
+أخدنا الآن أن Xi I و Gamma I تتمتئن among zero
+
+420
+00:34:35,830 --> 00:34:39,670
+sequences يعني في على الأقل term في كل واحدة مش
+
+421
+00:34:39,670 --> 00:34:47,190
+سفر ماشي طيبسمونك psi I تلده هذا الجسر اللي بدأ
+
+422
+00:34:47,190 --> 00:34:52,450
+عبره من خلاله بساويك psi I على القيمة هذه ماشي ايش
+
+423
+00:34:52,450 --> 00:34:58,930
+القيمة هذه اللي هو هذا ال summation اه اه واضح
+
+424
+00:34:58,930 --> 00:35:04,130
+واخدت الجامعة I بساوي الجامعة I تلده بساوي جامعة I
+
+425
+00:35:04,130 --> 00:35:11,660
+على ال summation هذا ماشيواضح؟ الان لو اجينا ضربنا
+
+426
+00:35:11,660 --> 00:35:17,940
+Xi I في Gamma I ماشي الحال حسب ال auxiliary
+
+427
+00:35:17,940 --> 00:35:23,480
+inequality هيها هيها هيها يعني بتاخد ال Alpha إيش
+
+428
+00:35:23,480 --> 00:35:30,040
+بتساوي Xi I تلده و ال Beta إيش بتساوي Gamma I تلده
+
+429
+00:35:30,040 --> 00:35:34,600
+هتساوي هذه أس بي على بي و هذه أس بي Q على مين؟ على
+
+430
+00:35:34,600 --> 00:35:41,390
+Q إذا صارت بالأماميالان لما أخدته هيك خد ال
+
+431
+00:35:41,390 --> 00:35:46,650
+summation اللي هو للجهتين من I1 I شماله إلى مالة
+
+432
+00:35:46,650 --> 00:35:50,150
+نهاية معايا؟ خد ال summation هنا و ال summation
+
+433
+00:35:50,150 --> 00:35:54,570
+هنا أخدنا ال summation و هي ال summation و هي ال
+
+434
+00:35:54,570 --> 00:36:00,270
+main ال summation ماشي الحالطبعا هذا هتلاقوه مضمون
+
+435
+00:36:00,270 --> 00:36:03,870
+ال summation اللي هو finite تبعا لإن هذا الأصل
+
+436
+00:36:03,870 --> 00:36:07,190
+finite و اللي تحت ما هو عبارة عن ياشعن عدد بتاخد
+
+437
+00:36:07,190 --> 00:36:12,630
+أعمل مشترك طيب .. الآن ما يساوي .. الآن نشوف هذا
+
+438
+00:36:12,630 --> 00:36:16,610
+إيش بده يطلع عنها اللي هو xi i في ال summation هنا
+
+439
+00:36:16,610 --> 00:36:23,330
+خدوا هذا و أس بي أس بيبعدين خدوله ال summation
+
+440
+00:36:23,330 --> 00:36:28,610
+مكان هذا معايا الان هذا بيصير رقم الواحدة والتانية
+
+441
+00:36:28,610 --> 00:36:35,810
+زيها الان xi i تلده بيساوي xi i على اللي هو خليني
+
+442
+00:36:35,810 --> 00:36:40,350
+أسمي هذا مثلا scene أو خليني أكتب ليه ليش
+
+443
+00:36:40,350 --> 00:36:47,690
+summation xi iأُس بي وكل أس واحد عالميا على بي
+
+444
+00:36:47,690 --> 00:36:51,670
+معايا إلا أن رفعولي يا أس بي هذا خدولي مدرس يرفعوا
+
+445
+00:36:51,670 --> 00:36:55,870
+أس بي خمدولي مدرس يرفعوا أس بي بتروح هذا ال بي صح
+
+446
+00:36:55,870 --> 00:37:01,050
+هذا رقم هذا رقم بين دايا خدولي ال summation I من
+
+447
+00:37:01,050 --> 00:37:04,530
+عند واحد إلى ما لنهاية خدولي ال summation I من عند
+
+448
+00:37:04,530 --> 00:37:07,750
+واحد إلى ما لنهاية عام مشترك بطلع لأنه عدا فبصير
+
+449
+00:37:07,750 --> 00:37:12,450
+هذا اللي فوق هو اللي تحت إذا مش هيساويوحد صح ولا
+
+450
+00:37:12,450 --> 00:37:17,550
+لأ فبصير عندى هذا المقدار واحد وهذا زيه بالظبط
+
+451
+00:37:17,550 --> 00:37:21,550
+واحد فبصير عبارة عن واحد عربي زي ادمين واحد عربي
+
+452
+00:37:21,550 --> 00:37:22,190
+واحد عربي واحد عربي واحد عربي واحد عربي واحد عربي
+
+453
+00:37:22,190 --> 00:37:22,550
+واحد عربي واحد عربي واحد عربي واحد عربي واحد عربي
+
+454
+00:37:22,550 --> 00:37:23,810
+واحد عربي واحد عربي واحد عربي واحد عربي واحد عربي
+
+455
+00:37:23,810 --> 00:37:27,870
+واحد عربي واحد عربي واحد عربي واحد عربي واحد عربي
+
+456
+00:37:27,870 --> 00:37:28,910
+واحد عربي واحد عربي واحد عربي واحد عربي واحد عربي
+
+457
+00:37:28,910 --> 00:37:28,910
+واحد عربي واحد عربي واحد عربي واحد عربي واحد عربي
+
+458
+00:37:28,910 --> 00:37:29,880
+واحد عربي واحد عربي واحد عربي واحد عربيالـ
+
+459
+00:37:29,880 --> 00:37:37,700
+Summation للـ Xi I Gamma I تلدة I من واحد إلى ما
+
+460
+00:37:37,700 --> 00:37:43,300
+لنهاية أصغر أو يساوي واحد على B زائد واحد على Q
+
+461
+00:37:43,300 --> 00:37:47,200
+اللي هو إيش بتساوي أكتبها واحد وخلاص مافيش داعي أن
+
+462
+00:37:47,200 --> 00:37:55,200
+أتكرر ماشي الحالة الآن بدي أعوض الآن هذه قيمتها Xi
+
+463
+00:37:55,200 --> 00:38:03,750
+I في Gamma Iاللي هي صارت عندي اللي هو automatic
+
+464
+00:38:03,750 --> 00:38:10,750
+منها لما عوض مكانها هذه و هذه، مظبوط؟ بيصير هذه في
+
+465
+00:38:10,750 --> 00:38:16,830
+هذه و هدول تحت بعض، ماشي الحال معايا؟ طيب خلينا
+
+466
+00:38:16,830 --> 00:38:24,150
+نشوف ال summation ل XI I تلدة في جامعة I تلدة I من
+
+467
+00:38:24,150 --> 00:38:30,400
+واحد إلى وين إلى ما إلى النهايةإيش بتساوي اللي هو
+
+468
+00:38:30,400 --> 00:38:37,400
+ال summation معايا أيه هذولة هذولة طلع عليها xi i
+
+469
+00:38:37,400 --> 00:38:44,640
+gamma i مظبوط على اللي هو مين هذولة عاوز مش شركة
+
+470
+00:38:44,640 --> 00:38:53,380
+بتطلع التانية اه اللي هو ال summation لل xi iSB S1
+
+471
+00:38:53,380 --> 00:38:58,540
+على B في الـ summation Gamma I SQ S1 على Q صح ولا
+
+472
+00:38:58,540 --> 00:39:03,880
+لا؟ ماشي، هذا كله إيش ماله؟ قلنا عنه أصغر أو يساوي
+
+473
+00:39:03,880 --> 00:39:10,540
+واحد خلاص، أدر بهذا في هذا، بطلع ال summation Xi I
+
+474
+00:39:10,540 --> 00:39:17,840
+Gamma I أصغر أو يساوي هذا المقدر و هو المخلوق،
+
+475
+00:39:17,840 --> 00:39:24,490
+واضح؟ إيش يا روحي؟بعيد زي ذلك هل جيت احنا هذا
+
+476
+00:39:24,490 --> 00:39:28,570
+عوضنا طاولة طلح هذا صار هذا ما هو احنا ما نقوله من
+
+477
+00:39:28,570 --> 00:39:31,230
+فوق ان هذا اصغر اصغر و واحد اذا صار هذا المقدر
+
+478
+00:39:31,230 --> 00:39:34,530
+اصغر اصغر واحد اضربه طرفين في وساطين بطلع اللي هو
+
+479
+00:39:34,530 --> 00:39:40,110
+ال inequality اللي بدنا اياها يلا اللي بعده نيجي
+
+480
+00:39:40,110 --> 00:39:47,450
+الان اللي هو بس ملاحظةلو كانت بي بتساوي كيو بساوي
+
+481
+00:39:47,450 --> 00:39:53,770
+اتنين بتطلع عندى XII I من واحد ده ماله نهاية باعود
+
+482
+00:39:53,770 --> 00:39:59,270
+بس عن اتنين اصغره ساوي XIK اص نص جامعان اص اتنين
+
+483
+00:39:59,270 --> 00:40:02,970
+اص مين اص نص هذا ال space محترم هذا ال space
+
+484
+00:40:02,970 --> 00:40:07,790
+هنفردله كلام كتير اللي هو بنسميه ال space العناصره
+
+485
+00:40:07,790 --> 00:40:11,950
+اللي هو في ال L2 اسمه ال L2 هذا اسمه Hilbert
+
+486
+00:40:11,950 --> 00:40:15,910
+Sequence Spaceهذا هنحكي عنه بالتفصيل جدا ان شاء
+
+487
+00:40:15,910 --> 00:40:22,470
+الله الان هو في الواقع تعميم .. تعميم هذا .. تعميم
+
+488
+00:40:22,470 --> 00:40:27,790
+للمترك تبعنا تبع زمان لما كنا ناخد ال .. لو أخدنا
+
+489
+00:40:27,790 --> 00:40:34,490
+في ال .. في ال R2 X بالساوي XI واحدو Psi 2 و Y
+
+490
+00:40:34,490 --> 00:40:38,470
+بتساوي Gamma 1 و Gamma 2 إيش كنا ناخد ال metric في
+
+491
+00:40:38,470 --> 00:40:45,330
+الزمان الجدر التربيعي يعني نقص نص Psi 1 ناقص Gamma
+
+492
+00:40:45,330 --> 00:40:50,230
+1 تربيع زاد Psi 2 ناقص Gamma 2 كل إيش ماله تربيع
+
+493
+00:40:50,740 --> 00:40:54,580
+فهذا في الواقع تعميم إلى مانا لنهاية مش عدد اللي
+
+494
+00:40:54,580 --> 00:40:58,780
+هي تنتين لمانا و أيضا تعميم هذا على الار تربيع
+
+495
+00:40:58,780 --> 00:41:01,680
+بنسميه metric عالمين على الار تربيع وهذا مثلا على
+
+496
+00:41:01,680 --> 00:41:04,800
+ال metric على الار تربيع على الار and in general
+
+497
+00:41:06,700 --> 00:41:12,940
+الـ Rn بيكون الـ Dxy بساوة الـ summation للـ Xi I
+
+498
+00:41:12,940 --> 00:41:18,840
+ناقص Gamma I لكل تربيع I من عند 1 لعند N لكل
+
+499
+00:41:18,840 --> 00:41:31,240
+أسمانه أس نص فالـ Rn و كأنه special case لـ L2 بس
+
+500
+00:41:31,240 --> 00:41:36,050
+العماصر من عند N زايد 1 و طالع كل مسفرواضح يعني
+
+501
+00:41:36,050 --> 00:41:39,170
+بتقدر نعملها ك sequence تصير اكساية واحد اكساية
+
+502
+00:41:39,170 --> 00:41:41,790
+اثنين عندك ساعة و بعدين سفر سفر سفر ناشي الحال
+
+503
+00:41:41,790 --> 00:41:46,250
+اطلع اللي بعده يعني لو أثبتنا ان ال LB metric
+
+504
+00:41:46,250 --> 00:41:50,190
+space بيكون أثبتنا ال RN تبعنا تبع زمان و ال R
+
+505
+00:41:50,190 --> 00:41:53,990
+تربيع كله من هذه ال metric spaces يلّا اللي بعده
+
+506
+00:41:53,990 --> 00:42:00,250
+طيب مينكوسكي inequality ناشي الحال ال
+
+507
+00:42:00,250 --> 00:42:06,010
+auxiliary هذهالآن استخدمناها في إثبات مين اللي هو
+
+508
+00:42:06,010 --> 00:42:09,310
+الـHolder in Quality اللي هو Absolute Value أو
+
+509
+00:42:09,310 --> 00:42:14,310
+Modulus XII Gamma I أصغر أو ساوي Summation XII أُس
+
+510
+00:42:14,310 --> 00:42:19,870
+B أُس واحد على B في الـSummation للـGamma I أُس Q
+
+511
+00:42:19,870 --> 00:42:24,890
+أُس واحد على Q هذه الآن هتلزمنا في إثبات اللي هو
+
+512
+00:42:24,890 --> 00:42:31,680
+مينالـ Minkowski Inquality اللي هي الأساس في إثبات
+
+513
+00:42:31,680 --> 00:42:35,960
+الـ Triangular Inquality دخل الواحد كمان لأنه
+
+514
+00:42:35,960 --> 00:42:40,020
+بيقولك إذا كانت B أكبر شو واحد وكان Xi I وGamma I
+
+515
+00:42:40,020 --> 00:42:45,080
+وين موجودة؟ في القلبي، إذا ال summation للXi I زاد
+
+516
+00:42:45,080 --> 00:42:49,540
+Gamma I أس B أس واحد على B أصغر شو ال summation Xi
+
+517
+00:42:49,540 --> 00:42:54,080
+K أس B أس واحد على B زاد ال summation Gamma B أس 2
+
+518
+00:42:54,080 --> 00:42:58,440
+أس واحد على Bالأن حالة الـ B بيساوي واحد هي حالتنا
+
+519
+00:42:58,440 --> 00:43:01,440
+تبعت زمان الـ Triangling Quality لإنه بتصير
+
+520
+00:43:01,440 --> 00:43:06,480
+أشمالها Xi I زائد Gamma I و بس أصغر بساعة الصممشن
+
+521
+00:43:06,480 --> 00:43:11,100
+Xi K زائد الصممشن من Gamma N وهذه نين هي من ال
+
+522
+00:43:11,100 --> 00:43:16,560
+Triangling Quality العادية، ماشي؟ طيب إذا الأن
+
+523
+00:43:16,560 --> 00:43:19,800
+بدنا نبدأ نشتغل على الـ B أكبر من واحد اللي
+
+524
+00:43:19,800 --> 00:43:27,900
+نظريتنا هذه هي إلها صحيحة، ماشي؟ليجي الآن تطلعوا
+
+525
+00:43:27,900 --> 00:43:34,900
+لها الفكرة اللي بده يشتغل فيها ويطبق الـholding
+
+526
+00:43:34,900 --> 00:43:41,360
+quality عليها شوفوا هاي هدفه هو، باشي، بعدين بياخد
+
+527
+00:43:41,360 --> 00:43:44,900
+الـsummation، بعدين، من الحاجين اللي هانجلك خدوا B
+
+528
+00:43:44,900 --> 00:43:48,180
+أكبر من واحد وخد A fixed I يعني بنحكي عن I
+
+529
+00:43:48,180 --> 00:43:54,330
+arbitrarily لكن يشمله I محددوشوفوا Xi I زي Gamma I
+
+530
+00:43:54,330 --> 00:44:00,350
+أُس B بتساوي، بتدفرطها جزئين جزء أُس واحد وجزء أُس
+
+531
+00:44:00,350 --> 00:44:04,650
+B minus واحد، ماشي الحال؟ لأن حاصل الدرب هدولة
+
+532
+00:44:04,650 --> 00:44:09,850
+التنتين شكله بياخد واحدة هذه وواحدة هذه ويشتغل على
+
+533
+00:44:09,850 --> 00:44:15,720
+مين؟ على المنكوسكي طيب، الأن أصغر أو يساوي؟XII
+
+534
+00:44:15,720 --> 00:44:19,460
+زائد gamma I في المقدار هذا وهي الجزء الأول وهي
+
+535
+00:44:19,460 --> 00:44:23,240
+الجزء مين الثاني وقال ال code اللي هو ال summation
+
+536
+00:44:23,240 --> 00:44:27,770
+من عند واحد لعند مين لعند اناهتلاقيه حسب ال
+
+537
+00:44:27,770 --> 00:44:29,770
+equality اللي هنا أصغر أو سوى ال summation على
+
+538
+00:44:29,770 --> 00:44:33,890
+الجهتين هسير ال summation لهذا أصغر أو سوى ال
+
+539
+00:44:33,890 --> 00:44:37,410
+summation لهذا زائد ال summation للثاني أصغر أو
+
+540
+00:44:37,410 --> 00:44:41,710
+سوى ال summation xi i في ال summation هذا أقصى b-1
+
+541
+00:44:41,710 --> 00:44:45,390
+زائد ال summation للثاني أقسمين b-1 وسميها دي إيش
+
+542
+00:44:45,390 --> 00:44:49,970
+واحد، خليني أكتب هنا عشان هتروح من عندنا الآن ال
+
+543
+00:44:49,970 --> 00:44:57,060
+summation لل xi i زائد gamma iأُس بي أصغر أو ساوي
+
+544
+00:44:57,060 --> 00:45:01,860
+طبعا أخد I من واحدة من عند أنه لأنه لسه مش ضامن من
+
+545
+00:45:01,860 --> 00:45:04,880
+واحد إلى ما لا نهاية يكون converge ولا لأ عشان هيك
+
+546
+00:45:04,880 --> 00:45:10,120
+في الآخر حتلاقي أخدها لما يصير الأمر ناضج أنه كل
+
+547
+00:45:10,120 --> 00:45:13,580
+اللي معناه converge فبشتغل عليها اللي هي إلى ما لا
+
+548
+00:45:13,580 --> 00:45:22,500
+نهاية أصغر أو ساوي summation xi Iفي xi i زائد
+
+549
+00:45:22,500 --> 00:45:27,500
+gamma i أس بي ماينس واحد هذه الأولانة زائد
+
+550
+00:45:27,500 --> 00:45:35,780
+summation gamma i في xi i زائد gamma i أس بي ماينس
+
+551
+00:45:35,780 --> 00:45:39,920
+واحد مظبوط؟
+
+552
+00:45:39,920 --> 00:45:46,240
+طيب الآن هذه سموها واحد و أطلع لفوق واستخدموا الآن
+
+553
+00:45:46,240 --> 00:45:51,080
+ال holding quality بدي أستخدمها للأولىأولات تانية
+
+554
+00:45:51,080 --> 00:45:55,300
+خلّينا نستخدم الأولى و نعوض و بعدين بنشتغل الأولى
+
+555
+00:45:55,300 --> 00:46:02,320
+هي هذه و كأنها اللي هي هذه و هذه و كأنها مين جامعة
+
+556
+00:46:02,320 --> 00:46:06,760
+فبيصير أصغر أو ساوي على هذه بدي أطبّق الأولى Exile
+
+557
+00:46:06,760 --> 00:46:11,480
+is بيوس واحد على بيه ماشي الحال هديك على أي من
+
+558
+00:46:11,480 --> 00:46:15,660
+واحد المالانهاية و غيره و تقولولي fine I تانية اه
+
+559
+00:46:15,660 --> 00:46:17,820
+ما هي اللي بتطبق على مالانهاية بتطبق عليها تبعد
+
+560
+00:46:17,820 --> 00:46:23,450
+تبرهن كل الناس فار البجياتماشي فبتصير
+
+561
+00:46:23,450 --> 00:46:26,930
+أس بي أس واحد على بي والتانية بتصير هذه أس بي
+
+562
+00:46:26,930 --> 00:46:31,190
+ماينوس واحد الكل أس كيو أس واحد على مين على كيو
+
+563
+00:46:31,190 --> 00:46:35,690
+مظبوط طبقت مين ال holder inequality اللي هي اللي
+
+564
+00:46:35,690 --> 00:46:40,330
+هنا هي هذه أس كيو أس واحد على كيو هي أس كيو أس
+
+565
+00:46:40,330 --> 00:46:43,910
+واحد على كيو على هذه طبقت اللي هي الأولى هذه بتنزل
+
+566
+00:46:43,910 --> 00:46:47,130
+زي ما هي والتانية بيصير بي ماينوس واحد في مين في
+
+567
+00:46:47,130 --> 00:46:51,810
+كيوالان اللي هي ال .. ال .. ال .. ال .. و هذه أس
+
+568
+00:46:51,810 --> 00:46:56,870
+مين؟ أس واحد على Q، أه؟ الان B minus واحد في Q
+
+569
+00:46:56,870 --> 00:47:02,990
+بتساوي اللي هو مين؟ بتساوي اللي هي B، أه؟ في ده ..
+
+570
+00:47:02,990 --> 00:47:07,270
+في ده أنا أعملها؟ كده؟
+
+571
+00:47:07,270 --> 00:47:11,610
+أه، مظبوط؟
+
+572
+00:47:11,610 --> 00:47:17,380
+أعملها ولا خلاص؟كلهم جايات من مين؟ من 1 على B زائد
+
+573
+00:47:17,380 --> 00:47:23,800
+1 على Q بساوي 1 ماشي الحال طيب الأنصار عندي XI K
+
+574
+00:47:23,800 --> 00:47:30,780
+أس B أس 1 على B وهذه أس B أس 1 على مين؟ على Q واضح
+
+575
+00:47:30,780 --> 00:47:35,500
+اللي بحكيه؟ طيب التانية similarly بنفس الأسلوب
+
+576
+00:47:35,500 --> 00:47:41,320
+Gamma I في XI هذا عملناها مين يا جماعة؟ هذه هي
+
+577
+00:47:41,320 --> 00:47:48,930
+أصغر أو يساوي هذههذه التانية بالظبط زيها بس بدل
+
+578
+00:47:48,930 --> 00:47:53,410
+لكساي I بتاخد 100 Gram I ماشي الحال إذا خلّيني
+
+579
+00:47:53,410 --> 00:48:01,430
+أسجلها هادي هان أصغر أو يساوي summation XI K أُس B
+
+580
+00:48:01,430 --> 00:48:11,610
+أُس 1 على B في summation XI M زائد Gram M أُس B
+
+581
+00:48:11,610 --> 00:48:13,290
+أُس 1 على 100
+
+582
+00:48:16,590 --> 00:48:22,830
+واضح اه طيب التانية نفس الاشي بس بدل هذه بده احط
+
+583
+00:48:22,830 --> 00:48:27,510
+هذه ماشي فبصير هذه و هذه زي بعض هذه زي الأولى و
+
+584
+00:48:27,510 --> 00:48:32,810
+هذه زائد زائد summation بدل هذه مين هيكون gamma K
+
+585
+00:48:32,810 --> 00:48:41,320
+أس بي أس واحد على بي في ال summation نفسهنفسه
+
+586
+00:48:41,320 --> 00:48:45,280
+ناخده مين عالم المشترك بيصير هذا ويساوي ال
+
+587
+00:48:45,280 --> 00:48:49,400
+summation اللي عامل المشترك هذا هذا مضروب في مين
+
+588
+00:48:49,400 --> 00:48:53,960
+في ال summation gamma k أس بي زاد ال summation
+
+589
+00:48:53,960 --> 00:49:04,700
+اكسايكل ونفعله هذي gamma k أس واحد على بي أس بي أس
+
+590
+00:49:04,700 --> 00:49:10,150
+مينواحد على كيو صح اطلع على فوق نشوف ده عشان نقول
+
+591
+00:49:10,150 --> 00:49:23,850
+خربطنا مافي حاجة substitute
+
+592
+00:49:23,850 --> 00:49:28,210
+of the two inequalities in main in واحد فبصير اللي
+
+593
+00:49:28,210 --> 00:49:30,250
+هو ان شاء الله مانكون خربطناش في الحسابات
+
+594
+00:49:37,050 --> 00:49:47,950
+أه واحد على Q و لا .. خلّيني أرجع لها هذه
+
+595
+00:49:47,950 --> 00:49:54,610
+واحد على B وهذه اللي هي التانية واحد على B أظن
+
+596
+00:49:54,610 --> 00:49:57,750
+واحد على B خلّيني أرجع لها دقيقة .. دقيقة .. دقيقة
+
+597
+00:49:57,750 --> 00:50:00,170
+.. دقيقة .. دقيقة .. دقيقة .. دقيقة .. دقيقة ..
+
+598
+00:50:00,170 --> 00:50:00,170
+دقيقة .. دقيقة .. دقيقة .. دقيقة .. دقيقة .. دقيقة
+
+599
+00:50:00,170 --> 00:50:00,730
+.. دقيقة .. دقيقة .. دقيقة .. دقيقة .. دقيقة ..
+
+600
+00:50:00,730 --> 00:50:00,730
+دقيقة .. دقيقة .. دقيقة .. دقيقة .. دقيقة .. دقيقة
+
+601
+00:50:00,730 --> 00:50:00,730
+.. دقيقة .. دقيقة .. دقيقة .. دقيقة .. دقيقة ..
+
+602
+00:50:00,730 --> 00:50:00,730
+دقيقة .. دقيقة .. دقيقة .. دقيقة .. دقيقة .. دقيقة
+
+603
+00:50:00,730 --> 00:50:00,770
+.. دقيقة .. دقيقة .. دقيقة .. دقيقة .. دقيقة ..
+
+604
+00:50:00,770 --> 00:50:00,850
+دقيقة .. دقيقة
+
+605
+00:50:05,230 --> 00:50:21,290
+بـ-1 في Q أس واحد على Q لأ
+
+606
+00:50:21,290 --> 00:50:28,110
+تبقى تلعاب المشتراك التنتين واحد على Qوحد على بي
+
+607
+00:50:28,110 --> 00:50:34,350
+وحد على بي وحد على بي مظبوط ان هذه الواحد على بي و
+
+608
+00:50:34,350 --> 00:50:44,810
+هذه يشبهلها واحد على بي طيب شوف ال .. تبهوا لوين
+
+609
+00:50:44,810 --> 00:50:52,250
+احنا وصلنا .. خليني أمسح حاجة، ميمش؟ بصير عند ال
+
+610
+00:50:52,250 --> 00:50:55,690
+.. and summation
+
+611
+00:50:56,990 --> 00:51:02,850
+Summation هذا شايفينه هذا هذا هذا أصغر أو يساوي
+
+612
+00:51:02,850 --> 00:51:05,950
+اللي هو هذا ال summation و هذا ال summation زائد
+
+613
+00:51:05,950 --> 00:51:10,850
+هذا و قلنا هنا خد عامل مشترك اللي هو هذا شايفينه
+
+614
+00:51:10,850 --> 00:51:16,450
+هاي هاي هذا عامل مشترك دل هذا و دل هذا فطلعنا هذا
+
+615
+00:51:16,450 --> 00:51:20,630
+العامل المشترك هاي و هان و هذول الجمع هاي هان ماشي
+
+616
+00:51:20,630 --> 00:51:24,950
+الحالة الان لاحظوا على هذا و هذا
+
+617
+00:51:27,950 --> 00:51:32,510
+نفس الاشي بس هذا أس واحد على Q و هذا أس واحد فلما
+
+618
+00:51:32,510 --> 00:51:35,730
+أجسم عليها بيصير اللي هو اللي على الطرف هنا أس
+
+619
+00:51:35,730 --> 00:51:40,920
+واحد ماقص واحد على Qواضحة فبصير عنده الآن ال
+
+620
+00:51:40,920 --> 00:51:44,740
+summation هذا اللي حكيته عن نقص واحد ناقص مين واحد
+
+621
+00:51:44,740 --> 00:51:48,620
+على Q اللي هو أصغر أو أساوي هذا بيظل زي ما هو وهذا
+
+622
+00:51:48,620 --> 00:51:53,660
+بيظل زي ما هو قبل N واحد ناقص واحد على Q هو واحد
+
+623
+00:51:53,660 --> 00:51:59,000
+على P مصدود واحد على P واحد على P فبصير عنده الآن
+
+624
+00:51:59,000 --> 00:52:04,480
+هذاصار عبارة عن واحد على بيه ماعليش ده شو جودني
+
+625
+00:52:04,480 --> 00:52:08,140
+بتبقى كتير واحد على مين على بيه الان صار هذا
+
+626
+00:52:08,140 --> 00:52:10,940
+المقدار واحد على بيه و هذا واحد على بيه و هذا واحد
+
+627
+00:52:10,940 --> 00:52:15,360
+على بيه و ال submissions اتوزع زي اللي انا اصلا
+
+628
+00:52:15,360 --> 00:52:23,340
+بروح بدياها الان انا مرتاحهاخد الأن مالة تروح
+
+629
+00:52:23,340 --> 00:52:27,020
+لمالة نهاية ليش مرتاح لإنه ضامن هذا converge زي
+
+630
+00:52:27,020 --> 00:52:29,860
+إنه هذا في القلبي وضامن هذا converge زي إنه في
+
+631
+00:52:29,860 --> 00:52:35,300
+القلبي فبصير عندي هذا من واحد إلى مالة نهاية بالهو
+
+632
+00:52:35,300 --> 00:52:39,840
+اللي أنا بديه أزرع يساوي هذا أس واحد على بيه زائد
+
+633
+00:52:39,840 --> 00:52:42,420
+هذا أس واحد على بيه وكامن واحد إلى مالة نهاية
+
+634
+00:52:42,420 --> 00:52:47,800
+وبكون حصلت عالميا على المينكوسكي in quad واضح
+
+635
+00:52:49,660 --> 00:52:54,420
+طيب، صلى على النبل أسوأ السنة الآن أصلنا للثمرة
+
+636
+00:52:54,420 --> 00:52:58,160
+اللي بتنيها اللي هو الـ sequence space اللي هو مين
+
+637
+00:52:58,160 --> 00:53:04,100
+الـ LB space قلنا الآن consider the asset LB of
+
+638
+00:53:04,100 --> 00:53:08,160
+all sequences of numbers XI I such that الـ
+
+639
+00:53:08,160 --> 00:53:11,380
+summation هذا يكون أشماله converts أو is finite
+
+640
+00:53:11,380 --> 00:53:15,880
+هذه الـ sequences اللي بالخاصية هذه هي اللي بتعمل
+
+641
+00:53:15,880 --> 00:53:22,660
+للـ LBالـ B تحت الـ D اللي في الأول أنا عرفته اللي
+
+642
+00:53:22,660 --> 00:53:26,760
+هو هيه .. هيه عندي D X Y بساوية summation X I I
+
+643
+00:53:26,760 --> 00:53:31,100
+نقص جمعي أس بيقص واحد على B هيعملني metric على الـ
+
+644
+00:53:31,100 --> 00:53:37,610
+B فبصير الـ B عبارة عن metric spaceالان هى المث
+
+645
+00:53:37,610 --> 00:53:43,010
+هذا اللى بنثبته بحقق الخصية الأول واحد اتنين تلاتة
+
+646
+00:53:43,010 --> 00:53:46,130
+أربعة الخصية الأوله automatic أكبر بساوية صفر هين
+
+647
+00:53:46,130 --> 00:53:50,450
+اللى هو بساوية صفر F وان دول F هذى بتساوي هذى يعني
+
+648
+00:53:50,450 --> 00:53:56,480
+X بتساوي Yباللي هو الـ x و y هي نفسها y و x تبع
+
+649
+00:53:56,480 --> 00:53:59,500
+الهادي الآن الخاصية الأخيرة الاتنين in quality
+
+650
+00:53:59,500 --> 00:54:03,520
+جاهزين لها ليش جاهزين لها من ال min cost ك in
+
+651
+00:54:03,520 --> 00:54:07,960
+quality شوفوا كيف احنا جاهزين منها هتلاقوا الأمر
+
+652
+00:54:07,960 --> 00:54:13,490
+automatic بطلع خدوا اي x بساوي psi iو Y بيساوي
+
+653
+00:54:13,490 --> 00:54:16,830
+Gamma I و Z بيساوي Beta I كل هى اللى موجودات فى
+
+654
+00:54:16,830 --> 00:54:22,070
+القلبى خد المسافة X Y بين X Y اللى احنا عرفنا ال
+
+655
+00:54:22,070 --> 00:54:27,070
+metric على أساسها اللى هو بيساوي هذه قطعا اللى هو
+
+656
+00:54:27,810 --> 00:54:32,270
+اللي جوا بس بدي .. بعد إذن كُن بدي أكتبها بضاطيف
+
+657
+00:54:32,270 --> 00:54:36,750
+Beta I واش ونقص Beta I بصير أصغر أو يساوي
+
+658
+00:54:36,750 --> 00:54:40,350
+وأستخدمين الـ Triangling الـ Quality العادية اللي
+
+659
+00:54:40,350 --> 00:54:44,990
+هو XI I نقص Beta I زي ال Beta I نقص من XI I وخلّي
+
+660
+00:54:44,990 --> 00:54:49,610
+.. يعني اشتغل هذه أصغر أو يساوي هذه وهذه B وهذه B
+
+661
+00:54:49,610 --> 00:54:54,220
+واحدة على B واحدة على B فاهمين؟طيب، الآن هذا بيصير
+
+662
+00:54:54,220 --> 00:54:57,760
+عندى حسب المنكسك inequality اللى قبل بشوية هذا
+
+663
+00:54:57,760 --> 00:55:02,900
+لحاله و هذا لحاله هذا بيصير أس بي سواحد على بي و
+
+664
+00:55:02,900 --> 00:55:07,820
+هذا بيصير أس كيو سواحد على كيو فاهمين؟ هذا اللى هو
+
+665
+00:55:07,820 --> 00:55:14,800
+استخدام المنكسك اللى مسحتها مباشرة يعني هذا بيمثل
+
+666
+00:55:14,800 --> 00:55:18,660
+في المنكسك اللى قبل شوية XII و هذا بيمثل Gamma I
+
+667
+00:55:19,950 --> 00:55:26,370
+فطبقتها فطلعت هذه زائد هذه هذه اللي هي DXY DX و Z
+
+668
+00:55:26,370 --> 00:55:30,810
+هي طبعت ال XY ال Z و هذي DY و Z و هيك بيكون عندنا
+
+669
+00:55:30,810 --> 00:55:35,610
+أثبتنا أن هذا عبارة عن مين عن metric space في حالة
+
+670
+00:55:35,610 --> 00:55:40,030
+ال B بالساوة اتنين قولنا هذا metric محترم بنعتبره
+
+671
+00:55:40,490 --> 00:55:44,430
+اللي هو اسمه الهيلبارد سبايس الهيلبارد سيكوينس
+
+672
+00:55:44,430 --> 00:55:49,350
+سبايس الهيلبارد
+
+673
+00:55:49,350 --> 00:55:50,170
+سيكوينس سبايس الهيلبارد سيكوينس سبايس الهيلبارد
+
+674
+00:55:50,170 --> 00:55:50,170
+سيكوينس سبايس الهيلبارد سيكوينس سبايس الهيلبارد
+
+675
+00:55:50,170 --> 00:55:51,050
+سيكوينس سبايس الهيلبارد سيكوينس سبايس الهيلبارد
+
+676
+00:55:51,050 --> 00:55:51,110
+سيكوينس سبايس الهيلبارد سيكوينس سبايس الهيلبارد
+
+677
+00:55:51,110 --> 00:55:53,090
+سيكوينس سبايس الهيلبارد سيكوينس سبايس الهيلبارد
+
+678
+00:55:53,090 --> 00:55:55,810
+سيكوينس سبايس الهيلبارد سيكوينس سبايساللي هو
+
+679
+00:55:55,810 --> 00:55:59,390
+العناصر اللي هي X,Y,I,Y الـ R تكعيب اتبعنا اللي هو
+
+680
+00:55:59,390 --> 00:56:02,410
+الـ Ordered Pair اللي هو هذا الـDXY اللي هو الجذر
+
+681
+00:56:02,410 --> 00:56:06,410
+التربيهي اللي حكيته قبل وشوية حالة خاصة منه والـR
+
+682
+00:56:06,410 --> 00:56:13,170
+تكعيب اللي بنفس الأسلوب بنعرفه حالة خاصة لأرضه
+
+683
+00:56:13,170 --> 00:56:18,130
+منين من الـL2 Space وكل هنا بنكون أثبتناه
+
+684
+00:56:18,130 --> 00:56:22,310
+الـMetric Space مادام أثبتنا مين اللي هو الـB in
+
+685
+00:56:22,310 --> 00:56:25,830
+general is a metric spaceلأنه بنعتبر الباقي اللي
+
+686
+00:56:25,830 --> 00:56:30,930
+هو إيش اللي هي أصفار والـ RN برضه زي ما قلت قبل
+
+687
+00:56:30,930 --> 00:56:35,070
+شوية نفس الأسلوب في حالة الـCN الـCN برضه نفس
+
+688
+00:56:35,070 --> 00:56:38,050
+الاشي بس باخد بدل التربية إيش باخد للمدرس عشان
+
+689
+00:56:38,050 --> 00:56:43,350
+يصير إن أعداد يطلع قيمةلأن عشان يطلع DXY عبارة عن
+
+690
+00:56:43,350 --> 00:56:48,310
+عدد فباخد المدرس فبكون هذا عبارة عن ال CN و بيكون
+
+691
+00:56:48,310 --> 00:56:52,750
+كل الحلات خاصة من اللي حكيته قبل بشوية و بيكون
+
+692
+00:56:52,750 --> 00:56:58,310
+معكم exercise الآن هذا اللي عندى بالاضافة ده
+
+693
+00:56:58,310 --> 00:57:03,150
+تمانية و عشرة هدولكم السيرمونيان و هدولة اللي هو
+
+694
+00:57:03,150 --> 00:57:07,790
+حلون و فيها العمون الحلون الموجودة عندى اللي
+
+695
+00:57:07,790 --> 00:57:12,270
+ماعرفش حاجة بنعطيها ان شاء اللهوبرك الله فيكم و
+
+696
+00:57:12,270 --> 00:57:13,110
+الله يعطيكم العافية
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/T3dQGYbQlAQ_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/T3dQGYbQlAQ_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..cdf1a57684162257dadd0586c25726906ce3ae3a
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/T3dQGYbQlAQ_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2429, "start": 5.11, "end": 24.29, "text": "بسم الله الرحمن الرحيم الحمد لله رب العالمين والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى آله وصحبه أجمعين هذه المحاضرة رقم 27 مساق تحليل اقتراني أو تحليل دالي طلاب وطالبات الجامعة الإسلامية قسم الرياضيات للطلاب وطالبات الماجستير", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21542, 2304, 3215, 24976, 3224, 12602, 3555, 18863, 45340, 9957, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 8608, 25708, 9673, 2288, 3794, 1211, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 19753, 43761, 4032, 9381, 5016, 3555, 3224, 5551, 7435, 2304, 3615, 9957, 29538, 9673, 5016, 46958, 25720, 12602, 4587, 2304, 7634, 47524, 995, 4587, 6055, 5016, 20292, 1211, 1975, 38149, 2288, 7649, 1829, 34051, 6055, 5016, 20292, 1211, 11778, 6027, 1829, 23032, 15040, 3555, 4032, 9566, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 12174, 38251, 2423, 16572, 46958, 1829, 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0.9703776041666666}, {"start": 8.85, "end": 9.07, "word": " على", "probability": 0.58642578125}, {"start": 9.07, "end": 9.41, "word": " سيد", "probability": 0.9609375}, {"start": 9.41, "end": 9.91, "word": " المرسلين", "probability": 0.97412109375}, {"start": 9.91, "end": 10.29, "word": " سيدنا", "probability": 0.966796875}, {"start": 10.29, "end": 10.69, "word": " محمد", "probability": 0.9873046875}, {"start": 10.69, "end": 10.93, "word": " وعلى", "probability": 0.8640950520833334}, {"start": 10.93, "end": 11.21, "word": " آله", "probability": 0.870361328125}, {"start": 11.21, "end": 11.71, "word": " وصحبه", "probability": 0.89501953125}, {"start": 11.71, "end": 12.27, "word": " أجمعين", "probability": 0.9435546875}, {"start": 12.27, "end": 12.95, "word": " هذه", "probability": 0.88720703125}, {"start": 12.95, "end": 13.45, "word": " المحاضرة", "probability": 0.98291015625}, {"start": 13.45, "end": 13.71, "word": " رقم", "probability": 0.9480794270833334}, {"start": 13.71, "end": 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x بيساوي g of x إذا كانت x في domain الـ g ماشي خلوها دي في الداكرة", "tokens": [1211, 33456, 28242, 36764, 24401, 10320, 24976, 2655, 7649, 10632, 6156, 10721, 1829, 2031, 8978, 9274, 23758, 11331, 1829, 30544, 8978, 9274, 13672, 1829, 31439, 3714, 9957, 13672, 1829, 10874, 16758, 2655, 11296, 6156, 6027, 148, 48506, 290, 2385, 295, 2031, 4724, 1829, 3794, 995, 45865, 290, 295, 2031, 11933, 15730, 25961, 2655, 2031, 8978, 9274, 2423, 39184, 290, 3714, 33599, 1829, 16490, 1211, 2407, 11296, 11778, 1829, 8978, 32748, 995, 4117, 25720], "avg_logprob": -0.25865710748208537, "compression_ratio": 1.5406976744186047, "no_speech_prob": 4.1365623474121094e-05, "words": [{"start": 587.48, "end": 588.26, "word": "لأن", "probability": 0.6375732421875}, {"start": 588.26, "end": 588.46, "word": " كل", "probability": 0.77587890625}, {"start": 588.46, "end": 588.64, "word": " واحد", "probability": 0.988037109375}, {"start": 588.64, "end": 588.98, "word": " extension", "probability": 0.40771484375}, 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عن من؟ عن اللي هي الـ F لأن هدولة كلها extension للـ F فصارت الجيهة اللي هي معرفة على أكبر domain فين هدولة اللي هو عبارة عن extension صار extension functional، linear functional إذن", "tokens": [19096, 10874, 1829, 3224, 3660, 307, 257, 8213, 10320, 295, 11745, 25724, 1829, 3224, 3660, 6055, 15040, 38436, 14739, 3224, 20328, 9640, 5551, 8592, 2304, 6027, 11296, 4032, 41779, 34268, 8717, 5172, 2407, 8848, 11296, 18871, 9154, 22807, 18871, 13672, 1829, 39896, 2423, 39184, 479, 5296, 33456, 8032, 3215, 12610, 3660, 28242, 11296, 10320, 24976, 39184, 479, 6156, 9381, 9640, 2655, 25724, 1829, 3224, 3660, 13672, 1829, 39896, 20449, 28480, 3660, 15844, 5551, 4117, 26890, 9274, 8978, 1863, 8032, 3215, 12610, 3660, 13672, 1829, 31439, 6225, 3555, 9640, 3660, 18871, 10320, 20328, 9640, 10320, 11745, 12399, 8213, 11745, 11933, 8848, 1863], "avg_logprob": -0.27267156482911575, "compression_ratio": 1.8211009174311927, "no_speech_prob": 7.092952728271484e-06, "words": [{"start": 602.84, "end": 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"probability": 0.626220703125}, {"start": 607.7, "end": 608.68, "word": " ووسعت", "probability": 0.8528645833333334}, {"start": 608.68, "end": 609.64, "word": " نفوذها", "probability": 0.9701171875}, {"start": 609.64, "end": 610.46, "word": " عن", "probability": 0.953125}, {"start": 610.46, "end": 611.1, "word": " من؟", "probability": 0.4765625}, {"start": 611.1, "end": 611.44, "word": " عن", "probability": 0.94189453125}, {"start": 611.44, "end": 611.7, "word": " اللي", "probability": 0.903076171875}, {"start": 611.7, "end": 612.08, "word": " هي", "probability": 0.9482421875}, {"start": 612.08, "end": 612.74, "word": " الـ", "probability": 0.658447265625}, {"start": 612.74, "end": 612.96, "word": " F", "probability": 0.51171875}, {"start": 612.96, "end": 613.3, "word": " لأن", "probability": 0.81982421875}, {"start": 613.3, "end": 613.56, "word": " هدولة", "probability": 0.7774658203125}, {"start": 613.56, "end": 613.78, "word": " كلها", "probability": 0.828125}, {"start": 613.78, 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"probability": 0.8431396484375}, {"start": 619.46, "end": 620.0, "word": " اللي", "probability": 0.970703125}, {"start": 620.0, "end": 620.26, "word": " هو", "probability": 0.966796875}, {"start": 620.26, "end": 621.02, "word": " عبارة", "probability": 0.99365234375}, {"start": 621.02, "end": 621.24, "word": " عن", "probability": 0.99169921875}, {"start": 621.24, "end": 621.88, "word": " extension", "probability": 0.92236328125}, {"start": 621.88, "end": 622.46, "word": " صار", "probability": 0.880615234375}, {"start": 622.46, "end": 622.88, "word": " extension", "probability": 0.65185546875}, {"start": 622.88, "end": 623.4, "word": " functional،", "probability": 0.4788818359375}, {"start": 623.4, "end": 623.56, "word": " linear", "probability": 0.70166015625}, {"start": 623.56, "end": 623.98, "word": " functional", "probability": 0.88232421875}, {"start": 623.98, "end": 626.42, "word": " إذن", "probability": 0.5985514322916666}], "temperature": 1.0}, {"id": 29, "seek": 65137, "start": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/T3dQGYbQlAQ_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/T3dQGYbQlAQ_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c3a58b4ae2b22e3a371245ecaf189e424943a2c7
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/T3dQGYbQlAQ_raw.srt
@@ -0,0 +1,2348 @@
+1
+00:00:05,110 --> 00:00:07,970
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,970 --> 00:00:10,930
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,930 --> 00:00:15,650
+آله وصحبه أجمعين هذه المحاضرة رقم 27 مساق تحليل
+
+4
+00:00:15,650 --> 00:00:19,210
+اقتراني أو تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:19,210 --> 00:00:24,290
+الإسلامية قسم الرياضيات للطلاب وطالبات الماجستير
+
+6
+00:00:25,410 --> 00:00:29,350
+أوصلنا لعند ال section التاني في chapter أربعة و
+
+7
+00:00:29,350 --> 00:00:32,550
+ال section هذا اللي هو نيجي اللي هو اسمه أربعة
+
+8
+00:00:32,550 --> 00:00:36,670
+اتنين هان بنخ تيرم و هان هنحكي عن إحدى النظريات
+
+9
+00:00:36,670 --> 00:00:43,310
+الأساسية في اللي هو التحليل الدالي جابل ما نبدأ
+
+10
+00:00:43,310 --> 00:00:47,230
+نحكي عن النظرية بدنا اللي هو نحكي عنها لبعض
+
+11
+00:00:47,230 --> 00:00:52,670
+التعريفات اللي هتلزمنا في اللي هي النظرية القادمة
+
+12
+00:00:53,740 --> 00:00:56,320
+التعريف الأول اربعة اتنين واحد definition a
+
+13
+00:00:56,320 --> 00:00:59,060
+sublinear functional sublinear احنا بنعرف ال
+
+14
+00:00:59,060 --> 00:01:01,840
+linear functional اللي عن sublinear functional is
+
+15
+00:01:01,840 --> 00:01:06,760
+a real valued function B on a vector space X لما
+
+16
+00:01:06,760 --> 00:01:11,700
+نحكي عن sublinear بحكي عن ايش بحكي عن اللي هو a
+
+17
+00:01:11,700 --> 00:01:14,540
+real valued function لأنه انا بتحكي عن order أصغر
+
+18
+00:01:14,540 --> 00:01:16,460
+أو يساوي انتوا عارفين في ال complex فيش اصغر أو
+
+19
+00:01:16,460 --> 00:01:19,760
+يساوي فيش order بمعنى اخر في ال complex field اللي
+
+20
+00:01:19,760 --> 00:01:20,440
+احنا بنعرفه
+
+21
+00:01:24,990 --> 00:01:28,150
+بحقق الشروط التالية عشان نكون sub linear الشرط
+
+22
+00:01:28,150 --> 00:01:31,870
+الأول بيكس زائد واي أصغر شهو بيكس زائد بي واي for
+
+23
+00:01:31,870 --> 00:01:35,610
+all x و y element in x وهذا اللي استدعت انه يكون
+
+24
+00:01:35,610 --> 00:01:40,290
+real valued functionبـ Positive Homogeneous بألفة
+
+25
+00:01:40,290 --> 00:01:47,470
+X Positive و Homogeneous بألفة
+
+26
+00:01:47,470 --> 00:01:51,290
+X أو أكبر يساوي سفر الألف بألفة X يساوي ألفة في B
+
+27
+00:01:51,290 --> 00:01:54,570
+of X for all X limited in X and all ألف أكبر أو
+
+28
+00:01:54,570 --> 00:01:58,770
+يساوي سفر إذا اتحقق الشرطين اللي أمامنا هذول بنسمي
+
+29
+00:01:58,770 --> 00:02:02,550
+اللي هو الـ B is a sublinear اللي هي functional
+
+30
+00:02:02,550 --> 00:02:06,210
+لإنها بترمي في ال field اللي عندنا اللي هو فعلا ال
+
+31
+00:02:06,210 --> 00:02:10,000
+fieldالـ R اللي هو الـ Real Value يعني الان نجي
+
+32
+00:02:10,000 --> 00:02:14,940
+لانبنغثيورم الانبنغثيورم هذه اللي هو لان فيه أكثر
+
+33
+00:02:14,940 --> 00:02:18,980
+من Formة هناخده ال Formة اللي بتتعامل اول اشي مع
+
+34
+00:02:18,980 --> 00:02:22,280
+vector space بس بعد شوية بنحكي عن اللي هو ال
+
+35
+00:02:22,280 --> 00:02:24,500
+normed space اللي احنا نسبقله اللي هي النظرية اللي
+
+36
+00:02:24,500 --> 00:02:27,540
+بنحكي عنها النظرية الأساسية فهذه النظرية اللي
+
+37
+00:02:27,540 --> 00:02:31,320
+خلينا نقول اللي هي مقدمة للنظرية اللي بعد هيك اللي
+
+38
+00:02:31,320 --> 00:02:36,350
+هي بتحكي على اللي هو normed space in generalخلّينا
+
+39
+00:02:36,350 --> 00:02:39,770
+نشوف طبعا النظرية هي extension ل linear functional
+
+40
+00:02:39,770 --> 00:02:43,310
+يعني بمعنى أخر بدنا نمد فلاحية ال linear
+
+41
+00:02:43,310 --> 00:02:47,450
+functional بحيث أنه يشتغل على vector space أوسع من
+
+42
+00:02:47,450 --> 00:02:52,820
+اللي هو عليه وبخواص معينة خلّينا نشوفهيقولنا
+
+43
+00:02:52,820 --> 00:02:56,620
+extension of linear functional زي هي اللي بتتحدث
+
+44
+00:02:56,620 --> 00:03:00,140
+عنه ال handbanach theorem let X be a real vector
+
+45
+00:03:00,140 --> 00:03:03,060
+space إذا نحكي عن real vector space بعد شوية هنحكي
+
+46
+00:03:03,060 --> 00:03:07,120
+عن complex and B is a sublinear functional on X
+
+47
+00:03:07,120 --> 00:03:09,480
+طبعا لما نحكي عن complex بنعالج اللي هي قصة اللي
+
+48
+00:03:09,480 --> 00:03:13,240
+هي linear functional بطريقة معينة اللي هي real
+
+49
+00:03:13,240 --> 00:03:16,600
+valued هذه and B is a sublinear functional on X
+
+50
+00:03:17,790 --> 00:03:21,550
+Furthermore، خلّينا نعتبر F Linear Functional،
+
+51
+00:03:21,550 --> 00:03:27,570
+which is defined on جزء من الـ X، on Z، من عصابة
+
+52
+00:03:27,570 --> 00:03:33,810
+Space، اللي هو Z of X، and satisfies F of X أصغر
+
+53
+00:03:33,810 --> 00:03:34,830
+يسوا بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+54
+00:03:34,830 --> 00:03:35,550
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+55
+00:03:35,550 --> 00:03:35,770
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+56
+00:03:35,770 --> 00:03:38,640
+بيه بيه بيه بيه بيهإذن الآن المعطيات اللي عندي ال
+
+57
+00:03:38,640 --> 00:03:41,940
+functional اللي عندي هذه ال linear functional هي
+
+58
+00:03:41,940 --> 00:03:45,200
+عبارة عن linear functional على جزء من ال space X
+
+59
+00:03:45,200 --> 00:03:50,900
+على sub space من ال space X وتحقق شاطر شخصية F of
+
+60
+00:03:50,900 --> 00:03:54,100
+X أصغر سوا بيه F of X الغبط من هذه النظرية أن أنا
+
+61
+00:03:54,100 --> 00:03:59,520
+بتدوسع نفوذ ال F هذهأخليها بدل ما هي على Z أعملها
+
+62
+00:03:59,520 --> 00:04:02,380
+extension تشغل على مين؟ على كل ال X يعني تبقى
+
+63
+00:04:02,380 --> 00:04:06,760
+محافظة على شغل على ال Z بنفس الخواص ومن ثم تنطلق
+
+64
+00:04:06,760 --> 00:04:12,660
+لتكون أوسع على ال X الكبيرة وتحافظ على الخواص
+
+65
+00:04:12,660 --> 00:04:21,010
+الموجودة بمعنى الآناللي بحتيه then f has a linear
+
+66
+00:04:21,010 --> 00:04:25,070
+extension هذا المطلوب f تلده الان from z to b into
+
+67
+00:04:25,070 --> 00:04:28,950
+x يعني هال linear extension خطة z و هيشغل عالميا
+
+68
+00:04:28,950 --> 00:04:34,330
+على كل x f تلده على ال x هتصير satisfying برضه
+
+69
+00:04:34,330 --> 00:04:38,250
+هتحقق نفس الشروط f تلده of x أصغر أو أصغر بيه of x
+
+70
+00:04:38,250 --> 00:04:42,950
+لكل x من الموجودة لكل x element in x هذه هي اللي
+
+71
+00:04:42,950 --> 00:04:52,320
+هي اللي مطلوب انه انا اوسع كانت fموجودة من Z إلى R
+
+72
+00:04:52,320 --> 00:04:59,050
+أو إلى اللي هي و كأو بدأ و عند Zsub space من X بدي
+
+73
+00:04:59,050 --> 00:05:03,210
+أجيب F تلده طبعا لو كان اتدت حقق هواس ان F of X
+
+74
+00:05:03,210 --> 00:05:05,470
+أصغر يساوي بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+75
+00:05:05,470 --> 00:05:07,190
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+76
+00:05:07,190 --> 00:05:07,470
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+77
+00:05:07,470 --> 00:05:07,630
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+78
+00:05:07,630 --> 00:05:13,750
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+79
+00:05:13,750 --> 00:05:25,320
+بيه بيه بتحقق F تلدة of X أصغر يساوي P of X لكل X
+
+80
+00:05:25,320 --> 00:05:30,320
+الأنوار الموجودة مش في Z بس فكل X اللي عندي لأن
+
+81
+00:05:30,320 --> 00:05:34,920
+الفكرة .. الفكرة .. الفكرة من الحل أنه أنا بدي
+
+82
+00:05:34,920 --> 00:05:40,040
+أجيب عائلة و أسميها إيه؟ هذه عائلة من الدوال هي
+
+83
+00:05:40,040 --> 00:05:42,480
+فعلا عائلة .. هحكي عنها عائلة من extension
+
+84
+00:05:42,480 --> 00:05:48,960
+functions لل-Fو قادي اللي هو عرف عليها partial
+
+85
+00:05:48,960 --> 00:05:51,780
+order relation بطريقة معينة هتشوفوها بعد شوية
+
+86
+00:05:51,780 --> 00:05:57,720
+هتعمل هذه non-empty set of .. of .. of .. of .. of
+
+87
+00:05:57,720 --> 00:06:01,780
+ordered أو non-empty ordered set بالنسبة لهذه ال
+
+88
+00:06:01,780 --> 00:06:05,540
+partial order relation و هلاجي ان كل ال chain فيها
+
+89
+00:06:05,540 --> 00:06:11,630
+انها ايش انها upper boundمنها هذه طبعاً بتكون شروط
+
+90
+00:06:11,630 --> 00:06:17,510
+zones لما اتحققت هيكون في عندى في maximal element
+
+91
+00:06:17,510 --> 00:06:21,190
+الآن ال maximal element هذا هو after ده هو اللي
+
+92
+00:06:21,190 --> 00:06:24,970
+حاتبته ال maximal element هو اللي بأد الغرض لهيك
+
+93
+00:06:24,970 --> 00:06:29,730
+هذه الاستراتيجية تبعت برهان النظرية ودعونا ندخل
+
+94
+00:06:29,730 --> 00:06:32,030
+الآن إلى التفاصيل
+
+95
+00:06:34,700 --> 00:06:38,940
+صلوا على النبي عليه الصلاة والسلام نشوف تفاصيل
+
+96
+00:06:38,940 --> 00:06:44,500
+الحديث الان بقول لي let E اللي وعدتكم فيها be the
+
+97
+00:06:44,500 --> 00:06:47,760
+set of all linear extensions عبارة عن كل ال linear
+
+98
+00:06:47,760 --> 00:06:52,160
+extensions بتسميها G لمين؟ لل F اللي احنا بدأنا
+
+99
+00:06:52,160 --> 00:06:55,900
+فيها that satisfy برضه هذه ال extension ليش بديها
+
+100
+00:06:55,900 --> 00:07:00,520
+يحقق G of X أصغر يساوي ب X لكل X وين موجود في
+
+101
+00:07:00,520 --> 00:07:04,790
+domain ال extension تبع G هذاهي الـ Ne عبارة عن
+
+102
+00:07:04,790 --> 00:07:08,930
+هذه العائلة أول إشي بقولك مدام العائلة هي عبارة عن
+
+103
+00:07:08,930 --> 00:07:12,830
+هذا ال F نفسها اللي موجودة اللي معطيني إياها أنا
+
+104
+00:07:12,830 --> 00:07:17,490
+هي نفسها تحقق هذه الشروط هي extension لنفسها على
+
+105
+00:07:17,490 --> 00:07:21,210
+نفس ال domain بس بتصير هو تحقق أن F of X أصغر سوى
+
+106
+00:07:21,210 --> 00:07:25,550
+B of X وفي نفس ال .. لكل X والي موجودة في domainها
+
+107
+00:07:25,550 --> 00:07:30,060
+اللي هو مين كان Zإذا أكيد أكيد أكيد ال F نفسه
+
+108
+00:07:30,060 --> 00:07:36,170
+الموجود في ال E إذا ال E is a non-empty setالشغلة
+
+109
+00:07:36,170 --> 00:07:41,910
+الثانية define on E a partial ordering by بدي اعرف
+
+110
+00:07:41,910 --> 00:07:44,870
+على ال D ايش ماله partial order relation اكيد انا
+
+111
+00:07:44,870 --> 00:07:47,950
+جاعد شغال في ال extension فهكيد هفكر في ال partial
+
+112
+00:07:47,950 --> 00:07:51,690
+order relation بناء على هذا ال extension فبصير
+
+113
+00:07:51,690 --> 00:07:54,350
+عندي الان المعرفه انا define on E a partial order
+
+114
+00:07:54,350 --> 00:07:58,890
+relation by D أصغر أو شومين Hكيف يكون G أصغر و
+
+115
+00:07:58,890 --> 00:08:04,310
+أصغر H؟ if and only if H is an extension of مين of
+
+116
+00:08:04,310 --> 00:08:08,490
+G يعني الآن بقول التنتين العنصرين اللي في E
+
+117
+00:08:08,490 --> 00:08:12,730
+بيكونون اللي انعلاقة في بعض إذا كان A شماله الـG
+
+118
+00:08:12,730 --> 00:08:17,710
+الـH extension لمين؟ للـG واضح؟ هذه هي ال partial
+
+119
+00:08:17,710 --> 00:08:24,160
+order relation طيبالان بدي اجيب .. بدي اخد اي
+
+120
+00:08:24,160 --> 00:08:28,600
+chain C subset من ايه و بدي اثبتلك ان ال chain C
+
+121
+00:08:28,600 --> 00:08:32,500
+هذه زي ما قلت هنا ال chain C .. بدي احقق شروط
+
+122
+00:08:32,500 --> 00:08:35,500
+zones لما ال chain .. ال .. ال chain C اخد
+
+123
+00:08:35,500 --> 00:08:39,380
+arbitrary ال chain C و اقولك لازم يكون فيها upper
+
+124
+00:08:39,380 --> 00:08:42,120
+bound اذا كان فيها upper bound automatic صار كل
+
+125
+00:08:42,120 --> 00:08:44,860
+chain اللي لها upper bound اذا حسب zones لما لازم
+
+126
+00:08:44,860 --> 00:08:49,290
+يكون لها ايش ما لها maximum element طيبالان for
+
+127
+00:08:49,290 --> 00:08:55,730
+any chain C subset من E define G hat بي G hat of X
+
+128
+00:08:55,730 --> 00:09:01,070
+بيساوي G X إذا كان X وين موجود في ال domain G و G
+
+129
+00:09:01,070 --> 00:09:04,870
+وين موجود في ال chain C يعني فرضا فرضا فرضا هي في
+
+130
+00:09:04,870 --> 00:09:12,120
+عند ال chain ال chain هي G واحدG2 G3 G4 إلى آخره
+
+131
+00:09:12,120 --> 00:09:14,720
+عنده هاي الـ Chain اللي موجودة عندي ماشي الحال
+
+132
+00:09:14,720 --> 00:09:18,560
+هدول ال Chain موجودة في الـ E كل واحدة كسنش لتالية
+
+133
+00:09:18,560 --> 00:09:24,760
+معايا اللي هم بده أعرف الـ G hat of X بساوي اللي
+
+134
+00:09:24,760 --> 00:09:29,050
+هو G of Xنفسها يعني الـ g hat of x هتساوي g واحد
+
+135
+00:09:29,050 --> 00:09:33,110
+of x إذا كان ال x في domain مين ال g واحد ويساوي g
+
+136
+00:09:33,110 --> 00:09:36,130
+اتنين of x إذا كان ال x في domain التالية و لا إيه
+
+137
+00:09:36,130 --> 00:09:40,810
+آخرية ونظرا لإنهم اتشينت هتلاقي إن ال g hat of x
+
+138
+00:09:40,810 --> 00:09:44,550
+لو كان عددهم finite هيكون ال g hat of x في الواقع
+
+139
+00:09:44,550 --> 00:09:48,980
+بساوي مين؟ g أربعة of xلأن كل واحد extension
+
+140
+00:09:48,980 --> 00:09:52,660
+للتانية فأي x في domain هذا حيكون في domain اللي
+
+141
+00:09:52,660 --> 00:09:57,640
+هو مين اللي جابتها فالآن g hat of x بيساوي g of x
+
+142
+00:09:57,640 --> 00:10:01,840
+إذا كانت x في domain الـ g ماشي خلوها دي في
+
+143
+00:10:01,840 --> 00:10:05,000
+الداكرةthen جيهة is a linear extension of
+
+144
+00:10:05,000 --> 00:10:08,680
+functional الجيهة تلاقي أنه صار أشمالها ووسعت
+
+145
+00:10:08,680 --> 00:10:13,780
+نفوذها عن من؟ عن اللي هي الـ F لأن هدولة كلها
+
+146
+00:10:13,780 --> 00:10:17,800
+extension للـ F فصارت الجيهة اللي هي معرفة على
+
+147
+00:10:17,800 --> 00:10:21,880
+أكبر domain فين هدولة اللي هو عبارة عن extension
+
+148
+00:10:21,880 --> 00:10:26,420
+صار extension functional، linear functional إذن
+
+149
+00:10:28,730 --> 00:10:33,410
+ذن جيهات is a linear functional and دي domain
+
+150
+00:10:33,410 --> 00:10:37,350
+جيهات بساوي الـun لمين لل domains اللي عندى اذا
+
+151
+00:10:37,350 --> 00:10:41,210
+بدك تتأكد ان هذه الجيهات linear functional يعني
+
+152
+00:10:41,210 --> 00:10:43,910
+عشان linear خد linear ماانتوا عارفين كيف linear
+
+153
+00:10:43,910 --> 00:10:49,890
+لذن تتأكد انها linear let x و y element ال main
+
+154
+00:10:49,890 --> 00:10:56,370
+and domainG hat ماشي الحال في domain الـ G hat ما
+
+155
+00:10:56,370 --> 00:10:58,790
+هي الـ G hat اللي هو domain هيه أشماله بيحتوي كل
+
+156
+00:10:58,790 --> 00:11:02,590
+ال domainات اللي عندي إذا عندي أو Alpha scalar
+
+157
+00:11:02,590 --> 00:11:07,970
+مثلا Alpha scalar بيصير عندي ال X و ال Y اللي هو
+
+158
+00:11:07,970 --> 00:11:11,090
+في domain الـ G hat اللي هو مين بيساوي ال union ل
+
+159
+00:11:11,090 --> 00:11:15,090
+domain الـ G G element المين in the chain ال chain
+
+160
+00:11:15,090 --> 00:11:21,290
+اللي مش عالق عليها بيصير عندي XElement X في ال
+
+161
+00:11:21,290 --> 00:11:24,150
+union و Y في element في ال union يعني هتكون X
+
+162
+00:11:24,150 --> 00:11:28,250
+element اللي هو في واحدة من هدول يعني only element
+
+163
+00:11:28,250 --> 00:11:34,530
+in domain G for some G element in main and C و ال
+
+164
+00:11:34,530 --> 00:11:40,030
+Y هتكون في domain G prime مثلا for some G element
+
+165
+00:11:40,030 --> 00:11:44,630
+in main .. G prime element in main and C واضح اللي
+
+166
+00:11:44,630 --> 00:11:49,660
+بحكيه؟ طيب يعني عند X و Y في domain G hatو domain
+
+167
+00:11:49,660 --> 00:11:52,740
+جي هات هو ال union إذا انصرت ال X و ال Y في ال
+
+168
+00:11:52,740 --> 00:11:57,160
+union بتكون ال X في واحدة من .. في واحدة من هدول و
+
+169
+00:11:57,160 --> 00:11:59,320
+ال Y في واحدة من هدول مش شرط تكونوا في نفس الوحدة
+
+170
+00:11:59,320 --> 00:12:02,940
+فX موجودة في domain الجي مثلا و Y في domain الجي
+
+171
+00:12:02,940 --> 00:12:06,860
+هات و الجي و الجي هات .. جي و الجي أبرايم موجودات
+
+172
+00:12:06,860 --> 00:12:12,570
+في ال C في ال chainالان في واحدة من هدولة تنتمي في
+
+173
+00:12:12,570 --> 00:12:15,890
+ال chain مادام في ال chain اكيد في واحد extension
+
+174
+00:12:15,890 --> 00:12:19,610
+لك تاني حسب التعريف ماشي الحال لأن كل اللي في ال
+
+175
+00:12:19,610 --> 00:12:23,870
+chain هي علاقة في بعض الان لو كانت ال جهات هي ال
+
+176
+00:12:23,870 --> 00:12:28,460
+extension بيصير ال x و ال y في دمية الجهاتمظبوط؟
+
+177
+00:12:28,460 --> 00:12:31,480
+لأنه extension إذا صارت الـ X والـ Y في domain الـ
+
+178
+00:12:31,480 --> 00:12:35,680
+G hat طيب ما هو صارت عندى في هذه الحالة اللى هو
+
+179
+00:12:35,680 --> 00:12:40,120
+الـ G الـ G اللى بدأنا فيها الـ X في domain الـ G
+
+180
+00:12:40,120 --> 00:12:43,400
+عشان إيش؟ بتبتلكم إن الـ G hat إيش معناه linear
+
+181
+00:12:43,400 --> 00:12:50,720
+إذا صارت عندى G hat of X أو Alpha X زائد Y بساوى
+
+182
+00:12:53,030 --> 00:12:58,890
+الان التنتين في domain مين الـ G prime إذا صارت
+
+183
+00:12:58,890 --> 00:13:01,010
+هذه الـ G hat هي نفس الـ G prime لأن الـ G hat
+
+184
+00:13:01,010 --> 00:13:04,150
+extension لها هتساويها في domainها و برا domainها
+
+185
+00:13:04,150 --> 00:13:09,930
+بتشتغل شغل تاني في G prime of Alpha X زائد Y و هي
+
+186
+00:13:09,930 --> 00:13:15,550
+ساوي Alpha G prime of X زائد G prime of Y وهذه
+
+187
+00:13:15,550 --> 00:13:20,390
+بتساوي Alpha G hat of X لأن G prime of X هي نفس
+
+188
+00:13:20,390 --> 00:13:26,720
+الـ G hat of Xdomainها زائد g hat of y وهذا يعني
+
+189
+00:13:26,720 --> 00:13:32,480
+أنه صارت الـ g hat إشمالها is linear إذن .. إذن يا
+
+190
+00:13:32,480 --> 00:13:36,500
+جماعة اللي أثبتناه الآن أن الـ g hat is a linear
+
+191
+00:13:36,500 --> 00:13:39,920
+functional و domain الـ g hat هو ال union لل
+
+192
+00:13:39,920 --> 00:13:43,040
+domains اللي عندنا كله العالمين اللي على الـ C
+
+193
+00:13:43,040 --> 00:13:47,640
+لإنه أنا معرفها الـ g hat عبارة عناللي هي
+
+194
+00:13:47,640 --> 00:13:55,120
+extension .. اه اللي هي ل .. معرفها ان جهات of X
+
+195
+00:13:55,120 --> 00:13:58,480
+بيساوي G of X لكل X في domain الجيه و .. ننزل ..
+
+196
+00:13:58,480 --> 00:14:04,520
+لأ و اللي هي ال .. ال domain ها هيكون اللي هو ال
+
+197
+00:14:04,520 --> 00:14:09,740
+union ل domain الجيه حسب التعريف الموضوع طيبالأن
+
+198
+00:14:09,740 --> 00:14:13,040
+الـ Union للـ Domains برضه بنفس الطريقة اللي أخدت
+
+199
+00:14:13,040 --> 00:14:17,040
+المشابهة لهذه برضه بتقدر تثبتها إن هي شمالها
+
+200
+00:14:17,040 --> 00:14:20,280
+Vector Space ماعش الحال اللي هي شئة الـ Vector
+
+201
+00:14:20,280 --> 00:14:23,920
+Space لو X و Y في Domain الجيهات مع أنها الـ X و
+
+202
+00:14:23,920 --> 00:14:25,820
+الـ Y موجودة في الـ Union مدام في الـ Union زي ما
+
+203
+00:14:25,820 --> 00:14:28,640
+عملت حيكون في واحدة منهم في ال .. إذن في ال
+
+204
+00:14:28,640 --> 00:14:32,300
+extension ل .. الأكبر في التنتين إذن حيكون و بما
+
+205
+00:14:32,300 --> 00:14:35,040
+إن Domain كل واحدة من ال extension Vector Space
+
+206
+00:14:35,040 --> 00:14:39,250
+إذن Automatic بتطلع فياللي هي ال union اتوكل الله
+
+207
+00:14:39,250 --> 00:14:45,090
+اذا vector space ارجع ليش جيت هان عندي ماشي اذا
+
+208
+00:14:45,090 --> 00:14:51,670
+عندي اللي هي اللي اللي اللي اللي صارت الجيهات فيها
+
+209
+00:14:51,670 --> 00:14:55,610
+اللي محقق كل الشروط الجيهات صارت عبارة عن
+
+210
+00:14:55,610 --> 00:15:01,720
+extension extension linear extension نفسهاوصارت
+
+211
+00:15:01,720 --> 00:15:06,400
+كمان الـ G hat أكبر يسوى G لكل مين لكل G وين
+
+212
+00:15:06,400 --> 00:15:10,320
+موجودة في ال chain إذا صارت الـ G hat نفسها عبارة
+
+213
+00:15:10,320 --> 00:15:13,900
+عن إيه؟ عبارة عن upper bound للـ C وكانت الـ C
+
+214
+00:15:13,900 --> 00:15:18,260
+مخدها يعني arbitrary chain إذا صار عند الـ non
+
+215
+00:15:18,260 --> 00:15:22,700
+-empty set الإيه اللي بحكي عنها is a non-empty
+
+216
+00:15:22,700 --> 00:15:28,370
+ordered setوالتي تحتوي على الـ Probability أن كل
+
+217
+00:15:28,370 --> 00:15:31,450
+قطعة تحتوي على قطعة أعلى ثم تحتوي على قطعة أعلى
+
+218
+00:15:31,450 --> 00:15:40,330
+باقية إذا بيزونز لما E لديه قطعة أعلى باقية افتل
+
+219
+00:15:40,330 --> 00:15:46,310
+ده افتل ده هذا اللي بتدعي أنه العنصر المطلوب هو
+
+220
+00:15:46,310 --> 00:15:50,360
+اللي هيكون ال extension اللي أنا طالبه على كل Xand
+
+221
+00:15:50,360 --> 00:15:54,240
+by the definition of E this is a linear extension
+
+222
+00:15:54,240 --> 00:15:57,920
+لأنه واحد من مين من اللي هو ال elements اللي في E
+
+223
+00:15:57,920 --> 00:16:02,360
+مظبوط ولا لأ؟ إذا هو ال E عبارة عن extensions إذا
+
+224
+00:16:02,360 --> 00:16:07,520
+ال F تلدة هيكون معله عبارة عن extension لل F ويحقق
+
+225
+00:16:07,520 --> 00:16:11,900
+حسب اللي هو تعريفه لل E هيحقق إنه F تلدة هو بيكس
+
+226
+00:16:11,900 --> 00:16:16,220
+أصغر سوى بيكس لكل X و M موجودة في domain ال F تلدة
+
+227
+00:16:17,330 --> 00:16:22,010
+الان اللى بدى أثبتلكم اللى ضال عليا انا هلجيت
+
+228
+00:16:22,010 --> 00:16:27,790
+اثبتتلكم ان F تلد عبارة عن extension لل F ويحقق F
+
+229
+00:16:27,790 --> 00:16:31,110
+تلد اصغر بساوية P of X لكل X و M موجودة في ال
+
+230
+00:16:31,110 --> 00:16:34,310
+domain F تلدة لو أثبتتلكم ال domain لل F تلدة
+
+231
+00:16:34,310 --> 00:16:38,660
+بساوية X بكون خلصتإذا نضل عليه إيش أثبت أنه domain
+
+232
+00:16:38,660 --> 00:16:42,780
+F تلده بساوي X لو أثبتتوا معيناته صار أنه F تلده
+
+233
+00:16:42,780 --> 00:16:47,400
+عبارة عن linear extension لل F و ال F تلده of X
+
+234
+00:16:47,400 --> 00:16:51,100
+أصغر بساوي P of X لكل X و إيه الموجودة في ال X وهو
+
+235
+00:16:51,100 --> 00:16:55,880
+المطلوب خلّينا نشوف اللي هو رحلة إثبات اللي هو
+
+236
+00:16:55,880 --> 00:16:59,820
+domain ال F تلده بساوي X بدنا نفترض العكس
+
+237
+00:17:08,320 --> 00:17:16,640
+خلّيني اختار Y1 في الـ X-Main-Domain Fماشي الحال
+
+238
+00:17:16,640 --> 00:17:21,380
+اللي بدأصلكم فيها contradiction انه بدأثبتلكم انه
+
+239
+00:17:21,380 --> 00:17:24,200
+في اشي اكبر من ال F تلد و هي ال maximum صار
+
+240
+00:17:24,200 --> 00:17:27,920
+contradiction شوف كيف يعني choose y واحد في ال X
+
+241
+00:17:27,920 --> 00:17:30,900
+minus main minus domain F تلد احنا بنقول domain F
+
+242
+00:17:30,900 --> 00:17:33,240
+تلد ده بتسويش X طبعا domain F تلد ده في نهاية
+
+243
+00:17:33,240 --> 00:17:38,550
+subset من X إذا في element هنا مش موجود هناY1 بطله
+
+244
+00:17:38,550 --> 00:17:41,630
+اللي موجود في domain الـ F اللي هان بدي أركب
+
+245
+00:17:41,630 --> 00:17:45,270
+subspace هو اللي هيجيب لي ال contradiction let Y1
+
+246
+00:17:45,270 --> 00:17:48,670
+be the subspace spanned by يعني الـ Y1 هو ال
+
+247
+00:17:48,670 --> 00:17:52,730
+subspace اللي spanned by domain الـ F تلد هذا اللي
+
+248
+00:17:52,730 --> 00:17:56,650
+بقول عنه ماسويش X بالإضافة لمين للـ Y1 اللي أخدتها
+
+249
+00:17:56,650 --> 00:18:02,810
+من هنا وموجودة هناالان واضح .. واضح ان الـ Y1 ده
+
+250
+00:18:02,810 --> 00:18:07,050
+مش هتساوي سفر ليش؟ لأن السفر موجود وين؟ في domain
+
+251
+00:18:07,050 --> 00:18:12,250
+F تلدة في الـ space أو vector space طيب .. مذا من
+
+252
+00:18:12,250 --> 00:18:16,250
+الـ zero element في domain F تلدة وانا ماخد الـ Y1
+
+253
+00:18:16,250 --> 00:18:19,430
+من ال X وبرّت ال domain F تلدة أكيد هو الـ Y1 ماله
+
+254
+00:18:19,430 --> 00:18:24,550
+مش السفر طيب .. إذا then Y1 ده تساوي سفر وكل X
+
+255
+00:18:24,550 --> 00:18:35,280
+الآن مدام أخدت الـ Y1الـ Y1 الـ
+
+256
+00:18:35,280 --> 00:18:44,000
+Y1 أخدتها عبارة عن الـ span بين الـ Y1 small و
+
+257
+00:18:44,000 --> 00:18:49,220
+domain الـ F تل ده فحقول لها أخدت ال span يعني أي
+
+258
+00:18:49,220 --> 00:18:52,300
+element هنا هيكون هنا combination بين هذه و بين
+
+259
+00:18:52,300 --> 00:18:58,010
+العناصر اللي هنا ماشي طيبالان اي x element y واحد
+
+260
+00:18:58,010 --> 00:19:02,030
+اللي وكّبته هذا can be written as x بتساوي element
+
+261
+00:19:02,030 --> 00:19:07,550
+من ال domain الاف تل ده زائد alpha between y واحد
+
+262
+00:19:07,550 --> 00:19:10,710
+واحد يقول لبيطا y هو البيطا y برضه وين موجود في ال
+
+263
+00:19:10,710 --> 00:19:15,070
+domain الاف تل ده فاهمين؟ فبتسميه y او بسميه z او
+
+264
+00:19:15,070 --> 00:19:19,690
+بسميه حرنة لإن اي mean اي أي scalar مضروف في هذا
+
+265
+00:19:20,460 --> 00:19:22,240
+عشان تقول الـ Linear combination ليش الـ Linear
+
+266
+00:19:22,240 --> 00:19:26,060
+combination X بالساوية Beta Y زايد Alpha Y واحد طب
+
+267
+00:19:26,060 --> 00:19:29,260
+ما هو الـ Beta Y موجود هان؟ لأن هذا عبارة عن
+
+268
+00:19:29,260 --> 00:19:31,960
+vector space فلو كانت الـ Y جوا ال Beta Y ورده جوا
+
+269
+00:19:31,960 --> 00:19:38,440
+فبتسميه Y أريح ليه طيب إذا أي X الآن موجودة في الـ
+
+270
+00:19:38,440 --> 00:19:42,600
+Y واحد can be written uniquely as Y زايد Alpha Y
+
+271
+00:19:42,600 --> 00:19:45,720
+واحد حيث Y في ال domain والـ Y واحد هي اللي احنا
+
+272
+00:19:45,720 --> 00:19:49,380
+حكينا عنها خلينا نقول إن عشان نثبت إن هذا واحد
+
+273
+00:19:50,060 --> 00:19:54,640
+إثبات بسيط سهل to see this to see أنه أنه واحد
+
+274
+00:19:54,640 --> 00:19:57,840
+suppose that فيه تنتين x بتساوي y زائد alpha y
+
+275
+00:19:57,840 --> 00:20:02,940
+واحد and x بتساوي y تلدة زائد مين beta y واحد يعني
+
+276
+00:20:02,940 --> 00:20:08,340
+عنصرين اللي هنا هذا و هذا يكون اللي هنا x بتساوي
+
+277
+00:20:08,340 --> 00:20:11,620
+كده يعني إنها صورتين بمعنى أخر ونتبت إن الصورتين
+
+278
+00:20:11,620 --> 00:20:15,320
+نفس الشيء يعني هتكون ال y هي ال y تلدة و ال alpha
+
+279
+00:20:15,320 --> 00:20:21,810
+هي مين ال beta شوفواخد الآن اترحم من بعض اترحم من
+
+280
+00:20:21,810 --> 00:20:25,670
+بعض او قول هذه بتساوي وهذه لان هذه بتساوي هذه
+
+281
+00:20:25,670 --> 00:20:29,810
+وانقل اللي هي ال Y تلده مع ال Y وانقل ال Y واحد مع
+
+282
+00:20:29,810 --> 00:20:33,250
+ال Y واحد بيصير عنده Alpha ناقص Beta في Y واحد
+
+283
+00:20:33,250 --> 00:20:37,770
+فاهمين؟ بيساوي Y تلده ناقص مين؟ ناقص Y ماشي الحل
+
+284
+00:20:37,770 --> 00:20:42,730
+هذه الان Y تلده وY واحد موجوديات في domain F تلده
+
+285
+00:20:42,730 --> 00:20:48,610
+صح ولا لا؟والـ Alpha نقص Beta في Y1 معروف الـ Y1
+
+286
+00:20:48,610 --> 00:20:52,790
+اللي موجودة في الـ X minus اللي هي domain F تلدة
+
+287
+00:20:52,790 --> 00:20:56,950
+هذه موجودة في domain الـ F تلدة والـ Y1 برا domain
+
+288
+00:20:56,950 --> 00:21:00,650
+الـ F تلدة إذا مستحيل هذا يساوي هذا إلا في حالة
+
+289
+00:21:00,650 --> 00:21:04,530
+واحدة إن هذا اللي هو يساوي يعني هذا سفر بساوي هياش
+
+290
+00:21:04,530 --> 00:21:11,720
+سفر إذا هذا العنصر في domain الـ F تلدةوهذا العنصر
+
+291
+00:21:11,720 --> 00:21:14,900
+في برّا domain الـ F تلدة لأنه ماخدينه في إئم الـ
+
+292
+00:21:14,900 --> 00:21:18,380
+X ناقص domain الـ F تلدة إذاً هذا يستحيل يكون
+
+293
+00:21:18,380 --> 00:21:22,180
+المساواة إلا إذا كانت Alpha ناقص Beta بتساوي سفر
+
+294
+00:21:22,180 --> 00:21:26,160
+وBot اللي هو Y واحد مش في domain الـ F تلدة وY
+
+295
+00:21:26,160 --> 00:21:30,040
+تلدة ناقص Y مش في domain الـ F إذاً Alpha ناقص
+
+296
+00:21:30,040 --> 00:21:33,320
+Beta بتساوي سفر ومن ثم Alpha بتساوي سفر ومعناته أن
+
+297
+00:21:33,320 --> 00:21:38,780
+Y تلدة هي الـ Y ومعناته أن الصورة صارت هذه وحيدةأه
+
+298
+00:21:38,780 --> 00:21:42,620
+والـ Alpha هي الـ Beta and this proves the
+
+299
+00:21:42,620 --> 00:21:46,860
+uniqueness of اللي هو representation لأن بدنا نعرف
+
+300
+00:21:46,860 --> 00:21:50,500
+اللي هو function اتوصلنا ل اللي هو ال
+
+301
+00:21:50,500 --> 00:21:55,900
+contradiction اللي بدنا يعرف طولوا
+
+302
+00:21:55,900 --> 00:22:01,780
+روحكم، البرهان طويل Define
+
+303
+00:22:01,780 --> 00:22:07,360
+G واحدمن Y1 لعنده Rπي عناصر الـ G1 اتفاقنا على هاي
+
+304
+00:22:07,360 --> 00:22:12,760
+شكلها G1 of Y زي الـ α Y1 بدي اعرفها كتالة بتساوي
+
+305
+00:22:12,760 --> 00:22:16,420
+اللي هو ال Y في domain ال F تلده فبدي أسويها بدي
+
+306
+00:22:16,420 --> 00:22:20,920
+أرسلها ل F تلده في domain of Y و هذه ال α Y1 بدي
+
+307
+00:22:20,920 --> 00:22:25,360
+ارسلها لالف في مين؟ في C في C for some constant
+
+308
+00:22:25,360 --> 00:22:30,080
+ماشي؟ إذا هاي ال G1 ال function اللي عندى where C
+
+309
+00:22:30,080 --> 00:22:34,840
+is any real constantIt is easy to see that G1 is
+
+310
+00:22:34,840 --> 00:22:38,400
+linear G1
+
+311
+00:22:38,400 --> 00:22:42,880
+is a linear functional خد شوف الـ G1 كيف ليناير خد
+
+312
+00:22:42,880 --> 00:22:48,000
+الآن any two elements فيه خلّينا ناخد Z بساوي
+
+313
+00:22:48,000 --> 00:22:56,600
+Alpha Y زائد Alpha Y واحد و Z prime بساوياللي هو
+
+314
+00:22:56,600 --> 00:23:05,440
+Y' زائد Beta Y1 مش هي شكل العناصر اللي في الـ Y1
+
+315
+00:23:05,440 --> 00:23:13,040
+اللي في الـ domain الان بتاخد الالد G1of Z زائد
+
+316
+00:23:13,040 --> 00:23:17,040
+Gamma زيد واحد مش هيك ابقنا نثبت انها Linear Y
+
+317
+00:23:17,040 --> 00:23:23,940
+ساوي الان جي واحد of Z ايش بتساوي Y زائد Alpha Y
+
+318
+00:23:23,940 --> 00:23:33,100
+واحد وهادي Y Prime هيها زائد Gamma في Y واحد زائد
+
+319
+00:23:33,100 --> 00:23:42,830
+Gamma في Beta في Y واحد صح ولا لأ Y ساويالأن جمعوا
+
+320
+00:23:42,830 --> 00:23:49,290
+اللي في domain الـ F تلدة مع بعض وتبعات الـ Y1 مع
+
+321
+00:23:49,290 --> 00:23:55,050
+بعض بيصير G1 of Y زائد Gamma Y1 هدولة كلهين وين
+
+322
+00:23:55,050 --> 00:24:00,610
+مالها في domain الـ F تلدة زائد هادي مع هادي اللي
+
+323
+00:24:00,610 --> 00:24:09,410
+عبارة عن Alpha Y1 زائد Gamma Beta Y1 وخلّي الـ Y1
+
+324
+00:24:09,410 --> 00:24:15,680
+مالهابرة فاهمين؟ حسب القانون اللي هو ايش معرفينه
+
+325
+00:24:15,680 --> 00:24:21,180
+احنا J1 بساوي F تلدة of هذه الكتلة زائد Alpha في C
+
+326
+00:24:21,180 --> 00:24:26,880
+بدل Y واحد Y ساوي هذا عبارة عن مين حسب التعريف
+
+327
+00:24:26,880 --> 00:24:34,410
+اللي هي F تلدة of Y زائد Gamma Y Primeوهذا كله
+
+328
+00:24:34,410 --> 00:24:39,630
+بيصير ايش ماله؟ زائد Alpha زائد Gamma في Beta في
+
+329
+00:24:39,630 --> 00:24:47,970
+مين؟ في C واضح هاه؟ ويساوي طويل
+
+330
+00:24:47,970 --> 00:24:53,900
+لكن سهل الهواء ويساويعندي ال F تلده نفسها Linear
+
+331
+00:24:53,900 --> 00:24:59,820
+مظبوط او لا اذا انا اخليك معناه انا F تلده of Y
+
+332
+00:24:59,820 --> 00:25:05,240
+زائد Gamma ف F تلده of Y Prime هذا الاولى لان F
+
+333
+00:25:05,240 --> 00:25:08,360
+تلده ليهاش معناه Linear وهذه constant بتوزع ال
+
+334
+00:25:08,360 --> 00:25:15,090
+constant زائدألفة في C زائد Gamma في Beta في مين
+
+335
+00:25:15,090 --> 00:25:19,910
+في C معايا خلّيني أجمح هدولة مع بعض هدولة التامتين
+
+336
+00:25:19,910 --> 00:25:28,370
+أيش بيساون تعريفها G1 of Y زائد Alpha Y واحد صح
+
+337
+00:25:28,370 --> 00:25:36,990
+ولا لأ هذي زائد هدولة عبارة عن Gamma في G1 of Y
+
+338
+00:25:36,990 --> 00:25:44,340
+واحد زائد Betaفى مين؟ فى Y1 صح ولا لأ؟ من التعريف
+
+339
+00:25:44,340 --> 00:25:51,580
+المباشرة وهذا معناته انه صارت هذا اللي هي Z وهذا
+
+340
+00:25:51,580 --> 00:26:01,160
+Z' يعني بسوء G1 of Z زائد G القامة G1 of Z' فبدأت
+
+341
+00:26:01,160 --> 00:26:09,490
+بهذه وانتهيت بهذه إذا فعلا G1 إيش مالها؟Is Linear
+
+342
+00:26:09,490 --> 00:26:16,420
+نيجي الآنفالفا بتساوي سفر إذا كانت الفا بتساوي سفر
+
+343
+00:26:16,420 --> 00:26:18,860
+عند الالفة هذه اللي .. اللي .. اللي اشتغلت فيها
+
+344
+00:26:18,860 --> 00:26:22,220
+هذه إذا كانت الفا واحد بتساوي .. الالفة بتساوي سفر
+
+345
+00:26:22,220 --> 00:26:27,780
+بيصير عند جي واحد of Y هيو جي واحد of Y هذا بيصير
+
+346
+00:26:27,780 --> 00:26:33,520
+سفر بيساوي F تلد مين of Y لكل Y موجودة في دمين ال
+
+347
+00:26:33,520 --> 00:26:38,400
+F تلدة وهذا معناته إيش أنه جي واحد is a proper
+
+348
+00:26:38,400 --> 00:26:42,840
+extension of مينو F tilde جي واحد extension لأنها
+
+349
+00:26:42,840 --> 00:26:48,000
+اشتغلت عالميا على ال elements هدولة و ساوت جي واحد
+
+350
+00:26:48,000 --> 00:26:53,020
+ساوت ال F تلد لل Y و فيها نفوذ أخرى ماشي الحال و
+
+351
+00:26:53,020 --> 00:26:56,080
+ليش هو proper لإن في element هذا ما هو احنا قولنا
+
+352
+00:26:56,080 --> 00:26:59,340
+عنه براة ال X هان المشكلة أصلا براة اللي هي ال
+
+353
+00:26:59,340 --> 00:27:04,480
+domain ال F tilde ماشي صارت عندنا جي واحد و Y زايد
+
+354
+00:27:04,480 --> 00:27:09,110
+Alpha Y واحداللي هي اللي بتساوي F tilde Y زائد
+
+355
+00:27:09,110 --> 00:27:14,870
+Alpha C هذا تعبر عن انه G1 extension لمين للـ F
+
+356
+00:27:14,870 --> 00:27:20,950
+tilde لإنه G1 هتساوي الـ F tilde لكل عناصر الـ Y و
+
+357
+00:27:20,950 --> 00:27:26,030
+M في دمية الـ F tildeوفي نفوذ أخر إلها اللي هو Y
+
+358
+00:27:26,030 --> 00:27:29,830
+زي الألف و Y واحد للألف لا تساوي سفر بترسل الأف تل
+
+359
+00:27:29,830 --> 00:27:34,130
+ده of Y زي الألف C يعني اشتغلت على اللي هو الأف تل
+
+360
+00:27:34,130 --> 00:27:37,490
+ده اللي هي domain الأف تل ده وما بعده اللي هو مين
+
+361
+00:27:37,490 --> 00:27:40,750
+ما بعد domain الأف تل ده اللي هو ال Y واحد هذا
+
+362
+00:27:40,750 --> 00:27:46,350
+اللي هو domain أف تل ده اتحاد ميناللي هو مش domain
+
+363
+00:27:46,350 --> 00:27:51,150
+الـ Y1 مين هو عبارة عن لسبان الـ Y1 عبارة عن هدى
+
+364
+00:27:51,150 --> 00:27:54,250
+عبارة عن مين؟ عن لسبان ل domain الـ F تلدى
+
+365
+00:27:54,250 --> 00:27:59,650
+بالاضافة للـ Y1 small ماشي؟ إذا أكيد صارت عندي GY1
+
+366
+00:27:59,650 --> 00:28:04,770
+of بتساوي F تلدى of Y for all ال domain F تلدى أدى
+
+367
+00:28:04,770 --> 00:28:09,030
+للسببين إنه G1 is a proper extension of مين؟ و F
+
+368
+00:28:09,030 --> 00:28:12,850
+تلدى يعني F تلدى X اللي هو G1 extension للـ F تلدى
+
+369
+00:28:13,450 --> 00:28:17,650
+وفي كمان اللي هو أكبر منه أو أوسع منه إذا أعرفنا
+
+370
+00:28:17,650 --> 00:28:21,810
+الأكبر أو يساوي كيف احنا في الـA إيش عرفنا الأكبر
+
+371
+00:28:21,810 --> 00:28:24,690
+أو يساوي؟ إنه G أكبر أو يساوي H ده كانت H
+
+372
+00:28:24,690 --> 00:28:30,130
+exceptional من 100 للـG لإن صارت أندي G واحد أكبر
+
+373
+00:28:30,130 --> 00:28:35,750
+أو يساوي من F تلدة وهنا ال contradiction لإنه إيش
+
+374
+00:28:35,750 --> 00:28:39,730
+ماله؟ اللي هو الـF تلدة .. قبل شوية قولنا maximum
+
+375
+00:28:39,730 --> 00:28:44,920
+elementماشي الحال اذا صار عندى بس في شغل ابنان
+
+376
+00:28:44,920 --> 00:28:49,400
+اثبتها however صار عند بروبر existential لكن انا
+
+377
+00:28:49,400 --> 00:28:52,580
+بدي اتجاوز هذه و بدي افترض ان الـG1 of X أصغر
+
+378
+00:28:52,580 --> 00:28:57,440
+شؤميا ب X لكل X where موجودة في domain G1 هذه الآن
+
+379
+00:28:57,440 --> 00:29:01,750
+بدي اثبتهابس خلّينا و كأننا مثبتينها صارت عندي
+
+380
+00:29:01,750 --> 00:29:06,410
+اللي هو لإنه أنا شغل في الإيدي لبالك شغل بقول إن
+
+381
+00:29:06,410 --> 00:29:11,150
+الـG أصغر يساوي H بيحتمل .. ال .. ال .. ال .. ال
+
+382
+00:29:11,150 --> 00:29:14,850
+.. خلّيني أقول شرطين الشرط الأول إن الـH تكون
+
+383
+00:29:14,850 --> 00:29:19,870
+extension للـG هذه واحدة و الشرط الثاني إنه يحقق
+
+384
+00:29:19,870 --> 00:29:25,350
+إن الـH of X أصغر يساوي P of X لكل X موجودة في
+
+385
+00:29:25,350 --> 00:29:30,230
+domain main الـHالان اللي حققته انا بالنسبة للأفتل
+
+386
+00:29:30,230 --> 00:29:33,750
+ده الـ G1 حققت شغلة انه الـ G1 هو Property
+
+387
+00:29:33,750 --> 00:29:38,450
+Essential له لكن لسه ضال بده حقق انه الـ G1 of X
+
+388
+00:29:38,450 --> 00:29:44,190
+أصغر سواء P of X لكل X و N موجود في Domain الـ G1
+
+389
+00:29:44,530 --> 00:29:50,590
+ماشي الحل فضلنا نحققنا صرنا حصلين على g1 اللي هو
+
+390
+00:29:50,590 --> 00:29:54,430
+extension لـ f تل ده و يحقق هذه يعني الـ g1 صار
+
+391
+00:29:54,430 --> 00:29:58,170
+وين موجود؟ في الـ E و أكبر من مين؟ من الـ f تل ده
+
+392
+00:29:58,170 --> 00:30:04,050
+Contradiction فبصير الآن hence g1 element الـ E
+
+393
+00:30:04,050 --> 00:30:07,190
+which is contradicts the maximality of f تل ده
+
+394
+00:30:07,190 --> 00:30:10,330
+Therefore ال domain لـ f تل ده إيش بساوي؟ بساوي x
+
+395
+00:30:10,330 --> 00:30:17,070
+و هيك بكون نهينا البرهان لوأثبتنا هذه اللي انا بدأ
+
+396
+00:30:17,070 --> 00:30:22,210
+أثبتها دل عليها خلّينا نثبتها وهذه برضه قصة اللي
+
+397
+00:30:22,210 --> 00:30:24,630
+انا اشضل عنديا يا جماعة انا بدأ أثبتلكم الـ G1 و
+
+398
+00:30:24,630 --> 00:30:29,770
+Fx أظهر سوء بيه و Fx لكل X والي موجود في domain
+
+399
+00:30:29,770 --> 00:30:34,610
+الـ G1 دلع فوق يا عزيزي دلع فوق يا عزيزي دلع فوق
+
+400
+00:30:34,610 --> 00:30:38,150
+يا عزيزي دلع فوق يا عزيزي دلع فوق يا عزيزي دلع فوق
+
+401
+00:30:38,150 --> 00:30:38,870
+يا عزيزي دلع فوق يا عزيزي دلع فوق يا عزيزي دلع فوق
+
+402
+00:30:38,870 --> 00:30:41,670
+يا عزيزي دلع فوق يا عزيزي دلع فوق يا عزيزي دلع فوق
+
+403
+00:30:41,670 --> 00:31:00,880
+ياالتالي بكون خلصت نظرية هضل
+
+404
+00:31:00,880 --> 00:31:04,420
+عليّ أنه اتصلوا على النبي و بدأ اثبتلكم عليه
+
+405
+00:31:04,420 --> 00:31:11,230
+الصلاة والسلام انه G1 of X أظهر يساوي P of Xلكل X
+
+406
+00:31:11,230 --> 00:31:16,310
+بتساوي Y زي Alpha Y واحد اللي هنا و هنا موجودات في
+
+407
+00:31:16,310 --> 00:31:19,010
+domain الجي واحد اللي هو كان عبارة عن ال span
+
+408
+00:31:19,010 --> 00:31:23,470
+لاللي هو domain الاف تلده بالاضافة لل Y واحد هاي
+
+409
+00:31:23,470 --> 00:31:27,790
+اللي بتثبته ماشي الحال خلينا ناخد حلوات الآن
+
+410
+00:31:27,790 --> 00:31:33,370
+finally to prove one اللي حكينا عنها let Y و Z
+
+411
+00:31:33,370 --> 00:31:36,590
+element in domain mean الاف تلده ده ماخدينه في
+
+412
+00:31:36,590 --> 00:31:38,730
+domain الاف تلده صبر عليها عشان نصركم للي بتكونوا
+
+413
+00:31:38,730 --> 00:31:47,250
+يعنيfor any y1 element in x f tilde of y ناقص f
+
+414
+00:31:47,250 --> 00:31:55,230
+tilde of z بساوية f .. هذه لأي y1 وين من ضمنها ال
+
+415
+00:31:55,230 --> 00:31:59,050
+y1 اللي فوق لأي واحد في الدنيا في ال x من ضمنها
+
+416
+00:31:59,050 --> 00:32:02,870
+مين ال y1 اللي فوق f tilde of y ناقص f tilde of z
+
+417
+00:32:02,870 --> 00:32:03,510
+ايش بتساوي
+
+418
+00:32:10,210 --> 00:32:13,770
+الآن الـ y و الـ z دول الموجودة في الـ F تلدة والـ
+
+419
+00:32:13,770 --> 00:32:17,850
+F تلدة دول الموجودة في الـ E إذا تحقق الشرط إن
+
+420
+00:32:17,850 --> 00:32:24,550
+أصغر يساوي P of y minus z و P اللي عندي بتساويالذى
+
+421
+00:32:24,550 --> 00:32:28,870
+ضيف رقم او اطرح رقم الذى ضيف بي of y زائد y واحد
+
+422
+00:32:28,870 --> 00:32:33,010
+ناقص y واحد ناقص z اللي مين هذا اللي اطرحته واضفته
+
+423
+00:32:33,010 --> 00:32:36,790
+ماشي الحال هذا الان ماهي ال b عبارة عن linear
+
+424
+00:32:36,790 --> 00:32:40,510
+extension sub linear مدام ال b sub linear ده
+
+425
+00:32:40,510 --> 00:32:46,030
+الأصغر شوي بي y واحد زائد y زائد b للتاني مظبوط
+
+426
+00:32:46,030 --> 00:32:49,990
+اللي هو ناقص y ناقص z استخدمت خاصية main انه
+
+427
+00:32:49,990 --> 00:32:56,650
+extensionthen خلّينا أهل جهة حسابات بدي قاعد أنجل
+
+428
+00:32:56,650 --> 00:33:01,830
+أي عندي هذه وصلت أصغر أو أسوأ هذه ماشي هذه مع هذه
+
+429
+00:33:01,830 --> 00:33:05,030
+هذه مع هذه شوف الآن بدي أنجل هذه أجيبها على الطرف
+
+430
+00:33:05,030 --> 00:33:09,450
+التاني بيصير سالب سالب P minus Y واحد ناقص Z ناقص
+
+431
+00:33:09,450 --> 00:33:13,310
+F tilde of Z و بدي ألجأ أودي F tilde of Y وين على
+
+432
+00:33:13,310 --> 00:33:16,450
+الجهة التانية اللي هي أصغر أو أسوأ P of Y واحد
+
+433
+00:33:16,450 --> 00:33:19,710
+زائد Y اللي ما نجلتاش ناقص F tilde of Z اللي
+
+434
+00:33:19,710 --> 00:33:26,580
+نجلتهاالان هذا الكلام صحيح .. صحيح لأي y و z و لأي
+
+435
+00:33:26,580 --> 00:33:35,420
+mean y واحد صحيح دايما الان صارت عندي الان for any
+
+436
+00:33:35,420 --> 00:33:39,840
+fixed y for any fixed y صار هذا أكبر أو يساوي هذا
+
+437
+00:33:39,840 --> 00:33:45,720
+لكل mean لكل ال z صار هذا upper bound للمجموعة هذه
+
+438
+00:33:46,480 --> 00:33:50,200
+اللي هي the set of all اللي هي .. اللي هي القيم
+
+439
+00:33:50,200 --> 00:33:53,780
+اللي على الصورة هذه لكل Z في الدنيا، ماشي الحال؟
+
+440
+00:33:53,780 --> 00:33:56,900
+صار هذا upper bound لهذا، for any fixed Y واحد،
+
+441
+00:33:56,900 --> 00:34:00,580
+اعمل fixation للـY واحد، و fixation لمين؟ للـY،
+
+442
+00:34:00,580 --> 00:34:04,420
+لكن Y والـY واحد اربترا ليه، صار هذا المقدار أكبر
+
+443
+00:34:04,420 --> 00:34:08,060
+أو يساوي هذا المقدار لكل Z في الدنيا، إذا صار هذا
+
+444
+00:34:08,060 --> 00:34:11,440
+المقدار upper bound لهذه، إذا أكيد أكبر أو يساوي
+
+445
+00:34:11,440 --> 00:34:15,420
+السبريمام إلهم،ماشي الحال إذا صار عبارة هذا أكبر
+
+446
+00:34:15,420 --> 00:34:19,380
+أو يساوي ال supremum لهدولة من المتغير الآن هو
+
+447
+00:34:19,380 --> 00:34:22,540
+الذنب ماشي الحال إذا صار اللي هو اللي سميته ال
+
+448
+00:34:22,540 --> 00:34:27,060
+supremum هذا ال U هذا ال U لأن هذا upper bound و
+
+449
+00:34:27,060 --> 00:34:30,760
+ال supremum ليس upper bound فطبيعي اللي هو عبارة
+
+450
+00:34:30,760 --> 00:34:34,700
+عن ال supremum هيكون أصغر أو ساوي من هذا فاهمين؟
+
+451
+00:34:34,700 --> 00:34:39,720
+إذا صار U أصغر أو ساوي هذا صار الآن ال U نفسهاللي
+
+452
+00:34:39,720 --> 00:34:44,260
+هو Lower Bound Lower Bound صار الـ U أصغر أو يساوي
+
+453
+00:34:44,260 --> 00:34:48,120
+هذا لكل الوايات اللي في الدنيا صار الـ U Lower
+
+454
+00:34:48,120 --> 00:34:52,180
+Bound لهذا إذا مدام Lower Bound إذا الـ U أكيد
+
+455
+00:34:52,180 --> 00:34:56,220
+أصغر أو يساوي من الـ Greatest Lower Bound ماشي؟
+
+456
+00:34:56,220 --> 00:34:58,780
+اللي هو الـ Infamous إذا صار عندي الآن الـ
+
+457
+00:34:58,780 --> 00:35:01,540
+Supremum هذا اللي هو الـ U أصغر أو يساوي الـ
+
+458
+00:35:01,540 --> 00:35:04,980
+Infamous لهذه اللي هو من الـ W صار عندي اللي هو
+
+459
+00:35:04,980 --> 00:35:11,540
+الـ U أصغر أو يساوي إيش الـ Wالان مادام هذا الرقم
+
+460
+00:35:11,540 --> 00:35:16,220
+اصغر شوهو هذا اذا اكيد بقدر الاقي فيه ايش then
+
+461
+00:35:16,220 --> 00:35:20,120
+there is a real number C بينهم such that C أكبر
+
+462
+00:35:20,120 --> 00:35:24,740
+شوهو U و اصغر شوهو مين W قطعا between any two real
+
+463
+00:35:24,740 --> 00:35:28,000
+numbers there exist infinite number of real
+
+464
+00:35:28,000 --> 00:35:28,400
+numbers
+
+465
+00:35:31,730 --> 00:35:34,850
+حتى لو كان واحد اصغر اشتوى التاني بيصير هو اللي
+
+466
+00:35:34,850 --> 00:35:39,510
+المساواة هو الرقم اللي بنحكي عنه و لو كان strictly
+
+467
+00:35:39,510 --> 00:35:48,850
+بتلاقي فترة مش عددها بعايا اه اطلع لفوق الان saw
+
+468
+00:35:48,850 --> 00:35:54,430
+that هيصير عندى لأ بس خليني ازل شوية عشان انا اعرف
+
+469
+00:35:54,430 --> 00:36:01,840
+انها الان عندى اللي هو ناقصناقص بي واحد ناقص كذا
+
+470
+00:36:01,840 --> 00:36:08,680
+هذا ال U ال U هذا اه و هذا مين ال W صار عند ال C
+
+471
+00:36:08,680 --> 00:36:14,900
+أصغر أو يساوي اللي هو ال W اه معايا اه و صارت اللي
+
+472
+00:36:14,900 --> 00:36:20,800
+هو ال U أصغر أو يساوي مين ال C لأن هذا ال U و هذا
+
+473
+00:36:20,800 --> 00:36:26,970
+مين ال Wمعايا؟ طيب إذن الآن صار عندي so that نشتغل
+
+474
+00:36:26,970 --> 00:36:30,630
+على هذه ناقص B minus Y واحد ناقص Z ناقص كذا أصغر
+
+475
+00:36:30,630 --> 00:36:34,450
+أو شواء و C لكل Z و N في domain F تلتة سميه اتنين
+
+476
+00:36:34,450 --> 00:36:38,310
+هذا هنرجعله و ال C أصغر أو شواء هذا المقدار لكل Y
+
+477
+00:36:38,310 --> 00:36:41,370
+و N في domain F تلتة و سميه تلتة اتنين هذا وهذا
+
+478
+00:36:41,370 --> 00:36:45,730
+وهذا هو اللي هستخدمه للوصول اللي بديه طيب اطلع على
+
+479
+00:36:45,730 --> 00:36:49,870
+فوق to prove one to prove one اللي احنا بدنا
+
+480
+00:36:49,870 --> 00:36:56,460
+نثبتهاWe have three steps بدنا ناخد case للألفة هي
+
+481
+00:36:56,460 --> 00:36:59,700
+بدأت بتهون هيها هيها بدأ أخد ألفة مرة اللي هي
+
+482
+00:36:59,700 --> 00:37:05,240
+سالبة مرة موجبة مرة بصفر ماشي الحال بصفر سهلة نيجي
+
+483
+00:37:05,240 --> 00:37:08,540
+الآن الموجبة بدأ استخدم فيها مثلا ال upper bound
+
+484
+00:37:08,540 --> 00:37:14,300
+ال U والأصغر من صفر بدأ استخدم التاني أو العكس
+
+485
+00:37:14,300 --> 00:37:18,620
+واضح ليش جسمت؟ عشان واحدة بنفعلها اللي هي السالب
+
+486
+00:37:18,620 --> 00:37:23,830
+وواحدة بنفعلها الأمين للموجب بس هي كل القصةطيب
+
+487
+00:37:27,020 --> 00:37:28,460
+أول خطوة أول خطوة أول خطوة أول خطوة أول خطوة أول
+
+488
+00:37:28,460 --> 00:37:29,860
+ألف أصغر من مين من سفر أول خطوة أول خطوة أول خطوة
+
+489
+00:37:29,860 --> 00:37:31,420
+أول ألف أصغر من مين من سفر أول خطوة أول خطوة أول
+
+490
+00:37:31,420 --> 00:37:37,900
+خطوة أول خطوة أول ألف أصغر من مين من سفر أول خطوة
+
+491
+00:37:37,900 --> 00:37:40,060
+أول خطوة أول خطوة أول خطوة أول ألف أصغر من مين من
+
+492
+00:37:40,060 --> 00:37:40,760
+سفر أول خطوة أول خطوة أول خطوة أول خطوة أول أصغر
+
+493
+00:37:40,760 --> 00:37:47,600
+من مين من سفر أول خطوة أول خطوة أول خطوة أول أصغر
+
+494
+00:37:47,600 --> 00:37:54,300
+من مين من سفر
+
+495
+00:37:54,430 --> 00:37:59,750
+التفاصيل اللي عندكم في دي حسابات يعني ناقص بي لأن
+
+496
+00:37:59,750 --> 00:38:08,190
+بتدعوا بتدعملكم إيه هش بتسويش شوف هي عندي اللي هي
+
+497
+00:38:08,190 --> 00:38:17,130
+اتنين ناقص بي of y واحد ناقص zناقص F of Z أصغر أو
+
+498
+00:38:17,130 --> 00:38:22,290
+شوه 100 أصغر أو شوه C بقوللي أول حاجة حط Z أيش
+
+499
+00:38:22,290 --> 00:38:28,090
+بيساوي Alpha inverse في Y حط ليه ناقص B ناقص Y وحط
+
+500
+00:38:28,090 --> 00:38:32,150
+مكان ال Z 100 Alpha inverse في Y ليه بيصير ناقص
+
+501
+00:38:32,150 --> 00:38:39,990
+Alpha inverse Y صح ولا لأ ناقص F of Alpha inverse
+
+502
+00:38:39,990 --> 00:38:46,160
+100 Yأصغره يساوي عياش اللي هو عياش C و بعدين
+
+503
+00:38:46,160 --> 00:38:50,980
+بقوللي اضرب اضرب اللي هو الجهتين اللي هو then
+
+504
+00:38:50,980 --> 00:38:55,120
+multiply both sides by ناقص Alpha اضرب الجهتين في
+
+505
+00:38:55,120 --> 00:38:58,940
+ناقص Alpha ال Alpha سالبة ناقص Alpha موجلة إذا انه
+
+506
+00:38:58,940 --> 00:39:02,480
+خلاص كمية موجلة بتبقى لها إشارة هذي بيصير Alpha و
+
+507
+00:39:02,480 --> 00:39:08,200
+هذي بيصير Alpha و هذي بيصير صح سالب Alpha في C
+
+508
+00:39:09,970 --> 00:39:14,350
+معايا؟ هي طلعت عندنا اللي بدوياها الان بدك ال ..
+
+509
+00:39:14,350 --> 00:39:19,050
+ال .. ال .. خد الان انا بدي اثبت انه g1 of x اه؟
+
+510
+00:39:19,050 --> 00:39:22,210
+هي بدي اثبتها اصغر شوة ومين بيه of x خد g1 of x
+
+511
+00:39:22,210 --> 00:39:27,730
+انت صار عندى g1 of x اللي هي g1 of y زي ده alpha
+
+512
+00:39:27,730 --> 00:39:32,750
+y1 واضحة تاني اه؟ اللي هي بتساوي حسب تعريف الـ g1
+
+513
+00:39:32,750 --> 00:39:42,180
+ايش بتساوي؟أف تلدة لل Y زي ألفة في C أف
+
+514
+00:39:42,180 --> 00:39:45,140
+تلدة لل Y زي ألفة في C أف تلدة لل Y زي ألفة في C
+
+515
+00:39:45,140 --> 00:39:45,140
+أف تلدة لل Y زي ألفة في C أف تلدة لل Y زي ألفة في
+
+516
+00:39:45,140 --> 00:39:46,480
+C أف تلدة لل Y زي ألفة في C أف تلدة لل Y زي ألفة
+
+517
+00:39:46,480 --> 00:39:47,580
+في C أف تلدة لل Y زي ألفة في C أف تلدة لل Y زي
+
+518
+00:39:47,580 --> 00:39:48,840
+ألفة في C أف تلدة لل Y زي ألفة في C أف تلدة لل Y
+
+519
+00:39:48,840 --> 00:39:53,060
+زي ألفة في C أف تلدة لل Y زي ألفة في C أف تلدة لل
+
+520
+00:39:53,060 --> 00:39:58,760
+Y زي ألفة في C أف تلدة لل Y زي ألفة في C أف تلدة
+
+521
+00:39:58,760 --> 00:40:04,650
+لل Y زي ألفة فيهذه صارت Alpha F tilde of Alpha
+
+522
+00:40:04,650 --> 00:40:09,830
+inverse Y أصغر أو يساوي أنجلها على الطرف التاني
+
+523
+00:40:09,830 --> 00:40:15,830
+Alpha في Beta ناقص Y ناقص Alpha inverse Y ناقص صح
+
+524
+00:40:15,830 --> 00:40:22,410
+ولا لأ ناقص مين Alpha في C صحيك هاه هي هذه بس نجلت
+
+525
+00:40:22,410 --> 00:40:28,300
+هذه على الجهة التانية عشان بس اعملها هنادخلها دي
+
+526
+00:40:28,300 --> 00:40:34,460
+جوا لانه بدوش إياها دخلها
+
+527
+00:40:34,460 --> 00:40:41,780
+جوا بتسيرواضح هاه؟ اذا صار عندي جي واحد of X
+
+528
+00:40:41,780 --> 00:40:46,720
+بتساوي Alpha of Y زي Alpha C شيل هذه بتصير أصغر أو
+
+529
+00:40:46,720 --> 00:40:51,200
+ساوي هذا المقدار أصغر أو ساوي ناقص Alpha في ال
+
+530
+00:40:51,200 --> 00:40:56,320
+Beta ناقص Alpha C و ال Alpha C وين ال Alpha C اللي
+
+531
+00:40:56,320 --> 00:41:03,960
+في الأصل ما هي ناقص Alpha C جي واحد of X بتساوي
+
+532
+00:41:03,960 --> 00:41:06,640
+كده ناقص
+
+533
+00:41:09,190 --> 00:41:12,430
+زائد alpha c زائد alpha c مع نقص ال alpha c بروح
+
+534
+00:41:12,430 --> 00:41:17,190
+مع بعض واضح هادي زائد هادي إذا أنت بدك تريح حالك
+
+535
+00:41:17,190 --> 00:41:21,370
+من الأول ان جيه زي ما بدك تريح حالك بصير زائد هادي
+
+536
+00:41:21,370 --> 00:41:25,550
+زي هاديهذه الكاملة أصغر أو ساوي هذا المقدار هيك
+
+537
+00:41:25,550 --> 00:41:30,930
+ممكن أسهلها أصغر أو ساوي ناقص Alpha في Beta وكذا
+
+538
+00:41:30,930 --> 00:41:36,450
+إلى آخرين دخل ناقص Alpha جوا بيصير عبارة عن ناقص
+
+539
+00:41:36,450 --> 00:41:41,860
+Alpha في Alpha inverse بيصير Y لحالهاY وناقص Alpha
+
+540
+00:41:41,860 --> 00:41:46,000
+في هذه ناقص يصبح Alpha Y واحد اللي هي في الواقع
+
+541
+00:41:46,000 --> 00:41:49,300
+هذه مين اسمها X فصارت عندي الان D واحد of X أصغر
+
+542
+00:41:49,300 --> 00:41:50,980
+شويه مين بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+543
+00:41:50,980 --> 00:41:52,500
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+544
+00:41:52,500 --> 00:41:52,500
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+545
+00:41:52,500 --> 00:41:52,920
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+546
+00:41:52,920 --> 00:42:08,100
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بي
+
+547
+00:42:08,130 --> 00:42:11,730
+اللي أصغر من واحد الـ α أكبر من واحد نفس الأشياء
+
+548
+00:42:11,730 --> 00:42:15,470
+بس بتستخدم مين بدل ما تستخدم اللي هي الاتنين
+
+549
+00:42:15,470 --> 00:42:19,430
+بتستخدم تلاتة بدل ما تستخدم الـ U و علاقتها بالـ C
+
+550
+00:42:19,430 --> 00:42:23,770
+بتستخدم الـ W و علاقتها بالـ C يلا اقولنا تجمع الـ
+
+551
+00:42:23,770 --> 00:42:28,690
+W اطلع لفوق خد الـ α الصفر سهلةالـ second step هو
+
+552
+00:42:28,690 --> 00:42:32,550
+الـ α بتساوي صفر ثم X أيش بتساوي؟ فهتصير الـ X
+
+553
+00:42:32,550 --> 00:42:35,670
+بتساوي الـ α Y زايد كده هتصير بتساوي إيش مالها؟ Y
+
+554
+00:42:35,670 --> 00:42:39,390
+وين موجودة؟ في الـ domain الـ F تلدة و G1 of X أيش
+
+555
+00:42:39,390 --> 00:42:42,870
+هيساوي؟ F تلدة of Y حسب التعريف اللي هي أصغر يساوي
+
+556
+00:42:42,870 --> 00:42:46,390
+مين؟ P of Y لأن الـ Y هدم هي الـ F تلدة من تعريفها
+
+557
+00:42:46,390 --> 00:42:48,930
+extension وتحقق خادة لأن الـ F تلدة موجودة في الـ
+
+558
+00:42:48,930 --> 00:42:52,030
+Eاذا انصرت الافتيل ده y أصغر ساوي P of Y اللي هي
+
+559
+00:42:52,030 --> 00:42:55,050
+بيساوي P of X لإنه Alpha سفر Thus one is true إن
+
+560
+00:42:55,050 --> 00:42:59,510
+Alpha بيساوي سفر Third step وإن Alpha أشمالها أكبر
+
+561
+00:42:59,510 --> 00:43:02,490
+من سفر انزل عشان تشوف تلاتة بنفس الوثنوب دي شعيده
+
+562
+00:43:04,030 --> 00:43:07,470
+بنفس الأسلوب اطلع خلّيها بس هذه اطلع لفوق شوية
+
+563
+00:43:07,470 --> 00:43:13,950
+ايوة بقى لأ خلّي ايوة اكملي شوية بس طيب الان when
+
+564
+00:43:13,950 --> 00:43:18,810
+alpha الان اكبر من سفر by تلاتة ماشي الحال but
+
+565
+00:43:18,810 --> 00:43:24,250
+triples y by minus مين ما لها alpha ناقص y ماشي
+
+566
+00:43:24,250 --> 00:43:28,370
+الحال and then multiply both sides by مين by alpha
+
+567
+00:43:28,370 --> 00:43:31,260
+to getأكيد بتحصلوا على هذا المقدار نفس الأسلوب
+
+568
+00:43:31,260 --> 00:43:33,980
+اللي قبل بشوية بالظبط اللي شراحته Alpha C أصغر
+
+569
+00:43:33,980 --> 00:43:37,840
+ساوي هذا المقدار هذا المقدار الآن Alpha بتدخله ال
+
+570
+00:43:37,840 --> 00:43:41,500
+Alpha جوه و بتشتغل و كده بنفس الأسلوب هتطلع عندى
+
+571
+00:43:41,500 --> 00:43:45,620
+هذه لما تدخلها دي بيصير بي و اي زايد Alpha Y واحد
+
+572
+00:43:45,620 --> 00:43:49,140
+اللي هي X بي of X فبيصير هذه بي of X و هذه ال
+
+573
+00:43:49,140 --> 00:43:52,240
+Alpha بتدخلوها جوه بيصير اللي هي F tilde of Y
+
+574
+00:43:52,240 --> 00:43:56,640
+مفهوم اه فبيصير عندي الآن Alpha C أصغر ساوي بي of
+
+575
+00:43:56,640 --> 00:44:00,750
+X زايد هذه اطلع لفوق الآنحصلنا على هذه منها بدنا
+
+576
+00:44:00,750 --> 00:44:03,490
+نحصل جي واحد و فيكس اللي هو اش مساوي بنفس الأسلوب
+
+577
+00:44:03,490 --> 00:44:07,210
+برضه اللي هو F تلد of Y زائد Alpha C Alpha tilde
+
+578
+00:44:07,210 --> 00:44:11,790
+of Y هيها زائد Alpha C أصغر من مين من بي و فيكس
+
+579
+00:44:11,790 --> 00:44:16,120
+لما نجلها هيها هادي هادي نجلها هان بالسيرaf tilde
+
+580
+00:44:16,120 --> 00:44:20,120
+of y زي ده alpha c أصغر من b of x ده حسابات كلها و
+
+581
+00:44:20,120 --> 00:44:23,140
+حسبنا زيها فبصير عند af tilde of y زي ده alpha c
+
+582
+00:44:23,140 --> 00:44:26,860
+أصغر سواء بيه of x إذا كانت برضه صحيحة في حالة مين
+
+583
+00:44:26,860 --> 00:44:29,520
+ال alpha أكبر من سفره ولا أصغر من سفره و بيه أصغر
+
+584
+00:44:29,520 --> 00:44:29,860
+من أصغر من أصغر من أصغر من أصغر من أصغر من أصغر من
+
+585
+00:44:29,860 --> 00:44:32,360
+أصغر من أصغر من أصغر من أصغر من أصغر من أصغر من
+
+586
+00:44:32,360 --> 00:44:35,260
+أصغر من أصغر من أصغر من أصغر من أصغر من أصغر من
+
+587
+00:44:35,260 --> 00:44:41,860
+أصغر من أصغر من أصغر من أصغر من أصغر من أص
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/VEACdbo-6Yo.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/VEACdbo-6Yo.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7905f6bc793483cbf37db0ac73b3ec8c80ed42de
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/VEACdbo-6Yo.srt
@@ -0,0 +1,2111 @@
+1
+00:00:05,040 --> 00:00:07,720
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,720 --> 00:00:10,680
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:10,680 --> 00:00:15,420
+آله وصحبه أجمعين هذه المحاضرة رقم 24 مساق تحليل 
+
+4
+00:00:15,420 --> 00:00:19,000
+الاقتران أو تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:19,000 --> 00:00:23,160
+الإسلامية ماجستير رياضيات وكل عام وأنتم بخير
+
+6
+00:00:23,160 --> 00:00:27,860
+مناسبة عيد الفطر المبارك اليوم إن شاء الله هيكون 
+
+7
+00:00:27,860 --> 00:00:31,100
+في عندنا الحديث عن اللي هي 3.9 اللي هو 
+
+8
+00:00:31,100 --> 00:00:33,080
+Hilbert Adjoint Operator
+
+9
+00:00:35,310 --> 00:00:40,750
+الموضوع اليوم هو موضوع خلّنا نقول من الموضوعات
+
+10
+00:00:40,750 --> 00:00:45,170
+المهمة في الـ operator theory طبعًا بدايات الحديث في
+
+11
+00:00:45,170 --> 00:00:50,430
+الـ operator theory هنشوف أنواع لـ operators هنحكي عن 
+
+12
+00:00:50,430 --> 00:00:53,790
+الـ Adjoint Operator هنحكي عن اللي هو الـ Normal 
+
+13
+00:00:53,790 --> 00:00:57,070
+Operator والـ Unitary والـ Self Adjoint إلى آخره
+
+14
+00:00:57,070 --> 00:01:00,410
+من هذه الـ Operators اللي لها استعمالات طبعًا واسعة 
+
+15
+00:01:00,410 --> 00:01:06,110
+في اللي هي مجالات عديدة  مش على  جد اللي هو التحليل
+
+16
+00:01:06,110 --> 00:01:11,110
+الدالي أو الرياضيات بل لها تطبيقات أخرى في الكهرباء
+
+17
+00:01:11,110 --> 00:01:14,630
+و الميكانيكا والهندسة إلى آخره في أمور عديدة
+
+18
+00:01:16,090 --> 00:01:21,930
+التعريف 3.9.1 هو definition لو كان عندي H1 وH2 two
+
+19
+00:01:21,930 --> 00:01:26,490
+Hilbert spaces and T من H1 لـ H2 بيكون bounded
+
+20
+00:01:26,490 --> 00:01:29,710
+linear operator إذا نتحدث عن bounded linear 
+
+21
+00:01:29,710 --> 00:01:33,730
+operator من Hilbert space لـ Hilbert space بدنا نعرف 
+
+22
+00:01:33,730 --> 00:01:37,650
+الآن حاجة اسمها الـ Hilbert Adjoint Operator الـ
+
+23
+00:01:37,650 --> 00:01:42,800
+Hilbert Adjoint Operator بدنا نرمزه بالرمز T* (of T)
+
+24
+00:01:42,800 --> 00:01:45,980
+is the operator هو عبارة عن operator اللي هو برضه
+
+25
+00:01:45,980 --> 00:01:48,920
+الـ adjoint operator هو عبارة عن operator إيش تعريفه؟
+
+26
+00:01:48,920 --> 00:01:54,620
+تعريفه هيكون من H2 لعند H1 T من H1 لعند H2 بينما 
+
+27
+00:01:54,620 --> 00:01:58,860
+اللي هو الـ adjoint له أو اللي هو الـ operator 
+
+28
+00:01:58,860 --> 00:02:03,300
+المساعد زي اللي هو دعنا نقول هذا تعميم للـ adjoint
+
+29
+00:02:03,300 --> 00:02:08,250
+matrix الآن such that for all x belonging to H1 and all
+
+30
+00:02:08,250 --> 00:02:11,890
+y belonging to H2 هيكون الـ inner product بين Tx وTy 
+
+31
+00:02:11,890 --> 00:02:18,050
+بيساوي x وT*y اللي بيحقق هذا اللي بيحقق هذا هو
+
+32
+00:02:18,050 --> 00:02:22,410
+اللي بنسميه إيش؟ ماله الـ adjoint operator إذا اللي هو 
+
+33
+00:02:22,410 --> 00:02:29,570
+عند T من H1 لعند H2 bounded linear operator بنعرف T
+
+34
+00:02:29,570 --> 00:02:37,520
+* من H2 لعند H1 كما يلي أنه اللي هو لكل X
+
+35
+00:02:37,520 --> 00:02:44,260
+element in H1 وY element in H2 بده يتحقق التالي X
+
+36
+00:02:44,260 --> 00:02:54,720
+TX وY يساوي اللي هو الـ X وT*Y الـ operator 
+
+37
+00:02:54,720 --> 00:02:59,420
+اللي بتحقق… اللي بيحقق هذه اللي هي الخاصية بنسميه 
+
+38
+00:02:59,420 --> 00:03:03,640
+الـ Adjoint Operator خلينا نتعرف عليه بشكل أكبر
+
+39
+00:03:03,640 --> 00:03:08,060
+اطلع لفوق هل هذا الـ operator اللي هو well defined
+
+40
+00:03:08,060 --> 00:03:13,320
+موجود؟ مش موجود؟ وحيد؟ مش وحيد؟ إلى آخره النظرية 3.9.2
+
+41
+00:03:13,320 --> 00:03:17,230
+بتجاوب على كل هذه الأسئلة بتقول إن ده هي 
+
+42
+00:03:17,230 --> 00:03:21,070
+الـ well-defined operator T* of T اللي في الـ
+
+43
+00:03:21,070 --> 00:03:24,110
+definition 3.9.1 أعلى اللي حكينا عنه قبل 
+
+44
+00:03:24,110 --> 00:03:29,450
+شوية أول شيء exist و unique و linear and bounded
+
+45
+00:03:29,450 --> 00:03:34,410
+with norm هو نفس norm من الـ operator الأصلي إذا
+
+46
+00:03:34,410 --> 00:03:37,250
+هيطلع عندي هذا الـ operator اللي عرفناه على هذا
+
+47
+00:03:37,250 --> 00:03:42,780
+الأساس عبارة عن bounded linear operator وفي نفس 
+
+48
+00:03:42,780 --> 00:03:47,000
+الوقت اللي هو norm هو norm الـ operator الأصلي و
+
+49
+00:03:47,000 --> 00:03:52,600
+طبعًا موجود ووحيد طيب نيجي إن أنا أعرف مالي عشان 
+
+50
+00:03:52,600 --> 00:03:56,400
+نبرهن إن أنا أعرف مالي البرهان consider H Y وX
+
+51
+00:03:56,400 --> 00:04:01,860
+بتساوي Y وTX  عرفت الآن اللي هو operator أو
+
+52
+00:04:01,860 --> 00:04:09,580
+function أو اللي هي H من اللي هو H2 لعند H1 اللي 
+
+53
+00:04:09,580 --> 00:04:16,140
+هي Y من H2 وX من H1 بيساوي الـ inner product Y وTX 
+
+54
+00:04:16,800 --> 00:04:20,840
+طبعًا هذا الـ operator عرفته بالشكل هذا <Y,TX> معرفات 
+
+55
+00:04:20,840 --> 00:04:24,840
+لأنه هو عبارة عن inner product اللي هي الـ <Y,TX> معرف
+
+56
+00:04:24,840 --> 00:04:28,320
+طبعًا الـ inner product هذا inner product وين في
+
+57
+00:04:28,320 --> 00:04:34,520
+الواقع هيكون في الـ H2 لأن الـ TX هي صورة X عنصر في 
+
+58
+00:04:34,520 --> 00:04:37,840
+الـ H1 وTX هيكون في الـ H2 والـ Y في الـ H2
+
+59
+00:04:37,840 --> 00:04:40,440
+فبيكون هذا الـ inner product والـ inner product تبع
+
+60
+00:04:40,440 --> 00:04:45,960
+مين؟ تبع الـ H2 طيب، which defines a sesquilinear
+
+61
+00:04:45,960 --> 00:04:50,820
+form على مين؟ على H2 × H1؟ إيه الـ sesquilinear
+
+62
+00:04:50,820 --> 00:04:59,100
+form؟ سهلة أن نثبتها يعني الآن H(Y,X) بتساوي اللي
+
+63
+00:04:59,100 --> 00:05:04,120
+هو <Y,TX> هي اللي عرفنا الـ H هذه زي ما قلنا الـ H 
+
+64
+00:05:04,120 --> 00:05:09,100
+هذه من وين لوين يا جماعة؟ الـ H هي عبارة عن اللي هو 
+
+65
+00:05:09,100 --> 00:05:21,580
+الـ H عبارة عن function من H اللي هو 2 معي across
+
+66
+00:05:21,580 --> 00:05:32,500
+H1 من H2 × H1 لعند مين؟ لعند H2 لعند H2 هذا اللي 
+
+67
+00:05:32,500 --> 00:05:40,320
+هو الـ operator عبارة عن اللي هو operator اللي هو
+
+68
+00:05:40,320 --> 00:05:45,820
+عبارة عن إيش ماله؟ sesquilinear ليش sesquilinear 
+
+69
+00:05:45,820 --> 00:05:48,340
+شوفوا كيف ليش sesquilinear
+
+70
+00:05:50,580 --> 00:05:59,300
+بتعرفوا إيش معنى if أخذنا Y1 وY2 element in H2 و
+
+71
+00:05:59,300 --> 00:06:07,100
+X1 وX2 element in H1 والـ α scalar فبيكون H(Y1
+
+72
+00:06:07,100 --> 00:06:14,800
++ Y2,X) بيساوي الـ inner product <Y1 + Y2,X> و
+
+73
+00:06:14,800 --> 00:06:23,240
+بيساوي <Y1,X> + <Y2,X> واضح إنه إيش ماله؟ هو نفسه 
+
+74
+00:06:23,240 --> 00:06:30,120
+عبارة عن H(Y1,X) + H(Y2,X) يعني الآن 
+
+75
+00:06:30,120 --> 00:06:34,180
+linear in the first entry additive in the first 
+
+76
+00:06:34,180 --> 00:06:40,880
+entry linear سهلة H(αY,X) بيساوي الـ inner
+
+77
+00:06:40,880 --> 00:06:46,080
+product بين <αY,X> وبيساوي α في <Y,X> إذا 
+
+78
+00:06:46,080 --> 00:06:49,780
+صار عنده Linear في الـ first entry وفي الـ second
+
+79
+00:06:49,780 --> 00:06:53,220
+entry رح يطلع إيش ماله؟ Conjugate Linear عشان يكون 
+
+80
+00:06:53,220 --> 00:06:55,860
+sesquilinear مش معنى sesquilinear إنه يكون
+
+81
+00:06:55,860 --> 00:06:58,640
+Linear في الأول وConjugate Linear في الثاني في 
+
+82
+00:06:58,640 --> 00:07:08,810
+الجزء الثاني سهل برضه خذ H(Y,X1 + X2) الـ H
+
+83
+00:07:08,810 --> 00:07:16,610
+(Y,X1 + X2) = <Y,T(X1 + X2)>
+
+84
+00:07:20,990 --> 00:07:27,390
+هو يساوي الآن هذا بيساوي <Y,TX1 + 
+
+85
+00:07:27,390 --> 00:07:32,650
+TX2> الآن اللي قبل إن نخلص اللي هنا product بيصير <Y,
+
+86
+00:07:32,650 --> 00:07:42,870
+TX1> + <Y,TX2> صار عبارة عن H(Y,X1)
+
+87
+00:07:42,870 --> 00:07:47,830
++ H(Y,X2) يعني صارت عبارة عن additive female
+
+88
+00:07:47,830 --> 00:07:54,890
+في الـ second entry linear كمان اكتبوا H(Y,αX)
+
+89
+00:07:54,890 --> 00:07:58,950
+بتساوي لأن أنا بدأت كبيرة حسب التعريف اللي 
+
+90
+00:07:58,950 --> 00:08:05,070
+عرفناها <Y,T(αX)> ما هي الـ T Linear إذا
+
+91
+00:08:05,070 --> 00:08:09,630
+الـ α بتطلع بيصير <Y,αTX> طب ما هي من بعيد 
+
+92
+00:08:09,630 --> 00:08:12,430
+في الـ inner product إيش بتطلع؟ Conjugate وبيساوي 
+
+93
+00:08:12,430 --> 00:08:18,270
+α Conjugate في <Y,TX> وبيساوي α Conjugate H
+
+94
+00:08:18,270 --> 00:08:22,590
+(Y,X) إذا طلعت عندي اللي هو Conjugate Linear إذا 
+
+95
+00:08:22,590 --> 00:08:28,310
+فعلاً طلعت عندي الـ H عبارة عن إيش؟ sesquilinear form
+
+96
+00:08:28,310 --> 00:08:32,770
+طيب ليش هذه بدأناها؟ بدأناها عشان أطبّق نظرية اللي هو 
+
+97
+00:08:32,770 --> 00:08:37,750
+أخذناها المرة الماضية، الآن صارت عندي هذه عبارة عن
+
+98
+00:08:37,750 --> 00:08:43,370
+sesquilinear وlinear، الآن ومش هيك ومش was inequality، لو 
+
+99
+00:08:43,370 --> 00:08:47,950
+أجيت أخذت الـ absolute value للـ H(Y,X) إيش 
+
+100
+00:08:47,950 --> 00:08:50,920
+هتطلع؟ الـ absolute value للـ inner product و
+
+101
+00:08:50,920 --> 00:08:54,800
+بـ Cauchy-Schwarz inequality أصغر أو يساوي norm الـ Y في norm من
+
+102
+00:08:54,800 --> 00:08:59,240
+TX وT is bounded إذا أصغر أو يساوي norm الـ Y في norm 
+
+103
+00:08:59,240 --> 00:09:04,020
+الـ T في norm من الـ X لأن هذه صارت عندي H(Y,X) 
+
+104
+00:09:04,020 --> 00:09:07,520
+أصغر أو يساوي norm الـ Y في norm الـ X في norm من الـ
+
+105
+00:09:07,520 --> 00:09:12,800
+T لهذا معناته this implies that الـ H ماله؟ is
+
+106
+00:09:12,800 --> 00:09:18,760
+bounded إذا الآن من هنا صار عندي الـ absolute value 
+
+107
+00:09:19,880 --> 00:09:27,360
+للـ H(Y,X) أصغر أو يساوي norm الـ T في norm
+
+108
+00:09:27,360 --> 00:09:34,300
+اللي هو الـ X في norm الـ Y إذا هيكون عندي اللي هو 
+
+109
+00:09:34,300 --> 00:09:41,140
+على للـ X في الـ Y بيصير نشوف بصير على norm الـ X 
+
+110
+00:09:41,140 --> 00:09:47,280
+في norm الـ Y أصغر أو يساوي norm الـ T ماشي الحال
+
+111
+00:09:47,280 --> 00:09:51,180
+إذا هذه صارت upper bound لهذه الـ set إذا الـ supremum
+
+112
+00:09:51,180 --> 00:09:57,040
+لها هيظل أصغر أو يساوي هذا لـ X وY X في الـ X وY
+
+113
+00:09:57,040 --> 00:10:02,700
+في الـ H1 وY في مين؟ في الـ H2 وهذا نفسه عبارة عن 
+
+114
+00:10:02,700 --> 00:10:08,450
+مين؟ عن norm الـ H إذا صارت norm الـ H أصغر أو يساوي
+
+115
+00:10:08,450 --> 00:10:13,230
+norm مين؟ الـ T إذا أثبتنا إن H is a sesquilinear
+
+116
+00:10:13,230 --> 00:10:19,470
+form which is bounded ونورمها أصغر أو يساوي مين؟
+
+117
+00:10:19,470 --> 00:10:21,570
+norm الـ T من جهة أخرى 
+
+118
+00:10:24,290 --> 00:10:27,690
+الـ norm H هو عبارة عن الـ supremum للـ absolute 
+
+119
+00:10:27,690 --> 00:10:31,110
+value H(Y,X) على norm Y في norm X للـ Y في الـ 
+
+120
+00:10:31,110 --> 00:10:35,250
+H2 مع دومين السفر طبعًا والـ X في الـ H1 مع دومين
+
+121
+00:10:35,250 --> 00:10:39,910
+السفر هذا الآن هو عبارة عن الـ supremum حطه مكان
+
+122
+00:10:39,910 --> 00:10:43,150
+هذه قيمتها اللي هي ماله؟ الـ inner product بين Y
+
+123
+00:10:43,150 --> 00:10:46,330
+وTX حسب ما إحنا معرفينها على norm Y في norm 
+
+124
+00:10:46,330 --> 00:10:49,950
+X Y في الـ H2 وminus zero والـ X في الـ H1 نقص 
+
+125
+00:10:49,950 --> 00:10:56,050
+zero الآن هذه المجموعة اللي هي في مجموعة حالة خاصة
+
+126
+00:10:56,050 --> 00:11:00,210
+منها فبتكون هذه جزئية منها أخذت بس الوايات اللي
+
+127
+00:11:00,210 --> 00:11:04,850
+مين؟ اللي هي عبارة عن صور شيء يعني TX لأنه
+
+128
+00:11:04,850 --> 00:11:07,770
+مش شرط تكون الـ T الـ function on it عشان تكون كل
+
+129
+00:11:07,770 --> 00:11:11,750
+واي لها X فبتكون هذه اللي هي المجموعة اللي هي
+
+130
+00:11:11,750 --> 00:11:15,770
+عبارة عن تحتوي المجموعة اللي أخذنا بدل الوايات مين؟
+
+131
+00:11:15,770 --> 00:11:19,890
+بس الـ TX فبيصير عبارة عن هذا اللي هو مدام هذه 
+
+132
+00:11:19,890 --> 00:11:22,210
+المجموعة بتحتوي هذه دا من الـ supremum لهذه أكبر 
+
+133
+00:11:22,210 --> 00:11:24,650
+أو يساوي الـ supremum لهذه اللي هو الـ supremum للـ
+
+134
+00:11:24,650 --> 00:11:28,850
+absolute value للـ <TX,TX> على الـ norm بدل الـ YTX في 
+
+135
+00:11:28,850 --> 00:11:33,990
+norm الـ X الآن هذا اللي هذا هو بقى عن مين؟ عن norm 
+
+136
+00:11:33,990 --> 00:11:37,350
+الـ ||TX|| تربيع ||TX|| بتروح مع ||TX|| والـ norm بيضل فوق norm 
+
+137
+00:11:37,350 --> 00:11:40,070
+الـ ||TX|| على norm الـ X norm الـ ||TX|| على norm الـ X الـ
+
+138
+00:11:40,070 --> 00:11:44,090
+supremum اللي هو مين؟ هيطلع norm اللي هو مين؟ الـ T
+
+139
+00:11:44,650 --> 00:11:47,790
+واضح إذا صار عندي برضه norm of H أكبر أو يساوي
+
+140
+00:11:47,790 --> 00:11:50,790
+norm of T واللي جاب الـ norm of H أصغر أو يساوي norm 
+
+141
+00:11:50,790 --> 00:11:55,530
+of T together norm of H إيش بيساوي norm of T إذا 
+
+142
+00:11:55,530 --> 00:12:02,070
+الآن .. الآن جهزت للنظرية اللي هي 3.8.4 أنه اللي هو
+
+143
+00:12:02,070 --> 00:12:06,650
+لجيت H is a bounded sesquilinear form إذا من theorem
+
+144
+00:12:06,650 --> 00:12:12,380
+3.8.4 إيش قلنا there exists a bounded linear operator
+
+145
+00:12:12,380 --> 00:12:16,120
+call it إيش ماله T* that is uniquely
+
+146
+00:12:16,120 --> 00:12:19,820
+determined by H and H(Y, X) بيساوي ال inner
+
+147
+00:12:19,820 --> 00:12:25,620
+product (T*Y, X) إذا بتتذكروا احنا قلنا إذا 
+
+148
+00:12:25,620 --> 00:12:32,980
+كانت H عبارة عن bounded sesquilinear form إذا بقدر
+
+149
+00:12:32,980 --> 00:12:36,300
+أكتبها uniquely as an inner product بقدر أحولها 
+
+150
+00:12:36,300 --> 00:12:37,940
+عبارة عن H وعندي
+
+151
+00:12:44,890 --> 00:12:48,770
+و H(Y, X) بيساوي اللي هو بقدر أحولها إلى inner block
+
+152
+00:12:48,770 --> 00:12:54,450
+سميناها S أيامها S(Y, X) ده بتتذكره ماشي الحال أنا 
+
+153
+00:12:54,450 --> 00:13:01,270
+سميته هذا is unique اللي هو و exist من نظرية تلاتة
+
+154
+00:13:01,270 --> 00:13:04,530
+وتمانية أربعة بدي أسميه S هنا اسمهاش بدي أسميه هنا 
+
+155
+00:13:04,530 --> 00:13:10,840
+T* حرنا إذا من نظرية 3.8.4 بما نستطيع أن نجد
+
+156
+00:13:10,840 --> 00:13:17,360
+bounded linear operator تسمى T*  أسقى بالهيك تسمى
+
+157
+00:13:17,360 --> 00:13:18,540
+T* تسمى T* تسمى T* تسمى T* تسمى T* تسمى T*
+
+158
+00:13:18,540 --> 00:13:19,140
+تسمى T* تسمى T* تسمى T* تسمى T* تسمى T* تسمى 
+
+159
+00:13:19,140 --> 00:13:19,240
+T* تسمى T* تسمى T* تسمى T* تسمى T* تسمى T*
+
+160
+00:13:19,240 --> 00:13:19,660
+تسمى T* تسمى T* تسمى T* تسمى T* تسمى T* تسمى
+
+161
+00:13:19,660 --> 00:13:19,960
+تسمى T* تسمى T* تسمى T* تسمى T* تسمى T* تسمى
+
+162
+00:13:19,960 --> 00:13:26,500
+T* تسمى T* تسمى T* تسمى T* تنورم الـ T* برضه
+
+163
+00:13:26,500 --> 00:13:30,400
+من نفس النظرية بيساوي مين؟ norm of H الأصل اللي
+
+164
+00:13:30,400 --> 00:13:34,660
+هو مين هو الـ sesquilinear form و أنا أثبتت قبل
+
+165
+00:13:34,660 --> 00:13:37,800
+بشوية norm of H بيساوي norm of T إذا صار عندي 
+
+166
+00:13:37,800 --> 00:13:42,640
+norm of T* هو نفسه مين؟ norm of T و H(Y, X)
+
+167
+00:13:42,640 --> 00:13:50,200
+بيساوي الان اللي هو (Y, TX) اللي أنا بنيت عليه توةوأنا
+
+168
+00:13:50,200 --> 00:13:54,320
+أثبتته من النظرية (T*Y, X) بيساوي إذا التنتين
+
+169
+00:13:54,320 --> 00:13:59,160
+مع بعض بيطلع عندي (Y, TX) بيساوي (T*Y, X) ومنه
+
+170
+00:13:59,160 --> 00:14:02,380
+خد ال conjugate لجهتين بيصير عبارة عن conjugate
+
+171
+00:14:02,380 --> 00:14:05,400
+لهذا بيساوي conjugate لهذا ال conjugate لهذا بيصير
+
+172
+00:14:05,400 --> 00:14:08,960
+(TX, Y) بيساوي conjugate لهذا اللي هو (X, مين و T
+
+173
+00:14:08,960 --> 00:14:14,920
+*Y) فهيك بكون أنا أثبتت اللي هو وجود T* و
+
+174
+00:14:14,920 --> 00:14:18,520
+أثبتت أنه عبارة عن bounded linear operator و أثبتت
+
+175
+00:14:18,520 --> 00:14:24,310
+أنه normهو norm الـ T يعني بمعنى آخر اللي هو
+
+176
+00:14:24,310 --> 00:14:27,930
+ال adjoint operator اللي سميته في ال definition قبل
+
+177
+00:14:27,930 --> 00:14:32,270
+شوية exist and unique and norm T* و نفسه norm
+
+178
+00:14:32,270 --> 00:14:37,390
+ال T نيجي
+
+179
+00:14:39,030 --> 00:14:44,770
+هيبقى نتعرف على الخواص بشكل أكبر على اللي هو الـ
+
+180
+00:14:44,770 --> 00:14:48,630
+adjoint Operator عشان أتعرف على هذا الخواص بالذمن
+
+181
+00:14:48,630 --> 00:14:52,860
+أول شيء نبرهن هذه اللملة البسيطة اللمّه دا
+
+182
+00:14:52,860 --> 00:14:55,820
+هنستخدمها كتير بعد شوية في البراهين فهذه اللمّه
+
+183
+00:14:55,820 --> 00:14:59,880
+بتقول اللمّه 3.9.3 let X and Y be inner product
+
+184
+00:14:59,880 --> 00:15:03,760
+spaces and Q from X to Y be a bounded linear
+
+185
+00:15:03,760 --> 00:15:07,480
+operator مش الحال إذا عندي فيه Q عبارة عن bounded
+
+186
+00:15:07,480 --> 00:15:09,920
+linear operator على inner product spaces
+
+187
+00:15:12,620 --> 00:15:16,020
+الـ Q هيساوى 0 if and only if .. الـ Q هذا هيساوى
+
+188
+00:15:16,020 --> 00:15:19,600
+0 if and only if .. اللي إنه مبروضكته (QX, Y)
+
+189
+00:15:19,600 --> 00:15:23,200
+بساوى 0 لكل X في الـ X و Y وين موجودة في الـ Y
+
+190
+00:15:23,200 --> 00:15:30,220
+واضح؟ طيب (B) إذا كانت Q من X لـ X مش من X لعند Y من X
+
+191
+00:15:30,220 --> 00:15:34,130
+لـ X وكانت X is a complexاللي هو Complex inner product
+
+192
+00:15:34,130 --> 00:15:38,050
+space مش real Complex inner product space and ال
+
+193
+00:15:38,050 --> 00:15:42,130
+inner product (QX, X) بيساوي صفر لكل X في ال X
+
+194
+00:15:42,130 --> 00:15:46,710
+إذاً Q بتساوي صفر Automatically إذا الأن خففنا الشرط
+
+195
+00:15:46,710 --> 00:15:51,050
+اللي فوق بس في حالة مين ال Q من X لعند X و X is
+
+196
+00:15:51,050 --> 00:15:55,130
+Complex لو كان عند (QX, X) و X بيساوي صفر لكل X في 
+
+197
+00:15:55,130 --> 00:16:00,280
+ال X هعطيه Automatically Q أشبه تساوي صفر لكن لو كان 
+
+198
+00:16:00,280 --> 00:16:04,520
+هذا الشرط مش موجود X is complex ليس شرط أنها تكون 
+
+199
+00:16:04,520 --> 00:16:08,320
+النظرية صحيحة وبعد شوية هنشوف في مثل Medium درهم
+
+200
+00:16:08,320 --> 00:16:14,410
+الآن بتمّا نبرهن الأولى أول إشي بدنا نفترض Q يساوي
+
+201
+00:16:14,410 --> 00:16:17,510
+صفر و نصل لهذه وبعدين لهذه و نصل لمن Q يساوي صفر 
+
+202
+00:16:17,510 --> 00:16:21,390
+بس قبلها خلينا نحضر هالكلمتين للبرهان عشان اللي هو
+
+203
+00:16:21,390 --> 00:16:27,430
+الآن الجزء الأول سهل لكن برضه مافيش مانع أن نبرهنه
+
+204
+00:16:27,430 --> 00:16:31,880
+لو كانت Q يساوي صفر Q بيساوي صفر Automatically 
+
+205
+00:16:31,880 --> 00:16:37,820
+اللي هو QX هيكون صفر معناته (QX, أي Y) هيساوي صفر
+
+206
+00:16:37,820 --> 00:16:43,920
+لكل X و لكل مين لكل Y طيب لو الآن كان عندى ال QX
+
+207
+00:16:43,920 --> 00:16:49,020
+لو أخدنا X arbitrary لو كان عندى (QX, Y) بتساوي صفر
+
+208
+00:16:49,020 --> 00:16:53,800
+لكل X و لكل Y في ال .. في ال .. بيصير عندى الآن 
+
+209
+00:16:53,800 --> 00:16:59,060
+conversely .. conversely صفر برضه لو كانت (QX, Y)
+
+210
+00:16:59,060 --> 00:17:05,380
+بساوة 0 لكل X في الـ H1 و Y في مين في الـ H2 هذا
+
+211
+00:17:05,380 --> 00:17:11,000
+المعطب نفسي بتقوله Q=0 معناه تخوض الآن let X
+
+212
+00:17:11,000 --> 00:17:15,640
+element الـ H1 بي arbiter دي انتفذ ماهاش الحال من
+
+213
+00:17:15,640 --> 00:17:20,480
+اللي فوق ما هي QX برضه هتكون في مين؟ في الـ H2
+
+214
+00:17:20,480 --> 00:17:26,620
+واحدة من الـ Y إذا بنطبق عليها إذن (QX, QX) هيساوة 0
+
+215
+00:17:26,620 --> 00:17:32,200
+حسب الفرضية و منه نعمل ||QX||² بيساوي صفر و منه الـ
+
+216
+00:17:32,200 --> 00:17:38,020
+QX بتساوي نفسها صفر إذا هذا الكلام لكل X لأنه كانت
+
+217
+00:17:38,020 --> 00:17:42,500
+X اللي هي كانت X arbitrarily إذا الـ Q بتساوي صفر
+
+218
+00:17:42,500 --> 00:17:46,480
+إذا الجزء الأول هذه سهلة نيجي لما يجي لجزء ثاني
+
+219
+00:17:46,480 --> 00:17:50,440
+اللي بدنا اللي هو انبرهنه خلينا نحضرله الكلمتين و
+
+220
+00:17:50,440 --> 00:17:54,660
+بعدين نروح باتجاه البرهن طيب صلوا على النبي عليه
+
+221
+00:17:54,660 --> 00:17:56,040
+الصلاة والسلام
+
+222
+00:18:10,310 --> 00:18:13,690
+طبعا هو اللي يمكن يسيس كلنا from ال H اللي عملناها 
+
+223
+00:18:13,690 --> 00:18:18,830
+قبل شوية أنا قولت من H2 × H1 اللي عند H2 هي من
+
+224
+00:18:18,830 --> 00:18:22,250
+H2 × H1 إلى اللي هي ال scalar field لأن ال
+
+225
+00:18:22,250 --> 00:18:27,810
+inner product عبارة عن اللي هو القيمة عددية from
+
+226
+00:18:27,810 --> 00:18:34,170
+assumption from assumption ما عطينا إن (QX, Y) بيساوي Y
+
+227
+00:18:34,170 --> 00:18:38,830
+بيساوي صفر لكل X في ال X الآن (QV, V) إيش بتساوي صفر
+
+228
+00:18:38,830 --> 00:18:43,050
+لكل V في ال main في ال X من ضمن هن قيلنا ال
+
+229
+00:18:43,050 --> 00:18:46,310
+linear combination V بتساوي αX + Y اللي هو
+
+230
+00:18:46,310 --> 00:18:49,610
+element in X ماشي الحاجة ده خدها الصورة ده عشان
+
+231
+00:18:49,610 --> 00:18:56,280
+أصلحها ده الآن حسبولي بناء على هذا الكلام بيصير QV
+
+232
+00:18:56,280 --> 00:18:59,620
+اللي هي أخدتها (αX + Y, αX + Y) إيش
+
+233
+00:18:59,620 --> 00:19:05,360
+هتساوي؟ هتساوي و صفر فردوها الآن اللي هو بتصير هذه
+
+234
+00:19:05,360 --> 00:19:11,940
+α(QX, X) + (QY, Y) و (αX + Y, αX + Y) بتساوي الآن بأخد
+
+235
+00:19:11,940 --> 00:19:15,260
+اللي هو ال (QX, X) مع ال X يعني و بطلع ال α برة
+
+236
+00:19:15,260 --> 00:19:20,200
+فبيصير α من ال α في برة واحدة أه واضح اه في
+
+237
+00:19:20,200 --> 00:19:25,700
+داعية أفصل α² (QX, X) التانية بتظهر هي (QY, Y) 
+
+238
+00:19:25,700 --> 00:19:33,720
+مع مين مع Y (QY, Y) اللي بعدها α(QX, Y) + (QY, 
+
+239
+00:19:33,720 --> 00:19:37,560
+Y) مع مين مع αX اللي من بعيد بطلع α كون
+
+240
+00:19:37,560 --> 00:19:42,310
+جيغيتو من الجاري بطلع α إذا زائد اللي هو قلنا
+
+241
+00:19:42,310 --> 00:19:45,830
+الـ α في (QX, Y) و مين و Y لأن هذه طلعت من مين من
+
+242
+00:19:45,830 --> 00:19:49,110
+الجريبة زائد اللي هو α conjugate اللي طلعت من
+
+243
+00:19:49,110 --> 00:19:55,070
+هنا في (QY, X) و مين و X و يساوي الآن ما هو احنا 
+
+244
+00:19:55,070 --> 00:20:01,940
+مفترضين إن (QX, X) بيتساوى 0 لكل X و الموجودة في
+
+245
+00:20:01,940 --> 00:20:05,140
+الـ X هذا الفرضية وبناء على أننا خلصنا من الأول
+
+246
+00:20:05,140 --> 00:20:08,200
+لإن أنا ببرهن في التاني أسف في الـ (B) فصار عندي
+
+247
+00:20:08,200 --> 00:20:11,900
+الآن ال .. ال .. ال .. ال .. ال (QV, V) بيساوى 0 و
+
+248
+00:20:11,900 --> 00:20:15,020
+(QX, X) بيساوى 0 و (QY, Y) بيساوى 0 دايما هيك
+
+249
+00:20:15,020 --> 00:20:18,380
+الموضوع طيب إذا صار عندي بدأت أخلص من هنا دولة
+
+250
+00:20:18,380 --> 00:20:23,810
+هادو هذه صفر صح ولا لأ إذا بيظل عندي بس هذه و
+
+251
+00:20:23,810 --> 00:20:29,050
+هذه بيصير α في (QX, Y) زائد α conjugate (QY, X)
+
+252
+00:20:29,050 --> 00:20:34,850
+الآن خده بياخد قيمتين عشان يعمل ال ايه الآن هذه 
+
+253
+00:20:35,500 --> 00:20:39,320
+زائدها دي بساوة صفر بدي أخد قيمتين لل α و α
+
+254
+00:20:39,320 --> 00:20:44,060
+كنت جيت عشان وكأني حلم اقم عادلتين بيمجهولين ويطلع 
+
+255
+00:20:44,060 --> 00:20:48,220
+عند الحل ماشي الحل شوفوا كيف أخدوا α بتساوي 1
+
+256
+00:20:48,220 --> 00:20:53,580
+فبتطلع هي دي (QX, Y) + (QY, X) بساوي مين بساوي صفر
+
+257
+00:20:53,580 --> 00:20:59,250
+هي واحدة أخدوا α بتساوي i هلجيت بتشوفوا كيف ليش
+
+258
+00:20:59,250 --> 00:21:04,250
+i لما أخد i بتصير i في هذا المقدار اللي كنت جيتله 
+
+259
+00:21:04,250 --> 00:21:09,090
+i ناقص i ناقص i اللي هو في هذا المقدار بيساوي صفر
+
+260
+00:21:09,090 --> 00:21:13,250
+ضيعوا ال i مع ال i فبتصير هذا ناقص هذا بيساوي صفر
+
+261
+00:21:13,250 --> 00:21:16,970
+فصار عندي الآن هذا المقدار ناقص هذا بيساوي صفر و
+
+262
+00:21:16,970 --> 00:21:19,810
+هذا زائد هذا بيساوي صفر صار معادلتين بمجهولين
+
+263
+00:21:19,810 --> 00:21:25,990
+فبنجمحل لبعض بيصير عنده إيش ماله؟ 2(QX, Y) بيساوي صفر و منه الـ
+
+264
+00:21:25,990 --> 00:21:31,270
+(QX, Y) بتساوي صفر ومن ثم Q بتساوي صفر من مين؟ من النظرية اللي فوق لإنه صار 
+
+265
+00:21:31,270 --> 00:21:34,730
+عندي وكانت عندي (QX, Y) arbitrary elements in X 
+
+266
+00:21:34,730 --> 00:21:39,550
+وصار عندي (QX, Y) بيساوي صفر لكل X و Y إذا الـ Q 
+
+267
+00:21:39,550 --> 00:21:44,050
+بتساوي صفر من اللي هي (A) و منه بيكون حصلنا على اللي
+
+268
+00:21:48,390 --> 00:21:55,020
+هي النتيجة الآن زي ما قلتلكم اللي لو كانت اللي هي
+
+269
+00:21:55,020 --> 00:21:58,540
+طبعا عندنا الشرط اللي محطوط في بيه انه تكون X is 
+
+270
+00:21:58,540 --> 00:22:03,240
+complex طب لو كانت X is real لو كانت X is real ليس
+
+271
+00:22:03,240 --> 00:22:07,760
+شرطا انه يكون في عندي نتيجة صحيحة إيش يعني مش 
+
+272
+00:22:07,760 --> 00:22:13,420
+صحيحة نزل عن النظرية هنلاقي يعني هنلاقي إن (QX, X)
+
+273
+00:22:13,420 --> 00:22:17,500
+بالساعة و صفر لكل X في ال X لكن Q أي شمالها مش صفر
+
+274
+00:22:17,500 --> 00:22:22,760
+شوف إيش اللي بده أخده بدي أخد الـ Q من ℝ² 
+
+275
+00:22:22,760 --> 00:22:28,500
+لعند مين لعند ℝ² و بدي أخد لكم اللي هو ..
+
+276
+00:22:28,500 --> 00:22:33,880
+اللي هي أي عنصرين واحد اسمه α و β Ordered
+
+277
+00:22:33,880 --> 00:22:38,520
+pair α و β هذه α و هذه مين β مثلا و
+
+278
+00:22:38,520 --> 00:22:41,100
+بدي .. هاي ال vector تبعي اللي في الـ ℝ² هي
+
+279
+00:22:41,100 --> 00:22:46,670
+ال vector بتاخد vector تاني اللي هو بتدرسل اللي هو
+
+281
+00:22:46,670 --> 00:22:50,610
+الـ function اللي عندنا الـ Q of Alpha و Beta
+
+282
+00:22:50,610 --> 00:22:55,490
+بتدرسلها لعند الـ vector اللي هو Beta و ناقص Alpha
+
+283
+00:22:55,490 --> 00:23:01,580
+Beta هي Beta وعندي بنزل ناقص Alpha فبتكون هذا اللي
+
+284
+00:23:01,580 --> 00:23:05,640
+هو الـ vector هذا اللي بتكون اللي عبارة عن Beta
+
+285
+00:23:05,640 --> 00:23:10,840
+وناقص Alpha يعني أنها لها Beta وهاد إيش ما لها
+
+286
+00:23:10,840 --> 00:23:16,000
+ناقص Alpha يعني وكأنه هذا طوله Beta و هذا طوله إيه
+
+287
+00:23:16,000 --> 00:23:20,380
+إيش Alpha ماشي و هاي الزاوية هاي المقابلها و هاي
+
+288
+00:23:20,380 --> 00:23:25,260
+المجاورها هذه الثانية بيصير اللي هو مقابلها اللي
+
+289
+00:23:25,260 --> 00:23:30,500
+هو عبارة عن Alpha طوله كطول و مجاورها مين هو Beta
+
+290
+00:23:30,500 --> 00:23:34,540
+فبتصير هذه و هذه متممة لهذه يعني هذه 90 درجة يعني
+
+291
+00:23:34,540 --> 00:23:37,820
+هذا هيكون عمودي على هذا إذا الـ inner product
+
+292
+00:23:37,820 --> 00:23:42,600
+بينهن إيش حيساوي صفر إذا الـ Q اللي هو هذا دائماً
+
+293
+00:23:42,600 --> 00:23:47,040
+حيكون عنده صفر لكن الـQ نفسه أشماله مش صفر هذا
+
+294
+00:23:47,040 --> 00:23:52,300
+الهندسيا،  دبريا هيه to see this consider the
+
+295
+00:23:52,300 --> 00:23:56,160
+mapping Q من R تربيع لـ R تربيع given by الـQ Alpha
+
+296
+00:23:56,160 --> 00:24:00,520
+و Beta بيساوي Beta وناقص Alpha it is clear that
+
+297
+00:24:00,520 --> 00:24:02,880
+for any X element in Alpha و Beta element in R
+
+298
+00:24:02,880 --> 00:24:05,660
+تربيع لو جئتم أخذتم الـ inner product بحكي عن
+
+299
+00:24:05,660 --> 00:24:07,860
+inner product في الـ .. في الـ .. في الـ .. في الـ  R تربيعي
+
+300
+00:24:07,860 --> 00:24:11,600
+الـ Q X و X إيش بيساوي؟ اللي هو Q X عبارة
+
+301
+00:24:11,600 --> 00:24:14,620
+عن Beta ونقص Alpha في الـ X اللي هي Alpha في Beta
+
+302
+00:24:14,620 --> 00:24:18,140
+الـ inner product بينهم Beta في Alpha نقص Alpha في 
+
+303
+00:24:18,140 --> 00:24:23,000
+مين؟ Beta بيساوي صفر بطي Q أشماله لا تساوي صفر لكن
+
+304
+00:24:23,000 --> 00:24:27,520
+لو كان .. لو كان أخذته اللي هو اللي هي .. لو كان
+
+305
+00:24:27,520 --> 00:24:30,920
+اللي هو عندي اللي هو Complex يعني بدنا نرسله
+
+306
+00:24:30,920 --> 00:24:34,540
+لـ Complex بتطلعش اللي هو اللي هي بتساوي صفر و جربه
+
+307
+00:24:34,540 --> 00:24:38,060
+اعمل inner product بينهم في c تربيع حتى جو أشماله
+
+308
+00:24:38,060 --> 00:24:42,920
+اللي هو ما بتطلعش اللي هو inner product بينهم صفر
+
+309
+00:24:42,920 --> 00:24:45,300
+يعني مش متحقق لإن الـ inner product بينهم صفر
+
+310
+00:24:45,300 --> 00:24:48,280
+معناته لازم يطلع Q صفر رسميًا حسب النظرية اللي جابت
+
+311
+00:24:51,060 --> 00:24:56,920
+نجي الآن لنظرية اللي بتتعلق بخواص الـ Adjoint
+
+312
+00:24:56,920 --> 00:25:05,120
+Operators شوف خلينا نتطلع على الخواص احنا نزلنا بس
+
+313
+00:25:05,120 --> 00:25:09,540
+على اللي هو التعريف الأصلي اللي عرفنا فيه الـ
+
+314
+00:25:09,540 --> 00:25:17,300
+Adjoint Operator قلنا الـ Adjoint T من H1 لعند H2 و
+
+315
+00:25:17,300 --> 00:25:22,880
+T* من H2 لعند H1 تحقق ما يلي
+
+316
+00:25:25,890 --> 00:25:33,290
+و Y بسوء X و T* Y لكل X element in H1 و Y
+
+317
+00:25:33,290 --> 00:25:39,310
+element in H2 معايا يا جماعة هذا اللي هي التعريف
+
+318
+00:25:39,310 --> 00:25:48,130
+الأصلي بدنا ننطلق من هذا التعريف عشان نحقق الخواص 
+
+319
+00:25:48,130 --> 00:25:49,450
+اللي حكيناها اطلع لفوق يا أخي
+
+320
+00:25:52,820 --> 00:26:01,180
+لأن let H1 و H2 بيهي البرت السباسيس و S و T عبارة عن
+
+321
+00:26:01,180 --> 00:26:05,640
+two bounded linear operators من H1 لعند H2 و Alpha
+
+322
+00:26:05,640 --> 00:26:11,920
+and scalar then we have مالي A T* Y و X بيساوي
+
+323
+00:26:11,920 --> 00:26:18,360
+Y و T mean X لكل X و Y element in H1 و Y element in
+
+324
+00:26:18,360 --> 00:26:23,730
+H2 و S زائد T لكل * بيساوي اللي هو الـ conjugate
+
+325
+00:26:23,730 --> 00:26:27,570
+للأول الـ adjoint للأول زائد من الـ adjoint للتاني
+
+326
+00:26:27,570 --> 00:26:31,330
+يعني الـ adjointness بتوزع على الجميع و alpha في الـ
+
+327
+00:26:31,330 --> 00:26:35,270
+T لكل * اللي كان التوزيع على الـ scalar of 
+
+328
+00:26:35,270 --> 00:26:38,190
+multiplication بيحول الـ alpha إلى alpha conjugate
+
+329
+00:26:38,190 --> 00:26:41,130
+فبيكون الـ adjoint هو عبارة عن alpha conjugate في 
+
+330
+00:26:41,130 --> 00:26:45,050
+مين؟ في T* و لو أخذتم الـ conjugate مرتين زي
+
+331
+00:26:45,050 --> 00:26:47,810
+.. زي و كأنه بناخد الـ .. آسف لو أخذتم الـ
+
+332
+00:26:47,810 --> 00:26:51,550
+adjointness مرتين برجع مين؟ نفس الأصل زي الـ
+
+333
+00:26:51,550 --> 00:26:55,040
+conjugation اللي هو T* الـ * كله إيش بيساوي
+
+334
+00:26:55,040 --> 00:27:01,100
+بيساوي اللي هو T and in this case طبعًا في هذه
+
+335
+00:27:01,100 --> 00:27:03,980
+الحالة عشان نعمل هيك بيكون actually هو مين أشته
+
+336
+00:27:03,980 --> 00:27:07,780
+عشان نقدر نعرف يكون التعريف full defined الآن الـ S
+
+337
+00:27:07,780 --> 00:27:11,660
+و الـ T لكل * إيش بيساوي T* في مين فاس الـ 
+
+338
+00:27:11,660 --> 00:27:15,690
+* زي الـ inverse اسمه لو برجع الجوا اللي هو بيصير
+
+339
+00:27:15,690 --> 00:27:21,490
+T* في S* Norm T* في T هو نفسه Norm T 
+
+340
+00:27:21,490 --> 00:27:25,810
+في T* مش حتفرق معانا ويساوي Norm T أشماله لكل 
+
+341
+00:27:25,810 --> 00:27:28,410
+تربيع طبعًا أسبابه برضه من الأسباب أنه Norm T هو 
+
+342
+00:27:28,410 --> 00:27:30,110
+Norm T*
+
+343
+00:27:38,810 --> 00:27:42,890
+واضح اللي بنحكيه خلّينا نبدأ اللي هو في مين في إيه
+
+344
+00:27:42,890 --> 00:27:45,190
+الآن إيش بده في إيه
+
+345
+00:27:48,310 --> 00:27:55,370
+نبدأ في T* Y T* Y O X T* Y O X هي اللي 
+
+346
+00:27:55,370 --> 00:28:01,550
+بدنا إياها لو جينا أخذناها اللي هو بيساوي اللي هو X
+
+347
+00:28:01,550 --> 00:28:10,030
+و T* Y conjugate صح ولا أكيد ماشي Y ساوي هذه 
+
+348
+00:28:10,030 --> 00:28:17,890
+بدأت فيها هذه بتوصلها لمين بتساوي Y T X الآن قولت T
+
+349
+00:28:17,890 --> 00:28:21,490
+* Y X بتساوي هذه يعني الآن لو غطيت هذا و قولت
+
+350
+00:28:21,490 --> 00:28:25,270
+لكم X و T* Y الكل كنتوا ما جتاش بيساوي شو اللي 
+
+351
+00:28:25,270 --> 00:28:29,010
+كنتم بيصير T* Y مين و X طيب حسب اللي هو 
+
+352
+00:28:29,010 --> 00:28:33,190
+التعريف اللي فوق هاي X و T* Y بده نستبدلها 
+
+353
+00:28:33,190 --> 00:28:38,010
+بقاش قيمتها و هي ساوي T X و Y و في Conjugate فوق
+
+354
+00:28:38,010 --> 00:28:43,630
+صح؟ لأن الـ Conjugation إيش حيِطلع عبارة عن Y و T X 
+
+355
+00:28:43,630 --> 00:28:50,870
+إذا حصلت عن T* Y بيساوي Y و T X و كأنه بيقول الـ 
+
+356
+00:28:50,870 --> 00:28:54,750
+T* Y و X لما بدك تنجل هذا على الجهة التانية
+
+357
+00:28:54,750 --> 00:29:00,920
+بيشيل الـ Conjugation اه ماشي الآن و كأنه تنجل هذه 
+
+358
+00:29:00,920 --> 00:29:03,960
+هنا بتصير بدلها إيش بدل ما هي T* بتصير هنا T
+
+359
+00:29:03,960 --> 00:29:07,740
+اه و لما تنجل هذه هنا برضه بتشيل إيش بتصير ..
+
+360
+00:29:07,740 --> 00:29:12,500
+بتشير .. بتحط Conjugation الآن هنا Txy عشان تنجلها
+
+361
+00:29:12,500 --> 00:29:16,680
+على الجهة التانية يعني عملية النقل من entry لثاني 
+
+362
+00:29:16,680 --> 00:29:19,580
+يا بتحط Conjugation يا بتشير Conjugation هذا حيسير
+
+363
+00:29:19,580 --> 00:29:22,400
+السلوك بعد شوية بس احنا قاعدين بنشرع لهذا السلوك
+
+364
+00:29:22,930 --> 00:29:27,650
+واضح طيب صلي على النبي عليه الصلاة والسلام نيجي
+
+365
+00:29:27,650 --> 00:29:31,150
+الآن اطلعلي على الكتاب خلينا نيجي لمين لـ اللي هي 
+
+366
+00:29:31,150 --> 00:29:38,610
+الفرع B طيب طيب
+
+367
+00:29:38,610 --> 00:29:47,550
+نيجينا اللي هي الفرع B بدنا نثبت اللي هو الـ 
+
+368
+00:29:47,550 --> 00:29:53,330
+T أس زائد T لكل * بيساوي S* زائد مين T*
+
+369
+00:29:53,330 --> 00:30:02,250
+ده أثبت أنه S زائد T لكل * بيساوي S* زائد
+
+370
+00:30:02,250 --> 00:30:07,030
+مين T* شوفوا كيف بتثبتها نشوف الآن خدولي أي x و 
+
+371
+00:30:07,030 --> 00:30:10,970
+y الآن أي x و y الـ x في الـ H1 و الـ y في مين في الـ
+
+372
+00:30:10,970 --> 00:30:15,630
+H2 احسمولي الآن اللي هو x و S زائد T كل * في 
+
+373
+00:30:15,630 --> 00:30:20,390
+مين في y بيساوي حسب الخاصية اللي عملناها قبل و شوية
+
+374
+00:30:20,390 --> 00:30:26,030
+إيش حيساوي اللي هو هذه هتنتقل على الجهة هذه بـ S
+
+375
+00:30:26,030 --> 00:30:31,310
+زائد T x of y هيها من اللي حكيناها هنا مظبوط طيب من
+
+376
+00:30:31,310 --> 00:30:36,290
+التعريف Y ساوي ما حنعرفيه S زي T of X مش ساوي SX
+
+377
+00:30:36,290 --> 00:30:42,030
+زي TX مظبوط الآن و الـ product هو linear في الـ 
+
+378
+00:30:42,030 --> 00:30:48,960
+entry الأول فبيصير SX و Y زي TX و Y الـ ALC
+
+379
+00:30:48,960 --> 00:30:53,160
+بدي أرجع أستخدم الخاصية S X Y إيش بتساوي X و S
+
+380
+00:30:53,160 --> 00:30:58,400
+* Y مظبوط و T X Y إيش بتساوي X و T* Y ردحهم 
+
+381
+00:30:58,400 --> 00:31:01,960
+كمان مرة لعبا بعض لإن أنا بدأت بيصير X و S*
+
+382
+00:31:01,960 --> 00:31:06,100
+زائد T* Y صار هذا الكلام صحيح لمين؟ لكل X و Y
+
+383
+00:31:06,100 --> 00:31:12,600
+يعني بمعنى آخر اللي وصلت له أنه أنا أن X و S زائد T
+
+384
+00:31:12,600 --> 00:31:22,970
+* Y ناقص الـ X و S* زي الـ T* of Y كله
+
+385
+00:31:22,970 --> 00:31:28,750
+أش بيساوي صفر وهذا الكلام لكل مين؟ لكل X و Y يعني 
+
+386
+00:31:28,750 --> 00:31:35,380
+بمعنى آخر صار عبارة عن X أو S زي الـ T* ناقص 
+
+387
+00:31:35,380 --> 00:31:42,160
+معايا S* زي الـ T* الكل of Y الكل إيش
+
+388
+00:31:42,160 --> 00:31:45,360
+بيساوي اللي أنا أقدر أقتله بيساوي صفر هذا الكلام
+
+389
+00:31:45,360 --> 00:31:49,780
+لكل XY من اللي قبل بشوية هذا اللي اسمه Q إذا إيش
+
+390
+00:31:49,780 --> 00:31:54,940
+حيساوي هذا؟ صفر إذا صار عندي S زي الـ T لكل *
+
+391
+00:31:54,940 --> 00:31:59,980
+بيساوي S* زي الـ T* لأن هذا حيساوي صفر إذا
+
+392
+00:31:59,980 --> 00:32:04,260
+على الجهة التانية بيسير بيساوي الثانية واضح؟ طيب،
+
+393
+00:32:04,260 --> 00:32:09,280
+إيه اللي بعده؟
+
+394
+00:32:09,280 --> 00:32:12,580
+اطلعلي
+
+395
+00:32:12,580 --> 00:32:16,360
+بس على النص، خلّيني أشوف النص على اللي هو النص في
+
+396
+00:32:16,360 --> 00:32:21,260
+الـ .. في الـ .. إيه بقى؟ عندي اللي هو Alpha T*
+
+397
+00:32:21,260 --> 00:32:25,540
+بس هو Alpha conjugate في مين؟ في T* Similarly
+
+398
+00:32:25,540 --> 00:32:29,060
+.. Similarly اللي هي .. خليك عليها اللي هي Alpha 
+
+399
+00:32:29,060 --> 00:32:36,080
+في T الكل * بيساوي Alpha conjugate في مين في T
+
+400
+00:32:36,080 --> 00:32:42,700
+الـ * نفس الشيء بدنا ناخد أي واحدة منهم مش
+
+401
+00:32:42,700 --> 00:32:46,220
+مشكلة لو دخلت على هذه اللي هو تيجي تاخد Alpha
+
+402
+00:32:46,220 --> 00:32:54,980
+Alpha T الكل * Y و X ماشي بيساوي و في الآخر 
+
+403
+00:32:54,980 --> 00:32:58,210
+ناخدهم الـ Conjugation مش مشكلة كثيرة بيساوي اللي هو 
+
+404
+00:32:58,210 --> 00:33:03,210
+عبارة عن مين؟ عن Y الـ inner product بيساوي الـ inner
+
+405
+00:33:03,210 --> 00:33:06,590
+product و لو بدأت في الأولى يعني بدأت في الـ .. في
+
+406
+00:33:06,590 --> 00:33:09,870
+هذه و أنت جالبت فيها برضه بنفع بيساوي الـ inner
+
+407
+00:33:09,870 --> 00:33:12,250
+product ده خليه Alpha conjugate في مين في T*
+
+408
+00:33:12,250 --> 00:33:17,630
+بيساوي الـ inner product بين Y و Alpha معايا يا 
+
+409
+00:33:17,630 --> 00:33:23,970
+جماعة اه T X من هذه جاعة بنجل اه معايا اه و بيساوي 
+
+410
+00:33:23,970 --> 00:33:28,720
+أها باستخدامها T* Y و X بيساوي .. خلوكم 
+
+411
+00:33:28,720 --> 00:33:32,800
+معيهانة .. Alpha T* Y و X إيش بيساوي Y و Alpha
+
+412
+00:33:32,800 --> 00:33:36,800
+T X .. مظبوط؟ و بيساوي .. شلوني الـ Alpha برة .. و 
+
+413
+00:33:36,800 --> 00:33:42,720
+بيساوي Alpha كل Conjugate .. صح؟ في Y و TX رجعوليها
+
+414
+00:33:42,720 --> 00:33:46,480
+الأصلها بيساوي Alpha conjugate فيه هذه بيصير T*
+
+415
+00:33:46,480 --> 00:33:52,020
+Y و Min و X صارت الآن هذا الصحيح لكل Min لكل كده و
+
+416
+00:33:52,020 --> 00:33:57,340
+رجعيها كمان مرة رجعيها دي جوا في الجريد بتحط Alpha
+
+417
+00:33:57,340 --> 00:34:00,860
+conjugate نفسها بيصير Alpha conjugate T* هيش 
+
+418
+00:34:00,860 --> 00:34:05,720
+بتساوي Alpha T كل هيش الـ * ماضح ها طيب ماشي
+
+419
+00:34:05,720 --> 00:34:08,280
+الحال يالا اللي بعده اطلع
+
+420
+00:34:13,490 --> 00:34:18,890
+طيب، الآن عندي .. لأ خليني أرجع لـ .. للبرهان إيش 
+
+421
+00:34:18,890 --> 00:34:24,470
+بده نثبت؟ T star star بساوي T، نفسها، نفس الحاجة،
+
+422
+00:34:24,470 --> 00:34:28,150
+طلعي الآن خذي ال inner product الآن، T star star X
+
+423
+00:34:28,150 --> 00:34:32,690
+و مع Y إحنا لما ننجل اللي هو هي هذا و كأنه اسمه
+
+424
+00:34:32,690 --> 00:34:36,860
+S هذا كله اسمه S S Star لما تجيبه هان ايش بده يصير
+
+425
+00:34:36,860 --> 00:34:40,000
+بيطلع ال Star اللي برا فبصير اللي هي ال S في Y
+
+426
+00:34:40,000 --> 00:34:43,640
+اللي هي مين S قلت عنها T Star فبصير X و T Star
+
+427
+00:34:43,640 --> 00:34:48,220
+الآن X و T Star Y برضه ايش هتساويه؟ رجعها لأصلها من
+
+428
+00:34:48,220 --> 00:34:52,720
+التعريف فبصير T X و مع Y يا التعريف يا ال
+
+429
+00:34:52,720 --> 00:34:56,940
+property هذه هم برجع لك اللي هو بشيل أو بحط زي ما
+
+430
+00:34:56,940 --> 00:35:01,360
+اتفقنا فهمك؟ واضح اه؟ فبصير عندي الآن اللي هي
+
+431
+00:35:04,910 --> 00:35:08,390
+طبعا نفسها كيف؟ لإن ننجل هذه بتصير صفر لكل x و y من
+
+432
+00:35:08,390 --> 00:35:13,550
+اللمة تصير T star T star ناقص T تساوي صفر تساوي
+
+433
+00:35:13,550 --> 00:35:14,490
+تساوي تساوي T تساوي T تساوي T تساوي T تساوي T
+
+434
+00:35:14,490 --> 00:35:15,050
+تساوي T تساوي T تساوي T تساوي T تساوي T تساوي T
+
+435
+00:35:15,050 --> 00:35:15,890
+تساوي T تساوي T تساوي T تساوي T تساوي T تساوي T
+
+436
+00:35:15,890 --> 00:35:19,490
+تساوي T تساوي T تساوي T تساوي T تساوي T تساوي T
+
+437
+00:35:19,490 --> 00:35:20,030
+تساوي T تساوي T تساوي T تساوي T تساوي T تساوي T
+
+438
+00:35:20,030 --> 00:35:28,000
+تساوي T تساوي T تساوي T تساوي T  إذن بدنا نثبت
+
+439
+00:35:28,000 --> 00:35:33,040
+ارجع لي بالله على النص اللي عندك بدك تثبت الآن
+
+440
+00:35:33,040 --> 00:35:40,840
+خلصنا اللي هو A وخلصنا B وخلصنا هاي C عندي S T لكل 
+
+441
+00:35:40,840 --> 00:35:44,380
+Star بيساوي T Star S Star خلينا نثبتها مع بعض برضه
+
+442
+00:35:44,380 --> 00:35:50,980
+بنفس الأسلوب كلها حسابات مشابهة لحاجتنا الآن ابدأ
+
+443
+00:35:50,980 --> 00:35:56,640
+في مين S زي ال T لكل Star S T لكل Star طبعا ال
+
+444
+00:35:56,640 --> 00:36:01,210
+Star بدخل على مين؟ على ال Y اللي هي last two Y
+
+445
+00:36:01,210 --> 00:36:05,330
+واللي في الـ H1 اتفقنا عليه اسمه ايش؟ اسمه X Y
+
+446
+00:36:05,330 --> 00:36:12,950
+يساوي اللي هو رجعوها بيصير Y و S T المفهومة لـ X Y
+
+447
+00:36:12,950 --> 00:36:20,610
+يساوي اللي هو عبارة عن Y و S of T X Y يساوي بدي أجيب
+
+448
+00:36:20,610 --> 00:36:24,210
+هذا على الجهة الثانية بيصير S Star فاهمين؟ بيصير S
+
+449
+00:36:24,210 --> 00:36:30,270
+Star Y و T X بتجيب الـ T على الجهة الثانية بيساوي
+
+450
+00:36:30,270 --> 00:36:36,430
+اللي هو عبارة عن T star S star Y و مع X إذا صار
+
+451
+00:36:36,430 --> 00:36:42,010
+هذا الـ N و هذا صحيح لمين لكل X و Y إذا هذا ناقص
+
+452
+00:36:42,010 --> 00:36:44,670
+هذا بيساوي صفر للأخرى للأخرى اللمة اللي احنا
+
+453
+00:36:44,670 --> 00:36:48,590
+عارفينها فبتطلع عند S of T الكل star بيساوي T star
+
+454
+00:36:48,590 --> 00:36:53,810
+في S star إذا حسابات كلها حسابات سهلة الآن الجزء
+
+455
+00:36:53,810 --> 00:36:58,820
+اللي هو الجابر الأخير norm اللي هو الـ T star في T
+
+456
+00:36:58,820 --> 00:37:01,840
+بيساوي norm لـ T في T star بيساوي norm من الـ T
+
+457
+00:37:01,840 --> 00:37:05,440
+تربيع خلينا نبرهن هذه من اللي عندها وبعدين نرجع 
+
+458
+00:37:05,440 --> 00:37:12,700
+لهذه اطلع لفوق شوية اطلع لفوق شوية الآن T star في
+
+459
+00:37:12,700 --> 00:37:20,340
+T الـ T طبعا من وين جايه؟ من H1 إلى H2 لأن الـ T*)
+
+460
+00:37:20,340 --> 00:37:25,300
+هتكون شغالة من وين؟ من H1 هترجع لمين؟ للـ H1 اللي هي
+
+461
+00:37:25,300 --> 00:37:29,520
+تبقى هتطلع من H2 لـ H1 فهترجع T*) T من H1 لعند مين؟
+
+462
+00:37:29,520 --> 00:37:34,580
+لعند H1 لكن T في T*) الـ T*) شغالة على الـ H2 فالـ
+
+463
+00:37:34,580 --> 00:37:37,620
+T T*) هتسيطر لـ H2 لعند الـ H2 composition of two
+
+464
+00:37:37,620 --> 00:37:41,770
+functions T من H1 لعند H2 و T Star من H2 لعند H1
+
+465
+00:37:41,770 --> 00:37:46,610
+فبصير ال composition الأول لما نبدأ T Star T من H1
+
+466
+00:37:46,610 --> 00:37:50,610
+لعند H1 ال composition الثاني T في T Star من H2
+
+467
+00:37:50,610 --> 00:37:54,570
+لعند مين؟ لعند H1 عشان أنتوا يهلا الشغل بس طيب الآن
+
+468
+00:37:54,570 --> 00:37:59,550
+احسبوا لي norm ال T X لكل تربيع ماشي الحال بدي 
+
+469
+00:37:59,550 --> 00:38:02,090
+أسالكم في الآخر norm ال T Star في T هو نفسه norm
+
+470
+00:38:02,090 --> 00:38:05,250
+ال T في T Star هو norm من مين؟ ال T تربيع أمر برضه
+
+471
+00:38:05,250 --> 00:38:09,950
+حسابات سهلة لو جينا حسبنا norm الـ TX الكل تربيع
+
+472
+00:38:09,950 --> 00:38:12,750
+هو اللي هو ال product بين الـ TX و الـ TX يساوي
+
+473
+00:38:12,750 --> 00:38:17,950
+بنجيب هذه هنا فبصير T start TX اللي هي أكيد
+
+474
+00:38:17,950 --> 00:38:21,570
+بالشوارزين quality طبعا ال absolute value لهذه هو
+
+475
+00:38:21,570 --> 00:38:24,890
+نفسه هذا مدام هذا صار absolute value لأن هذا عبارة
+
+476
+00:38:24,890 --> 00:38:28,690
+عن كمية تربيعية يعني بما عبارة عن اللي هو ال
+
+477
+00:38:28,690 --> 00:38:31,570
+absolute value لها واضح اه؟ ف بيشوار zin quality
+
+478
+00:38:31,570 --> 00:38:35,670
+أصغر أو يساوي هذا، norm هذا في norm هذا أو هذا أصغر
+
+479
+00:38:35,670 --> 00:38:38,130
+أو يساوي هذا، T is bounded و T star is bounded إذا
+
+480
+00:38:38,130 --> 00:38:41,430
+أنا أصغر أو يساوي norm ال X norm ال T في صرف T في
+
+481
+00:38:41,430 --> 00:38:47,010
+norm ال X لكل ماله لكل تربيع، واضح كيف اه؟ طيب،
+
+482
+00:38:47,010 --> 00:38:52,110
+الآن أنا بدأت عن صغر هذا أصغر أو يساوي هذا أنا بديها
+
+483
+00:38:52,110 --> 00:38:55,770
+هذا كله على بعضه معناه فيه، فبصير norm of T X الكل
+
+484
+00:38:55,770 --> 00:38:58,990
+تربيع على norm of X التربيع أصغر أو يساوي norm of T
+
+485
+00:38:58,990 --> 00:39:01,830
+star في T، إذا الأكيد بيصير عندي norm of T تربيع
+
+486
+00:39:01,830 --> 00:39:06,260
+لأن هذا عبارة عن supremum لكل تربيع، فاهمين؟ أصغر
+
+487
+00:39:06,260 --> 00:39:08,980
+أو يساوي اللي هو بيساوي sup norm ل T X في كل تربيع
+
+488
+00:39:08,980 --> 00:39:12,020
+اللي هو أصغر أو يساوي norm ال .. norm ال T star في T
+
+489
+00:39:12,020 --> 00:39:14,700
+اللي هو أصغر أو يساوي norm ال T star في norm ال T اللي
+
+490
+00:39:14,700 --> 00:39:17,900
+هو .. فاهمين طبعا في norm ال T تقل .. في norm ال T
+
+491
+00:39:17,900 --> 00:39:20,800
+لإن هذا هو norm ال T نفسه من النظرية الأولى بيصير
+
+492
+00:39:20,800 --> 00:39:25,160
+norm ال T تربيع لإن صار عندي norm ال T تربيع أصغر
+
+493
+00:39:25,160 --> 00:39:28,500
+أو يساوي هذا المقدار أصغر أو يساوي norm ال T تربيع لإن
+
+494
+00:39:28,500 --> 00:39:33,110
+صار في الطريق كلها متساويات فاهمين؟ حصرتهم بين نفس
+
+495
+00:39:33,110 --> 00:39:36,810
+الكمية الكميتين هدول هذه حصرتها بين norm الـT
+
+496
+00:39:36,810 --> 00:39:41,830
+تربيع و norm الـT تربيع صار عندي norm الـT star في
+
+497
+00:39:41,830 --> 00:39:46,310
+T هو نفسه norm الـT تربيع الآن يا بتعمل ما عملناه
+
+498
+00:39:46,310 --> 00:39:50,050
+قبل شوية بنفس الأسلوب بس بناخد T في T star بدل T
+
+499
+00:39:50,050 --> 00:39:53,910
+star في T و بنحصل نفس الشيء أو الآن بعد ما حصلنا
+
+500
+00:39:53,910 --> 00:39:57,550
+هذه ما هو اللي بيظبط على الـT بيظبط على الـT star
+
+501
+00:39:57,550 --> 00:40:02,870
+بيصير الآن مكان كل T star حطه مين؟ T replacing T by
+
+502
+00:40:02,870 --> 00:40:07,990
+T star to get T star star T star شيلنا بس اللي هو
+
+503
+00:40:07,990 --> 00:40:12,770
+ال T و حطيناه مكانه T star فاهمين؟ فبصير T star star
+
+504
+00:40:12,770 --> 00:40:17,730
+في T star بيساوي T star تربيع وهذه normها هي نفس ال
+
+505
+00:40:17,730 --> 00:40:22,170
+T تربيع وهذه هي T في T star فبكون حصلنا على اللي
+
+506
+00:40:22,170 --> 00:40:26,470
+هو T في T star و أنا T star في T فصار norm هذه
+
+507
+00:40:26,470 --> 00:40:30,420
+و norm هذه هو نفسه مين؟ norm ال T تربيع انزل خليني
+
+508
+00:40:30,420 --> 00:40:36,580
+ناخد اخر واحدة اللي هي E خليني نطلع على E برضه
+
+509
+00:40:36,580 --> 00:40:45,540
+حسابات و شغلات عشان كنت على الكتاب برضه 
+
+510
+00:40:45,540 --> 00:40:51,760
+حسابات كلها و حسابات سهلة زي ما قلنا T*) T من H1 إلى
+
+511
+00:40:51,760 --> 00:40:59,240
+H2 H2 لكن T تستار من H2 لعند HH التي هي 2 مصر على
+
+512
+00:40:59,240 --> 00:41:03,280
+أنه سهل norm TX لكل تربيع بسوء inner product هذا و
+
+513
+00:41:03,280 --> 00:41:09,320
+يساوي T*)TX عملنا هذا كله و اه ده ايه عملناها 
+
+514
+00:41:09,320 --> 00:41:10,260
+عملناها اطلع لفهم
+
+515
+00:41:20,350 --> 00:41:24,350
+انزل انزل انزل
+
+516
+00:41:24,350 --> 00:41:28,290
+انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+517
+00:41:28,290 --> 00:41:30,850
+انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+518
+00:41:30,850 --> 00:41:31,830
+انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+519
+00:41:31,830 --> 00:41:31,910
+انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+520
+00:41:31,910 --> 00:41:31,990
+انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+521
+00:41:31,990 --> 00:41:35,110
+انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+522
+00:41:35,110 --> 00:41:40,310
+انزل انزل
+
+523
+00:41:47,840 --> 00:41:55,100
+إذا كانت T بتساوي صفر T بتساوي صفر الـ T في T Star 
+
+524
+00:41:55,100 --> 00:42:02,600
+صفر أكيد اه معايا احنا الآن أثبتنا أنه ال norm هذا
+
+525
+00:42:02,600 --> 00:42:07,920
+بيساوي هذا مظبوط فلو كانت T Star في T بيساوي صفر
+
+526
+00:42:07,920 --> 00:42:11,600
+إذا ال norm هذا صفر صح؟ إذا ال norm هذا صفر إذا T
+
+527
+00:42:11,600 --> 00:42:17,260
+صفر conversely T صفر norm هي صفر، إذا norm هو صفر،
+
+528
+00:42:17,260 --> 00:42:21,220
+إذا هو صفر، صح؟ يبقى تحسبوها حسابك، بأي طريقة 
+
+529
+00:42:21,220 --> 00:42:25,060
+بنفعل، أي سؤال وإلى لقاء آخر
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/WmXLCzkJRL8_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/WmXLCzkJRL8_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0be99dc27112998f06b990e244454a7ec5d224d9
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/WmXLCzkJRL8_raw.srt
@@ -0,0 +1,2304 @@
+1
+00:00:05,970 --> 00:00:08,510
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,510 --> 00:00:12,170
+والصلاة والسلامة على سيد المرسلين سيدنا محمد وعلي
+
+3
+00:00:12,170 --> 00:00:16,670
+آله وصحبه أجمعين هذه المحاضرة رقم تلاتين نساق
+
+4
+00:00:16,670 --> 00:00:20,810
+تحليل اقتراني أو تحليل دالي طلاب طالبات الجامعة
+
+5
+00:00:20,810 --> 00:00:24,850
+الإسلامية قسم الرياضيات ماجستير وصلنا لعند اللي هو
+
+6
+00:00:24,850 --> 00:00:28,370
+ال section السادس في شبطر أربعة اللي هو تحت عنوان
+
+7
+00:00:28,370 --> 00:00:29,710
+reflexive spaces
+
+8
+00:00:32,710 --> 00:00:36,690
+نبدأ في البداية بها اللمّة الصغيرة على أساس
+
+9
+00:00:36,690 --> 00:00:41,570
+تأهيلنا لإنه نعرف شو معناه بعد شوية لما بعدين نعرف
+
+10
+00:00:41,570 --> 00:00:48,270
+شو معناه reflexive space اللمّة بتقول التالي for
+
+11
+00:00:48,270 --> 00:00:53,310
+every fixed X in a normed space X the functional
+
+12
+00:00:53,310 --> 00:00:58,610
+GX defined on X' يعني عندي X عبارة عن normed space
+
+13
+00:01:01,290 --> 00:01:06,730
+وعندي x arbitrary element in X لكن اللي هو بنحكي
+
+14
+00:01:06,730 --> 00:01:10,370
+عن إيش محدد أخدته arbitrary but fixed يعني بدي
+
+15
+00:01:10,370 --> 00:01:13,590
+أسير أحكي عن ال element العشوائي اللي في ال X اللي
+
+16
+00:01:13,590 --> 00:01:18,230
+أخدته عشوائي بس بدي أحكي عن element معين بعد ما
+
+17
+00:01:18,230 --> 00:01:21,690
+أخده عشوائي بدي أحكي عنه بدي نعرف ال functional DX
+
+18
+00:01:23,550 --> 00:01:29,470
+معرفة defined on X' يعني تاخد من X' و ترمى في الـ
+
+19
+00:01:29,470 --> 00:01:35,010
+scalar field تبعته اللي هو الـ K كيف بدي أعرفها؟
+
+20
+00:01:35,010 --> 00:01:41,130
+DX of العناصر اللي هنا dual functional لإن هذا
+
+21
+00:01:41,130 --> 00:01:45,470
+الdual اسم بياسم of F بساوي، إيش بدي أعرفها؟ بدي
+
+22
+00:01:45,470 --> 00:01:49,050
+أعرف قيمة الـ F دي اللي أخدتها من هنا عند مين عنده
+
+23
+00:01:49,050 --> 00:01:55,550
+النقطة X الـ Fixed هذه بساوي F of Xالان هذه صارت
+
+24
+00:01:55,550 --> 00:01:59,270
+عندي اللي هي function هو بتدعي الآن اللي ما بتقول
+
+25
+00:01:59,270 --> 00:02:03,890
+هتطلع هذا ال function is a bounded linear
+
+26
+00:02:03,890 --> 00:02:07,770
+functional يعني بمعنى آخر هتطلع اللي عالميا على ال
+
+27
+00:02:07,770 --> 00:02:11,310
+X' إذا هتكون في الدول اسمه إسلاميا لل X' يعني في
+
+28
+00:02:11,310 --> 00:02:15,370
+ال second دول و كأنها DX element in X double prime
+
+29
+00:02:15,370 --> 00:02:19,550
+و هيطلع عندي نورم ال DX هو نورمين ال X طلع ليها
+
+30
+00:02:19,550 --> 00:02:24,190
+الكتابالان بدنا نبرهن هذه اللي هي ال linearity
+
+31
+00:02:24,190 --> 00:02:29,770
+اللي هي يعني بالطرق العادية يعني لو جينا أخدنا G X
+
+32
+00:02:29,770 --> 00:02:40,700
+of Alpha Fمثلا زائد F إبراهيم أو F واحد بندن نشوف
+
+33
+00:02:40,700 --> 00:02:45,580
+إيش قيمتها بقى هتكون قيمتها بالساوي Alpha F زائد F
+
+34
+00:02:45,580 --> 00:02:50,780
+واحد الكل of مين حسب التعريف of X صح ولا لأ ويساوي
+
+35
+00:02:50,780 --> 00:02:57,620
+Alpha F of X زائد F واحد of X وهذه فعلا مين هي
+
+36
+00:02:57,620 --> 00:03:06,750
+عبارة عن Alpha DX of Fصحيح؟ زائد مين زائد g of dx
+
+37
+00:03:06,750 --> 00:03:14,210
+of f واحد فعلاً طلعت اشملها easily لان لان المرة
+
+38
+00:03:14,210 --> 00:03:18,790
+الماضية اللي هي ال chapter اللي في ال section اللي
+
+39
+00:03:18,790 --> 00:03:25,690
+فات أخدنا ال norm بدلالة ال xيعني نورم الـ X
+
+40
+00:03:25,690 --> 00:03:29,450
+بدلالة الـ F آسف غير إن أحنا بنوجد النورم بدلالة
+
+41
+00:03:29,450 --> 00:03:35,430
+مين اللي هو ال X نفسها اللي بقصده يعني نقول نورم
+
+42
+00:03:35,430 --> 00:03:41,810
+ال X أو نورم ال F بساوي ال supremum هذا اللي
+
+43
+00:03:41,810 --> 00:03:49,190
+بنعرفه F of X على X نورم ل X element in X minus
+
+44
+00:03:49,190 --> 00:03:54,930
+مين Zero هذا التعريف العادي مافي الحالالان اخدنا
+
+45
+00:03:54,930 --> 00:03:58,870
+احنا المره الفاتحة الكورولارى انه Normal X بنقدر
+
+46
+00:03:58,870 --> 00:04:05,230
+نقول عنها عبارة عن ال supreman لل F of X عالمياعلى
+
+47
+00:04:05,230 --> 00:04:11,050
+norm الـ F والـ F element in X' ماشي الحال الأخرى
+
+48
+00:04:11,050 --> 00:04:13,890
+هذا خدمة المرة الفاتتة اللي هي النتيجة بس أعملها
+
+49
+00:04:13,890 --> 00:04:18,450
+الآن الان عشان أثبت لكم إنه GX is bounded وNorm ما
+
+50
+00:04:18,450 --> 00:04:22,850
+بيسوي نورم الـ X الأمر سهل نورم الـ GX حسب تعريف
+
+51
+00:04:22,850 --> 00:04:26,490
+اللي هو النورم العادي هو أبداً ال supremum لقيمة
+
+52
+00:04:26,490 --> 00:04:28,990
+هذه عند اللي هو الـ arbitrary F اللي هي في
+
+53
+00:04:28,990 --> 00:04:33,240
+domainها domainها مين هو؟ X'الان بيصير absolute
+
+54
+00:04:33,240 --> 00:04:37,420
+value of g x of f على mean normal f دي اللي هي ال
+
+55
+00:04:37,420 --> 00:04:40,220
+element اللي هو الموجود في الـ x' للفاتي اللي
+
+56
+00:04:40,220 --> 00:04:44,440
+بيساوي النشتفر الان هذا نفسه بيساوي g x of f ايش
+
+57
+00:04:44,440 --> 00:04:49,500
+هي هايها g x of f بتساوي meanF of X إذا بيساوي الـ
+
+58
+00:04:49,500 --> 00:04:54,480
+absolute value الـ F of X على نورم الـ F F limit
+
+59
+00:04:54,480 --> 00:04:58,260
+X' وهذه من الكورولر اللي حكيت عنها قبل شوية إيش
+
+60
+00:04:58,260 --> 00:05:02,320
+بتساوي نورم ال X إذا صار عندي نورم ال GX بيساوي
+
+61
+00:05:02,320 --> 00:05:09,430
+مين نورم اللي هو LX اطلع لفوقإذا صار عندي اللي هي
+
+62
+00:05:09,430 --> 00:05:13,390
+اللي اللي صارت عندي bounded وصارت عندي اللي هو
+
+63
+00:05:13,390 --> 00:05:17,810
+normها بسواه norm هذا إذا ال GX هذه اللي عندي صارت
+
+64
+00:05:17,810 --> 00:05:22,050
+bounded linear functional و norm هو norm ال X هذه
+
+65
+00:05:22,050 --> 00:05:25,990
+بتستختمها بعد شوية أطلع لها على التلخيص إلى أن نجي
+
+66
+00:05:25,990 --> 00:05:30,650
+للملة اللي باعدها الملة اللي باعدها كانت تاليبتقول
+
+67
+00:05:30,650 --> 00:05:35,250
+لي let X be a known space هذا كله عشان أصل اللي هو
+
+68
+00:05:35,250 --> 00:05:38,530
+تعريف ال reflexive space let X be a known space
+
+69
+00:05:38,530 --> 00:05:41,670
+then the canonical mapping هذا بنسميه canonical
+
+70
+00:05:41,670 --> 00:05:47,090
+mapping C هياخد من مين من X لمين لل X double prime
+
+71
+00:05:47,090 --> 00:05:52,410
+هذا اللي هيحددلي اللي هو هوية ال reflexive space
+
+72
+00:05:52,410 --> 00:05:56,290
+من خلاله بدي أعرف ال reflexive spaceإيه هذا ال
+
+73
+00:05:56,290 --> 00:05:59,170
+mapping؟ then the canonical mapping C من X ليند X
+
+74
+00:05:59,170 --> 00:06:03,050
+double prime defined by إيش بده ياخد هذا؟ بده ياخد
+
+75
+00:06:03,050 --> 00:06:08,190
+ال C of X أي X المتنهانة يرميه لمين ل G X وين
+
+76
+00:06:08,190 --> 00:06:12,140
+موجودة في ال X double prime اللي تاية مهتلهااللي
+
+77
+00:06:12,140 --> 00:06:16,840
+هي ايش DX الـ Double Prime تعريفها؟ انه DX of F هي
+
+78
+00:06:16,840 --> 00:06:20,220
+اللي عرفتها قبل شوية بساوة F of X لكل F element in
+
+79
+00:06:20,220 --> 00:06:23,300
+X prime ايش هيعمللي ال canonical mapping هذا؟
+
+80
+00:06:23,300 --> 00:06:27,440
+المعرف على هذا الأساس هيعمللي is an isomorphism
+
+81
+00:06:27,440 --> 00:06:32,140
+from X onto mean R of C يعني هيعمللي one to one و
+
+82
+00:06:32,140 --> 00:06:37,540
+isometric و linear لكن مش هيقوللي ان هو ontoاللي
+
+83
+00:06:37,540 --> 00:06:41,660
+هو بس isomorphism من وين؟ من X onto mean range of
+
+84
+00:06:41,660 --> 00:06:45,700
+C the range of mean of C يعني قال له كلمة بتمتعي
+
+85
+00:06:45,700 --> 00:06:49,840
+بكل شيء مع ده خاصية اللي هو الـ onto ممكن أه و
+
+86
+00:06:49,840 --> 00:06:54,100
+ممكن لأ حسب اللي موجود واضح اللي بحكيه؟ طيب الآن
+
+87
+00:06:54,100 --> 00:06:57,500
+لنثبت هذا الكلام عشان نثبت اللي هو isomorphism
+
+88
+00:06:57,500 --> 00:07:03,060
+بنثبت ال linearityالـ Linearity كالعادة خدوا أي أف
+
+89
+00:07:03,060 --> 00:07:07,080
+في ال X براي أنا الآن ال .. ال mapping تبعي من وين
+
+90
+00:07:07,080 --> 00:07:18,580
+لوين ال mapping ال
+
+91
+00:07:18,580 --> 00:07:25,700
+mapping Cمن X لعند X مين double prime الـ C هتاخد
+
+92
+00:07:25,700 --> 00:07:28,760
+الـ X و هترنيها في مين في ال element هنا سميناه
+
+93
+00:07:28,760 --> 00:07:32,660
+مين هو الـ GX الـ GX هذا هيكون اللي هو في الـ X
+
+94
+00:07:32,660 --> 00:07:35,700
+double prime يعني هيكون الـ GX من X prime لعند مين
+
+95
+00:07:35,700 --> 00:07:40,060
+لعند K تحت القانون GX of F بيساوي مين F of X لكل F
+
+96
+00:07:40,060 --> 00:07:44,000
+موجودة في الـ X primeطب إذن الآن عشان أثبت Linear
+
+97
+00:07:44,000 --> 00:07:49,640
+بدي أثبتلكم إن C α X زائد Y عند كل نقطة من النقاط
+
+98
+00:07:49,640 --> 00:07:52,280
+F F F F F F F F F F F F F F F F F F F F F F F F F
+
+99
+00:07:52,280 --> 00:07:53,200
+F F F F F F F F F F F F F F F F F F F F F F F F F
+
+100
+00:07:53,200 --> 00:07:54,060
+F F F F F F F F F F F F F F F F F F F F F F F F F
+
+101
+00:07:54,060 --> 00:07:54,300
+F F F F F F F F F F F F F F F F F F F F F F F F F
+
+102
+00:07:54,300 --> 00:07:57,660
+F F
+
+103
+00:07:57,660 --> 00:07:57,720
+F F F F F F F F F F F F F F F F F F F F F F F F F
+
+104
+00:07:57,720 --> 00:07:57,760
+F F F F F F F F F F F F F F F F F F F F F F F F F
+
+105
+00:07:57,760 --> 00:07:57,760
+F F F F F F F F F F F F F F F F F F F F F F F F F
+
+106
+00:07:57,760 --> 00:08:04,030
+F F F F F Fلان خد arbitrary f element in X' وخد ل
+
+107
+00:08:04,030 --> 00:08:07,510
+X و Y وين موجودات في الـ domain اللي بنحكي عنها و
+
+108
+00:08:07,510 --> 00:08:13,130
+الـ α scalar احسبلي C α X زي Y عند مين؟ عند الـ F
+
+109
+00:08:13,130 --> 00:08:17,870
+واضح؟ الـ F arbitrary element in وين؟ in X' بساوي
+
+110
+00:08:17,870 --> 00:08:22,210
+حسب التعريف اللي قبله بشوية بصير G هذه of هذه،
+
+111
+00:08:22,210 --> 00:08:27,290
+مظبوط؟ G α X زي Y of F وهذه تعريفة إيش؟ F لهذا
+
+112
+00:08:27,880 --> 00:08:32,480
+ويساوي f of α x زائد y ويساوي f is linear ما هي f
+
+113
+00:08:32,480 --> 00:08:36,700
+element in x' إذا هتتوزع α f of x زائد f of mean
+
+114
+00:08:36,700 --> 00:08:42,000
+of y الآن هذه بدرجة حال أصلها هذه عبارة عن مين هذه
+
+115
+00:08:42,000 --> 00:08:46,080
+الحالها اللي هو g x of f وهذه ال alpha زي ما هي
+
+116
+00:08:46,080 --> 00:08:51,510
+وهذه ايش أصلها g of y of fالآن هذه اللي هي Alpha
+
+117
+00:08:51,510 --> 00:08:56,490
+DX of F هي عبارة عن هذه كلها عبارة عن مين هي C of
+
+118
+00:08:56,490 --> 00:09:01,370
+X of مين of F زي ما احنا معرفينها CXاشو بتساوي DX
+
+119
+00:09:01,370 --> 00:09:06,290
+CX of F بيساوي DX of F هي عندك DX of F بيصير عبارة
+
+120
+00:09:06,290 --> 00:09:10,530
+عن C of X of مين of F والألفة معاها ونفس ال
+
+121
+00:09:10,530 --> 00:09:15,710
+relation DY of F هي عبارة عن C of Y of مين of F
+
+122
+00:09:16,160 --> 00:09:19,700
+الان هذا الكلام صار صحيح لكل F إذا صارت عند C of
+
+123
+00:09:19,700 --> 00:09:24,220
+Alpha X زائد Y بتساوي Alpha C of X زائد C of Y
+
+124
+00:09:24,220 --> 00:09:31,560
+وهذا يعني ان الـ C is Linear طيب الان note that
+
+125
+00:09:31,560 --> 00:09:39,120
+بدي أحصلكم الآن على إنها bounded و isometric معاية
+
+126
+00:09:39,120 --> 00:09:45,530
+نشوف كيفخدوا الآن أي F element in main in X' والـ
+
+127
+00:09:45,530 --> 00:09:49,350
+X وY are arbitrary points in main in X نفسها
+
+128
+00:09:49,350 --> 00:09:55,350
+ويحسبولي GX-Y of F إيش هيساوي حسب التعريف الجبل
+
+129
+00:09:55,350 --> 00:10:02,710
+شويةهي عبارة عن F of X minus Y والـ F is Linear
+
+130
+00:10:02,710 --> 00:10:05,930
+إذا بيسوا F of X ناقص F of Y طب الـ F of X ما هي
+
+131
+00:10:05,930 --> 00:10:10,290
+عبارة عن GX F of F والـ F of Y هي عبارة عن GY of F
+
+132
+00:10:10,290 --> 00:10:14,730
+إلى أن بيصير عبارة عن GX ناقص GY of مين of F حصل
+
+133
+00:10:14,730 --> 00:10:20,440
+طرح دالكين إلى أن صار عندي الآن هذا المقداربساوي
+
+134
+00:10:20,440 --> 00:10:25,900
+هذا المقدار عند كل F اذا اكيد هيصير عندى GX-Y هو
+
+135
+00:10:25,900 --> 00:10:30,480
+نفسه G GX ناقص GY لأنه دالتين متساويتين عند كل
+
+136
+00:10:30,480 --> 00:10:32,740
+نقطة من النقطة ال domain هنا اللي هو ال F اذا
+
+137
+00:10:32,740 --> 00:10:38,500
+هيكون GX-Y بساوي GX ناقص GY من لمّة أربعة ستة واحد
+
+138
+00:10:38,500 --> 00:10:43,530
+اللي قبل بشوية خدولي ال norm CX ناقص CYماذا يساوي
+
+139
+00:10:43,530 --> 00:10:49,650
+CX GX نقص مين GY يساوي نورم GX نقص Y هذه اللي
+
+140
+00:10:49,650 --> 00:10:53,710
+أثبتناها اللي هي هذه من اللي قبل بشوية ماذا يساوي
+
+141
+00:10:53,710 --> 00:10:58,730
+نورم X minus Y إذا صار عندي اللي هو C of X نقص C
+
+142
+00:10:58,730 --> 00:11:02,890
+of Y يساوي نورم X minus Yوهذا معناته أن هذا يعني
+
+143
+00:11:02,890 --> 00:11:04,810
+أن C هي عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+144
+00:11:04,810 --> 00:11:08,070
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+145
+00:11:08,070 --> 00:11:09,350
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+146
+00:11:09,350 --> 00:11:10,410
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+147
+00:11:10,410 --> 00:11:12,790
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+148
+00:11:12,790 --> 00:11:13,430
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+149
+00:11:13,430 --> 00:11:13,950
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+150
+00:11:13,950 --> 00:11:19,460
+عن عبارة عن عبارة عن عبارة عن عبارة عن عهلقال الـ
+
+151
+00:11:19,460 --> 00:11:24,480
+Spaces الـ Spaces اللي بيكون Range of C هو الـ X
+
+152
+00:11:24,480 --> 00:11:26,880
+double prime يعني الدلة اللي جابله شوية لما تكون
+
+153
+00:11:26,880 --> 00:11:31,020
+on two على طول بنسمي الـ Space هذا X أشماله is
+
+154
+00:11:31,020 --> 00:11:35,020
+reflexive إذا الـ Space X is reflexive إذا لجينا
+
+155
+00:11:35,020 --> 00:11:42,330
+ال canonical mapping اللي هو الـ C الـ Cمن X لعند
+
+156
+00:11:42,330 --> 00:11:47,570
+X double prime ويكون onto لأن دائما هذا C إيش ماله
+
+157
+00:11:47,570 --> 00:11:52,250
+عبارة عن isomorphism لل range of C إذا لجينا اللي
+
+158
+00:11:52,250 --> 00:11:56,910
+هو onto هذا أو بمعنى آخر ال range of C بيساوي ال X
+
+159
+00:11:56,910 --> 00:12:00,930
+double prime على طول بنقول إن ال X نفسها إيش ماله
+
+160
+00:12:00,930 --> 00:12:07,630
+is a reflexive space واضح؟ طيب ونشوف الآن Notes
+
+161
+00:12:08,980 --> 00:12:14,140
+بينما 4 6 2 the non-space x is isomorphic to a
+
+162
+00:12:14,140 --> 00:12:17,700
+subspace of mean of x w برايف x w برايف اللي هو
+
+163
+00:12:17,700 --> 00:12:24,020
+mean ال range of Cهنس .. هنس بنقول X is embedable
+
+164
+00:12:24,020 --> 00:12:27,740
+in مين؟ in X double prime X is embedable in X
+
+165
+00:12:27,740 --> 00:12:32,180
+double prime لأنه في canonical mapping بين ال X و
+
+166
+00:12:32,180 --> 00:12:35,120
+بين مين؟ اللي هو X double prime يعني في
+
+167
+00:12:35,120 --> 00:12:39,340
+isomorphism بين ال X و بين اللي هو subspace منها
+
+168
+00:12:39,340 --> 00:12:43,720
+فهذه الحاجة بنسميها طبعا إيش؟ X is embedable in X
+
+169
+00:12:43,720 --> 00:12:49,080
+double prime يعني isomorphicلـ subspace من XW' وفي
+
+170
+00:12:49,080 --> 00:12:53,620
+هذه الحالة C يسمى كالونيكال اللي هي أدات الـ
+
+171
+00:12:53,620 --> 00:12:59,200
+embedding من X إلى مين إلى XW' لأن إذا كانت الـ
+
+172
+00:12:59,200 --> 00:13:05,600
+subspace X عرفية فهي عيزومورفية من مين من XW' لكن
+
+173
+00:13:05,600 --> 00:13:11,400
+لو اقل الليل عنديلو فيه isomorphism بين X وXW' ليس
+
+174
+00:13:11,400 --> 00:13:15,780
+شرطًا هيكون reflexive لأن اللي يعمل isomorphism
+
+175
+00:13:15,780 --> 00:13:18,900
+عشان يكون reflexive اللي بيعمل isomorphism بيه هو
+
+176
+00:13:18,900 --> 00:13:25,720
+الـ canonical map واضح؟ اطلع لفوق طيب
+
+177
+00:13:25,720 --> 00:13:34,240
+theorem if
+
+178
+00:13:34,240 --> 00:13:39,840
+unknown spaceX is reflexive it is إيش ما له
+
+179
+00:13:39,840 --> 00:13:45,060
+complete يعني ال space اللي مش complete تدوروش على
+
+180
+00:13:45,060 --> 00:13:48,720
+إنه reflexive على طول إيش ما له is not reflexive
+
+181
+00:13:48,720 --> 00:13:52,620
+مجرد ما يكون ال norm of the space X is reflexive
+
+182
+00:13:52,620 --> 00:13:58,040
+على طول بيكون إيش ما له complete نيجي الآن الأمر
+
+183
+00:13:58,040 --> 00:14:02,220
+سهل since X is reflexive then X is isomorphic to
+
+184
+00:14:02,220 --> 00:14:04,800
+مين؟ to X double prime مين X double prime؟
+
+185
+00:14:04,800 --> 00:14:08,140
+completeمش الـdual space complete سواء الـX
+
+186
+00:14:08,140 --> 00:14:11,400
+complete أو لا الـX'' أكيد complete إذا على طول
+
+187
+00:14:11,400 --> 00:14:13,980
+اللي هو الـisomorphic اللي هو إيش هيكون is
+
+188
+00:14:13,980 --> 00:14:19,720
+complete يعني الآن صار عندي اللي هو any reflexive
+
+189
+00:14:19,720 --> 00:14:23,660
+space is a complete space أو إذا بنخ space طيب
+
+190
+00:14:23,660 --> 00:14:28,120
+theorem every
+
+191
+00:14:28,120 --> 00:14:33,200
+finite dimensional every finite dimensional normed
+
+192
+00:14:33,200 --> 00:14:38,870
+space is reflexiveأي finite dimensional normed
+
+193
+00:14:38,870 --> 00:14:43,690
+space is reflexive اخدنا .. اعملنا قبل هيك هذا
+
+194
+00:14:43,690 --> 00:14:46,390
+اللي هو ال canonical mapping في حالة ال .. في حالة
+
+195
+00:14:46,390 --> 00:14:51,070
+مين اللي هو ال finite dimensional ليش؟ إذا بتذكروا
+
+196
+00:14:52,180 --> 00:14:55,100
+لما كنا نقول ان الـdimensional لـ X is finite على
+
+197
+00:14:55,100 --> 00:15:00,420
+طول اللي هو بيصير any linear functional is bounded
+
+198
+00:15:00,420 --> 00:15:04,880
+معناته انه صار الـ X' و الـ X'' و الـ X*) إيش ما
+
+199
+00:15:04,880 --> 00:15:07,640
+يلوزي بعض الـ X*) اللي هو the set of all linear
+
+200
+00:15:07,640 --> 00:15:10,400
+اللي هو functional مافيش bounded نفسي، احنا
+
+201
+00:15:10,400 --> 00:15:13,280
+مابنحكيش عنها الان X' في حالة الـ finite
+
+202
+00:15:13,280 --> 00:15:18,440
+dimensional بتكون هي مين طلعت الـ X*)الأن من الـ
+
+203
+00:15:18,440 --> 00:15:22,500
+Theorem 2.9.3 الـ Dimension للـ X*) لجيناها إيش
+
+204
+00:15:22,500 --> 00:15:27,580
+بتساوي؟ الـ Dimension للـ X إذا صار عندي الآن الـ
+
+205
+00:15:27,580 --> 00:15:29,760
+X double prime .. يعني صارت هذه برضه finite
+
+206
+00:15:29,760 --> 00:15:34,780
+dimensional للـ X والـ X*) إذا الـ X*) Star هتكون
+
+207
+00:15:34,780 --> 00:15:38,160
+برضه مين هي؟ الـ X double prime الـ Second Dual
+
+208
+00:15:38,160 --> 00:15:43,370
+Spaceالان however .. however اللي هو C من X لعند X
+
+209
+00:15:43,370 --> 00:15:48,290
+double star إيش كانت أثبتناها is an isomorphism
+
+210
+00:15:48,290 --> 00:15:53,510
+مدام isomorphism هذه و هو ال X double prime مين هو
+
+211
+00:15:53,510 --> 00:15:56,990
+ال X double star هو نفسه ال X double prime إذا
+
+212
+00:15:56,990 --> 00:16:01,770
+صارت C من X لعند X double star is an isomorphism
+
+213
+00:16:01,770 --> 00:16:06,640
+hence ال X هتطلعis reflexive إذن الآن كلها الـ
+
+214
+00:16:06,640 --> 00:16:10,780
+finite dimensional spaces طلعت لنا إشمالها are
+
+215
+00:16:10,780 --> 00:16:20,200
+reflexive spaces طيب الآن القلبي
+
+216
+00:16:22,330 --> 00:16:26,930
+Ibrahim طلعت عنها LQ صح؟ اللي هي 1 على P زي 1 على
+
+217
+00:16:26,930 --> 00:16:31,550
+Q بيساوي 1 كمان Ibrahim لها هترجع منين؟ للـ LB إذا
+
+218
+00:16:31,550 --> 00:16:34,750
+ال second هو اللي هو ال LB إذا على طول هتطلع
+
+219
+00:16:34,750 --> 00:16:39,210
+أشماله أكيد الكلمة بين هذا و بين هذا هي نفسها لو
+
+220
+00:16:39,210 --> 00:16:43,930
+أنتوا جاهز مدام وانتوا وانتوا وانتوا وانتوا وانتوا
+
+221
+00:16:43,930 --> 00:16:44,150
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+222
+00:16:44,150 --> 00:16:46,330
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+223
+00:16:46,330 --> 00:16:47,150
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+224
+00:16:47,150 --> 00:16:49,700
+وانتوا وانتوا وانتوا وانتوا وانتوا وreflexive
+
+225
+00:16:49,700 --> 00:16:54,560
+space إذن الان كل ال ال B spaces are reflexive
+
+226
+00:16:54,560 --> 00:16:59,880
+spaces طيب الان في عندي كمان عنوان كبير theorem 6
+
+227
+00:16:59,880 --> 00:17:07,620
+6 اللي هو every Hilbert space is reflexive any
+
+228
+00:17:07,620 --> 00:17:15,280
+Hilbert space is reflexive اللي بعده .. خسرناش
+
+229
+00:17:15,280 --> 00:17:22,250
+الوران اللي بعدهلما أربعة ستة سبعة let y be a
+
+230
+00:17:22,250 --> 00:17:35,310
+proper closed subspace خلّيني أطلع إليه هذا let
+
+231
+00:17:35,310 --> 00:17:39,770
+y be a proper closed subspace of a normed space x
+
+232
+00:17:44,190 --> 00:17:48,690
+وProper Closed Subspace منه يعني بمعنى آخر هذا
+
+233
+00:17:48,690 --> 00:17:53,710
+Closed وفي Elements بين الـ aY و بين مين و بين ال
+
+234
+00:17:53,710 --> 00:17:57,890
+X على الأقل في عندي Element هنا ماشي الحال Let X
+
+235
+00:17:57,890 --> 00:18:00,550
+not element in X minus Y خلّيني أخد X not وين
+
+236
+00:18:00,550 --> 00:18:06,470
+موجودة في ال X minus Y بيه Arbitrary و خلّيني أعرف
+
+237
+00:18:06,470 --> 00:18:10,400
+ال Deltaاللي هو بيساوي الـ infimum المسافة يعني
+
+238
+00:18:10,400 --> 00:18:15,940
+المسافة بين اللي هي ال X note و مين و ال Y ال
+
+239
+00:18:15,940 --> 00:18:23,140
+infimum لأ اللي هي ال norm Y note أو أيه Y ناقص X
+
+240
+00:18:23,140 --> 00:18:27,020
+noteوهي بيسميها D تلدة زي ما هو بيسميها such that
+
+241
+00:18:27,020 --> 00:18:31,660
+Y تلدة element in mean in Y الانفمان بين هذه و بين
+
+242
+00:18:31,660 --> 00:18:35,000
+الست اللي عندى هو سميها mean الدلتة هي اللي هي في
+
+243
+00:18:35,000 --> 00:18:38,180
+الواقع اللي هي ال distance the distance from X
+
+244
+00:18:38,180 --> 00:18:43,450
+node to Yبقولني then .. then بضمانكم there exists
+
+245
+00:18:43,450 --> 00:18:48,490
+F تلدى وين موجودة في ال X' بحيث أنه norm ال F تلدى
+
+246
+00:18:48,490 --> 00:18:53,370
+بيساوي واحد و ال F تلدى ل Y بتساوي سفر لكل Y وين
+
+247
+00:18:53,370 --> 00:18:57,450
+موجودة بلي هي بيكون موجودة في ال Y يعني بلاقي اللي
+
+248
+00:18:57,450 --> 00:19:06,830
+هو F تلدى element in X' و ال F تلدى normهابس هو
+
+249
+00:19:06,830 --> 00:19:14,150
+واحد والـ F تلدىof أي element هنا y بساوي 0 ومش
+
+250
+00:19:14,150 --> 00:19:21,450
+هيك و ال F لل X note هذه هي اللي هتساوي مين؟ اللي
+
+251
+00:19:21,450 --> 00:19:25,610
+هي المسافة F تلدة لل X note بساوي مين؟ بساوي
+
+252
+00:19:25,610 --> 00:19:28,630
+المسافة يعني لجأت ال F تلدة ده ال functional
+
+253
+00:19:28,630 --> 00:19:31,290
+بتساوي المسافة و في نفس ال issue و ال norm هو
+
+254
+00:19:31,290 --> 00:19:35,850
+بساوي 1 و F تلدة of Y لكل element هنا بساوي اللي
+
+255
+00:19:35,850 --> 00:19:37,770
+هو 0 خليني نبره مع بعض
+
+256
+00:19:42,940 --> 00:19:47,300
+اللي هن consider the subspace Z عبارة عن كل
+
+257
+00:19:47,300 --> 00:19:52,040
+الـlinear combinations اللي هي Y زاد Alpha X0 يعني
+
+258
+00:19:52,040 --> 00:19:57,000
+هو كأنه span بين الـ X0 و بين مين الـ Y نفسها such
+
+259
+00:19:57,000 --> 00:20:00,020
+that Alpha is the scalar of X هذا subspace من مين؟
+
+260
+00:20:00,020 --> 00:20:05,160
+من X لأن Y جزئية من X و الـ X0 موجودة في الـ X بظل
+
+261
+00:20:05,160 --> 00:20:08,940
+span عبارة عن subspace من الـ X and define the
+
+262
+00:20:08,940 --> 00:20:18,410
+functional Fon z يعني عرف الان f من z لعند
+
+263
+00:20:18,410 --> 00:20:23,610
+اللي هو ال scalar field تبعنا الآن هذه العناصر
+
+264
+00:20:23,610 --> 00:20:27,970
+اللي هنا اللي هي f of z اللي هو كيف شكل العنصر z
+
+265
+00:20:27,970 --> 00:20:32,770
+بساوي f of y زي ال alpha x not عملنا زيه المرة
+
+266
+00:20:32,770 --> 00:20:37,350
+الفاتة اللي هو بساوي ايه اش f of هذا بساوي مين ال
+
+267
+00:20:37,350 --> 00:20:44,900
+alpha هذه في مين في ال deltaالألفة في مين؟ في
+
+268
+00:20:44,900 --> 00:20:49,700
+الـDelta تنشوف كيف then
+
+269
+00:20:49,700 --> 00:20:52,840
+F is linear F is linear عاملة زيها المرة اللي فاتت
+
+270
+00:20:52,840 --> 00:20:56,180
+F is linear تاخدوا two elements بتكون عاملها
+
+271
+00:20:56,180 --> 00:21:03,680
+بعملها اللي هو F خلينا نقول of Gamma زد واحد زائد
+
+272
+00:21:03,680 --> 00:21:09,930
+زد اتنين بساوي تبقى معايا خلينا نتبتها linearزد
+
+273
+00:21:09,930 --> 00:21:12,870
+واحد وزد اتنين arbitrarily elementين وين أخدناهين
+
+274
+00:21:12,870 --> 00:21:18,810
+نزد اللي عندى بدا اثبت انه F is linear معايا Y
+
+275
+00:21:18,810 --> 00:21:25,170
+ساوي اللي هو F of جامعة زد واحد اللي هي جامعة في Y
+
+276
+00:21:25,170 --> 00:21:31,950
+زائد او Y واحد دعنا نسميها زائد Alpha واحد X Note
+
+277
+00:21:31,950 --> 00:21:36,690
+ماشي هذا زد واحد سميتها زد واحد اللي هو زد اتنين
+
+278
+00:21:37,600 --> 00:21:42,360
+اللي عبارة عن إيش Y2 مش هيك شكلها هي هنا يا جماعة
+
+279
+00:21:42,360 --> 00:21:51,560
+هي من هنا باخد زائد Alpha 2 X Note ويساوي جمّحن مع
+
+280
+00:21:51,560 --> 00:21:59,840
+بعض يصير F of Gamma Y1 زائد Y2 Gamma Y1 زائد Y2
+
+281
+00:21:59,840 --> 00:22:05,180
+مضروبة في مين زائد مين زائد اللي هو Alpha 1 زائد
+
+282
+00:22:05,180 --> 00:22:11,070
+Alpha 2 في X Noteو يساوي ايش قانونة هذه على طول
+
+283
+00:22:11,070 --> 00:22:16,550
+بتنمي مين معامل x0 في مين في دلتا و يساوي معامل x0
+
+284
+00:22:16,550 --> 00:22:22,590
+اللي هو Alpha 1 أه Gamma هذا مضروبة برضه Gamma
+
+285
+00:22:22,590 --> 00:22:27,870
+Gamma مضروبة في Alpha 1 أه صح Gamma مضروبة في
+
+286
+00:22:27,870 --> 00:22:33,170
+Alpha 1 طيب Gamma Alpha 1 زائد مين Alpha 2 كله
+
+287
+00:22:33,170 --> 00:22:36,410
+مضروب في مين في دلتا واضح أه
+
+288
+00:22:39,850 --> 00:22:46,930
+هي بترمي اللي هو العنصر هذا Alpha اللي هو معامل X
+
+289
+00:22:46,930 --> 00:22:52,750
+Note في Delta هاي معامل X Note في مين؟ في Delta
+
+290
+00:22:52,750 --> 00:22:56,590
+وهذا ال element فيها كلها بعض فبيصير Y ساوي اللي
+
+291
+00:22:56,590 --> 00:23:03,710
+هو Gamma Alpha 1 Delta زائد Alpha 2 في Delta Y
+
+292
+00:23:03,710 --> 00:23:09,120
+ساوية رجّح الاصلها هذه Gamma 1Gamma فالف واحد
+
+293
+00:23:09,120 --> 00:23:14,340
+Delta اللي هي عبارة عن مين هادي مع بعض هو ال
+
+294
+00:23:14,340 --> 00:23:19,160
+element، مظبوط؟ لو بمعنى أخر، عندي بدي أطلع جابة
+
+295
+00:23:19,160 --> 00:23:27,840
+برا، Gamma، بيصير عندي F of Y واحد زائد الف واحد
+
+296
+00:23:27,840 --> 00:23:35,800
+في Delta، زائد، التاني نفس الاشيF of Y2 زي الألف
+
+297
+00:23:35,800 --> 00:23:43,680
+اتنين اللي هو لأ بدون دلتا X0 أسف في X0 إذا صارت
+
+298
+00:23:43,680 --> 00:23:48,980
+اللي هي عبارة عن Linear هاي F اللي هي طبعا هادي و
+
+299
+00:23:48,980 --> 00:23:56,600
+يسوى Gamma F of Z1 زي F of Z2 و راجعوا الحسابات
+
+300
+00:23:56,600 --> 00:24:01,430
+لايكون خربطنا في إشيطيب then F is معناه إزلينا
+
+301
+00:24:01,430 --> 00:24:06,550
+خلصنا من ال linearity لأن since Y is closed then
+
+302
+00:24:06,550 --> 00:24:11,390
+Delta strictly أكبر من مين من سفر المسافة اللي هو
+
+303
+00:24:11,390 --> 00:24:15,430
+بتسير اللي هي بين هذي و هذي بتساوي سفر وعملناها
+
+304
+00:24:15,430 --> 00:24:18,670
+إذا بتتذكروا هذي عملتها في برهان نظرية في شبطر
+
+305
+00:24:18,670 --> 00:24:24,380
+اللي هو في شبطر 2إنه ليش Delta أكبر من سفر و
+
+306
+00:24:24,380 --> 00:24:28,940
+أرجعولها لأن then Delta أكبر من سفر and so F لا
+
+307
+00:24:28,940 --> 00:24:33,200
+تساوي إياش لاتساوي Zero مدام Delta أكبر من سفر
+
+308
+00:24:33,200 --> 00:24:37,600
+فالـ F مش ال Zero function لأن F إيش معرفة F of Z
+
+309
+00:24:37,600 --> 00:24:41,780
+بيساوي Alpha في Delta و ال Delta هذه مش سفر معناته
+
+310
+00:24:41,780 --> 00:24:45,300
+اللي هو صار عندى لما ما تكونش هذه سفر على طول ال F
+
+311
+00:24:45,300 --> 00:24:48,420
+of Z بتساوي قيمة غير السفر إذا أكيد مش ال Zero
+
+312
+00:24:48,420 --> 00:24:52,190
+functionوعنا اللي هو ال elements اللي زيها دي y زي
+
+313
+00:24:52,190 --> 00:24:57,930
+x0 نفسها هي قيمتها مش سفر مظبوط ولا لأ ايش قيمتها
+
+314
+00:24:57,930 --> 00:25:02,730
+بدأ تطلع تطلع
+
+315
+00:25:02,730 --> 00:25:13,210
+عبارة عن f of y زي x0 ايش بساوي دلتا نفسها مش
+
+316
+00:25:13,210 --> 00:25:16,690
+معامد x0 طيب
+
+317
+00:25:19,770 --> 00:25:23,870
+طيب اتفجنا عليها دي note that for all y element in
+
+318
+00:25:23,870 --> 00:25:28,910
+y f of y ايش بيساوي بيساوي اللي هي او انا انزل
+
+319
+00:25:28,910 --> 00:25:31,130
+عشان اقولكم مين رايح اذا اذكركم ان ايش بدي ابدل
+
+320
+00:25:31,130 --> 00:25:34,350
+ايه اف تل ده اللي هي نور ما بيساوي واحد و قابلة
+
+321
+00:25:34,350 --> 00:25:37,470
+سفر و ايش ما لو اف تل ده و في x not بيساوي اللي هو
+
+322
+00:25:37,470 --> 00:25:41,350
+دلتا الان انا بشر العلق اللي هو subspace ومنه
+
+323
+00:25:41,350 --> 00:25:47,600
+هنطلق في اللي اللي بديه طيبثم اقول لنا ان for all
+
+324
+00:25:47,600 --> 00:25:51,740
+y into y, f of y بيساوي اطلع لفوق اللي هو f of y
+
+325
+00:25:51,740 --> 00:25:55,840
+زائد مين زائد سفر في x not صح ولا لأ اللي هو ايش
+
+326
+00:25:55,840 --> 00:26:00,100
+هيطلع بساوي بساوي سفر في دلتا اللي هو سفر and f of
+
+327
+00:26:00,100 --> 00:26:03,460
+x not هنا او ده بتجداش بتساوي بساوي اللي هو دلتا
+
+328
+00:26:03,870 --> 00:26:08,470
+واضح طيب طبعا هي التفسير يتواي بساوي صفر و الف
+
+329
+00:26:08,470 --> 00:26:11,310
+بساوي واحد في الجهتين تطلع عندها دي بساوي صفر وهذا
+
+330
+00:26:11,310 --> 00:26:16,230
+بساوي واحد الان now we show that F is bounded ده
+
+331
+00:26:16,230 --> 00:26:20,110
+اثبتنا ان F لينيا و اثبتنا F مش هي الصفر و اثبتنا
+
+332
+00:26:20,110 --> 00:26:25,770
+قيمة ال F عند ال Y اي Y في ال Y هداك بساوي صفر و F
+
+333
+00:26:25,770 --> 00:26:30,700
+of X not بتساوي دلتاكل هدولة خلّيني لأنه بلزم اني
+
+334
+00:26:30,700 --> 00:26:34,860
+بعد شوية Now we show that F is bounded if Alpha
+
+335
+00:26:34,860 --> 00:26:38,260
+بتساوي سفر اذا F of Z automatically مش هتساوي
+
+336
+00:26:38,260 --> 00:26:41,140
+هتساوي سفر وهذا طبعا ال boundedness بيطلع
+
+337
+00:26:41,140 --> 00:26:46,200
+automatic يعني لو Alpha مش سفر بدي أسالكم انه F is
+
+338
+00:26:46,200 --> 00:26:50,940
+boundedأو أوصلكم لـ Boundedness لـ F الان مدام
+
+339
+00:26:50,940 --> 00:26:53,200
+Alpha مش ساوي مش ساوي ليش ساوي سيفرزن شكل اللي بده
+
+340
+00:26:53,200 --> 00:26:57,120
+أجسم على Alpha إذا بيصير عندي لأي Y element in Y
+
+341
+00:26:57,120 --> 00:27:01,340
+ناقص واحدة لـ Alpha وين هيكون برضه في Y ماشي الحال
+
+342
+00:27:01,340 --> 00:27:06,900
+طيب بحسبلي الآن absolute value لـ F of Zبتساوي F
+
+343
+00:27:06,900 --> 00:27:11,820
+of Y زائد ألفة مين X Note حسب اللي هو تعريف هذه
+
+344
+00:27:11,820 --> 00:27:15,120
+هيطلع Alpha في Delta و Absolute Value بيصير
+
+345
+00:27:15,120 --> 00:27:18,300
+Absolute Value في الألفة في المين في الدلتة لأن
+
+346
+00:27:18,300 --> 00:27:23,930
+الدلتة أكبر أو يساوي أكبر Circle من سفرY ساوي الـ
+
+347
+00:27:23,930 --> 00:27:26,550
+Absolute value لـ Alpha في مين في الـ infimum لهذه
+
+348
+00:27:26,550 --> 00:27:30,890
+الأشياء الـ infimum هي الـ distance الان الـ
+
+349
+00:27:30,890 --> 00:27:35,910
+infimum هذا سيكون أصغر أو يساوي اللي هي نجامة هي
+
+350
+00:27:35,910 --> 00:27:40,630
+الـ Absolute value لـ Alpha زي ما هي و هذه اللي هي
+
+351
+00:27:40,630 --> 00:27:44,190
+الـ infimum أصغر أو يساوي واحدة منهم من الواحدة
+
+352
+00:27:44,190 --> 00:27:47,590
+منهم ياخد Y تلدة عبارة عن ناقص واحد على الألفة في
+
+353
+00:27:47,590 --> 00:27:51,510
+مين في Y ناقص X nodeواخدتها بالشكل هذا عشان لما
+
+354
+00:27:51,510 --> 00:27:55,550
+أنا أدخل Alpha اللي جوا هيصير عبارة عن Y زائد
+
+355
+00:27:55,550 --> 00:27:59,010
+Alpha X naught، مظبوط؟ اللي هي Y زائد Alpha X
+
+356
+00:27:59,010 --> 00:28:02,350
+naught اللي هي مين؟ الـ Z اللي بدأت فيها، إذا صار
+
+357
+00:28:02,350 --> 00:28:07,110
+ال absolute value لل F of Z أصغر أو ساوي مين؟ نورم
+
+358
+00:28:07,110 --> 00:28:10,470
+الـ Z، اجسموا انتهتين أو خدوا ال suprem على نورم
+
+359
+00:28:10,470 --> 00:28:14,890
+الـ Z بساوي واحد، بتطلع اللي هو نورم ال F أصغر أو
+
+360
+00:28:14,890 --> 00:28:20,850
+ساوي إيش؟ أصغر أو ساوي واحداللي بعده اطلع لفوق
+
+361
+00:28:20,850 --> 00:28:24,250
+لنثبت انها اكبر او يساوي ايش اكبر او يساوي واحد
+
+362
+00:28:24,250 --> 00:28:30,350
+طيب by the definition of infimum there is exist a
+
+363
+00:28:30,350 --> 00:28:34,230
+sequence y and of elements in NY such that normal
+
+364
+00:28:34,230 --> 00:28:38,970
+y and not six note ايش ماله؟converge لمن؟ لـDelta،
+
+365
+00:28:38,970 --> 00:28:44,030
+ماشي الحال؟ الان الـ infimum بيساوي هذا المقدار،
+
+366
+00:28:44,030 --> 00:28:47,750
+ماشي الحال؟ إذا بقدر ألاقي sequence من ال elements
+
+367
+00:28:47,750 --> 00:28:51,630
+اللي في Y بحيث norm الـ Y الناقص اللي هو X0 يروح
+
+368
+00:28:51,630 --> 00:28:57,510
+لمن؟ لهذه الـ Delta، وثباته سهل هذا الكلام، طيب
+
+369
+00:29:00,530 --> 00:29:05,310
+صار عندى اللى هو sequence من العناصر اللى موجودة
+
+370
+00:29:05,310 --> 00:29:09,930
+في الـY نورم الـEI أنقص X0 وتروح لمين لـDelta منها
+
+371
+00:29:09,930 --> 00:29:14,350
+هذه الـsequence بتاخدها كعلخاصة توصلى لشق الثاني
+
+372
+00:29:14,350 --> 00:29:17,610
+اللى و أف النورم أكبر أو يساوي واحد خدوا بتقياد
+
+373
+00:29:17,610 --> 00:29:20,510
+النورم للأف أكبر أو يساوي واحد اللى هي أكبر أو
+
+374
+00:29:20,510 --> 00:29:24,250
+يساوم هي supreme أكبر أو يساوم القيمة عند نقطة ما
+
+375
+00:29:24,950 --> 00:29:28,410
+أو عند نقاطنا إذا أكبر أو ساوي F of Y N نقص X Note
+
+376
+00:29:28,410 --> 00:29:33,290
+اللي لجاتهم ع نورم Y N نقص X Note هذا الكلام لكل
+
+377
+00:29:33,290 --> 00:29:38,990
+اللي هي N element هناقيمة هذه اللي هي عبارة عن ال
+
+378
+00:29:38,990 --> 00:29:42,970
+absolute value لناقص واحد لناقص Delta ال absolute
+
+379
+00:29:42,970 --> 00:29:46,930
+value لناقص Delta هو مين؟ ال Delta على ال norm هذا
+
+380
+00:29:46,930 --> 00:29:51,010
+نفسه as n goes to infinity هذا بتروح ل Delta إذا
+
+381
+00:29:51,010 --> 00:29:55,530
+هذا norm ال F أكبر أو يساوي هذي for every n إذا
+
+382
+00:29:55,530 --> 00:29:58,130
+خدوا ال limit as n goes to infinity فتطلع دلتة ع
+
+383
+00:29:58,130 --> 00:30:00,570
+دلتة اللي هي ساوي واحد يصير نورم ال F أكبر أو
+
+384
+00:30:00,570 --> 00:30:04,450
+يساوي ال واحد و جابل أصغر أو يساوي ال واحد إذا صار
+
+385
+00:30:04,450 --> 00:30:08,360
+عند نورم ال F إيش بيساوي؟ بيساوي واحدهذه الـ F
+
+386
+00:30:08,360 --> 00:30:15,000
+اللي اشتغلت عليها لزد subspace من مين؟ من ال X
+
+387
+00:30:15,000 --> 00:30:20,560
+بقدر اعمل له extension أنا معتمد الآن على مين؟ على
+
+388
+00:30:20,560 --> 00:30:23,920
+اللي هو ال hand-benach theorem الان by hand-benach
+
+389
+00:30:23,920 --> 00:30:28,860
+theorem أربعة تلاتة اتنين there exist F مين؟
+
+390
+00:30:31,840 --> 00:30:36,780
+بتوسع نفوذها بدل ما كانت على الـ subspace Z هتوسع
+
+391
+00:30:36,780 --> 00:30:40,320
+نفوذها على الـ X' وبنفس الخواص such that norm of F
+
+392
+00:30:40,320 --> 00:30:45,720
+تلده بسوء واحد و F تلده of Y بسوء سفر و F تلده of
+
+393
+00:30:45,720 --> 00:30:51,040
+X0 بسوء دلتا وهيك هتكون حصلت على النتيجة اللي
+
+394
+00:30:51,040 --> 00:30:53,280
+بديها وهو المطلوب
+
+395
+00:31:02,880 --> 00:31:04,340
+يوجد كثير من الـ 4,6,8
+
+396
+00:31:08,580 --> 00:31:11,420
+إذا كان الـ Dual Space X' من نفسه نفسه نفسه نفسه
+
+397
+00:31:11,420 --> 00:31:21,600
+نفسه نفسه نفسه نفسه نفسه نفسه
+
+398
+00:31:21,600 --> 00:31:36,380
+نفسه نفسه نفسه
+
+399
+00:31:36,800 --> 00:31:41,680
+A separable normed space X with a non-separable
+
+400
+00:31:41,680 --> 00:31:46,940
+dual space X' can't be reflexive يعني لو كان عندي
+
+401
+00:31:46,940 --> 00:31:53,240
+separable normed space X وكان ال X' إيش ماله؟ non
+
+402
+00:31:53,240 --> 00:31:58,640
+-separableالآن لو كانت X' separable، فهي Automatic
+
+403
+00:31:58,640 --> 00:32:02,440
+X separable لكن ممكن يكون الـ X' non-separable
+
+404
+00:32:02,440 --> 00:32:06,560
+وهذه تكون يشمالها separable فالآن فرضينا أن X
+
+405
+00:32:06,560 --> 00:32:12,120
+separable و X' non-separable الآن يقول لي مستحيل
+
+406
+00:32:12,120 --> 00:32:15,560
+تطلع الـ X يشمالها reflexive لازم تطلع يشمالها، X
+
+407
+00:32:15,560 --> 00:32:19,440
+is not reflexive suppose that X' is non-separable
+
+408
+00:32:19,440 --> 00:32:25,130
+زي ما هو حاكيو X separable و X أشمالها و X
+
+409
+00:32:25,130 --> 00:32:28,890
+reflexive تقولوا إن كانت بيه reflexive فبنرسلها
+
+410
+00:32:28,890 --> 00:32:32,790
+contradiction الآن X اللي هي ساعة أشمال في تردنها
+
+411
+00:32:32,790 --> 00:32:38,050
+reflexive مدام X reflexive إذن الـ X double-brane
+
+412
+00:32:38,050 --> 00:32:43,740
+isomorphicمدام XW' أزو مورفك تاكس which implies
+
+413
+00:32:43,740 --> 00:32:48,500
+that XW' أشمالها separable then by theorem اللي
+
+414
+00:32:48,500 --> 00:32:53,140
+حكينا عنها فوق اللي هي الأجال درجة منها X' أسبرابل
+
+415
+00:32:53,140 --> 00:32:57,040
+بظبط ولا لأ بناء على هذه إنه إذا كانت ال XW'
+
+416
+00:32:57,300 --> 00:33:02,080
+أسبرابل هتكون اللي هي X أشمالها براي أسبرابل
+
+417
+00:33:04,580 --> 00:33:07,720
+فاهمين أه؟ الان صار عندي which is a contradiction
+
+418
+00:33:07,720 --> 00:33:14,840
+therefore x can't be reflexive الان بتسمحوا لي
+
+419
+00:33:14,840 --> 00:33:20,800
+عادة ديش أيضا .. دي ده مش فاهمين عليها example ال
+
+420
+00:33:20,800 --> 00:33:27,720
+one is not reflexive ال one is not reflexive since
+
+421
+00:33:27,720 --> 00:33:33,730
+ال one is separableأخدناها but الـ one prime
+
+422
+00:33:33,730 --> 00:33:38,670
+بتساوي ال infinity إيش ما لها is not اللي هي
+
+423
+00:33:38,670 --> 00:33:46,250
+separable then ال one is not reflexive أخدناها ده
+
+424
+00:33:46,250 --> 00:33:53,590
+الكلام سابقا خليني أرجع بس لهذه الشغلة قبل ما ..
+
+425
+00:33:53,590 --> 00:33:54,410
+بعد إذنكم يعني
+
+426
+00:34:08,250 --> 00:34:12,950
+اللي خاطر أشرحها هذه اللي هي ال .. الـ Hilbert
+
+427
+00:34:12,950 --> 00:34:16,530
+space أنه every Hilbert space is reflexive أنه هي
+
+428
+00:34:16,530 --> 00:34:21,070
+مهمة يعني فالشغلة بس بسيطة مش كبيرة بس اللي أنتوا
+
+429
+00:34:21,070 --> 00:34:24,810
+اللي بدنا نثبته فخليني أطلع عليه بال .. يعني
+
+430
+00:34:24,810 --> 00:34:29,350
+المعلومات اللي فيه بتقدروا يعني خليني أقول متوفرة
+
+431
+00:34:29,350 --> 00:34:32,830
+بين إيديكم خليني أشوفها أيش اللي بدنا نثبت أنه
+
+432
+00:34:32,830 --> 00:34:36,390
+every Hilbert space is reflexive
+
+433
+00:34:40,950 --> 00:34:45,670
+الان عشان نثبت reflexive بدنا نثبت الـ canonical
+
+434
+00:34:45,670 --> 00:34:50,840
+mapping ايش معله اذا انتهبدنا نركّب لنا ناخد الـ
+
+435
+00:34:50,840 --> 00:34:53,100
+Arbitrary Element هنا و نركّب لنا Element بحيث انه
+
+436
+00:34:53,100 --> 00:34:56,840
+يكون اللي هو صورته يعني تكون هي اللي بدأنا فيها
+
+437
+00:34:56,840 --> 00:35:00,520
+الان every Hilbert space H is reflexive we shall
+
+438
+00:35:00,520 --> 00:35:05,040
+prove surjectivity of the canonical mapping C من H
+
+439
+00:35:05,040 --> 00:35:07,920
+لعند H double prime ان احنا نعرف ان H .. C من H
+
+440
+00:35:07,920 --> 00:35:11,560
+لعند H double prime قبل بشوية قولنا دايما اللي هو
+
+441
+00:35:11,560 --> 00:35:13,940
+.. اللي هو فيه أزيومرفيزي من عند ال range of C
+
+442
+00:35:13,940 --> 00:35:18,490
+عشان نكمل القصة بس نثبت ان هي H ontoBy showing
+
+443
+00:35:18,490 --> 00:35:21,350
+that for every G element in H double prime داخد G
+
+444
+00:35:21,350 --> 00:35:25,090
+وين موجودة في الـ H double prime و ألاقي element
+
+445
+00:35:25,090 --> 00:35:28,830
+هنا بحيث انه CX هو يصير اللي هو الـ G اللي بدأت
+
+446
+00:35:28,830 --> 00:35:32,210
+فيه ماشي الحال ستلاقي اللي هو الأمور المشابهة اللي
+
+447
+00:35:32,210 --> 00:35:36,330
+حكيناها قبل شوية لذن for every G element in H
+
+448
+00:35:36,330 --> 00:35:40,170
+double prime we want to find X element in H such
+
+449
+00:35:40,170 --> 00:35:47,950
+that G بتساوي CXالآن خلّينا نحضر للوصول لهذا اللي
+
+450
+00:35:47,950 --> 00:35:51,030
+هي .. و نستعمل بعض الشغلات اللي أخدناها قبل هيك
+
+451
+00:35:51,030 --> 00:35:54,010
+خصوصا الـ ResRepresentation Theorem اللي هي اللي
+
+452
+00:35:54,010 --> 00:35:58,070
+.. اللي بناخد F بدلالة الـ inner product زي ما
+
+453
+00:35:58,070 --> 00:36:00,110
+عملنا المرة الفاتتة في المحاضرة الفاتتة عملنا زي
+
+454
+00:36:00,110 --> 00:36:03,850
+هيك شوفوا كده as a preparation we define A من H'
+
+455
+00:36:04,090 --> 00:36:07,930
+لعند Hπ عملتها قبل هيك المرة الفاتة اللي هو بي A F
+
+456
+00:36:07,930 --> 00:36:12,980
+إيش بيساوي Zالـ F من أين جاء من أتش براين و بساوي
+
+457
+00:36:12,980 --> 00:36:16,640
+Z مين الـ Z هي احنا بنقول لكل F Element من أتش
+
+458
+00:36:16,640 --> 00:36:21,400
+براين اللي هو there exist a unique Z such that F
+
+459
+00:36:21,400 --> 00:36:24,460
+of X can be written as any product X و Z هذا الـ
+
+460
+00:36:24,460 --> 00:36:29,580
+representation theoryاللي بيدا استخدمه أنه أخد أي
+
+461
+00:36:29,580 --> 00:36:32,400
+أف اللي متناقش prime و بال race representation
+
+462
+00:36:32,400 --> 00:36:36,260
+theorem for any أف اللي متناقش prime there exist a
+
+463
+00:36:36,260 --> 00:36:40,400
+unique z such that f of x بيساوي ال x ومين و ال z
+
+464
+00:36:40,400 --> 00:36:43,780
+ماشي الحال إذا انجدرت اللي أنا عرف أي أف مش متساوي
+
+465
+00:36:43,780 --> 00:36:46,580
+بيساوي ال z اللي لجيتها اللي بتدللتها عرفت اللي هي
+
+466
+00:36:46,580 --> 00:36:53,050
+الأف as another productالان عندى طبعا هذا الكلام
+
+467
+00:36:53,050 --> 00:36:56,870
+كله from تلاتة تمانية واحد we know that a is
+
+468
+00:36:56,870 --> 00:37:00,910
+bijective and isometric ال a is bijective and
+
+469
+00:37:00,910 --> 00:37:03,850
+isometric عملتها المرة الفاتتة في المحاضرة اللى
+
+470
+00:37:03,850 --> 00:37:07,430
+فاتتها عملتها الان و a is conjugate linear برضه
+
+471
+00:37:07,430 --> 00:37:10,940
+عملتها المرة الفاتتةA is going to get linear إذا
+
+472
+00:37:10,940 --> 00:37:16,460
+بتتذكروا as we see from 16 section 4-5 اللي المرة
+
+473
+00:37:16,460 --> 00:37:20,240
+الفاتتة عندي الأثبتنا لـA is going to get linear
+
+474
+00:37:20,240 --> 00:37:24,540
+رجعوه رجعوه رجعوه كله حكيته بالتفصيل المرة الفاتتة
+
+475
+00:37:25,700 --> 00:37:32,040
+الأن الـ H براين هو مجتمع مكتمل إذا من اتنين عشرة
+
+476
+00:37:32,040 --> 00:37:35,940
+أربعة اللي هو and a Hilbert space with inner
+
+477
+00:37:35,940 --> 00:37:39,680
+product space defined by برضه أثبتنا أنه لما يكون
+
+478
+00:37:39,680 --> 00:37:43,780
+الـ Hاللي هو inner product space أو Hilbert space
+
+479
+00:37:43,780 --> 00:37:48,340
+الـ H prime تبعه برضه هيكون ماله Hilbert space و
+
+480
+00:37:48,340 --> 00:37:52,220
+ال inner product تبعي اللي هو ال H prime اللي صار
+
+481
+00:37:52,220 --> 00:37:55,040
+Hilbert space بقدر اخده من ال inner product تبع
+
+482
+00:37:55,040 --> 00:37:58,580
+مين؟ تبع ال H واخدناه بالطريقة التالية ان ال inner
+
+483
+00:37:58,580 --> 00:38:04,860
+product F1 F2 تبع ال H prime بساوي اللي هو AF2
+
+484
+00:38:04,860 --> 00:38:09,730
+اللي هي AF2 و AF1 اللي هو elementين وين هذا؟هذا
+
+485
+00:38:09,730 --> 00:38:13,710
+بغض النظر إيش هو هذا بساوي Element من من من ال ..
+
+486
+00:38:13,710 --> 00:38:17,370
+هذا مش عليه inner product لأن هذا الـ H prime
+
+487
+00:38:17,370 --> 00:38:21,480
+هيكون عبارة عن Hilbert spaceوهيكون ال product
+
+488
+00:38:21,480 --> 00:38:25,660
+تبعته بقدر اخده من هذا كيف باخده من هذا لو عندي x
+
+489
+00:38:25,660 --> 00:38:30,460
+و y هنا في هذا بيصير عندي ال F1 و ال F2 تبعته
+
+490
+00:38:30,460 --> 00:38:33,680
+بيساوي inner product بس مجلوب بين الجهتين اللي هو
+
+491
+00:38:33,680 --> 00:38:38,360
+في هذه الحالة هيكون عندي F1 و F2 بيساوي A F2 هيكون
+
+492
+00:38:38,360 --> 00:38:43,280
+في ال H و ال A F1 برضه هيكون وين في ال H طيب
+
+493
+00:38:48,060 --> 00:38:52,340
+الان بيقولني لاحظ احنا قبل شوية قولنا ايه is
+
+494
+00:38:52,340 --> 00:38:56,660
+conjugate linear conjugate linear والترتيب القدر
+
+495
+00:38:56,660 --> 00:39:02,720
+اللي هو عندك ال inner product هذا اللي هو عكس اللي
+
+496
+00:39:02,720 --> 00:39:09,420
+هي بدل F2 F1 هنا مين عنده بعرفه بال F2 و ال
+
+497
+00:39:09,420 --> 00:39:12,280
+conjugate linear مع هذا العكس هيطلع اللي هو اللي
+
+498
+00:39:12,280 --> 00:39:16,920
+بديهشوفوا كيف الان note that the order of F1 و F2
+
+499
+00:39:16,920 --> 00:39:22,280
+on both sides اللي هو هذا عكس التاني الان هذا
+
+500
+00:39:22,280 --> 00:39:25,140
+هيعمل inner product ال inner product كلها إيه
+
+501
+00:39:25,140 --> 00:39:27,940
+جمال؟ لأن الخواص اللي بتعملوها و بتلاجوها على طول
+
+502
+00:39:27,940 --> 00:39:31,820
+inner product دي شكل في تفصيلها الان ماعطيكم
+
+503
+00:39:31,820 --> 00:39:35,360
+ملاحظة عالمين على الخاصية التانية اللي بتستخدم
+
+504
+00:39:35,360 --> 00:39:39,360
+فيها ال conjugate linear يعني بمعنى أخر Alpha F1 و
+
+505
+00:39:39,360 --> 00:39:45,160
+F2هذه بتحقق اللي هو إيش بتساوي Alpha ف F1 و مين؟
+
+506
+00:39:45,160 --> 00:39:48,380
+F2 اللي حققه الليال هو ال conjugate linear مع
+
+507
+00:39:48,380 --> 00:39:54,320
+تعريفه هذا كيف Alpha F1 F2 إيش بتساوي؟ بتساوي A F2
+
+508
+00:39:54,320 --> 00:40:00,290
+هذه لهذه و A لهذهA α 1 أهلاً لكن الـ A conjugate
+
+509
+00:40:00,290 --> 00:40:02,630
+ليه؟ يعني إذا اللي بده يطلع منها بتطلع إيه؟
+
+510
+00:40:02,630 --> 00:40:06,790
+conjugate فبتصير الـ α conjugate في A F 1 وده A F
+
+511
+00:40:06,790 --> 00:40:09,930
+2 لأن هذه لما تطلع من اللي بعيد اللي هو بتطلع
+
+512
+00:40:09,930 --> 00:40:12,250
+إليها كمان conjugate فبتصير لها conjugate
+
+513
+00:40:12,250 --> 00:40:16,470
+conjugate بتطلع Alpha فبتطلع اللي هي فعلا محققة من
+
+514
+00:40:16,470 --> 00:40:19,990
+اللي هو الشرط التاني تبع ال inner product والشرط
+
+515
+00:40:19,990 --> 00:40:24,310
+الأول وبجاعة الشروط برضه اللي هي سريعة وسهلةالان
+
+516
+00:40:24,310 --> 00:40:29,090
+اذا صار فعلا عندى هذا عمللى اللى هو inner product
+
+517
+00:40:29,090 --> 00:40:34,750
+على اللى هو ال H prime و هيكون complete
+
+518
+00:40:38,270 --> 00:40:42,870
+الان let g element .. كله عشان .. بدي أركب مين؟
+
+519
+00:40:42,870 --> 00:40:47,230
+بدي أركب .. أخدت اللي هو g arbitrary اللي هي ال ..
+
+520
+00:40:47,230 --> 00:40:48,750
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+521
+00:40:48,750 --> 00:40:48,790
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+522
+00:40:48,790 --> 00:40:49,070
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+523
+00:40:49,070 --> 00:40:49,090
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+524
+00:40:49,090 --> 00:40:49,430
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+525
+00:40:49,430 --> 00:40:50,130
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+526
+00:40:50,130 --> 00:40:50,410
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+527
+00:40:50,410 --> 00:40:51,230
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+528
+00:40:51,230 --> 00:40:51,810
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+529
+00:40:51,810 --> 00:40:51,810
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+530
+00:40:51,810 --> 00:40:59,970
+ال .. ال .. ال .. ال .. ال ..
+
+531
+00:40:59,970 --> 00:41:04,590
+ال .. ال ..
+
+532
+00:41:06,450 --> 00:41:10,450
+ما هي برضه الـ G في الـ H double prime يعني بمعنى
+
+533
+00:41:10,450 --> 00:41:16,690
+آخر G element in H prime الكل أشماله الـ prime بدا
+
+534
+00:41:16,690 --> 00:41:19,810
+أطبق ال race representation theorem عليها اللي هو
+
+535
+00:41:19,810 --> 00:41:22,350
+there exist لكل element هنا there exist a unique
+
+536
+00:41:22,350 --> 00:41:28,310
+element جوا بحيث انه اللي هو G of ال F أي element
+
+537
+00:41:28,310 --> 00:41:32,830
+بساوي اللي هو ال inner product بين اللي هو A of No
+
+538
+00:41:32,830 --> 00:41:40,810
+اللي هو أسف Fو F note اللي هو واحد كمان مرة ايش ال
+
+539
+00:41:40,810 --> 00:41:44,270
+reservation presentation بتفهم بتقول هذا اسم اللي
+
+540
+00:41:44,270 --> 00:41:47,810
+بدكم إياه اش برايم سمونيه اللي بدكم إياه اي inner
+
+541
+00:41:47,810 --> 00:41:54,150
+product X ماشي الان لكل element في ال X برايم بقدر
+
+542
+00:41:54,150 --> 00:42:01,390
+انادي unique element اللي هو بحيث انه Gof هذي
+
+543
+00:42:01,390 --> 00:42:09,190
+شغالة وين؟ G من H' شغالة وين من H' لمن؟ ل K فح؟
+
+544
+00:42:09,190 --> 00:42:15,290
+بتاخد ال element G of F و بترميه في شغلة لإن ال
+
+545
+00:42:15,290 --> 00:42:17,910
+research presentation بتقول لك مدام أن ال product
+
+546
+00:42:17,910 --> 00:42:22,250
+هو ال birth space أنا بقدر أجيلك unique element
+
+547
+00:42:22,250 --> 00:42:27,590
+فيه اللي هو ال H' بدلالتهبتقدر تكتب هذه as inner
+
+548
+00:42:27,590 --> 00:42:32,050
+product يعني G of F بيصير بساوى inner product بين
+
+549
+00:42:32,050 --> 00:42:36,230
+الـ F هذه ال arbitrary والـ F note اللي لديته اللي
+
+550
+00:42:36,230 --> 00:42:39,850
+عملته Z قبل شوية في الثانية فصار عندى الآن G of F
+
+551
+00:42:39,850 --> 00:42:44,030
+اللي هي عبارة عن كان بالwritten as ال inner
+
+552
+00:42:44,030 --> 00:42:47,110
+product بين F و F note مين لل inner product تبعنا
+
+553
+00:42:47,110 --> 00:42:50,270
+اللي بنشتغل عليه على مين على اللي هو ال space اللي
+
+554
+00:42:50,270 --> 00:42:55,530
+عندىهذا قبل بشوية احنا عرفناه كالتالي بيصير A F
+
+555
+00:42:55,530 --> 00:43:03,870
+Note و مين A F إذا هذا حصلته بالشكل هذا طيب الان
+
+556
+00:43:03,870 --> 00:43:08,090
+عندي لكن F of X أشبه ساوي X زد اللي قبل بشوية
+
+557
+00:43:08,090 --> 00:43:15,650
+حكيته و Z أشبه ساوي A F وعندي ال A F Note هيكون
+
+558
+00:43:15,650 --> 00:43:20,670
+اللي هيقيمةأف نوت أف بساوي زد الأف نوت حقوقه
+
+559
+00:43:20,670 --> 00:43:26,070
+يسموني إيه إيه إيش X إذا الأف نوت كإنه هي اللي
+
+560
+00:43:26,070 --> 00:43:30,250
+لجيتها اللي بدا توصلني لل element اللي لجيته اللي
+
+561
+00:43:30,250 --> 00:43:38,160
+C اللي عنده اللي هو Cاللي هو من HW' لعند H الان
+
+562
+00:43:38,160 --> 00:43:42,380
+انا بتاخد ال CG اللي بتهيأله دي لها إشي ماشي حال
+
+563
+00:43:42,380 --> 00:43:46,700
+صورة الان انا اللي بيوصللي اللي لجأته ال F هذا
+
+564
+00:43:46,700 --> 00:43:52,660
+بيوصللي لل X اللي ال CG إيش يساوي؟ يساوي ال X طيب
+
+565
+00:43:52,660 --> 00:43:57,640
+الان ال F note لجأته ال A F note طبيعي هيكون إيش
+
+566
+00:43:57,640 --> 00:44:01,990
+بيساوي؟ بيساوي اللي هو ال Xماشي الحال لإنه element
+
+567
+00:44:01,990 --> 00:44:06,330
+في H لإن هذه الصورة will هتكون موجودة في الـ H إذا
+
+568
+00:44:06,330 --> 00:44:10,250
+ال A of note بيساوي X إذا صار عندي we have اللي هو
+
+569
+00:44:10,250 --> 00:44:15,930
+A of note و A of إيش هيساوي اللي هو X مكان هذه و
+
+570
+00:44:15,930 --> 00:44:18,190
+هذه ال A of اللي جيتها من جبل اللي هي عبارة عن مين
+
+571
+00:44:18,190 --> 00:44:24,150
+عن Z و هذه نفسها إيش بتساوي F of Xفعند الان مع بعض
+
+572
+00:44:24,150 --> 00:44:30,530
+هذه g of f ايش بيساوي f of x g of f صارت بيساوي f
+
+573
+00:44:30,530 --> 00:44:34,110
+of x مدام g of f بيساوي f of x اللي هو هذا معناته
+
+574
+00:44:34,110 --> 00:44:38,730
+انه cx ايش هتساوي هتساوي ال g وهذا معناته صارت
+
+575
+00:44:38,730 --> 00:44:43,710
+اللي هي c ال subjective او انتوا وبهيك وكون خلصنا
+
+576
+00:44:43,710 --> 00:44:45,830
+البرهان وإلى لقاء ناخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Y0ewTrfR1Fk.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Y0ewTrfR1Fk.srt
new file mode 100644
index 0000000000000000000000000000000000000000..42deb8ab6bdc5d99efce5469f33aafe423ede367
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Y0ewTrfR1Fk.srt
@@ -0,0 +1,1272 @@
+
+1
+00:00:05,550 --> 00:00:08,150
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,150 --> 00:00:10,970
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:10,970 --> 00:00:16,750
+آله وصحبه أجمعين هذه هي المحاضرة رقم 15 مساق تحليل 
+
+4
+00:00:16,750 --> 00:00:19,630
+اقتراني أو تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:19,630 --> 00:00:20,790
+الإسلامية مساق 
+
+6
+00:00:23,450 --> 00:00:27,730
+ماجستير وصلنا اليوم لعند اللي هو الـ section التاسع 
+
+7
+00:00:27,730 --> 00:00:31,290
+في الـ chapter الثاني اللي هو 2.9 تحت عنوان 
+
+8
+00:00:31,290 --> 00:00:35,050
+linear operators and functionals يعني linear
+
+9
+00:00:35,050 --> 00:00:38,530
+operators and linear functionals on finite
+
+10
+00:00:38,530 --> 00:00:40,990
+dimensional spaces على الـ finite dimensional
+
+11
+00:00:40,990 --> 00:00:43,470
+spaces والدنيا كلها بتكون سهلة على الـ finite
+
+12
+00:00:43,470 --> 00:00:47,270
+dimensional spaces وحسينا هذا الكلام في اللي هي 
+
+13
+00:00:47,270 --> 00:00:50,900
+succession سابقًا والشيء بس نحطها الـ remark
+
+14
+00:00:50,900 --> 00:00:56,820
+عشان بدنا نبدأ الآن نبدأ نبني spaces اليوم هنبني
+
+15
+00:00:56,820 --> 00:01:01,240
+space مقدمة لبناء الـ space اللي هو اللي هنسميه
+
+16
+00:01:01,240 --> 00:01:04,740
+قدام The Dual Space هذا هنسميه The Algebraic Dual
+
+17
+00:01:04,740 --> 00:01:09,460
+Space هذا عائلة من الـ linear functionals
+
+18
+00:01:09,460 --> 00:01:13,280
+بعدها هنحكي عن عائلة من الـ bounded linear
+
+19
+00:01:13,280 --> 00:01:16,780
+functionals وهنشوف الآن التفاصيل شوفوا صلوا على 
+
+20
+00:01:16,780 --> 00:01:21,730
+النبي عليه الصلاة والسلام. لـ X Star كتابنا هيك أما
+
+21
+00:01:21,730 --> 00:01:24,970
+أخذه طبعًا في بعض الكتب يعني بتعمل الـ X Star ذات
+
+22
+00:01:24,970 --> 00:01:28,310
+Dual Space احنا خلينا نلتزم مع كتابنا الـ X Star
+
+23
+00:01:28,310 --> 00:01:32,770
+إيش هو؟ Be the set of all linear functionals Linear 
+
+24
+00:01:32,770 --> 00:01:38,710
+functionals ماشي Defined on a vector space X. إذن 
+
+25
+00:01:38,710 --> 00:01:44,530
+الـ N X Star نتفج من الـ N وطالع X Star يمثل عائلة 
+
+26
+00:01:44,530 --> 00:01:48,730
+الـ Linear Functionals على مين؟ على Vector Space
+
+27
+00:01:48,730 --> 00:01:52,210
+أنا مش قاعد بحكي عن مين، عن Topologies ولا بحكي عن 
+
+28
+00:01:52,210 --> 00:01:55,310
+Norm يعني أنا بحكي بس عن موجود جرد Vector Space 
+
+29
+00:01:55,310 --> 00:01:59,830
+يعني درس جبل خطوة كأننا بنحكي For any f و g element
+
+30
+00:01:59,830 --> 00:02:04,930
+in x*) بدي أعرف و skill أعرفها بدي أعرف الآن إيش
+
+31
+00:02:04,930 --> 00:02:07,790
+معنى f زي الـ g يعني إيش معنى linear functional
+
+32
+00:02:07,790 --> 00:02:10,950
+زي الـ linear functional وإيش معنى الـ f في الـ f by
+
+33
+00:02:10,950 --> 00:02:16,030
+با أعرف اللي أنتو عارفينه F زائد G of X بيساوي F of
+
+34
+00:02:16,030 --> 00:02:19,970
+X زائد مين؟ G of X هاي معنى الجامع فيه اللي هو في
+
+35
+00:02:19,970 --> 00:02:23,990
+الـ elements اللي في الـ X*) الآن Alpha في F of X 
+
+36
+00:02:23,990 --> 00:02:27,110
+معناها Alpha في F of X يعني pointwise scalar
+
+37
+00:02:27,110 --> 00:02:29,610
+multiplication pointwise addition و الـ scalar 
+
+38
+00:02:29,610 --> 00:02:32,410
+multiplication اللي أعمامنا For all X element in X
+
+39
+00:02:32,680 --> 00:02:36,720
+then X star نفسه هيعمل لي إيه تحت العملتين هذول
+
+40
+00:02:36,720 --> 00:02:41,800
+is a vector space called the algebraic dual space
+
+41
+00:02:41,800 --> 00:02:47,200
+of X إذا الـ algebraic dual space of X ما هو إلا 
+
+42
+00:02:47,200 --> 00:02:50,940
+عبارة عن vector space أو the vector space of all 
+
+43
+00:02:50,940 --> 00:02:55,560
+linear functionals in X star يعني بتاخد من X
+
+44
+00:02:55,560 --> 00:02:59,460
+العناصرها بتاخد F من X لعند scalar field تبعته
+
+45
+00:03:00,000 --> 00:03:04,780
+العنوان X Star Star is the base of all linear 
+
+46
+00:03:04,780 --> 00:03:09,380
+functionals defined on X Star يعني برد بعرف اللي 
+
+47
+00:03:09,380 --> 00:03:13,620
+هو الـ functional إيش بتسميها؟ إيش بتسميها؟ G من X
+
+48
+00:03:13,620 --> 00:03:17,840
+Star وبرميها وين؟ في الـ R هذه الآن صارت Lena
+
+49
+00:03:17,840 --> 00:03:21,880
+function على هذه هذول العناصر بقى سميه موجودات في 
+
+50
+00:03:21,880 --> 00:03:27,920
+الـ X** يعني the second algebraic dual space اللي
+
+51
+00:03:27,920 --> 00:03:33,220
+هو بنسميه second algebraic dual space واضح؟ اطلع
+
+52
+00:03:33,220 --> 00:03:40,220
+لفوق الآن نيجي لـ هالنظرية اللي بتلزمنا Let X be an
+
+53
+00:03:40,220 --> 00:03:44,240
+n-dimensional vector space بحكي عن كل جابر خط الآن
+
+54
+00:03:44,240 --> 00:03:50,200
+وعند E بتساوي E1 E2 EN مدام انديمشنال هو مين بيه
+
+55
+00:03:50,200 --> 00:03:56,400
+a basis for X. then الآن بدي أعرفلكم أو بدي أجيبلكم 
+
+56
+00:03:56,400 --> 00:04:00,520
+bases للـ X star يعني بدي أجيب من الـ X .. من bases 
+
+57
+00:04:00,520 --> 00:04:05,840
+الـ X bases لمين؟ للـ X star شوفوا هالحلوة And then 
+
+58
+00:04:05,840 --> 00:04:09,260
+the set of all linear functionals F اللي هي F1,
+
+59
+00:04:09,400 --> 00:04:17,190
+F2, Fn عدد مثل هدول Given by fk of ej بيساوي صفر لما
+
+60
+00:04:17,190 --> 00:04:21,430
+نتجي أشمالها لتساول k وواحد لما نتجي أشمالها
+
+61
+00:04:21,430 --> 00:04:28,770
+تساول k يعني F1E11 F2E22 لكن F1E البجيات صفر F2
+
+62
+00:04:28,770 --> 00:04:34,940
+للبجيات بدون E2 صفر وهكذا واضح؟ طيب إذا a basis
+
+63
+00:04:34,940 --> 00:04:39,860
+بتدعي إنه هذه الـ FK هدول يعملوا in basis for X and
+
+64
+00:04:39,860 --> 00:04:43,260
+dimension للـ X*) هو نفسه dimension من مين؟ للـ X الـ
+
+65
+00:04:43,260 --> 00:04:46,760
+basis شغلتين Linear لاندبندن زاد spanning يعمل
+
+66
+00:04:46,760 --> 00:04:50,200
+spanning لكل مين؟ الـ space اللي احنا نسبق إليه مين؟
+
+67
+00:04:50,200 --> 00:04:54,430
+space نا اللي هو الـ X*) ماشي الحال طيب To show that
+
+68
+00:04:54,430 --> 00:04:57,670
+F is a linearly independent هذي is a linearly
+
+69
+00:04:57,670 --> 00:05:00,610
+independent set عارفين إيه؟ إيش بدنا نسويه؟ goal الـ
+
+70
+00:05:00,610 --> 00:05:04,430
+summation لها Beta 1 F1 زي Beta 2 F2 زي Beta 
+
+71
+00:05:04,430 --> 00:05:07,510
+N بيساوي صفر بيساوي صفر ونوصل لـ Beta 1 Beta 2
+
+72
+00:05:07,510 --> 00:05:12,320
+Beta N كل هنا إيه شمالهم صفر شغل جبر خطر. then الـ
+
+73
+00:05:12,320 --> 00:05:15,740
+summation beta k fk of xk من واحد لعند n إيش
+
+74
+00:05:15,740 --> 00:05:20,720
+بيساوي؟ لكل الـ X اللي موجودة Element in X in
+
+75
+00:05:20,720 --> 00:05:24,420
+particular in particular مش هذا سوى لكل X in
+
+76
+00:05:24,420 --> 00:05:30,000
+particular for EJ اللي هي X بيساوي EJ فبيصير عندي 
+
+77
+00:05:30,000 --> 00:05:33,740
+الصفر هذا بيساوي summation beta K FK of EJ K من 
+
+78
+00:05:33,740 --> 00:05:38,020
+واحد لعند n تنسوش إن هدول كلها صفر ما عدا عندك
+
+79
+00:05:38,020 --> 00:05:42,240
+J بتساوي K صح؟ يعني هيصير عندي بيساوي من Beta J
+
+80
+00:05:42,240 --> 00:05:47,180
+في FJ EJ اللي هي واحد فصارت الـ BJ بيساوي صفر، 
+
+81
+00:05:47,180 --> 00:05:50,700
+والـ EJ أنا صرتها arbitrarily زي ما بختار لأي واحد و
+
+82
+00:05:50,700 --> 00:05:53,560
+لأي اتنين ولأي تلاتة لعندي ليه؟ يعني بتطلع إن كلهم 
+
+83
+00:05:53,560 --> 00:05:57,620
+الـ Beta إيه شمالهم Beta 1, Beta 2, Beta N صفر إذا
+
+84
+00:05:57,620 --> 00:06:01,840
+صار عندي This implies that Beta J بيساوي 0 for all 
+
+85
+00:06:01,840 --> 00:06:05,760
+J. معناته Therefore F is a linearly independent set
+
+86
+00:06:05,760 --> 00:06:09,620
+اللي هان يجي لإن الـ span اطلع لفوق جاوبه صحيح Let 
+
+87
+00:06:09,620 --> 00:06:15,670
+F الآن Let F اطلع لفوق كمان Let لنزل أنت اللي ..
+
+88
+00:06:15,670 --> 00:06:19,690
+Let F be any fixed element in M in X star بدي أخد 
+
+89
+00:06:19,690 --> 00:06:22,770
+أقفل X star وأقول لك بقدر أكتب الأفعار زي الـ
+
+90
+00:06:22,770 --> 00:06:26,380
+linear combination إذا انخلصنا اه مش هيك اللي معنى
+
+91
+00:06:26,380 --> 00:06:30,000
+الـ .. الـ .. الـ little bit bases for any x إذا 
+
+92
+00:06:30,000 --> 00:06:33,340
+أنا أخدت f أي element fixed element منين؟ And x 
+
+93
+00:06:33,340 --> 00:06:37,060
+star بدك تبقى أزالينا combination من f1, f2, f3، 
+
+94
+00:06:37,060 --> 00:06:41,100
+اللي عندي الـ fn طيب For any x بالثماثين x, i,
+
+95
+00:06:41,140 --> 00:06:43,980
+k, a, k, كامن عند 1 عند n ليش كتبت هيك؟ لإن
+
+96
+00:06:43,980 --> 00:06:46,440
+هدول bases وأي element ما أقدر أكتبه في الـ .. في 
+
+97
+00:06:46,440 --> 00:06:49,240
+الـ x ما أقدر أكتبه على هذه الصورة By using the
+
+98
+00:06:49,240 --> 00:06:53,870
+linearity of f we have F is linear by الـ F of X
+
+99
+00:06:53,870 --> 00:06:58,570
+بيساوي الـ summation لـ XI K F of EK K من عند واحد
+
+100
+00:06:58,570 --> 00:07:02,530
+لعند مين؟ لعند n هذا من الـ linearity طيب خلي هذه 
+
+101
+00:07:02,530 --> 00:07:07,270
+إيش؟ واحد On the other hand for أي fixed J بين واحد
+
+102
+00:07:07,270 --> 00:07:12,940
+وبين n احسبلي الآن F J of X إيش بتساوي خلي هذه في 
+
+103
+00:07:12,940 --> 00:07:16,500
+الذاكرة وحسب هذه Fj of summation بدخل لإن كل
+
+104
+00:07:16,500 --> 00:07:20,220
+أحده Linear بيساوي الـ summation لـ EK Fj of EK كل
+
+105
+00:07:20,220 --> 00:07:24,280
+هي صفر معدى عند مين؟ عند اللي هي ياش J بتلتقي مع 
+
+106
+00:07:24,280 --> 00:07:28,820
+الـ K اللي هي عند مين؟ Xij إذا صارت Fj of X إيش
+
+107
+00:07:28,820 --> 00:07:35,570
+بتساوي؟ E Ej من هذه ومن هذه خلصنا القصة بيصير F of
+
+108
+00:07:35,570 --> 00:07:40,570
+X بتساوي الـ EK بحط مكانها مين؟ F K بيساوي الـ 
+
+109
+00:07:40,570 --> 00:07:46,160
+summation لـ FK of X في E في F of E K for all X هذا
+
+110
+00:07:46,160 --> 00:07:49,500
+الكلام صحيح لكل الـ .. لكل الـ X في الدنيا إذا صارت 
+
+111
+00:07:49,500 --> 00:07:55,760
+الـ F إيش بكتبها على صورة FK في F of EK K من واحد
+
+112
+00:07:55,760 --> 00:07:58,300
+لعند مين؟ لإن function هذه لما كنتوا functions 
+
+113
+00:07:58,300 --> 00:08:00,840
+متساويات عند كل النقاط إنها متساويات مين الـ 
+
+114
+00:08:00,840 --> 00:08:05,220
+functions الـ F و الـ FK معايا؟ إذا صار عندي الـ F
+
+115
+00:08:05,220 --> 00:08:08,560
+بتساوي الـ summation هذا يعني قدرت أكتب F أزنين هو 
+
+116
+00:08:08,560 --> 00:08:12,960
+combination من هذا معناته صار الـ F لسبان للـ F و
+
+117
+00:08:12,960 --> 00:08:16,280
+لسبان للـ F طبيعي جزء من الـ X*) إذا صار لسبان للـ F
+
+118
+00:08:16,280 --> 00:08:20,080
+إيش بيساوي الـ X*) إذا صار عندي Hence F is a basis
+
+119
+00:08:20,080 --> 00:08:23,760
+for X*) and الـ dimension في الحالتين اللي هو كان
+
+120
+00:08:23,760 --> 00:08:27,520
+اللي هو F1 F2 FN هم الـ bases عدد هنا والأولانية
+
+121
+00:08:27,520 --> 00:08:29,980
+عدد هنا إذا الـ dimension للـ X بيساوي الـ dimension
+
+122
+00:08:29,980 --> 00:08:37,910
+للـ X*) وشوف اللي بعدها طيب لما نشوف اللي لما اللي 
+
+123
+00:08:37,910 --> 00:08:45,950
+عندي Let
+
+124
+00:08:45,950 --> 00:08:51,790
+C من X عند X Star Star يعني من الـ X نروح نشوف كيف
+
+125
+00:08:51,790 --> 00:08:58,810
+فيه إشي بده يعمل عند الـ X فيه لها Dual Space أو
+
+126
+00:08:58,810 --> 00:09:03,670
+الجبريك Dual Space اسمه X Star الآن الـ X Star فيه
+
+127
+00:09:03,670 --> 00:09:07,150
+لها Dual Space ثاني اللي هو X Star Star صار عندي 
+
+128
+00:09:07,150 --> 00:09:12,010
+الـ Second Dual Space شكله فيه له لقب الأصل لما 
+
+129
+00:09:12,010 --> 00:09:16,010
+نجيب مرتين مرتين زي تبع زمان الـ inverse لما نعمله
+
+130
+00:09:16,010 --> 00:09:19,630
+مرتين برجع للأصل يعني مش بالظبط هو فيه له اللي 
+
+131
+00:09:19,630 --> 00:09:23,290
+بيعمل هيك بنعطيه خاصية اللي شاطر بيعمل زيك بنعمله
+
+132
+00:09:23,290 --> 00:09:28,330
+خاصية الآن Let C من X لعند X ★ ★ هذا اسمه بنسميه
+
+133
+00:09:28,330 --> 00:09:32,250
+canonical mapping on a vector space X defined by
+
+134
+00:09:32,250 --> 00:09:39,790
+CX CX بتاخد الـ X لمين؟ لـ GX الـ GX ماله؟ هذا الـ GX
+
+135
+00:09:39,790 --> 00:09:52,450
+احنا الـ GX الآن C من X لعند X ★ ★ الآن بياخد الـ C
+
+136
+00:09:52,450 --> 00:09:56,030
+والـ X بياخدها الـ X من وين؟ بيوديها لـ Element
+
+137
+00:09:56,030 --> 00:10:01,350
+هنا بنسميه GX طب إيش هذا الـ GX؟ هذا الـ GX أكيد
+
+138
+00:10:01,350 --> 00:10:07,250
+function من وين؟ من X Star لعند اللي هو الـ R أو
+
+139
+00:10:07,250 --> 00:10:10,650
+الـ C حسب الـ field اللي بتشتغل فيه مش هو هذا عبارة
+
+140
+00:10:10,650 --> 00:10:13,210
+عن Element من X Star Star وهذا إيش هو X Star 
+
+141
+00:10:13,210 --> 00:10:16,970
+X*؟ عبارة عن The set of all linear functionals
+
+142
+00:10:16,970 --> 00:10:22,370
+on X* ماشي الحال طب إذا هذا إشماله هذا برضه
+
+143
+00:10:22,370 --> 00:10:28,570
+بيجي بياخد G<sub>X</sub>(F) من هنا و برميها هان كيف
+
+144
+00:10:28,570 --> 00:10:33,690
+بترميها هان الـ F إشماله F عبارة عن دالة من X لعند
+
+145
+00:10:33,690 --> 00:10:38,270
+R مش الـ F في الـ X السار إذا دالة من X لعند R إذا
+
+146
+00:10:38,270 --> 00:10:43,890
+G<sub>X</sub>(F) بدي أرميها في الـ R بدي أقول بتساوي F عند
+
+147
+00:10:43,890 --> 00:10:50,890
+مين عند الـ X صارت الـ F من X لعند الـ R إذا فعلا هذا
+
+148
+00:10:50,890 --> 00:10:56,390
+بنسميه canonical mapping هو بيه the canonical
+
+149
+00:10:56,390 --> 00:10:59,470
+mapping of vector space X defined by C<sub>X</sub> بيساوي G
+
+150
+00:10:59,470 --> 00:11:07,150
+X for any fixed X المتين X G<sub>X</sub> من X* لعند K
+
+151
+00:11:07,150 --> 00:11:10,270
+زي ما قولت K is the real or the complex حسب اللي
+
+152
+00:11:10,270 --> 00:11:13,190
+احنا نشتغل عليها is defined by G<sub>X</sub>(F) بيساوي F
+
+153
+00:11:13,190 --> 00:11:17,010
+of X for any F المتين X* then C اللي عم نثبت
+
+154
+00:11:17,010 --> 00:11:20,190
+إيهاش is a linear operator يعني C هذا الـ canonical
+
+155
+00:11:20,190 --> 00:11:23,150
+mapping هيطلع اللي برضه أيه شماله linear operator
+
+156
+00:11:23,150 --> 00:11:27,870
+سهل الدنيا إن شاء الله أولاً نظرح ذلك G<sub>X</sub> إليمنت
+
+157
+00:11:27,870 --> 00:11:30,850
+في الـ X** لكي نثبت أن هذا يشمل نفسه G<sub>X</sub> هذا
+
+158
+00:11:30,850 --> 00:11:34,110
+اللي بتقوله عنه في الـ X** يعني عبارة عن element
+
+159
+00:11:34,110 --> 00:11:36,890
+هذا هو هوين بيقدر ميه بيقدر ميه لازم أرميه هناك
+
+160
+00:11:36,890 --> 00:11:41,070
+الآن for any f<sub>1</sub> و f<sub>2</sub> عشان أثبت أنه هنا بيثبت أن هو
+
+161
+00:11:41,070 --> 00:11:45,700
+نفسه linear أه كيف بدأت بتقوله Linear خد أي two
+
+162
+00:11:45,700 --> 00:11:49,840
+elements Linear عالميا على الـ X* يعني باخد أي
+
+163
+00:11:49,840 --> 00:11:53,640
+two elements يعني هذا الـ G<sub>X</sub> بدأت بتقوله Linear هان
+
+164
+00:11:53,640 --> 00:11:58,860
+أه باخد أي عنصرين من هان و الـ scalar و بثبت أنه
+
+165
+00:11:58,860 --> 00:12:05,550
+Linear ده نشوف كيف مع بعض وين وصلنا؟ طيب for any f<sub>1</sub>
+
+166
+00:12:05,550 --> 00:12:09,490
+و f<sub>2</sub> element in X* and any scalar α we have G<sub>X</sub>
+
+167
+00:12:09,490 --> 00:12:14,450
+of α f<sub>1</sub> + f<sub>2</sub> بيساوي Alpha حسب التعريف α f<sub>1</sub>
+
+168
+00:12:14,450 --> 00:12:19,010
++ f<sub>2</sub> of x و يساوي α f<sub>1</sub> of x من
+
+169
+00:12:19,010 --> 00:12:22,290
+تعريف الـ function زي التعريف أنه توزيع الـ function
+
+170
+00:12:22,290 --> 00:12:26,970
+العادى و الـ scalar العادى + f<sub>2</sub> of x هذه اللي هي
+
+171
+00:12:26,970 --> 00:12:33,370
+f<sub>1</sub> of x اللي هي G<sub>X</sub> of f<sub>1</sub> وهذه G<sub>X</sub> f<sub>2</sub> وهي الـ α إذا
+
+172
+00:12:33,370 --> 00:12:38,650
+صار فعلاً الآن G هذا بيساوي هذا وهذا معناته G<sub>X</sub> is
+
+173
+00:12:38,650 --> 00:12:44,010
+linear on X* الآن صار عند G<sub>X</sub> وين موجودة في X
+
+174
+00:12:44,010 --> 00:12:48,390
+* الـ * بدي الآن أثبت أنه اللي هو الـ C linear
+
+175
+00:12:48,390 --> 00:12:52,110
+لما أنا على هيك بده أروح هنا for any X element in
+
+176
+00:12:52,110 --> 00:12:56,150
+X there is a unique G<sub>X</sub> element in X** such
+
+177
+00:12:56,150 --> 00:13:01,010
+that تعريف هذا such that C(X)(H) بيساوي D<sub>X</sub>
+
+178
+00:13:01,010 --> 00:13:06,650
+because الآن عشان أقولكم أن هذا الكلام فعلا well
+
+179
+00:13:06,650 --> 00:13:10,450
+defined الآن بقول أنا ادعاء انه لكل X element in X
+
+180
+00:13:10,450 --> 00:13:14,050
+بلاقي D<sub>X</sub> element in X** من تعريفها الجد حقولكم انه
+
+181
+00:13:14,050 --> 00:13:17,570
+فعلا هذا الكلام هيكون هو ينيك كيف ينيك لأن such
+
+182
+00:13:17,570 --> 00:13:21,410
+that C<sub>X</sub> بيساوي D<sub>X</sub> because لو كانت الـ C<sub>X</sub> بيساوي D<sub>X</sub>
+
+183
+00:13:21,410 --> 00:13:26,120
+و C<sub>X</sub> بيساوي H<sub>X</sub> معناته for some G<sub>X</sub> و H<sub>X</sub> المتنكستار
+
+184
+00:13:26,120 --> 00:13:33,190
+** حيصير ان عندي قنتين الآن بيصير G<sub>X</sub> of F
+
+185
+00:13:33,190 --> 00:13:36,170
+بيساوي F(X) وما لاقتش H<sub>X</sub> of F بيساوي F(X)
+
+186
+00:13:36,170 --> 00:13:39,530
+ومدامة الـ F function يستحيل هدول يكونين إيش
+
+187
+00:13:39,530 --> 00:13:43,810
+مالهين مختلفات لازم يكونين إيش مالهين متساويات
+
+188
+00:13:43,810 --> 00:13:48,470
+which is impossible لأ إذا كانت مختلفات because F
+
+189
+00:13:48,470 --> 00:13:51,870
+is a function إذا لازم غصب عننا يطلع الـ D<sub>X</sub> هو
+
+190
+00:13:51,870 --> 00:13:55,710
+نفسه ما لاقتش في X therefore C is well
+
+191
+00:13:55,710 --> 00:13:59,010
+defined لأن في الآخر بنتبه أنها C is Linear إذا
+
+192
+00:13:59,010 --> 00:14:01,530
+أثبتنا أنها و أنه بتودي و باتثبتنا أنها well
+
+193
+00:14:01,530 --> 00:14:05,370
+defined ظل نثبت علينا أنها Linear و Linearity سهلة
+
+194
+00:14:05,370 --> 00:14:10,110
+وينالي وي شوه أن C هي Linear لأي X و Y element in
+
+195
+00:14:10,110 --> 00:14:15,910
+X وأي Scalar α وأي F element in X* رحلنا لدينا
+
+196
+00:14:15,910 --> 00:14:19,530
+C التعريف على طول هالجيت C(αX + Y)(F)
+
+197
+00:14:19,530 --> 00:14:24,570
+إيش بيساوي اللي هو G<sub>αX + Y</sub> اللي هي
+
+198
+00:14:24,570 --> 00:14:29,470
+متعلقة بهذه of من؟ of F هذه إيش قيمتها؟ F( هذه
+
+199
+00:14:30,390 --> 00:14:34,130
+لكن تعرفناه و يساوي F( المقدار هذا و F is linear
+
+200
+00:14:34,130 --> 00:14:38,950
+إذا α F + اللي هي F، مظبوط؟ الآن هذه مين هي؟
+
+201
+00:14:38,950 --> 00:14:43,710
+هي α G<sub>X</sub>(F) و هذه مين هي؟ G<sub>Y</sub>(F) الآن هذه
+
+202
+00:14:43,710 --> 00:14:48,950
+إيش هي؟ اللي هي α C<sub>X</sub> عند الـ F، معايا؟ و هذه
+
+203
+00:14:48,950 --> 00:14:52,470
+مين هي؟ C<sub>Y</sub> عند مين؟ عند الـ F، صارت عندي هذه
+
+204
+00:14:52,470 --> 00:14:59,050
+المقدار بيساوي هذا عند كل F في الدنيا عند كل الـ X
+
+205
+00:14:59,050 --> 00:15:01,870
+والـ Y اللي حكيناها إذا صار عند الـ C(αX + 
+
+206
+00:15:01,870 --> 00:15:08,170
+Y) بيساوي α C<sub>X</sub> +  C<sub>Y</sub> فاهمين؟ إذا الـ C is
+
+207
+00:15:08,170 --> 00:15:12,830
+linear اللي بعدها اطلع اللي فوق لأن نيجي لها
+
+208
+00:15:12,830 --> 00:15:18,550
+الملاحظة Note that if R(C) بيساوي X**
+
+209
+00:15:18,550 --> 00:15:22,270
+اللي قلت كلكم عنها قبل ما شوية يعني لو لجئنا إنه
+
+210
+00:15:22,270 --> 00:15:32,110
+الـ C الـ C من X لعند X** بحيث أنه الـ
+
+211
+00:15:32,110 --> 00:15:35,290
+Range للـ C طلع X** يعني بمعنى الاخر سارة
+
+212
+00:15:35,290 --> 00:15:41,050
+تادي onto function بنسمي اللي هو X is said to be
+
+213
+00:15:41,050 --> 00:15:44,430
+algebraically reflexive إذا algebraically
+
+214
+00:15:44,430 --> 00:15:52,020
+reflexive وكأنه بصير عندي اللي هو الـ X والـ X**
+
+215
+00:15:52,020 --> 00:15:58,680
+R equivalent أو R equivalent أو R isomorphic بكل
+
+216
+00:15:58,680 --> 00:16:02,460
+مفاهيمين الجبرية يعني one to one one to function
+
+217
+00:16:02,460 --> 00:16:08,340
+وكمان اللي هو الـ linearity اللي هي أو المحافظة
+
+218
+00:16:08,340 --> 00:16:11,480
+preserve the algebraic operation
+
+219
+00:16:14,210 --> 00:16:23,450
+نأخد .. نأخد الآن اللمّة let
+
+220
+00:16:23,450 --> 00:16:27,570
+X be a finite dimensional vector space
+
+221
+00:16:36,360 --> 00:16:41,080
+إذا كان الجنة F(X) not بيساوي 0 لكل F في X*
+
+222
+00:16:41,080 --> 00:16:45,700
+لازم الـ X not إيش هتتطلع كل الأفات بيودنها الـ X
+
+223
+00:16:45,700 --> 00:16:50,750
+not للسفر مش هتكون الا السفر هادي طيب الـ proof لت
+
+224
+00:16:50,750 --> 00:16:55,790
+{e<sub>1</sub>, e<sub>2</sub>, ..., e<sub>n</sub>} بيبقى basis for مين؟ for X مدان basis
+
+225
+00:16:55,790 --> 00:16:58,190
+إن X not كان بيرتن أزالين الـ combination من هنا
+
+226
+00:16:58,190 --> 00:17:02,150
+إذا بيساوي Σ x<sub>j</sub> a<sub>j</sub> e<sub>j</sub> من وحدة لعندها هذا
+
+227
+00:17:02,150 --> 00:17:05,250
+هتكون طبعا وين موجودة في الـ X then حسب الكلام اللي
+
+228
+00:17:05,250 --> 00:17:10,430
+بيحكي المعطى X not هتساوي 0 هذه طيب الآن f
+
+229
+00:17:10,430 --> 00:17:13,670
+of X not اللي هو بيساوي الـ Σ بدخل الـ f على
+
+230
+00:17:13,670 --> 00:17:16,470
+اللي هو الـ Σ و linear f إذا بيساوي الـ
+
+231
+00:17:16,470 --> 00:17:20,250
+Σ x<sub>j</sub> f(e<sub>j</sub>) for all f element in X*
+
+232
+00:17:20,250 --> 00:17:23,250
+إذا صار الكلام هذا لكل مين؟ لكل الأفات اللي في
+
+233
+00:17:23,250 --> 00:17:27,850
+الدنيا إذا صار عندي الـ Σ هذا بيساوي 0 for
+
+234
+00:17:27,850 --> 00:17:33,630
+any choice لمن للـ F(e<sub>j</sub>) مادام هذا بيساوي
+
+235
+00:17:33,630 --> 00:17:37,810
+0 لكل الـ choices للـ F(e<sub>j</sub>) مستحيل إلا تكون
+
+236
+00:17:37,810 --> 00:17:40,270
+الـ F(e<sub>j</sub>) اللي .. اللي هي ال .. ال .. ال
+
+237
+00:17:40,270 --> 00:17:43,870
+e<sub>j</sub> هدول اللي أمامي كل واحدة أشمالها بتساوي 0
+
+238
+00:17:43,870 --> 00:17:49,150
+وهذا يعني ان X not بتساوي 0 وهو المطلوب يلا
+
+239
+00:17:49,150 --> 00:17:54,530
+لبعده theorem
+
+240
+00:17:56,300 --> 00:17:59,240
+A finite dimensional vector space is algebraically
+
+241
+00:17:59,240 --> 00:18:02,100
+reflexive الآن قلنا algebraically reflexive متى
+
+242
+00:18:02,100 --> 00:18:08,460
+بيكون إذا كان عندي اللي هو C من X عند X*** اللي هو
+
+243
+00:18:08,460 --> 00:18:12,830
+is one to function و one to one وهي Linear طيب،
+
+244
+00:18:12,830 --> 00:18:15,930
+تنشوف، يعني التنين isomorphic بمفهوم .. الـ
+
+245
+00:18:15,930 --> 00:18:21,690
+isomorphism بمفهوم اللي هو preserved the linearity
+
+246
+00:18:21,690 --> 00:18:26,330
+أو الـ algebraic operations and اللي هو الـ
+
+247
+00:18:26,330 --> 00:18:31,130
+cardinality أو اللي هو الـ one to one و الـ onto By
+
+248
+00:18:31,130 --> 00:18:36,550
+Lemma 2.9.2، C is linear، اتفقنا C(X<sub>0</sub>) بيساوي 0
+
+249
+00:18:36,550 --> 00:18:40,050
+عشان أنا أثبت اللي هو الـ main اللي هو ال .. ال .. ال
+
+250
+00:18:40,050 --> 00:18:43,510
+.. الـ one to one then for all F element in X*
+
+251
+00:18:43,510 --> 00:18:48,830
+هيكون عنده 0 بيساوي C(X<sub>0</sub>)(F) مظبوط ولا لا؟ الآن
+
+252
+00:18:48,830 --> 00:18:53,710
+0 بيساوي من تعريف C(X<sub>0</sub>)(F) بيساوي اللي هو G<sub>X<sub>0</sub></sub>(F)
+
+253
+00:18:55,330 --> 00:18:58,170
+هيك التعريف G<sub>X<sub>0</sub></sub>(F) G<sub>X<sub>0</sub></sub>(F) أيش؟
+
+254
+00:18:58,170 --> 00:19:00,970
+بيساوي F(X<sub>0</sub>) إذا صارت عندي F(X<sub>0</sub>)
+
+255
+00:19:00,970 --> 00:19:04,510
+بتساوي مين؟ بتساوي 0 لكل الأفات إذا من اللمّة
+
+256
+00:19:04,510 --> 00:19:08,030
+اللي قبل شوية حتى تطلع X<sub>0</sub> بيساوي 0 إذا صارت
+
+257
+00:19:08,030 --> 00:19:10,990
+الـ C is one to one لإن C(X<sub>0</sub>) بيساوي 0 أدت X
+
+258
+00:19:10,990 --> 00:19:14,350
+<sub>0</sub> بيساوي 0 إذا C is one to one and so C
+
+259
+00:19:14,350 --> 00:19:19,850
+inverse exist ماشي الآن من theorem 2.16 اللي قبل
+
+260
+00:19:19,850 --> 00:19:23,670
+بشوية الـ dimension للـ R(C) بيساوي الـ dimension
+
+261
+00:19:23,670 --> 00:19:29,740
+للـ X أه طيب الآن صارت two dimensions زي بعض by
+
+262
+00:19:29,740 --> 00:19:37,880
+theorem 2.9.1 ركزوا هذه بالساوية دي خلوها في دماغه
+
+263
+00:19:37,880 --> 00:19:42,200
+الآن من 2.9.1 قبل بشوية الـ dimension للـ X*
+
+264
+00:19:42,200 --> 00:19:44,660
+الـ dimension للـ X* بيساوي الـ dimension للـ X
+
+265
+00:19:44,660 --> 00:19:48,260
+أثبتناها وجهها الـ dimension X** هيساوي الـ
+
+266
+00:19:48,260 --> 00:19:51,060
+dimension للـ X* إذا صار ان هدول الـ
+
+267
+00:19:51,060 --> 00:19:55,010
+dimension اللي هنا شمال هنا زي بعض الآن هدولة مح
+
+268
+00:19:55,010 --> 00:19:59,210
+هدول صار عندي dimension للـ R(C) بيساوي بالظبط الـ
+
+269
+00:19:59,210 --> 00:20:02,290
+dimension لمين؟ للـ X** لأن هذا بيساوي الـ
+
+270
+00:20:02,290 --> 00:20:05,210
+dimension للـ X وهذا بيساوي الـ dimension للـ X إذا
+
+271
+00:20:05,210 --> 00:20:06,990
+أكيد الـ dimension للـ R(C) بيساوي الـ dimension
+
+272
+00:20:06,990 --> 00:20:11,570
+لمين؟ للـ X** كم هي الـ R(C) subspace من
+
+273
+00:20:11,570 --> 00:20:15,550
+مين؟ من الـ X** و الـ dimension زي بعض، إذا
+
+274
+00:20:15,550 --> 00:20:19,870
+هي، ماتكونش هي إذا however R(C) is a vector
+
+275
+00:20:19,870 --> 00:20:25,720
+subspace of X** there by corollary 2.1.8 R
+
+276
+00:20:25,720 --> 00:20:30,380
+(C) بيساوي X** hence C is onto therefore
+
+277
+00:20:30,380 --> 00:20:33,800
+صارت one to one و onto و بتحافظ على اللي هو الـ
+
+278
+00:20:33,800 --> 00:20:36,520
+linearity أو العمليات معناته صارت اللي هي
+
+279
+00:20:36,520 --> 00:20:41,500
+algebraically reflexive إذا في حالة الـ finite
+
+280
+00:20:41,500 --> 00:20:49,450
+dimensional space ارجع ل في حالة الـ finite 
+
+281
+00:20:49,450 --> 00:20:53,590
+dimensional space بكون الـ vector space أشمله
+
+282
+00:20:53,590 --> 00:20:57,870
+algebraically reflexي نيجي لل definition الأخيرة
+
+283
+00:20:57,870 --> 00:21:01,210
+two vector spaces are said to be isomorphic 
+
+284
+00:21:01,210 --> 00:21:04,450
+vector space is isomorphic قلته أنا عموما توه في
+
+285
+00:21:04,450 --> 00:21:08,430
+أثناء الحديث إنه if there وصولك هذا حكيناه قبل هذا
+
+286
+00:21:08,430 --> 00:21:13,430
+if there is a bijective or Objective
+
+287
+00:21:13,430 --> 00:21:16,690
+Linear Map between the two vector spaces يعني إيش
+
+288
+00:21:16,690 --> 00:21:20,490
+ماله؟ يعني بحق .. هو أصلا إيش؟ هو عبارة عن تركيبة
+
+289
+00:21:20,490 --> 00:21:25,610
+جبرية بالإضافة .. تركيبة جبرية بالإضافة ل .. ل ..
+
+290
+00:21:25,610 --> 00:21:29,310
+لست إحنا كنا نقول الست إن هم equipotent أو متكافئة
+
+291
+00:21:29,310 --> 00:21:31,690
+تانية ده كانت في one to one onto function يعني بس
+
+292
+00:21:31,690 --> 00:21:34,850
+اللي .. بس ال cardinality اللي هنا زي بعض الآن لما
+
+293
+00:21:34,850 --> 00:21:38,750
+صار في عند .. اللي .. اللي هي عمليات جبريةالعمليات
+
+294
+00:21:38,750 --> 00:21:41,050
+الجبرية عشان نقول الـ  equivalent أو الـ
+
+295
+00:21:41,050 --> 00:21:45,290
+isomorphic بدها تكون كتركيبة جبرية كاملة
+
+296
+00:21:45,290 --> 00:21:49,030
+تكافئت كتركيبة جبرية كاملة إيش التركيبة الجبرية
+
+297
+00:21:49,030 --> 00:21:52,810
+هان اللي هي الـ scalar multiplication و ال vector
+
+298
+00:21:52,810 --> 00:21:57,000
+addition إذا كانت linear بتحفظهاوالـ one to one on
+
+299
+00:21:57,000 --> 00:22:00,100
+to بتحفظ العدد إذا صارت isomorphic بين vector
+
+300
+00:22:00,100 --> 00:22:03,320
+spaces لو بدنا نحط norm ونقول isomorphic أو
+
+301
+00:22:03,320 --> 00:22:06,620
+isomorphism بينهم لازم يحافظ على كل اللي حكيته
+
+302
+00:22:06,620 --> 00:22:10,850
+بالإضافة على ال preserve the norm ولو في topology
+
+303
+00:22:10,850 --> 00:22:15,650
+نفس الشيء إذا يعني بيكون هنا نفس هنا بس بتغيرات
+
+304
+00:22:15,650 --> 00:22:19,950
+الأسماء يعني هذه باسم تاني هي بس ال isomorphic بين
+
+305
+00:22:19,950 --> 00:22:23,710
+المعانات و هم زي بعض لكن اللي هي تغيرت الأسماء
+
+306
+00:22:23,710 --> 00:22:25,250
+واحد اسمه X واحد اسمه TX
+
+307
+00:22:43,900 --> 00:22:48,980
+تركيبة الجبرية تركيبة التباليجية تركيبة التباليجية
+
+308
+00:22:48,980 --> 00:22:52,420
+تركيبة التباليجية تركيبة التباليجية هذا معناته اللي
+
+309
+00:22:52,420 --> 00:22:56,920
+هو الـ isomorphic أو الـ equivalence بين نظامين if
+
+310
+00:22:56,920 --> 00:22:59,780
+the vector space X is isomorphic with a subspace
+
+311
+00:22:59,780 --> 00:23:02,840
+of a vector space Y then we say that X is
+
+312
+00:23:02,840 --> 00:23:08,320
+embedable in Y لما يكون الـ X isomorphic لجزء من
+
+313
+00:23:08,320 --> 00:23:11,420
+الـ Y بنقول على هذا إيش embedable ابنه ابنه ابنه
+
+314
+00:23:11,420 --> 00:23:15,640
+ابنه زيه بالظبط زي اللي جوا بالظبط يعني الآن X هي
+
+315
+00:23:15,640 --> 00:23:28,670
+عندي Y Y Y Y كبير هيك وفي عندياللي هو X إشي تاني
+
+316
+00:23:28,670 --> 00:23:35,910
+وها نتيجة داخله Z لو كان ال X isomorphic مع ال Z
+
+317
+00:23:35,910 --> 00:23:43,070
+هو نفسه بس بسامة ثانية بنقول إن X is embedable in
+
+318
+00:23:43,070 --> 00:23:47,210
+Y وبرك الله فيكم وإلى لقاء آخر 
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Z5xeo5Xjt84.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Z5xeo5Xjt84.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a13e0ccf028abdce9250043abc88591eea520709
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Z5xeo5Xjt84.srt
@@ -0,0 +1,1783 @@
+1
+00:00:05,060 --> 00:00:07,800
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,800 --> 00:00:10,800
+والصلاة والسلام على سيد المسلمين سيدنا محمد وعلى 
+
+3
+00:00:10,800 --> 00:00:15,460
+أهله وصحبه أجمعين هذه هي المحاضرة رقم 32 مساق 
+
+4
+00:00:15,460 --> 00:00:20,340
+تحليل اقتراني أو تحليل دالي لطلاب وطالبات الجامعة 
+
+5
+00:00:20,340 --> 00:00:25,200
+الإسلامية ماجستير الرياضيات وصلنا لعند اللي هو 
+
+6
+00:00:25,200 --> 00:00:29,460
+أربعة ثمانية strong and weak convergence نشوف ايش 
+
+7
+00:00:29,460 --> 00:00:35,260
+اللي هو نقصد اللي هو strong و weak convergence
+
+8
+00:00:35,260 --> 00:00:39,380
+طبعا احنا اللي هنحكي عن اللي هو norm space 
+
+9
+00:00:39,380 --> 00:00:42,960
+نحكي عن ال convergence في داخل norm space
+
+10
+00:00:44,590 --> 00:00:48,030
+بنتعرف على نوعين من أنواع ال convergence في ال
+
+11
+00:00:48,030 --> 00:00:53,110
+normed space ونشوف أيش معنات كل نوع من النوعين 
+
+12
+00:00:53,110 --> 00:00:57,730
+a sequence xn in a normed space x is said to be
+
+13
+00:00:57,730 --> 00:01:01,970
+strongly convergent or convergent in the norm يعني
+
+14
+00:01:01,970 --> 00:01:04,290
+ال convergence with respect to the norm
+
+15
+00:01:11,440 --> 00:01:15,680
+وهذا الكلام احنا بنرمزله باسم limit xn = x أو 
+
+16
+00:01:15,680 --> 00:01:16,800
+xn converges to x
+
+17
+00:01:23,730 --> 00:01:28,990
+لذلك عندما نكتب xn converges للـ x بالشكل هذا اللي 
+
+18
+00:01:28,990 --> 00:01:33,310
+نقصد فيها هو xn is strongly convergence to the 
+
+19
+00:01:33,310 --> 00:01:39,030
+x مايعنيها؟ معناته أن ال limit للـ xn - x بيروح 
+
+20
+00:01:39,030 --> 00:01:42,990
+للـ 0 as n goes to infinity في هذه 
+
+21
+00:01:42,990 --> 00:01:46,590
+الحالة بنسمي الـ X the limit اللي هو the strong
+
+22
+00:01:46,590 --> 00:01:50,790
+limit of the sequence Xn الآن في 
+
+23
+00:01:50,790 --> 00:01:54,550
+convergence آخر اللي هو سنتعرف عليه اللي هو
+
+24
+00:01:54,550 --> 00:02:00,950
+a sequence بنقول عنه XN converts ل X weakly طبعا الـ
+
+25
+00:02:00,950 --> 00:02:06,210
+XN والـ X برضه الموجودات الـ XN والـ x elements in
+
+26
+00:02:06,210 --> 00:02:11,230
+the normed space x هذا الأولاني اللي هو الـ
+
+27
+00:02:11,230 --> 00:02:13,610
+strong convergence والآن بدنا نعرف الـ weak
+
+28
+00:02:13,610 --> 00:02:16,590
+convergence إيش معناته اللي هو xₙ تروح للـ x
+
+29
+00:02:16,590 --> 00:02:23,650
+weakly إذا كان اللي هو لكل f element اللي هو x'
+
+30
+00:02:23,650 --> 00:02:26,270
+يعني bounded linear operator bounded linear
+
+31
+00:02:26,270 --> 00:02:26,590
+function
+
+32
+00:02:30,120 --> 00:02:34,720
+converging to the f of X هذا معناته ان Xn 
+
+33
+00:02:34,720 --> 00:02:39,300
+converges لإكس  weakly  لحظة اللي هو احنا
+
+34
+00:02:39,300 --> 00:02:44,240
+حولنا الحدير من Xn ل X اللي هي في الـ normed spaces
+
+35
+00:02:44,240 --> 00:02:48,420
+إلى convergence في الواقع في الـ scalar field لأن
+
+36
+00:02:48,420 --> 00:02:52,480
+f of Xn و f of X شمالها عبارة عن number يعني
+
+37
+00:02:52,480 --> 00:02:54,980
+complex أو real حسب اللي هو ال complex field عشان
+
+38
+00:02:54,980 --> 00:03:01,110
+هيك بنسمي weekly convergence يعني باختصار بالنسبة
+
+39
+00:03:01,110 --> 00:03:08,550
+لـ Xn في الوضع X قد يكون مرتبطاً بـ X weakly إذا كان
+
+40
+00:03:08,550 --> 00:03:11,850
+هناك X أقل من X كما لو كان هناك X أقل من X كما لو
+
+41
+00:03:11,850 --> 00:03:19,290
+كان هناك X أقل من X كما لو كان هناك X أقل من X
+
+42
+00:03:22,940 --> 00:03:26,280
+لأن أكيد في علاقة بين الـ weak convergence وبين
+
+43
+00:03:26,280 --> 00:03:29,640
+الـ norm وبين ال strong convergence يعني انتبه عن
+
+44
+00:03:29,640 --> 00:03:32,900
+الواحد هيقول أكيد ال strong convergence إيش هيقدر
+
+45
+00:03:32,900 --> 00:03:35,680
+لل weak convergence لكن the convergence need not
+
+46
+00:03:35,680 --> 00:03:41,390
+to be true in general هنشوف اللي هو كيف نثبت الـ Xn
+
+47
+00:03:41,390 --> 00:03:47,810
+بتروح للـ X weakly بيؤدي لـ weakly و كيف اللي هو
+
+48
+00:03:47,810 --> 00:03:52,330
+انه احنا نثبت انه اللي هو ال converges need not to
+
+49
+00:03:52,330 --> 00:03:55,910
+be true عن طريق example ومن ثم نشوف ايش في
+
+50
+00:03:55,910 --> 00:04:00,570
+condition بنحطه على اللي هو normed space عشان
+
+51
+00:04:00,570 --> 00:04:03,470
+يصير اللي هو ال weak convergence و ال strong يشمله
+
+52
+00:04:03,470 --> 00:04:10,610
+زي بعض لاحظوا في الـ R كنا نحكي عن weak convergence
+
+53
+00:04:10,610 --> 00:04:13,550
+و strong convergence كنا نحكي عنه في الـ sequences
+
+54
+00:04:14,820 --> 00:04:17,620
+سنجد أن في الـ R وفي الـ C وفي الحاجات اللي زي 
+
+55
+00:04:17,620 --> 00:04:21,280
+... في كل الـ finite dimensional spaces سيكون اللي
+
+56
+00:04:21,280 --> 00:04:24,260
+هو الـ weak convergence و الـ strong ايش مالهين
+
+57
+00:04:24,260 --> 00:04:28,300
+are the same خلّينا الأن نشوف أول لمّة لمّة الأولى
+
+58
+00:04:28,300 --> 00:04:31,460
+let Xn be a weakly اللي هو convergence sequence
+
+59
+00:04:31,460 --> 00:04:36,620
+in normed space X سي Xn بتروح للـ X ما لها weakly أثناء
+
+60
+00:04:36,620 --> 00:04:41,280
+ذلك، قيمة الـ weak limit of Xn هي محدودة، وهي شمالها
+
+61
+00:04:41,280 --> 00:04:45,440
+وحيدة، إذن قيمة، في حالة، احنا بنحكي عن أهم حالة
+
+62
+00:04:45,440 --> 00:04:50,340
+مين؟ حالة الـ weak convergence قيمة اللي هي وحيدة،
+
+63
+00:04:50,340 --> 00:04:53,920
+اثنين، every subsequence of Xn converges شمالها
+
+64
+00:04:53,920 --> 00:04:59,010
+weakly to X الحالة في الـ sequence الـ norm لـ Xn 
+
+65
+00:04:59,010 --> 00:05:03,330
+شمالها is bounded إذا كل هذه الأمور اللي هو من
+
+66
+00:05:03,330 --> 00:05:06,050
+خواص الـ weak convergence يعني لو بدنا نيدي
+
+67
+00:05:06,050 --> 00:05:11,090
+نعطيكوا sketch للبرهان نفترض إن Xn بتروح لـ X
+
+68
+00:05:11,090 --> 00:05:16,450
+weakly و Xn بتروح لـ Y أيش برضه weakly يعني بروح
+
+69
+00:05:16,450 --> 00:05:19,790
+إني شمال إلى different limits وفي الآخر نثبت إنه
+
+70
+00:05:19,790 --> 00:05:24,120
+شمال و X و Y هي نفس الأشياء الان شو معنات xn بتروح 
+
+71
+00:05:24,120 --> 00:05:28,600
+لل x weakly لأن لكل f element in x' هيكون عند 
+
+72
+00:05:28,600 --> 00:05:35,000
+ال f of xn بتروح لمين لل f of x معايا نفس الشي 
+
+73
+00:05:35,000 --> 00:05:39,620
+مدام xn بتروح لل y weakly لكل f element in x' 
+
+74
+00:05:39,620 --> 00:05:47,170
+هتطلع f of xn برضه هتروح لمين لل f هذه sequence number 
+
+75
+00:05:47,170 --> 00:05:50,610
+و هذه sequence number واحنا نعرف ان sequence number 
+
+76
+00:05:50,610 --> 00:05:53,510
+عندما يكون مرتبط مع مرتبط مع نفس المقالة إلى نفس
+
+77
+00:05:53,510 --> 00:05:54,150
+المقالة
+
+78
+00:05:59,080 --> 00:06:04,280
+هي ساوي F of Y هذا الكلام لكل مين لكل F element in
+
+79
+00:06:04,280 --> 00:06:10,440
+X' هذا معناته أن F of X - Y هتساوي صفر لكل F
+
+80
+00:06:10,440 --> 00:06:14,720
+element in X' واحنا أخدنا نتيجة قبل هيك هتطلع مين
+
+81
+00:06:14,720 --> 00:06:20,300
+إذا ال X - Y هتساوي صفر إذا معناته X هتساوي Y
+
+82
+00:06:20,300 --> 00:06:24,620
+معناته إنه ال limit ما لها is unique under the
+
+83
+00:06:24,620 --> 00:06:32,930
+weak convergence هذا بالنسبة لمن؟ لـ B برضه 
+
+84
+00:06:32,930 --> 00:06:36,890
+نفس الأشياء اعتمادا على خواص الـ sequence of
+
+85
+00:06:36,890 --> 00:06:42,510
+numbers سنحصل على خواص الـ convergence للـ
+
+86
+00:06:42,510 --> 00:06:49,330
+sequence لو جيت الآن قلت خلّينا نفترض إن Xn مرتبط 
+
+87
+00:06:49,330 --> 00:06:53,990
+بالـ X ما لها weakly بتاخد الآن أي subsequence
+
+88
+00:06:53,990 --> 00:06:56,830
+منها واكتبت برضه انها مرتبط بالـ X ما لها weakly 
+
+89
+00:06:56,830 --> 00:07:07,930
+بدي أقول let Xnk be any subsequence of Xn ماشي
+
+90
+00:07:07,930 --> 00:07:14,780
+الحال؟ الآن مدام Xn بتروح للـ X weakly then أكيد 
+
+91
+00:07:14,780 --> 00:07:20,380
+الـ f of xn هتروح للـ f of x لكل الأثوين الموجودة 
+
+92
+00:07:20,380 --> 00:07:25,960
+في الـ x' الآن f عبارة عن sequence of 
+
+93
+00:07:25,960 --> 00:07:31,040
+numbers ال sequence of numbers أي subsequence منها 
+
+94
+00:07:31,040 --> 00:07:33,580
+هتكون في virtue of the same limit إذا ال
+
+95
+00:07:33,580 --> 00:07:39,910
+subsequence f of xnk اللي هو conveys لمين لل F of X
+
+96
+00:07:39,910 --> 00:07:46,690
+لكل FY موجودة برضه في الـ X' وهذا معناته هو تعريف 
+
+97
+00:07:46,690 --> 00:07:51,990
+إن X and K بتروح لل X weakly إذا أي subsequence
+
+98
+00:07:51,990 --> 00:07:55,610
+converges weakly to the same limit as الsequence
+
+99
+00:07:55,610 --> 00:07:56,310
+الأصلية
+
+100
+00:07:59,320 --> 00:08:04,400
+اللي هو الـ sequence اللي هو ما لها norm لـ Xn ايش
+
+101
+00:08:04,400 --> 00:08:09,680
+ما لها is اللي هي bounded ال sequence norm لـ Xn 
+
+102
+00:08:09,680 --> 00:08:14,460
+is bounded عند Xn بتروح لل X weakly ماشي الحال لل
+
+103
+00:08:14,460 --> 00:08:19,060
+X then F of Xn بتروح لل F of X لكل F الموجودة في 
+
+104
+00:08:19,060 --> 00:08:23,900
+ال X' هذا صار تعريف فهمنا الآن so that the 
+
+105
+00:08:23,900 --> 00:08:28,580
+sequence of numbers F of Xn is bounded أكيدلاحظوا
+
+106
+00:08:28,580 --> 00:08:32,620
+كل اعتمادي تحويل اللي هو convergence in the norm
+
+107
+00:08:32,620 --> 00:08:35,700
+اللي هو x as if convergence weakly in the norm ل
+
+108
+00:08:35,700 --> 00:08:41,180
+convergence of sequence of numbers اللي صارتها
+
+109
+00:08:41,180 --> 00:08:45,740
+bounded that is there exists cf اللي هي constant
+
+110
+00:08:45,740 --> 00:08:51,060
+depending on f لأن هذا الكلام هذه تطلع على 
+
+111
+00:08:51,060 --> 00:08:56,400
+فوق هذه ال sequence f of xn is bounded لمين؟ لل f 
+
+112
+00:08:56,400 --> 00:08:59,560
+اللي بحكي عنها إذا أكيد ال c تبعتها بتعتمد على
+
+113
+00:08:59,560 --> 00:09:02,300
+مين؟ على ال f إذا بصير عند ال absolute value أو ال 
+
+114
+00:09:02,300 --> 00:09:07,980
+modulus لل f of xn أصغر أو يساوي cf لكل n الآن using 
+
+115
+00:09:07,980 --> 00:09:11,580
+the canonical mapping C إذا بتذكره من X لعين X
+
+116
+00:09:11,580 --> 00:09:13,700
+double prime هذا ال canonical mapping كيف كنا
+
+117
+00:09:13,700 --> 00:09:20,880
+عارفينه where ناخد اللي هو can define Gn element
+
+118
+00:09:20,880 --> 00:09:23,900
+in X double prime by حكيناه المرة السابقة تفصيله 
+
+119
+00:09:23,900 --> 00:09:28,520
+المرة السابقة أخذناه Gn of F ايش متساوي F of XN 
+
+120
+00:09:29,020 --> 00:09:32,460
+لكل f الموجودة في الـ x' خُد الآن الـ absolute
+
+121
+00:09:32,460 --> 00:09:37,560
+value هذه لها ال absolute value of g of f بسوء ال
+
+122
+00:09:37,560 --> 00:09:42,060
+absolute value of f of xn اللي هو أصغر أو يساوي cf
+
+123
+00:09:42,060 --> 00:09:47,460
+إذا صار عنده الآن هذه نفسها is bounded هذه نفسها 
+
+124
+00:09:47,460 --> 00:09:51,140
+is bounded لإن هذه bounded إذا هذه ايش معناها is
+
+125
+00:09:51,140 --> 00:09:54,520
+bounded وهذا is bounded for all f element in x'
+
+126
+00:09:54,880 --> 00:10:02,660
+لكن x' is complete إذا باللي هي uniform 
+
+127
+00:10:02,660 --> 00:10:06,160
+boundedness اللي أخذناها المرة الماضية normها
+
+128
+00:10:06,160 --> 00:10:09,860
+هيكون bounded مظبوط ولا لأ حكيناه المرة الفاتة 
+
+129
+00:10:09,860 --> 00:10:15,060
+مدام أنها bounded إذا و ال X' is complete اللي 
+
+130
+00:10:15,060 --> 00:10:22,000
+عليها معرفة اللي هي اللي عندها GN معرفة على Complete
+
+131
+00:10:22,000 --> 00:10:26,560
+Space إذا بالـ Uniform Boundedness Theorem شروطها 
+
+132
+00:10:26,560 --> 00:10:30,760
+مطبقة حيكون الـ Normal GN is bounded معناته Normal 
+
+133
+00:10:30,760 --> 00:10:33,820
+GN is bounded معناته اللي هو Normal XN bounded
+
+134
+00:10:33,820 --> 00:10:38,700
+لأنه أثبتنا في 4، 6، 1 إن Normal XN هو 
+
+135
+00:10:38,700 --> 00:10:45,480
+Normal GN ومن ثم أثبتنا Normal XN is bounded طيب،
+
+136
+00:10:45,480 --> 00:10:46,720
+الـ theorem اللي بعدها
+
+137
+00:10:50,820 --> 00:10:56,160
+اللي وعدناكم فيه let Xn be a sequence in normed
+
+138
+00:10:56,160 --> 00:11:01,260
+space X then
+
+139
+00:11:01,260 --> 00:11:06,940
+a strong convergence implies ما له weak
+
+140
+00:11:06,940 --> 00:11:10,160
+convergence with the same limit يعني لو الآن Xn
+
+141
+00:11:10,160 --> 00:11:14,900
+بتروح للـ X strongly هتروح للـ X  أيش مالها weakly
+
+142
+00:11:15,620 --> 00:11:19,120
+الآن الـ Converse of A need not be true in
+
+143
+00:11:19,120 --> 00:11:23,380
+general يعني فيه اللي هو weak convergence مش 
+
+144
+00:11:23,380 --> 00:11:27,860
+strong convergence وهنأخذ مثال الشغل الثالثة بدنا 
+
+145
+00:11:27,860 --> 00:11:30,740
+نزيد شرط شوية على ال weak convergence اللي يخليه 
+
+146
+00:11:30,740 --> 00:11:34,100
+strong اللي قلناه قبل شوية ملاحظة أنه لو كان ال
+
+147
+00:11:34,100 --> 00:11:36,460
+dimension الـ X finite هيكون ال weak convergence
+
+148
+00:11:36,460 --> 00:11:40,360
+أيش ماله وبيعطي اللي هو ال strong convergence يجي
+
+149
+00:11:40,360 --> 00:11:43,840
+ناخد واحدة واحدة يجي ناخد الأولى الآن الآن لو
+
+150
+00:11:43,840 --> 00:11:50,340
+فرضنا أن xn بتروح للـ x اللي هو strongly ماشي؟ إيش
+
+151
+00:11:50,340 --> 00:11:56,280
+معناته هذا؟ إذا then norm ال xn ناقص x بيروح لمين؟
+
+152
+00:11:56,280 --> 00:12:01,030
+لصفر الآن بيثبت لك أن ال XN بتروح للـ XA شمالها
+
+153
+00:12:01,030 --> 00:12:05,970
+weakly إيش يعني؟ بيثبت لك بيثبت لك أن لكل F element
+
+154
+00:12:05,970 --> 00:12:11,870
+in X' يطلع F of XN بيروح لمين؟ للـ F of X ماشي الحال
+
+155
+00:12:11,870 --> 00:12:19,050
+هاي اللي بيثبته إيش يعني؟ يعني بمعنى بدي أثبت لك بدي
+
+156
+00:12:19,050 --> 00:12:23,010
+أثبت لك إنه لو أخدت ال absolute value of f of x n
+
+157
+00:12:23,010 --> 00:12:27,510
+ناقص f of x بدي أثبت لك إن هذا بيروح للسفر as n goes
+
+158
+00:12:27,510 --> 00:12:32,110
+to infinity معايا يا جماعة؟ الآن شوفوا هذا هذا 
+
+159
+00:12:32,110 --> 00:12:38,310
+طبعا أصغر اللي بيساوي ال f of x n ناقص x صح ولا
+
+160
+00:12:38,310 --> 00:12:42,950
+لأ؟ لأن f is linear وهذا أصغر أو يساوي normal f
+
+161
+00:12:44,140 --> 00:12:49,150
+بـ norm الـ x أهم ناقص x لأن f is bounded الـ N as
+
+162
+00:12:49,150 --> 00:12:53,410
+N goes to infinity هذا بيروح لمين؟ للـ Zero إذاً و
+
+163
+00:12:53,410 --> 00:12:59,850
+هذا أكبر و يساوي صفر إذاً F of X N هتروح للـ F of X و
+
+164
+00:12:59,850 --> 00:13:04,470
+كانت F arbitrary قيمة X Prime إذاً هذا معناته إذا 
+
+165
+00:13:04,470 --> 00:13:09,190
+X N بتروح للـ X weakly إذا اللي هو ال strong
+
+166
+00:13:09,190 --> 00:13:12,770
+convergence واضح أنه بيعطي مين؟ اللي هو ال weak
+
+167
+00:13:12,770 --> 00:13:16,610
+convergence يجي الآن بيقول لك if the converse of A
+
+168
+00:13:16,610 --> 00:13:20,570
+is not true in general وخلّينا نشوف المثال أو ال
+
+169
+00:13:20,570 --> 00:13:25,750
+counter example اللي معطينه اطلع لفوق شوية الآن
+
+170
+00:13:25,750 --> 00:13:30,830
+let E N let E N be an orthonormal sequence in
+
+171
+00:13:30,830 --> 00:13:34,650
+Hilbert space mean H وقولنا أن ال ال ال ال ال
+
+172
+00:13:34,650 --> 00:13:38,110
+Hilbert space has an orthonormal اللي هو بنقدر
+
+173
+00:13:38,110 --> 00:13:41,350
+ناخد فيه an orthonormal sequence By Riesz
+
+174
+00:13:41,350 --> 00:13:44,450
+Representation Theorem اللي استخدمناها كثير تلاتة
+
+175
+00:13:44,450 --> 00:13:48,030
+ثمانية واحد لدرجة أن إحنا حافظنا رقمها By Riesz
+
+176
+00:13:48,030 --> 00:13:51,970
+Representation Theorem Any F المتنقطش برايم has a
+
+177
+00:13:51,970 --> 00:13:55,010
+representation F of X مش بيساوي X و Z و الـ Z ده 
+
+178
+00:13:55,010 --> 00:13:59,590
+unique زي ما اتفقنا ماشي الحال طيب hence الآن مدام
+
+179
+00:13:59,590 --> 00:14:02,270
+F of X بيساوي X و Z أكيد ال F of En تبع 
+
+180
+00:14:02,270 --> 00:14:07,300
+الورتنورمال بيساوي En و 100 و Z ماشي هذا الكلام 
+
+181
+00:14:07,300 --> 00:14:12,380
+طبعا الآن أي F element الـ H' له Z اللي هي بقدر 
+
+182
+00:14:12,380 --> 00:14:19,180
+أكتب ال F بدللها اتفقنا؟ طيب الآن F of E N بساوي
+
+183
+00:14:19,180 --> 00:14:24,270
+ال inner product بين E N و Z الآن أنا بثبت لكم أن
+
+184
+00:14:24,270 --> 00:14:29,350
+اللي هو عند ال EN هذه converts to zero weakly لكن 
+
+185
+00:14:29,350 --> 00:14:33,890
+مش strongly ماشي ال EN هذه ال orthonormal sequence
+
+186
+00:14:33,890 --> 00:14:36,510
+اللي هو اللي خدناها في ال H بثبت لكم إنها تروح
+
+187
+00:14:36,510 --> 00:14:41,940
+weakly لل zero لكن مش strongly ده نشوف كده الآن 
+
+188
+00:14:41,940 --> 00:14:45,240
+بالـ Bessel Inequality عشان أوصل اللي .. اللي بديها
+
+189
+00:14:45,240 --> 00:14:48,460
+لو جيت أخدت اللي هو ال .. الـ Bessel Inequality
+
+190
+00:14:48,460 --> 00:14:51,260
+اللي مش ذاكرينها لقينا الربروضاكت بين الـ E ان
+
+191
+00:14:51,260 --> 00:14:55,360
+والـ Z تربيع من n = 1 إلى مالانهاية هذا أصغر أو 
+
+192
+00:14:55,360 --> 00:14:58,280
+يساوي norm من Z التربيع، هذه اللي هي الـ Bessel
+
+193
+00:14:58,280 --> 00:15:03,580
+Inequality اللي أخذناها طيب الآن معناته أن صارت هذه
+
+194
+00:15:03,580 --> 00:15:07,840
+ال series converge مجموعها محدودة بمين؟ بالقيمة اللي 
+
+195
+00:15:07,840 --> 00:15:11,240
+هي norm of z مدام إنها مرتبطة إذا ال limit اللي
+
+196
+00:15:11,240 --> 00:15:14,880
+جواها إيش مالها صفر أنا بحكي عن number صارت هذا 
+
+197
+00:15:14,880 --> 00:15:17,800
+absolute value معناته صارت number الآن limit اللي
+
+198
+00:15:17,800 --> 00:15:20,740
+جواها إيش مالها صفر إذا هذا المقدار بيروح ل zero as n
+
+199
+00:15:20,740 --> 00:15:26,040
+goes to infinity الآن و هذا بيعطيني هذا صار اللي هو 
+
+200
+00:15:26,040 --> 00:15:29,560
+ال absolute value له بيروح لل zero برضه إذا أكيد
+
+201
+00:15:29,560 --> 00:15:32,180
+اللي هو ال F of EN اللي هو بسوء EN و Z برضه بيروح 
+
+202
+00:15:32,180 --> 00:15:37,800
+لمين؟ لل zero واضح الآن هذا المقدار راح لل صفر و
+
+203
+00:15:37,800 --> 00:15:42,260
+أنا بعرف أن هذا المقدار تربيع ال FEN يعني صارت FEN
+
+204
+00:15:42,260 --> 00:15:45,600
+تربيع بتروح لل صفر إذا ال FEN نفسها هتروح لمين؟ لل
+
+205
+00:15:45,600 --> 00:15:51,080
+zero الـ 0 اللي هو عبارة عن الـ F of إيه عش؟ of 0
+
+206
+00:15:51,080 --> 00:15:58,420
+ماشي اللي هي as n goes since F المتنقضش prime هذا
+
+207
+00:15:58,420 --> 00:16:01,320
+اللي هو بيروح للـ 0 اللي هو بسوء إيه عش؟ F of 0
+
+208
+00:16:01,320 --> 00:16:06,540
+لأن F of 0 بسوء 0 لكل F linear functional عارفين
+
+209
+00:16:06,540 --> 00:16:09,440
+هذا المعلومة؟ since F المتنقضش prime was arbitrary
+
+210
+00:16:09,440 --> 00:16:16,070
+إذا EN هذه الـ EN هتروح لمين؟ للي هو يعني الآن 
+
+211
+00:16:16,070 --> 00:16:23,410
+أثبتت لكم F of E N بتروح للـ F of Zero لكل F element
+
+212
+00:16:23,410 --> 00:16:27,810
+in H' هذا اللي أثبته هذا إيش معناته؟ أن E N بتروح
+
+213
+00:16:27,810 --> 00:16:35,390
+لل Zero weakly إذا أثبتنا أن E N بتروح للصفر
+
+214
+00:16:35,390 --> 00:16:45,200
+weakly بل أثبت أن E N مستحيل تروح للسفر يعني مستحيل
+
+215
+00:16:45,200 --> 00:16:50,960
+أن يكون عندي Normal EN ناقص السفر ويساوي Normal EN
+
+216
+00:16:50,960 --> 00:16:58,280
+بيروح لمين؟ للسفر هذا الكلام مستحيل لسبب بسيط الآن
+
+217
+00:16:58,280 --> 00:17:08,300
+اطلع لفوق احسب لي الآن خد أي N لا تساوي M واحسب
+
+218
+00:17:08,300 --> 00:17:13,280
+المسافة بين E M و E N ال E M إيش هي؟ صفار صفار صفار
+
+219
+00:17:13,280 --> 00:17:17,420
+معدي عند ال Nth term واحد و ال E N صفار صفار صفار
+
+220
+00:17:17,420 --> 00:17:21,640
+معدي عند ال Nth term بيساوي واحد إذا سأقرأ هذا الـ a
+
+221
+00:17:21,640 --> 00:17:25,360
+الماقص يعني عبارة عن كل هن أسفار معاد جزئين فيه
+
+222
+00:17:25,360 --> 00:17:29,180
+هن إيش بيساوي؟ واحد واحد فال summation الهن تربيع
+
+223
+00:17:29,180 --> 00:17:32,420
+لكل واحد الكل أص نص اللي هو عبارة عن واحد وكمان
+
+224
+00:17:32,420 --> 00:17:35,460
+واحد اتنين الكل أص نص مايصير جذر إيش اللي هو جذر
+
+225
+00:17:35,460 --> 00:17:38,340
+الاثنين إذا هذا اللي جوا norm جذر الاثنين يعني 
+
+226
+00:17:38,340 --> 00:17:42,880
+تربيعه إيش بيساوي؟ اثنين فاهمين اللي بحكيه؟ أو إذا 
+
+227
+00:17:42,880 --> 00:17:46,800
+حسبته بالشكل هذا E M و E N و E N و E N هذا ال E M
+
+228
+00:17:46,800 --> 00:17:51,760
+وال E M اللي هو norm واحد وهذا norm واحد اللي هو 
+
+229
+00:17:51,760 --> 00:17:54,540
+بيصير norm اثنين وطبعا و ال E M من على ال E N لما
+
+230
+00:17:54,540 --> 00:17:59,880
+تفكه بيطلع صفر لإنهم orthonormal اثنين عامدين على
+
+231
+00:17:59,880 --> 00:18:03,440
+بعض و ال E M و ال E N برضه إيش بيساوي؟ بيساوي صفراً إذن 
+
+232
+00:18:03,440 --> 00:18:09,360
+الـ N صارت هذه الـ Sequence E N مش كوشي لإن البعد 
+
+233
+00:18:09,360 --> 00:18:12,360
+بينهم شامل و بيساوي و بيساوي و اثنين راحت N إلى مالانهاية 
+
+234
+00:18:12,360 --> 00:18:16,140
+ونهاية و لا ال M إلى مالانهاية لن يتغير الأبعاد
+
+235
+00:18:16,140 --> 00:18:20,560
+المسافات بين كل عنصر و الثاني أبعد عن بعض ففيش إيش 
+
+236
+00:18:20,560 --> 00:18:24,380
+بيروح له باتجاهه يعني بمعنى آخر E N صارت is not
+
+237
+00:18:24,380 --> 00:18:27,460
+cauchy إيش معنات is not cauchy و في إحنا في
+
+238
+00:18:27,460 --> 00:18:31,580
+complete space يعني معناها is not convergent إذاً
+
+239
+00:18:31,580 --> 00:18:36,880
+الآن EN is not .. does not converge مثلا does not
+
+240
+00:18:36,880 --> 00:18:41,760
+converge إذا normal EN هذا does not converge to
+
+241
+00:18:41,760 --> 00:18:47,340
+zero يعني بمعنى آخر EN does not converge strongly
+
+242
+00:18:47,340 --> 00:18:53,840
+to zero هاي مثلا نيجي الآن للي بعده اللي بعده في
+
+243
+00:18:53,840 --> 00:18:55,460
+حالة ال dimension
+
+244
+00:18:58,000 --> 00:19:02,080
+للـ X بيساوي مثلا ال K زي ما هو مسميها اللي هو
+
+245
+00:19:02,080 --> 00:19:07,860
+finite هيكون عند ال XM بتروح للـ X weakly if and 
+
+246
+00:19:07,860 --> 00:19:12,220
+only if XM بتروح للـ X شمالها strongly
+
+247
+00:19:15,220 --> 00:19:20,380
+الاتجاه هذا أثبتناه إذا ظلّينا نثبت أنه لما ال
+
+248
+00:19:20,380 --> 00:19:23,940
+dimension للـ X بيساوي كده و كائنة Xn بتروح للـ X 
+
+249
+00:19:23,940 --> 00:19:29,320
+weakly يعطيني إن Normal Xn ناقص ال X بيروح لمين؟
+
+250
+00:19:29,320 --> 00:19:33,220
+لل Zero أو بمعنى آخر Xn بتروح للـ X strongly واضح
+
+251
+00:19:33,220 --> 00:19:38,800
+الكلام، هي اللي بدي أثبته طيب شوفوا الآن كيف بدي 
+
+252
+00:19:38,800 --> 00:19:44,780
+أكيد استعمل اللي هو ال dimension للـ X is finite لما
+
+253
+00:19:44,780 --> 00:19:47,860
+الـ dimension للـ X is finite إذن فيه bases صحيح
+
+254
+00:19:47,860 --> 00:19:52,280
+طيب إذا الآن suppose that XM بتروح لـ X weakly and
+
+255
+00:19:52,280 --> 00:19:55,260
+dimension ل X بيساوي K وبيثبت إن XM بتروح لـ X
+
+256
+00:19:55,260 --> 00:19:59,240
+strongly لأن مدام الـ finite dimensional واسمه K
+
+257
+00:19:59,240 --> 00:20:03,460
+إذا بقدر أجرأ وأقول let E1 و E2 لعند الـ E كي بيه 
+
+258
+00:20:03,460 --> 00:20:07,500
+أي basis of مين؟ of X مدام basis ل X إذا أي
+
+259
+00:20:07,500 --> 00:20:12,730
+sequence Xn عناصرها X واحد في الـ X و الـ X اتنين في
+
+260
+00:20:12,730 --> 00:20:15,910
+الـ X و الـ Xn in general في الـ X إذا بقدر أكتبها 
+
+261
+00:20:15,910 --> 00:20:19,090
+على صورة linear combination من مين؟ من عناصر ال
+
+262
+00:20:19,090 --> 00:20:24,310
+bases إذا صار عندي الـ Xn بيساوي Alpha J N يعني EJ
+
+263
+00:20:24,310 --> 00:20:28,490
+J من واحد عند K و Alpha J N هذه إيش مالها؟ عبارة عن ال
+
+264
+00:20:28,490 --> 00:20:34,400
+scalars يعني الآن X واحد اللي بيصير Alpha 1 1 Alpha
+
+265
+00:20:34,400 --> 00:20:41,980
+2 1 Alpha 3 1 Alpha 4 1 Alpha 5 K Alpha 1 Alpha K
+
+266
+00:20:41,980 --> 00:20:47,590
+1 الآن X2 نفس الشيء X3 نفس الشيء إذا صارت عندي هذه
+
+267
+00:20:47,590 --> 00:20:51,030
+sequence of elements in mean in X الآن برضه نفس
+
+268
+00:20:51,030 --> 00:20:56,830
+الشيء خد X بتساوي اللي هو summation لألف ج أيه جه 
+
+269
+00:20:56,830 --> 00:20:59,710
+جه من عند واحد لعند مين؟ لعند كيه برضه ليه ال
+
+270
+00:20:59,710 --> 00:21:03,370
+compilation من مين؟ من العناصر الآن by assumption
+
+271
+00:21:03,370 --> 00:21:06,430
+إحنا ما إحنا قولنا X ان بتروح لمين؟ للـ X weakly
+
+272
+00:21:06,430 --> 00:21:10,130
+كترت ال X ان بصورة هذه و كترت ال X بصورة هذه بناء
+
+273
+00:21:10,130 --> 00:21:13,510
+على ال dimension للـ X بيساوي K و هذا هو ال basis طيب
+
+274
+00:21:13,510 --> 00:21:16,770
+by assumption مدام x1 بتروح إلى x weakly إذا أنا
+
+275
+00:21:16,770 --> 00:21:19,270
+هيطلع عندي f of x2 بتروح إلى ال f of x لكل mean
+
+276
+00:21:19,270 --> 00:21:24,550
+لكل f element in x prime in particular ما هو ال x
+
+277
+00:21:24,550 --> 00:21:29,310
+prime اللي هو برضه ال dimension ياله k إذا فيه
+
+278
+00:21:29,310 --> 00:21:35,670
+باسيس باسيس تبعه اللي هو مثلا نسميه f1, f2 أف تلاتة 
+
+279
+00:21:35,670 --> 00:21:39,450
+لأنها functions لعند أف كي مظبوط ولا لأ؟ نحن لا نعرف 
+
+280
+00:21:39,450 --> 00:21:43,510
+أن ال dimension للـ X كي الـ X برايم برضه دايما مش 
+
+281
+00:21:43,510 --> 00:21:47,710
+نقوله إيش بساوي؟ بساوي كِ إذن الآن in particular
+
+282
+00:21:47,710 --> 00:21:51,810
+مدام هذا الصحيح لكل العناصر تبعات الأف الـ X برايم
+
+283
+00:21:51,810 --> 00:21:55,710
+إذا صحيحة برضه العناصر من الـ bases اللي هي النمو
+
+284
+00:21:55,710 --> 00:21:58,590
+اللي من هنا مظبوط، هذا اللي هو الـ bases اللي هو
+
+285
+00:21:58,590 --> 00:21:59,610
+basis of
+
+286
+00:22:02,200 --> 00:22:07,520
+معايا؟ طيب شوفوا صارت عندي fj of xn بتروح للـ fj of 
+
+287
+00:22:07,520 --> 00:22:14,560
+x، يعني f1 و f2 و f3 و f4 لكل اللي عند مين؟ لعند الـ
+
+288
+00:22:14,560 --> 00:22:20,440
+k، طيب where fg of j من عناصر الـ basis هذوله بيكون
+
+289
+00:22:20,440 --> 00:22:23,580
+fg of ej أشبه ساوي و ساوي واحد، كل هذا مر علينا
+
+290
+00:22:23,580 --> 00:22:28,460
+سابقا، and fj of m إيش هتساوي؟ إك سفر لكل أملة تساوي
+
+291
+00:22:28,460 --> 00:22:33,260
+j، إذا صار عندي الآن بناء على هذا الكلام لو أجيت
+
+292
+00:22:33,260 --> 00:22:38,790
+دخلت الـ fj على الـ xn كلن هيتصفرن بس هيدلل مين عندي؟
+
+293
+00:22:38,790 --> 00:22:45,250
+Alpha J اللي هي الـ N معايا، كلن هيتصفرن فبصير F J
+
+294
+00:22:45,250 --> 00:22:50,850
+of X N بساوي Alpha J مين؟ N، و F J of X هيتلع مين هو؟
+
+295
+00:22:50,850 --> 00:22:58,790
+الـ Alpha J لأن F عملها
+
+296
+00:22:58,790 --> 00:23:09,330
+.. انتبهوا، الآن أحسبه Fj of xn بساوي Fj of الوه الـ
+
+297
+00:23:09,330 --> 00:23:18,010
+summation Alpha 1n E1 زائد لما أصل لآخر واحدة
+
+298
+00:23:18,010 --> 00:23:24,710
+Alpha الوه KN EK، ماشي
+
+299
+00:23:27,700 --> 00:23:37,740
+كل حيتصفر للجوا معدنين لرقمها Alpha J N E J حيصير
+
+300
+00:23:37,740 --> 00:23:41,040
+عنده هذا صفر و هذا صفر لأنه Linear تدخل عليها كل
+
+301
+00:23:41,040 --> 00:23:46,540
+زمان عند هدولة كلها نصفار معدنين لـ FJ of Alpha J
+
+302
+00:23:46,540 --> 00:23:51,040
+N E J و هد قيمتها إيش بتساوي؟ هد بتطلع برا و هد
+
+303
+00:23:51,040 --> 00:23:56,860
+قيمتها واحد فبصير Alpha J N، Similarly, Fj of X
+
+304
+00:23:56,860 --> 00:24:01,340
+هتطلع مين؟ Alpha J، بناء عليه مادام قولنا أن Fj of
+
+305
+00:24:01,340 --> 00:24:06,060
+X هتطلع Fj of X، معناته أصبحت عندي Fj أن بدل هذه
+
+306
+00:24:06,060 --> 00:24:08,540
+بتروح لمين؟ للـ Alpha J
+
+307
+00:24:12,070 --> 00:24:17,330
+ألفا جي أن هتروح للألفا جي as n goes to infinity
+
+308
+00:24:17,330 --> 00:24:21,730
+وهذا لكل جي، جي بتساوي واحد واثنين لعين جمين لعين
+
+309
+00:24:21,730 --> 00:24:26,310
+كي، كل هنا دول أشمالي الصحيحة اطلع then خلصنا، then
+
+310
+00:24:26,310 --> 00:24:31,190
+احسب للان normal xn ناقص normal x ايش بيساوي؟ ال xn
+
+311
+00:24:31,190 --> 00:24:35,350
+هيقبلتها والـ X هي قيمتها طرحناها من بعض طلعت هذا
+
+312
+00:24:35,350 --> 00:24:39,030
+القيمة، هذا اللي هو أصغر أو ساوي للـ triangle
+
+313
+00:24:39,030 --> 00:24:41,990
+inequality الـ absolute value هذا في الـ norm هذا
+
+314
+00:24:41,990 --> 00:24:45,710
+هذا ايش معنى هذا؟ الان الان الان الان الان الان
+
+315
+00:24:45,710 --> 00:24:46,150
+الان الان الان الان الان الان الان الان الان الان
+
+316
+00:24:46,150 --> 00:24:49,650
+الان الان الان الان إنه هذا as n goes to infinity
+
+317
+00:24:49,650 --> 00:24:52,490
+منها أنا alpha j ومن هنا ال alpha j تذهب إلى مين؟
+
+318
+00:24:52,490 --> 00:24:56,010
+إذن كل واحد منهم اللي جوه الـ zero، إذا المجموح اللي
+
+319
+00:24:56,010 --> 00:24:59,490
+هيروح للـ zero، إذا صارت عند الـ x أنه تتقل إلى مين؟
+
+320
+00:24:59,490 --> 00:25:04,390
+إلى الـ x weakly، strongly، under the condition x
+
+321
+00:25:04,390 --> 00:25:07,170
+أنه تذهب إلى الـ x weakly عند الـ dimension للـ x
+
+322
+00:25:07,170 --> 00:25:13,350
+بساوى k أو finite example
+
+323
+00:25:18,930 --> 00:25:24,970
+الأول مثلًا الـ Hilbert space، الـ Hilbert space Xn
+
+324
+00:25:24,970 --> 00:25:29,150
+تذهب إلى X weakly، فان دول F Xn و Z تذهب إلى X و Z
+
+325
+00:25:29,150 --> 00:25:31,410
+for all Z مين؟ in H
+
+326
+00:25:40,280 --> 00:25:44,740
+يكافئ أن نقول أن f of x which هي xn و z بتروح لل x
+
+327
+00:25:44,740 --> 00:25:47,820
+و z for all ليش هذا؟ هذا ما أحنا عارفينه، هذه
+
+328
+00:25:47,820 --> 00:25:54,300
+المعلومة سهلة، فشو معناه أن xn بتروح لل x weakly؟
+
+329
+00:25:54,300 --> 00:26:01,650
+معناته هذا يكافئ أن f of xn بتروح لل F of X لكل FY
+
+330
+00:26:01,650 --> 00:26:05,770
+الموجودة في الـ X' صح ولا لأ؟ اللي هي الـ H' في
+
+331
+00:26:05,770 --> 00:26:09,490
+هذا الحالة لكن أنا بعرف من جهة أخرى، من الـ 381
+
+332
+00:26:09,490 --> 00:26:12,390
+الـ Riesz Representation Theorem أنه لكل F element
+
+333
+00:26:12,390 --> 00:26:17,610
+في الـ H' اللي هو بقدر ألاجله F of X and can be
+
+334
+00:26:17,610 --> 00:26:23,160
+written as X ومين؟ وZ صح؟ ماشي؟ إذا يعني هذا الـ
+
+335
+00:26:23,160 --> 00:26:27,820
+condition ماقدر أستبدله بإنه اللي هو xn و z بتروح
+
+336
+00:26:27,820 --> 00:26:31,600
+لل x و z for all z in H والتفاصيل اللي لكم، طيب
+
+337
+00:26:31,600 --> 00:26:44,460
+اللي بعده الآن انقل بي .. انقل بي .. انقل بي أنا
+
+338
+00:26:44,460 --> 00:26:47,860
+طبعا بي أكبر واحدة صغيرة من infinity Xn بتروح لل X
+
+339
+00:26:47,860 --> 00:26:51,580
+weakly إذا وفقط إذا الشرطين التاليات، يعني الآن
+
+340
+00:26:51,580 --> 00:26:55,860
+عندي شرطين يكافئن Xn بتروح لل X weakly، الشرط الأول
+
+341
+00:26:55,860 --> 00:27:02,120
+ال sequence normal Xn أشماله is bounded، الشرط
+
+342
+00:27:02,120 --> 00:27:07,440
+الثاني for every prefix j we have alpha jn بتروح
+
+343
+00:27:07,440 --> 00:27:15,280
+للxi j as n goes to infinity اللي هي حيث xn هذه
+
+344
+00:27:15,280 --> 00:27:21,820
+عبارة عن xi jn والـ x يمين هي xi j يعني هذه بتروح الـ
+
+345
+00:27:21,820 --> 00:27:25,640
+Xn بتروح للـ X weakly إذا كانها bounded والجزء
+
+346
+00:27:25,640 --> 00:27:30,260
+الثاني إنه كل واحدة من الـ terms اللي هنا Alpha J
+
+347
+00:27:30,260 --> 00:27:35,880
+يعني Alpha واحد N بتروح للألف واحد، Alpha اتنين N
+
+348
+00:27:35,880 --> 00:27:39,380
+بتروح للألف اتنين فاهمين؟ إيه الأخر؟ إيه المعنى
+
+349
+00:27:39,380 --> 00:27:42,800
+النهاية؟ هذا هذولة التانية مع بعض وكافئن هذولة
+
+350
+00:27:42,800 --> 00:27:49,130
+الآن هذه النظرية أو هذه اللي هي الخاصية حنجيها اللي
+
+351
+00:27:49,130 --> 00:27:53,930
+هي خلّيني أقول automatic تطلع من مين؟ من اللمة بس
+
+352
+00:27:53,930 --> 00:27:57,050
+انت بيصير اللي .. اللي احنا بنحكي عنه ال ال ال ال
+
+353
+00:27:57,050 --> 00:27:57,950
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+354
+00:27:57,950 --> 00:27:58,490
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+355
+00:27:58,490 --> 00:27:58,670
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+356
+00:27:58,670 --> 00:27:59,830
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+357
+00:27:59,830 --> 00:28:03,030
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+358
+00:28:03,030 --> 00:28:10,750
+ال
+
+359
+00:28:14,670 --> 00:28:18,130
+ماشي، الحل هو جايلك أصلا في الكتاب هذي left to the
+
+360
+00:28:18,130 --> 00:28:20,790
+reader ب exercise من مين؟ من اللي تحته، وبوضح بعض
+
+361
+00:28:20,790 --> 00:28:25,070
+الشغلات، طيب خلّيني إن شاء الله أندي أشتغل على لمّة
+
+362
+00:28:25,070 --> 00:28:31,210
+أربعة تمانية سبعة اللي هي in general هذي بتقول لي
+
+363
+00:28:31,210 --> 00:28:36,890
+إن I know the space X in general we have X and
+
+364
+00:28:36,890 --> 00:28:42,900
+بتروح لل X weakly تكافئ إنه الـ sequence normal XN
+
+365
+00:28:42,900 --> 00:28:47,920
+is bounded، هاي واحدة، اتنين، for every element of
+
+366
+00:28:47,920 --> 00:28:52,340
+a total M، اللي subset M of X' في اللي فوق الـ
+
+367
+00:28:52,340 --> 00:28:58,260
+total subset، اللي هي الـ An، total subset، طيب،
+
+368
+00:28:58,260 --> 00:29:03,000
+for every element F of a total subset M of X'، we
+
+369
+00:29:03,000 --> 00:29:06,020
+have F of XN بتروح لمين؟ ال of X as M قصة نفيّل
+
+370
+00:29:06,020 --> 00:29:11,650
+تانية، يعني، شوفوا الآن لو جينا حللنا النظرية
+
+371
+00:29:11,650 --> 00:29:16,690
+بالمنبرهن Xn بتروح للـ X weakly، إيش معناتها؟ إن F
+
+372
+00:29:16,690 --> 00:29:21,030
+of Xn بتروح لل F of X لكل F element الـ main، الـ
+
+373
+00:29:21,030 --> 00:29:25,850
+X' اللي أنا هذا بقولك أنا هذا الشرط الكثير اللي
+
+374
+00:29:25,850 --> 00:29:31,530
+الهن كلهن بديش لكل أفوال من TX' بيثبت فيني ان يكون
+
+375
+00:29:31,530 --> 00:29:36,290
+لكل أفوال ما لها في total subset يعني جزء من X'
+
+376
+00:29:36,690 --> 00:29:41,130
+لكن بدها زجة شوية عشان تتفل الـ weakly إن يكون norm
+
+377
+00:29:41,130 --> 00:29:44,890
+لكسرني إيش ماله؟ is bounded بيعطيني هذا يؤدي إلى
+
+378
+00:29:44,890 --> 00:29:48,410
+هذا وهذا يؤدي لهذا هلاجيه اللي هو أمر سهل من
+
+379
+00:29:48,410 --> 00:29:52,680
+الخواص اللي قبل شوية حصلناه لأنه قبل بشوية قلنا
+
+380
+00:29:52,680 --> 00:29:57,160
+لما Xn تروح لل X weakly Normal Xn bounded برهنها
+
+381
+00:29:57,160 --> 00:30:00,520
+توه، هاي واحد اتنين، شو معناه Xn بتروح لل X
+
+382
+00:30:00,520 --> 00:30:05,140
+weakly؟ فإن F of Xn بتروح ل F of X لكل F من ضمن
+
+383
+00:30:05,140 --> 00:30:09,940
+انها دول، إذا هذا الاتجاه جاهز دل مين؟ اطلع للي
+
+384
+00:30:09,940 --> 00:30:13,420
+اتجاه الثاني، إذا if xn بتروح للي x weakly then a
+
+385
+00:30:13,420 --> 00:30:16,540
+follows from لما كذا and b follows from the
+
+386
+00:30:16,540 --> 00:30:18,860
+definition of weak convergence اللي حكيته قبل قليل
+
+387
+00:30:18,860 --> 00:30:23,620
+شوية، إذا نطلع فوق وبدنا نثبت مين؟ conversely، طيب
+
+388
+00:30:23,620 --> 00:30:27,280
+نيجي الان conversely ونعني بعض الشغلات هيك الحلوة
+
+389
+00:30:27,280 --> 00:30:35,620
+بنعملها و بنصل للي بدنا ايه، الآن شو معناته أن total
+
+390
+00:30:35,620 --> 00:30:43,520
+set، أن total set in X' معناته أن الـ span للأم
+
+391
+00:30:43,520 --> 00:30:49,340
+أقل جاب بساومين X'، هذا الان اللي هو الـ bridge اللي
+
+392
+00:30:49,340 --> 00:30:54,960
+بدصل من خلاله لالمطلوب، conversely suppose that A
+
+393
+00:30:54,960 --> 00:30:59,630
+and B hold و بدنا نتبط ان Xn بتروح للـ X weakly By
+
+394
+00:30:59,630 --> 00:31:06,580
+A، مدام Xn bounded لنوم Xn أصغر سوى C لكل N، والـ norm
+
+395
+00:31:06,580 --> 00:31:10,840
+الـ X أصغر أو يساوي C for sufficiently large mean
+
+396
+00:31:10,840 --> 00:31:15,520
+اللي هو mean C، مدام الـ XN بتروح الـ N، النورم الـ XN
+
+397
+00:31:15,520 --> 00:31:21,200
+أصغر أو يساوي C for all N، إذن automatically اللي
+
+398
+00:31:21,200 --> 00:31:25,580
+هي النورمها، اللي هو النورم الـ X، هيكون ماله؟ أصغر
+
+399
+00:31:25,580 --> 00:31:31,540
+أو يساوي C، اللي هو هذي طبعا أصغر يساوي C for all n
+
+400
+00:31:31,540 --> 00:31:35,880
+جارس نصف شالد ليه لاعيش C انك تختار C أشماله
+
+401
+00:31:35,880 --> 00:31:39,780
+كبيرة كفاية إنها تكفل ال .. ال .. ال .. since M is
+
+402
+00:31:39,780 --> 00:31:45,830
+total in X prime، ما دام total in X'، then for every
+
+403
+00:31:45,830 --> 00:31:49,530
+F in X'، there exists a sequence Fi in span لـM،
+
+404
+00:31:49,530 --> 00:31:54,710
+such that Fi بتروح لمين؟ لـF، dense، مش الآن هذه
+
+405
+00:31:54,710 --> 00:31:59,670
+dense في هذه A، إذا أي element هنا، بلاقي الـ
+
+406
+00:31:59,670 --> 00:32:03,310
+sequence في اللي جوا، كون ذالك له، ماشي، تعريف الـ
+
+407
+00:32:03,310 --> 00:32:08,600
+density، طيب الآن since M is total إذا الـ span لـ M
+
+408
+00:32:08,600 --> 00:32:13,560
+بساوي X' then لكل F element in X' there exist a
+
+409
+00:32:13,560 --> 00:32:17,700
+sequence of I in span M such that F I بتروح لمين؟
+
+410
+00:32:17,700 --> 00:32:22,660
+لل F هايو، since span ل M is dense in X'، إذا مدام F
+
+411
+00:32:22,660 --> 00:32:26,900
+I بتروح لل F، إذا بقدر أسغر المسافة جد ما بدي، Then,
+
+412
+00:32:27,100 --> 00:32:31,100
+for every Y أكبر من 0، there exists J such that
+
+413
+00:32:31,100 --> 00:32:39,810
+normal Fi-F أصغر من مين؟ من Y على 3C، راحظوا الـ
+
+414
+00:32:39,810 --> 00:32:43,790
+convergence في العالم
+
+415
+00:32:43,790 --> 00:32:49,050
+تبع x' يعني in the norm تبع x'، يعني أصلا كل الـ
+
+416
+00:32:49,050 --> 00:32:52,450
+convergence لما كنا نقول convergence في x زمان، الـ
+
+417
+00:32:52,450 --> 00:32:54,990
+convergence في الـ x لما نحكي عليه with respect to
+
+418
+00:32:54,990 --> 00:32:59,050
+the norm يعني الـ strong convergence، طيب إذا الأن
+
+419
+00:32:59,050 --> 00:33:02,790
+صار عندي normal fi ناقص f أصغر من أي إبسلون في
+
+420
+00:33:02,790 --> 00:33:05,970
+الدنيا من ضمنها y على تلاتة c، ده استخدمها للحسابات
+
+421
+00:33:05,970 --> 00:33:09,810
+بعد شوية زي ما أنتم عارفين لأن moreover, since fi
+
+422
+00:33:09,810 --> 00:33:15,290
+element مسبان لل M then by B there is n such that
+
+423
+00:33:15,290 --> 00:33:21,310
+fi of x n ناقص fi of x أصغر من y على ثلاثة for all
+
+424
+00:33:21,310 --> 00:33:27,420
+n أكبر من مين من اللي هي مين من n عندي FI of XN
+
+425
+00:33:27,420 --> 00:33:32,460
+ناقص FI of X التي أصغر من Y على 3 لكل N أكبر من
+
+426
+00:33:32,460 --> 00:33:40,420
+100 من N طيب أطلع لفوق then for all N أكبر من N we
+
+427
+00:33:40,420 --> 00:33:45,840
+have أحسب لـ FI of XN ناقص F of X هذه بالـ
+
+428
+00:33:45,840 --> 00:33:49,200
+Triangling Quality بدي أضيف ترم وأطرح ترم أصغر أو 
+
+429
+00:33:49,200 --> 00:33:53,140
+يساوي اللي هو norm أو absolute value للـ FI of XN
+
+430
+00:33:53,140 --> 00:33:59,800
+ناقص FI of XN هي اللي ضفتها وهنا طرحت أو ضفت a5x
+
+431
+00:33:59,800 --> 00:34:05,420
+أنا ناقص مين a5x زاد a5x ناقص a5x طرحت مين التنتين
+
+432
+00:34:05,420 --> 00:34:09,940
+ضفت التنتين اه ماشي الحل الآن صار عندي الآن الأولى
+
+433
+00:34:09,940 --> 00:34:16,450
+هذه اللي هو أصغر أو شوية normal FI ناقص F وهذه X
+
+434
+00:34:16,450 --> 00:34:24,210
+زائد المفهومة هذه أصغر من مين من Y ع تلاتة وهذه FI
+
+435
+00:34:24,210 --> 00:34:27,590
+of X ناقص نفس اللي عملته في اللي فوق Normal FI
+
+436
+00:34:27,590 --> 00:34:32,870
+ناقص F في Normal مين ال X هذه الواحدة فيها اللي هو
+
+437
+00:34:32,870 --> 00:34:37,650
+FI ناقص F أصغر من Y ع تلاتة C وهذه أصغر أو شوه C
+
+438
+00:34:38,610 --> 00:34:42,370
+هذه زي ما هي وهذه نفس الشيء أصغر أو يساوي y ع تلاتة c
+
+439
+00:34:42,370 --> 00:34:46,510
+وهذه أصغر من c إذا اللي هو صارت عندي y ع تلاتة y ع
+
+440
+00:34:46,510 --> 00:34:49,970
+تلاتة y ع تلاتة أو يساوي إبسلون الآن صار عندي الآن
+
+441
+00:34:49,970 --> 00:34:54,130
+ال absolute value لل F of X نقص F of X أصغر أو
+
+442
+00:34:54,130 --> 00:34:59,130
+يساوي إبسلون و F كانت arbitrary إذا هذا معناته إنه
+
+443
+00:34:59,130 --> 00:35:03,130
+F of X هان بتروح لل F of X ك number إذا معناته X
+
+444
+00:35:03,130 --> 00:35:07,870
+هان بتروح لل X إيش ماله weekly  وهيك بيكون احنا
+
+445
+00:35:08,660 --> 00:35:15,700
+خلصنا اللي هو المحاضرة نزل المحاضرة وإن شاء الله
+
+446
+00:35:15,700 --> 00:35:18,920
+إلى لقاء آخر 
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Z5xeo5Xjt84_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Z5xeo5Xjt84_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5e251d0b4a77b5c0871a9b69c2347e3a8b2cd9b8
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Z5xeo5Xjt84_postprocess.srt
@@ -0,0 +1,1784 @@
+1
+00:00:05,060 --> 00:00:07,800
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,800 --> 00:00:10,800
+والصلاة والسلام على سيد المسلمين سيدنا محمد وعلى
+
+3
+00:00:10,800 --> 00:00:15,460
+أهله وصحبه أجمعين هذه هي المحاضرة رقم 32 مساق
+
+4
+00:00:15,460 --> 00:00:20,340
+تحليل اقتراني أو تحليل دالي طلاب طالبات الجامعة
+
+5
+00:00:20,340 --> 00:00:25,200
+الإسلامية ماجستير الرياضياتوصلنا لعند اللي هو
+
+6
+00:00:25,200 --> 00:00:29,460
+اربعة تمانية strong and weak convergence نشوف ايش
+
+7
+00:00:29,460 --> 00:00:35,260
+اللي هو نقصد اللي هو strong و weak convergence
+
+8
+00:00:35,260 --> 00:00:39,380
+طبعا احنا اللي هنحكي عن اللي هو norm this base
+
+9
+00:00:39,380 --> 00:00:42,960
+نحكي عن ال convergence في داخل norm this base
+
+10
+00:00:44,590 --> 00:00:48,030
+بنتعرف على نوعين من أنواع ال convergence في ال
+
+11
+00:00:48,030 --> 00:00:53,110
+node space ونشوف أيش معنات كل نوع من النوعين a
+
+12
+00:00:53,110 --> 00:00:57,730
+sequence xn in a node space x is said to be
+
+13
+00:00:57,730 --> 00:01:01,970
+strongly convergent or convergent in the norm يعني
+
+14
+00:01:01,970 --> 00:01:04,290
+ال convergence with respect to mean to the norm
+
+15
+00:01:11,440 --> 00:01:15,680
+وهذا الكلام احنا بنرمزله باسم limit xn بساوة x او
+
+16
+00:01:15,680 --> 00:01:16,800
+xn converges to x
+
+17
+00:01:23,730 --> 00:01:28,990
+لذلك عندما نكتب xn converges للـ x بالشكل هذا اللي
+
+18
+00:01:28,990 --> 00:01:33,310
+نقصد فيها هو xn is strongly convergence to main to
+
+19
+00:01:33,310 --> 00:01:39,030
+x مايعنيها؟ معناته أن ال limit للـ xn ناقص xبروح
+
+20
+00:01:39,030 --> 00:01:42,990
+للـ 0 as N goes from mean to infinity في هذه
+
+21
+00:01:42,990 --> 00:01:46,590
+الحالة بنسمي الـ X the limit اللي هو the strong
+
+22
+00:01:46,590 --> 00:01:50,790
+limit of mean of the sequence XN الآن في
+
+23
+00:01:50,790 --> 00:01:54,550
+convergence آخر اللي هو سنتعرف عليه اللي هو
+
+24
+00:01:54,550 --> 00:02:00,950
+sequence بنقول عنه XN converts ل X weekly طبعا الـ
+
+25
+00:02:00,950 --> 00:02:06,210
+XN والـ X برضه الموجودات الـ XNوالـ x elements in
+
+26
+00:02:06,210 --> 00:02:11,230
+the non-dospace is x هذا الأولاني اللي هو الـ
+
+27
+00:02:11,230 --> 00:02:13,610
+strong convergence والآن بدنا نعرف الـ weak
+
+28
+00:02:13,610 --> 00:02:16,590
+convergence إيش معناته اللي هو xₙ تروح للـ x
+
+29
+00:02:16,590 --> 00:02:23,650
+weekly إذا كان اللي هو لكل f element اللي هو x برا
+
+30
+00:02:23,650 --> 00:02:26,270
+يعني bounded linear operator bounded linear
+
+31
+00:02:26,270 --> 00:02:26,590
+function
+
+32
+00:02:30,120 --> 00:02:34,720
+Converging to the off of X هذا معناته ان Xn
+
+33
+00:02:34,720 --> 00:02:39,300
+Converges لإكسية شمال و weekly لحظه اللي هو احنا
+
+34
+00:02:39,300 --> 00:02:44,240
+حولنا الحدير من Xn ل X اللي هي في الـ non spaces
+
+35
+00:02:44,240 --> 00:02:48,420
+إلى convergence في الواقع في الـ scalar field لأن
+
+36
+00:02:48,420 --> 00:02:52,480
+off of Xn و off of X شمالها عبارة عن number يعني
+
+37
+00:02:52,480 --> 00:02:54,980
+complex أو real حسب اللي هو ال complex field عشان
+
+38
+00:02:54,980 --> 00:03:01,110
+هيك بنسمي weekly convergence يعني باختصاربالنسبة
+
+39
+00:03:01,110 --> 00:03:08,550
+لـ Xn في الوضع X قد يكون مرتبطاً يومياً إذا كان
+
+40
+00:03:08,550 --> 00:03:11,850
+هناك X أقل من X كما لو كان هناك X أقل من X كما لو
+
+41
+00:03:11,850 --> 00:03:19,290
+كان هناك X أقل من X كما لو كان هناك X أقل من X
+
+42
+00:03:22,940 --> 00:03:26,280
+لأن أكيد في علاقة بين الـ weak convergence وبين
+
+43
+00:03:26,280 --> 00:03:29,640
+mean وبين ال strong convergence يعني انتبه عن
+
+44
+00:03:29,640 --> 00:03:32,900
+الواحد هيقول أكيد ال strong convergence إيش هيقدر
+
+45
+00:03:32,900 --> 00:03:35,680
+لل weak convergence لكن the convergence need not
+
+46
+00:03:35,680 --> 00:03:41,390
+to be true in general هنشوف اللي هوكيف نثبت الـ Xn
+
+47
+00:03:41,390 --> 00:03:47,810
+بتروح للـ X weakly بيؤدي لـ weakly و كيف اللي هو
+
+48
+00:03:47,810 --> 00:03:52,330
+انه احنا نثبت انه اللي هو ال converts need not to
+
+49
+00:03:52,330 --> 00:03:55,910
+be true عن طريق example و من ثم نشوف ايش في
+
+50
+00:03:55,910 --> 00:04:00,570
+condition بنحطه على اللي هو non displaced عشان
+
+51
+00:04:00,570 --> 00:04:03,470
+يصير اللي هو ال weak convergence و ال strong يشمله
+
+52
+00:04:03,470 --> 00:04:10,610
+زي بعضلاحظوا في الـ R كنا نحكي عن weak convergence
+
+53
+00:04:10,610 --> 00:04:13,550
+و strong convergence كنا نحكي عنه في الـ sequences
+
+54
+00:04:14,820 --> 00:04:17,620
+سنجد أن في الـ R و في الـ C و في الحاجات اللي زي
+
+55
+00:04:17,620 --> 00:04:21,280
+.. في كل الـ finite dimensional spaces سيكون اللي
+
+56
+00:04:21,280 --> 00:04:24,260
+هو الـ weak convergence و الـ strong Gاش مالهين
+
+57
+00:04:24,260 --> 00:04:28,300
+are the same خلّينا الأن نشوف أول لمّة لمّة الأولى
+
+58
+00:04:28,300 --> 00:04:31,460
+let Xn be a weakly اللي هو convergence sequence
+
+59
+00:04:31,460 --> 00:04:36,620
+around space X سي Xn بتروح للـ X مالها weaklyأثناء
+
+60
+00:04:36,620 --> 00:04:41,280
+ذلك، قيمة الـ weak X of Xn هي محدودة، وهي أشمالها
+
+61
+00:04:41,280 --> 00:04:45,440
+وحيدة، إذن قيمة، في حالة، احنا بنحكي عن أهم حالة
+
+62
+00:04:45,440 --> 00:04:50,340
+مين؟ حالة الـ weak convergence قيمة اللي هي وحيدة،
+
+63
+00:04:50,340 --> 00:04:53,920
+اتنين، every subsequence of Xn converges أشماله
+
+64
+00:04:53,920 --> 00:04:59,010
+weakly to Xالحالة في الـ sequence الـ norm لـ Xn
+
+65
+00:04:59,010 --> 00:05:03,330
+أشمالها is bounded إذا كل هذه الأمور اللي هو من
+
+66
+00:05:03,330 --> 00:05:06,050
+خواص الـ weak convergence يعني لو بدنا نيدي
+
+67
+00:05:06,050 --> 00:05:11,090
+نعطيكوا sketch للبرهان نفترض إن Xn بتروح لـ X
+
+68
+00:05:11,090 --> 00:05:16,450
+weekly و Xn بتروح لـ Y أيش برضه weekly يعني بروح
+
+69
+00:05:16,450 --> 00:05:19,790
+إني أشمال إلى different limits و في الآخر نثبت إنه
+
+70
+00:05:19,790 --> 00:05:24,120
+أشمال و X و Y هي نفس الأشياءالان شو معنات xn بتروح
+
+71
+00:05:24,120 --> 00:05:28,600
+لل x weekly لان لكل f element in x prime هيكون عند
+
+72
+00:05:28,600 --> 00:05:35,000
+ال f of xn بتروح لمين لل f of x معايا نفس الاشي
+
+73
+00:05:35,000 --> 00:05:39,620
+مدام xn بتروح لل y weekly لكل f element in x prime
+
+74
+00:05:39,620 --> 00:05:47,170
+هتطلع f of xn برضه هتروح لمين لل fهذه سيكوينس نمبر
+
+75
+00:05:47,170 --> 00:05:50,610
+و هذه سيكوينس نمبر و احنا نعرف ان سيكوينس نمبر
+
+76
+00:05:50,610 --> 00:05:53,510
+عندما يكون مرتبط مع مرتبط مع نفس المقالة إلى نفس
+
+77
+00:05:53,510 --> 00:05:54,150
+المقالة
+
+78
+00:05:59,080 --> 00:06:04,280
+هي ساوي F of Y هذا الكلام لكل مين لكل F element in
+
+79
+00:06:04,280 --> 00:06:10,440
+X' هذا معناته أن F of X minus Y هتساوي سفر لكل F
+
+80
+00:06:10,440 --> 00:06:14,720
+element in X' واحنا أخدنا نتيجة قبل هيك هتطلع مين
+
+81
+00:06:14,720 --> 00:06:20,300
+إذا ال X minus Y هتساوي سفر إذا معناته X هتساوي Y
+
+82
+00:06:20,300 --> 00:06:24,620
+معناته إنه ال limit ما لها is unique under the
+
+83
+00:06:24,620 --> 00:06:32,930
+weak convergenceهذا بالنسبة لمن؟ لـ B برضه
+
+84
+00:06:32,930 --> 00:06:36,890
+نفس الأشياء إعتمادا على خواص الـ sequence of
+
+85
+00:06:36,890 --> 00:06:42,510
+numbers سنحصل على خواص الـ convergence للـ
+
+86
+00:06:42,510 --> 00:06:49,330
+sequence لو جيت الآن قلتخلّينا نفترض إن Xn مرتبط
+
+87
+00:06:49,330 --> 00:06:53,990
+بالـ X ما لها weekly بتاخد الآن أي subsequence
+
+88
+00:06:53,990 --> 00:06:56,830
+منها و اكتبت برضه انها مرتبط بالـ X ما لها weekly
+
+89
+00:06:56,830 --> 00:07:07,930
+بدي أقول let Xnk be any subsequence of Xn ماشي
+
+90
+00:07:07,930 --> 00:07:14,780
+الحال؟ الآن مدام Xn بتروح للـ X weekly thenأكيد
+
+91
+00:07:14,780 --> 00:07:20,380
+الـ f of xn هتروح للـ f of x لكل الأثوين الموجودة
+
+92
+00:07:20,380 --> 00:07:25,960
+في الـ x' الان سارة تقدر عبارة عن sequence of
+
+93
+00:07:25,960 --> 00:07:31,040
+numbers ال sequence of numbers أي subsequence منها
+
+94
+00:07:31,040 --> 00:07:33,580
+هتكون في ال virtue of the same limit إذا ال
+
+95
+00:07:33,580 --> 00:07:39,910
+subsequence f of xnkاللي هو conveys لمين لل F of X
+
+96
+00:07:39,910 --> 00:07:46,690
+لكل FY موجودة برضه في الـ X' وهذا معناته هو تعريف
+
+97
+00:07:46,690 --> 00:07:51,990
+إن X and K بتروح لل X weekly إذا أي subsequence
+
+98
+00:07:51,990 --> 00:07:55,610
+conveys weekly to the same limit as الsequence
+
+99
+00:07:55,610 --> 00:07:56,310
+الأصلية
+
+100
+00:07:59,320 --> 00:08:04,400
+اللي هو الـ sequence اللي هو ما لها norm لـ Xn إيش
+
+101
+00:08:04,400 --> 00:08:09,680
+ما لها is اللي هي bounded ال sequence norm لـ Xn
+
+102
+00:08:09,680 --> 00:08:14,460
+is bounded عند Xn بتروح لل X weekly ماشي الحال لل
+
+103
+00:08:14,460 --> 00:08:19,060
+X then F of Xn بتروح لل F of X لكل F الموجودة في
+
+104
+00:08:19,060 --> 00:08:23,900
+ال X' هذا صار تعريف فهمنا الان so that the
+
+105
+00:08:23,900 --> 00:08:28,580
+sequence of numbers F of Xn is bounded أكيدلاحظوا
+
+106
+00:08:28,580 --> 00:08:32,620
+كل اعتمادي تحويل اللي هو convergence in the norm
+
+107
+00:08:32,620 --> 00:08:35,700
+اللي هو x as if convergence weekly in the norm ل
+
+108
+00:08:35,700 --> 00:08:41,180
+convergence of mean of numbers اللي صارتها
+
+109
+00:08:41,180 --> 00:08:45,740
+debounded that is there exists cf اللي هي constant
+
+110
+00:08:45,740 --> 00:08:51,060
+depending on mean on fلأن هذا الكلام هذه تطلع على
+
+111
+00:08:51,060 --> 00:08:56,400
+فوق هذه ال sequence f of xn is bounded لمين؟ لل f
+
+112
+00:08:56,400 --> 00:08:59,560
+اللي بحكي عنها إذا أكيد ال c تبعتها بتعتمد على
+
+113
+00:08:59,560 --> 00:09:02,300
+مين؟ على ال f إذا بصير عند ال absolute value أو ال
+
+114
+00:09:02,300 --> 00:09:07,980
+modulus لل f of xn أصغر يستوي cf لكل nالآن using
+
+115
+00:09:07,980 --> 00:09:11,580
+the canonical mapping C إذا بتذكره من X لعين X
+
+116
+00:09:11,580 --> 00:09:13,700
+double prime هذا ال canonical mapping كيف كنا
+
+117
+00:09:13,700 --> 00:09:20,880
+عارفينه where ناخد اللي هو can define GN element
+
+118
+00:09:20,880 --> 00:09:23,900
+in X double prime by حكيناه المرة السابقة تفصيله
+
+119
+00:09:23,900 --> 00:09:28,520
+المرة السابقة تاخدناه GN of F ايش متساوي F of XN
+
+120
+00:09:29,020 --> 00:09:32,460
+لكل f الموجودة في الـ x' خُد الآن الـ absolute
+
+121
+00:09:32,460 --> 00:09:37,560
+value هذه لها ال absolute value of g of f بسوء ال
+
+122
+00:09:37,560 --> 00:09:42,060
+absolute value of f of xn اللي هو أصغر أو شومين cf
+
+123
+00:09:42,060 --> 00:09:47,460
+إذا صار عنده الآن هذه نفسها is bounded هذه نفسها
+
+124
+00:09:47,460 --> 00:09:51,140
+is bounded لإن هذه bounded إذا هذه ايش معناها is
+
+125
+00:09:51,140 --> 00:09:54,520
+bounded وهذا is bounded for all f element in x'
+
+126
+00:09:54,880 --> 00:10:02,660
+لكن x' is completeإذا باى اللي هي uniform
+
+127
+00:10:02,660 --> 00:10:06,160
+boundedness اللي ناخدناها المرة الماضية نورمها
+
+128
+00:10:06,160 --> 00:10:09,860
+هيكون bounded مظبوط ولا لأ حكيناه المرة الفاتة
+
+129
+00:10:09,860 --> 00:10:15,060
+مدام أنها bounded إذا و ال X' is complete اللي
+
+130
+00:10:15,060 --> 00:10:22,000
+عليها معرفة اللي هي اللي عنده GNمعرفة على Complete
+
+131
+00:10:22,000 --> 00:10:26,560
+Space إذا بالـ Uniform Boundedness Theorem شروطها
+
+132
+00:10:26,560 --> 00:10:30,760
+مطبقة حيكون الـ Normal GN is bounded معناته Normal
+
+133
+00:10:30,760 --> 00:10:33,820
+GN is bounded معناته اللي هو Normal XN bounded
+
+134
+00:10:33,820 --> 00:10:38,700
+لإنه أثبتنا في أربعة، ستة، واحد إن Normal XN هو
+
+135
+00:10:38,700 --> 00:10:45,480
+Normal GN ومن ثم أثبتنا Normal XN is bounded طيب،
+
+136
+00:10:45,480 --> 00:10:46,720
+الـtheorem اللي بعدها
+
+137
+00:10:50,820 --> 00:10:56,160
+اللي وعدناكم فيه let Xn be a sequence in unknown
+
+138
+00:10:56,160 --> 00:11:01,260
+space X then
+
+139
+00:11:01,260 --> 00:11:06,940
+a strong convergence implies ما له weak
+
+140
+00:11:06,940 --> 00:11:10,160
+convergence with the same limit يعني لو الآن Xn
+
+141
+00:11:10,160 --> 00:11:14,900
+بتروح لل X strongly هتروح لل X أش ما لها weakly
+
+142
+00:11:15,620 --> 00:11:19,120
+الأن الـ Converse of A need not to be true in
+
+143
+00:11:19,120 --> 00:11:23,380
+general يعني فيه اللي هو weak convergence مش
+
+144
+00:11:23,380 --> 00:11:27,860
+strong convergence وحناخد مثال الشغل الثالثة بدنا
+
+145
+00:11:27,860 --> 00:11:30,740
+نزيد شرط شوية على ال weak convergence اللي يخلّيه
+
+146
+00:11:30,740 --> 00:11:34,100
+strong اللي قلناه قبل شوية ملاحظة انه لو كان ال
+
+147
+00:11:34,100 --> 00:11:36,460
+dimension ال X finite هيكون ال weak convergence
+
+148
+00:11:36,460 --> 00:11:40,360
+إيش ماله وبيعطي اللي هو ال strong convergence ديجي
+
+149
+00:11:40,360 --> 00:11:43,840
+ناخد واحدة واحدة ديجي ناخد الأولة الآنالان لو
+
+150
+00:11:43,840 --> 00:11:50,340
+فرضنا ان xn بتروح لل x اللي هو strongly ماشي؟ ايش
+
+151
+00:11:50,340 --> 00:11:56,280
+معناته هذا؟ اذا then norm ال xn ناقص x بروح لمين؟
+
+152
+00:11:56,280 --> 00:12:01,030
+لصفرالان بيثبتلك ان ال XN بتروح لل XA شمالها
+
+153
+00:12:01,030 --> 00:12:05,970
+weekly ايش يعني بيثبتلك بيثبتلك ان لكل F element
+
+154
+00:12:05,970 --> 00:12:11,870
+in X' يطلع F of XN بيروح لمين لل F of X ماشي الحال
+
+155
+00:12:11,870 --> 00:12:19,050
+هاي اللي بيثبتهإيش يعني؟ يعني بمعنى بدي أثبتلك بدي
+
+156
+00:12:19,050 --> 00:12:23,010
+أثبتلك إنه لو أخدت ال absolute value of f of x n
+
+157
+00:12:23,010 --> 00:12:27,510
+ماقص f of x بدي أثبتلك إن هذا بروح للسفر as n goes
+
+158
+00:12:27,510 --> 00:12:32,110
+to infinity معايا يا جماعة؟ الآن شوفوا هذا هذا
+
+159
+00:12:32,110 --> 00:12:38,310
+طبعا أصغر اللي بيساوي ال f of x n ماقص x صح ولا
+
+160
+00:12:38,310 --> 00:12:42,950
+لأ؟ لأن f is linear وهذا أصغر أو يساوي normal f
+
+161
+00:12:44,140 --> 00:12:49,150
+فنورمين الـ x أهم ناقص x لأن f is boundedالـ N as
+
+162
+00:12:49,150 --> 00:12:53,410
+N goes to infinity هذا بيروح لمين؟ للـ Zero إذاً و
+
+163
+00:12:53,410 --> 00:12:59,850
+هذا أكبر و سوء سفر إذاً F of X N هتروح لل F of X و
+
+164
+00:12:59,850 --> 00:13:04,470
+كانت F arbitrary قلمة X Prime إذاً هذا معناته إذا
+
+165
+00:13:04,470 --> 00:13:09,190
+X N بتروح لل X weekly إذا اللي هو ال strong
+
+166
+00:13:09,190 --> 00:13:12,770
+convergence واضح أنه بيعطي مين؟ اللي هو ال weak
+
+167
+00:13:12,770 --> 00:13:16,610
+convergenceيجي الآن بقول لك if the converse of A
+
+168
+00:13:16,610 --> 00:13:20,570
+is not true in general وخلّينا نشوف المثال أو ال
+
+169
+00:13:20,570 --> 00:13:25,750
+counter example اللي معطينيه اطلع لفوق شوية الان
+
+170
+00:13:25,750 --> 00:13:30,830
+let E N let E N be an orthonormal sequence in
+
+171
+00:13:30,830 --> 00:13:34,650
+Hilbert space mean H وقولنا ان ال ال ال ال ال
+
+172
+00:13:34,650 --> 00:13:38,110
+Hilbert space has an orthonormal اللي هو بنقدر
+
+173
+00:13:38,110 --> 00:13:41,350
+ناخد فيه an orthonormal sequenceBy Ray's
+
+174
+00:13:41,350 --> 00:13:44,450
+Representation Theorem اللي استخدمناها كثير تلاتة
+
+175
+00:13:44,450 --> 00:13:48,030
+تمانية واحد لدرجة ان احنا حافظنا رقمها By Ray's
+
+176
+00:13:48,030 --> 00:13:51,970
+Representation Theorem Any F المتنقطش برايم has a
+
+177
+00:13:51,970 --> 00:13:55,010
+representation F of X مش بيساوي X و Z و الـ Z ده
+
+178
+00:13:55,010 --> 00:13:59,590
+unique زي ما اتفجنا ماشي الحال طيب hence الان مدام
+
+179
+00:13:59,590 --> 00:14:02,270
+F of X بيساوي X و Z أكيد ال F of En تبع
+
+180
+00:14:02,270 --> 00:14:07,300
+الورتنورمال بيساوي En و 100 و Zماشي هذا الكلام
+
+181
+00:14:07,300 --> 00:14:12,380
+طبعا الان اي F element الـ H' له Z اللي هي بقدر
+
+182
+00:14:12,380 --> 00:14:19,180
+اكتب ال F بدللتها اتفقنا؟ طيب الان F of E N بساول
+
+183
+00:14:19,180 --> 00:14:24,270
+ال inner product بين E N و Zالان انا بتثبتلكم انه
+
+184
+00:14:24,270 --> 00:14:29,350
+اللي هو عند ال EN هذه converts to zero weekly لكن
+
+185
+00:14:29,350 --> 00:14:33,890
+مش strongly ماشي ال EN هذه ال orthonormal sequence
+
+186
+00:14:33,890 --> 00:14:36,510
+اللي هو اللي ماخدها في ال H بتثبتلكم انها تروح
+
+187
+00:14:36,510 --> 00:14:41,940
+weekly لل zero لكن مش strongly ده نشوف كدهالان
+
+188
+00:14:41,940 --> 00:14:45,240
+بالـ Bessel Inquality عشان أصل اللي .. اللي بديها
+
+189
+00:14:45,240 --> 00:14:48,460
+لو جيت أخدت اللي هو ال .. الـ Bessel Inquality
+
+190
+00:14:48,460 --> 00:14:51,260
+اللي مش ذاكرينها لقينا الربروضاكت بين الـ E ان
+
+191
+00:14:51,260 --> 00:14:55,360
+والـ Z تربيع من ان و نحد إلى مالة نهاية هذا أصغر و
+
+192
+00:14:55,360 --> 00:14:58,280
+ساوي من نور من Z التربيع، هذه اللي هي الـ Bessel
+
+193
+00:14:58,280 --> 00:15:03,580
+Inquality اللي أخدناها طيبالان معناته انه صارت هذه
+
+194
+00:15:03,580 --> 00:15:07,840
+ال series converge مزامها محدودة بمين بالقيمة اللي
+
+195
+00:15:07,840 --> 00:15:11,240
+هي norm of z مدام انها مرتبطت اذا ال limit اللي
+
+196
+00:15:11,240 --> 00:15:14,880
+جوا ايه شماله سفر انا بحكي عن number صرت هذا
+
+197
+00:15:14,880 --> 00:15:17,800
+absolute value معناه صرت number الان limit اللي
+
+198
+00:15:17,800 --> 00:15:20,740
+جوا ايه شماله سفر اذا هذا المقدار بروح ل zero as n
+
+199
+00:15:20,740 --> 00:15:26,040
+goes to infinityالان و هذا بيعطيني هذا صار اللي هو
+
+200
+00:15:26,040 --> 00:15:29,560
+ال absolute value له يروح لل zero برضه اذا اكيد
+
+201
+00:15:29,560 --> 00:15:32,180
+اللي هو ال F of EN اللي هو سوء EN و Z برضه هيروح
+
+202
+00:15:32,180 --> 00:15:37,800
+لمين لل zero واضح الان هذا المقدار راح لل صفر و
+
+203
+00:15:37,800 --> 00:15:42,260
+انا بعرف ان هذا المقدار تربيع ال FEN يعني صارت FEN
+
+204
+00:15:42,260 --> 00:15:45,600
+تربيع بتروح لل صفر اذا ال FEN نفسها هتروح لمين لل
+
+205
+00:15:45,600 --> 00:15:51,080
+zeroالـ 0 اللي هو عبارة عن الـ F of إيه عش؟ of 0
+
+206
+00:15:51,080 --> 00:15:58,420
+ماشي اللي هي as n goes since F المتنقضش prime هذا
+
+207
+00:15:58,420 --> 00:16:01,320
+اللي هو بيروح للـ 0 اللي هو بسوء إيه عش؟ F of 0
+
+208
+00:16:01,320 --> 00:16:06,540
+لأن F of 0 بسوء 0 لكل F linear functional عارفين
+
+209
+00:16:06,540 --> 00:16:09,440
+هذا المعلومة؟ since F المتنقضش prime was arbitrary
+
+210
+00:16:09,440 --> 00:16:16,070
+إذا EN هذه الـ EN هتروح لمين؟ للي هويعني الأن
+
+211
+00:16:16,070 --> 00:16:23,410
+أثبتتلكم F of E N بتروح لل F of Zero لكل F element
+
+212
+00:16:23,410 --> 00:16:27,810
+in H' هذا اللي أثبته هذا أيش معناته أن E N بتروح
+
+213
+00:16:27,810 --> 00:16:35,390
+لل Zero weekly إذا أثبتنا أن E N بتروح للصفر
+
+214
+00:16:35,390 --> 00:16:45,200
+weekly بل أثبت أن E N مستحيل تروحللسفر يعني مستحيل
+
+215
+00:16:45,200 --> 00:16:50,960
+ان يكون عندي Normal EN ناقص السفر ويساوي Normal EN
+
+216
+00:16:50,960 --> 00:16:58,280
+يروح لمين للسفر هذا الكلام مستحيل لسبب بسيط الان
+
+217
+00:16:58,280 --> 00:17:08,300
+اطلع لفوق احسبلي الانخُد أي N لا تساوى M وحسب
+
+218
+00:17:08,300 --> 00:17:13,280
+المسافة بين E M وE N ال E M إيش هي صفار صفار صفار
+
+219
+00:17:13,280 --> 00:17:17,420
+معدى عند ال Nth term واحد وال E N صفار صفار صفار
+
+220
+00:17:17,420 --> 00:17:21,640
+معدى عند ال Nth term بساوى واحدأذا سأقرا هذا الـ a
+
+221
+00:17:21,640 --> 00:17:25,360
+المقصي يعني عبارة عن كل هن أسفار معادة جزئين فيه
+
+222
+00:17:25,360 --> 00:17:29,180
+هن أش بيساوي واحد واحد فال summation الهن تربيع
+
+223
+00:17:29,180 --> 00:17:32,420
+لكل واحد الكل أص نص اللي هو عبارة عن واحد وكمان
+
+224
+00:17:32,420 --> 00:17:35,460
+واحد اتنين الكل أص نص مايصير جدياش اللي هو جدر
+
+225
+00:17:35,460 --> 00:17:38,340
+التنين إذا هذا اللي جوا نور مجدر التنين يعني
+
+226
+00:17:38,340 --> 00:17:42,880
+تربيعه أش بيساوي اتنين فاهمين اللي بحكيه؟أو إذا
+
+227
+00:17:42,880 --> 00:17:46,800
+حسبته بالشكل هذا E M و E N و E N و E N هذا ال E M
+
+228
+00:17:46,800 --> 00:17:51,760
+وال E M اللي هو norm واحد وهذا norm واحد اللي هو
+
+229
+00:17:51,760 --> 00:17:54,540
+بيصير norm اتنين وطبعا وال E M من علي ال E N لما
+
+230
+00:17:54,540 --> 00:17:59,880
+تفكه بيطلع سفر لإنهم orthonormal اتنين عامدين على
+
+231
+00:17:59,880 --> 00:18:03,440
+بعض وال E M وال E N برضه أيش بيساوي بيساوي سفرإذن
+
+232
+00:18:03,440 --> 00:18:09,360
+الـ N صارت هذه الـ Sequence E N مش كوشي لإن البعد
+
+233
+00:18:09,360 --> 00:18:12,360
+بينه نشمل و بساوي و بساوي و اتنين راحت N إلى مالة
+
+234
+00:18:12,360 --> 00:18:16,140
+نهاية و لا ال M إلى مالة نهاية لن يتغير الأبعاد
+
+235
+00:18:16,140 --> 00:18:20,560
+المسافات بين كل عنصر و الثاني ابعد عن بعض ففيش إيش
+
+236
+00:18:20,560 --> 00:18:24,380
+يروحه باتجاهه يعني بمعنى آخر E N صارت is not
+
+237
+00:18:24,380 --> 00:18:27,460
+cauchy إيش معنات is not cauchy و في إحنا في
+
+238
+00:18:27,460 --> 00:18:31,580
+complete space يعني معناها is not convergentإذا
+
+239
+00:18:31,580 --> 00:18:36,880
+الان EN is not .. does not converge مثلا does not
+
+240
+00:18:36,880 --> 00:18:41,760
+converge إذا normal EN هذا does not converge to
+
+241
+00:18:41,760 --> 00:18:47,340
+zero يعني بمعنى أخر EN does not converge strongly
+
+242
+00:18:47,340 --> 00:18:53,840
+to zero هاي مثلا نيجي الآن للي بعده اللي بعده في
+
+243
+00:18:53,840 --> 00:18:55,460
+حالة ال dimension
+
+244
+00:18:58,000 --> 00:19:02,080
+للـ X بيساوي مثلا ال K زي ما هو مسميها اللي هو
+
+245
+00:19:02,080 --> 00:19:07,860
+finite هيكون عند ال XM بتروح لل X weekly if and
+
+246
+00:19:07,860 --> 00:19:12,220
+only if XM بتروح لل X إشمالها strongly
+
+247
+00:19:15,220 --> 00:19:20,380
+الاتجاه هذا أثبتناه إذا نظل على يثبت أنه لما ال
+
+248
+00:19:20,380 --> 00:19:23,940
+dimension لل X بيساوي كده و كائنة Xn بتروح لل X
+
+249
+00:19:23,940 --> 00:19:29,320
+weekly يعطيني إن Normal Xn ناطس ال X بيروح لمين؟
+
+250
+00:19:29,320 --> 00:19:33,220
+لل Zero أو بمعنى آخر Xn بتروح لل X strongly واضح
+
+251
+00:19:33,220 --> 00:19:38,800
+الكلام، هي اللي بدي أثبته طيب شوفوا الآن كيف بدي
+
+252
+00:19:38,800 --> 00:19:44,780
+أكيد استعمل اللي هو ال dimension لل X is finiteلما
+
+253
+00:19:44,780 --> 00:19:47,860
+الـ dimension للـ X is finite إذن فيه bases صحيح
+
+254
+00:19:47,860 --> 00:19:52,280
+طيب إذا الأن suppose that XM بتروح ل X weakly and
+
+255
+00:19:52,280 --> 00:19:55,260
+dimension ل X بالساوة K وبيتثبت إن XM بتروح ل X
+
+256
+00:19:55,260 --> 00:19:59,240
+strongly لأن مدام الـ finite dimensional واسمه K
+
+257
+00:19:59,240 --> 00:20:03,460
+إذا بقدر أجرأ و أقول let E1 و E2 لعند الـ E كي بيه
+
+258
+00:20:03,460 --> 00:20:07,500
+أي basis of مين of X مدام basis ل X إذا أي
+
+259
+00:20:07,500 --> 00:20:12,730
+sequenceXn عناصرها X واحد في الـ X والـ X اتنين في
+
+260
+00:20:12,730 --> 00:20:15,910
+الـ X والـ Xn in general في الـ X إذا بقدر اكتبها
+
+261
+00:20:15,910 --> 00:20:19,090
+على صورة linear combination من مين؟ من عناصر ال
+
+262
+00:20:19,090 --> 00:20:24,310
+bases إذا صار عندي الـ Xn بيساوي Alpha J N يعني EJ
+
+263
+00:20:24,310 --> 00:20:28,490
+J من واحد عند K وAlpha J N هذي أشملها عبارة عن ال
+
+264
+00:20:28,490 --> 00:20:34,400
+scalars يعني الآن X واحداللي بيصير Alpha 1 1 Alpha
+
+265
+00:20:34,400 --> 00:20:41,980
+2 1 Alpha 3 1 Alpha 4 1 Alpha 5 K Alpha 1 Alpha K
+
+266
+00:20:41,980 --> 00:20:47,590
+1الأن X2 نفس الشيء X3 نفس الشيء إذا صارت عندي هذه
+
+267
+00:20:47,590 --> 00:20:51,030
+sequence of elements in mean in X الان برضه نفس
+
+268
+00:20:51,030 --> 00:20:56,830
+الشيء خد X بتساوي اللي هو summation لألف ج أيه جه
+
+269
+00:20:56,830 --> 00:20:59,710
+جه من عند واحد لعند مين لعند كيه برضه ليه ال
+
+270
+00:20:59,710 --> 00:21:03,370
+compilation من مين من العناصر الان by assumption
+
+271
+00:21:03,370 --> 00:21:06,430
+احنا ما احنا قولنا X ان بتروح لمين لل X weekly
+
+272
+00:21:06,430 --> 00:21:10,130
+كترت ال X ان بصورة هذه و كترت ال X بصورة هذه بناء
+
+273
+00:21:10,130 --> 00:21:13,510
+على ال dimension لل X بساوة K و هذا هو ال basisطيب
+
+274
+00:21:13,510 --> 00:21:16,770
+by assumption مدام x1 بتروح إلى x weekly إذا أنا
+
+275
+00:21:16,770 --> 00:21:19,270
+هيطلع عندي f of x2 بتروح إلى ال f of x لكل mean
+
+276
+00:21:19,270 --> 00:21:24,550
+لكل f element in x prime in particular ما هو ال x
+
+277
+00:21:24,550 --> 00:21:29,310
+prime اللي هو برضه ال dimension ياله k إذا فيه
+
+278
+00:21:29,310 --> 00:21:35,670
+باسيس باسيس تبعه اللي هو مثلا نسموه f1, f2أف تلاتة
+
+279
+00:21:35,670 --> 00:21:39,450
+لأنه functions لعند أف كي مظبوط ولا لأ نحن لا نعرف
+
+280
+00:21:39,450 --> 00:21:43,510
+ان ال dimension لل X كي ال X برايم برضه دايما مش
+
+281
+00:21:43,510 --> 00:21:47,710
+نقوله إيش بساوي بساوة كي إذن الآن in particular
+
+282
+00:21:47,710 --> 00:21:51,810
+مدام هذا الصحيح لكل العناصر تبعات الأف ال X برايم
+
+283
+00:21:51,810 --> 00:21:55,710
+إذا صحيحة برضه العناصر من ال bases اللي هى النمو
+
+284
+00:21:55,710 --> 00:21:58,590
+اللي من هنا مظبوط هذا اللي هو ال bases اللي هو
+
+285
+00:21:58,590 --> 00:21:59,610
+basis of
+
+286
+00:22:02,200 --> 00:22:07,520
+معايا؟ طيب شوفوا صارت عندي fj of xn بتروح لل fj of
+
+287
+00:22:07,520 --> 00:22:14,560
+x يعني f1 و f2 و f3 و f4 لكل اللي عند مين لعند ال
+
+288
+00:22:14,560 --> 00:22:20,440
+kطيب where fg of j من عناصر ال basis هذوله بيكون
+
+289
+00:22:20,440 --> 00:22:23,580
+fg of ej أشبه ساوي و ساوي واحد كل هذا مر علينا
+
+290
+00:22:23,580 --> 00:22:28,460
+سابقا and fj of m إيش هتساوي اك سفر لكل أملة تساوي
+
+291
+00:22:28,460 --> 00:22:33,260
+j إذا صار عندى الآن بناء على هذا الكلام لو أجيت
+
+292
+00:22:33,260 --> 00:22:38,790
+دخلت ال fj على ال xnكلن هيتصفرن بس هيدلل مين عندى
+
+293
+00:22:38,790 --> 00:22:45,250
+Alpha J اللي هي ال N معايا كلن هيتصفرن فبصير F J
+
+294
+00:22:45,250 --> 00:22:50,850
+of X N بسوا Alpha J مين N و F J of X هيتلع مين هو
+
+295
+00:22:50,850 --> 00:22:58,790
+ال Alpha J لأن F عملها
+
+296
+00:22:58,790 --> 00:23:09,330
+.. انتبهوالأن أحسبه Fj of xn بساوية Fj of الوه ال
+
+297
+00:23:09,330 --> 00:23:18,010
+summation Alpha 1n E1 زائد لما أصل لآخر واحدة
+
+298
+00:23:18,010 --> 00:23:24,710
+Alpha الوه KN EK ماشي
+
+299
+00:23:27,700 --> 00:23:37,740
+كل حيتصفر للجوا معدنين لرقمها Alpha J N E J حيصير
+
+300
+00:23:37,740 --> 00:23:41,040
+عنده هذا سفر و هذا سفر لأنه Linear تدخل عليها كل
+
+301
+00:23:41,040 --> 00:23:46,540
+زمان عند هدولة كلها نصفار معدنين لـ FJ of Alpha J
+
+302
+00:23:46,540 --> 00:23:51,040
+N E J و هد قيمتها إيش بتساوي هد بتطلع برا و هد
+
+303
+00:23:51,040 --> 00:23:56,860
+قيمتها واحد فبصير Alpha J NSimilarly, Fj of X
+
+304
+00:23:56,860 --> 00:24:01,340
+هتطلع مين؟ Alpha J بناء عليه مادام قولنا أن Fj of
+
+305
+00:24:01,340 --> 00:24:06,060
+X هتطلع Fj of X معناته أصبحت عندي Fj أن بدل هذه
+
+306
+00:24:06,060 --> 00:24:08,540
+بتروح لمين؟ للـ Alpha J
+
+307
+00:24:12,070 --> 00:24:17,330
+ألفا جي أن هتروح للألفا جي as n goes to infinity
+
+308
+00:24:17,330 --> 00:24:21,730
+وهذا لكل جي جي بتساوي واحد واثنين لعين جمين لعين
+
+309
+00:24:21,730 --> 00:24:26,310
+كي كل هنا دول أشمالي الصحيحة اطلع then خلصنا then
+
+310
+00:24:26,310 --> 00:24:31,190
+احسب للان normal xn ناقص normal x ايش بيساوي ال xn
+
+311
+00:24:31,190 --> 00:24:35,350
+هيقبلتهاوالـ X هي قيمتها طرحناها من بعض طلعت هذا
+
+312
+00:24:35,350 --> 00:24:39,030
+القيمة هذا اللي هو أصغر أو ساوي لل triangle
+
+313
+00:24:39,030 --> 00:24:41,990
+inequality ال absolute value هذا في ال norm هذا
+
+314
+00:24:41,990 --> 00:24:45,710
+هذا ايش معنى هذا الان الان الان الان الان الان
+
+315
+00:24:45,710 --> 00:24:46,150
+الان الان الان الان الان الان الان الان الان الان
+
+316
+00:24:46,150 --> 00:24:49,650
+الان الان الان الانإنه هذا as n goes to infinity
+
+317
+00:24:49,650 --> 00:24:52,490
+منها أنا alpha j ومن هنا ال alpha j تذهب إلى مين؟
+
+318
+00:24:52,490 --> 00:24:56,010
+إذن كل واحد منهم اللي جوه ال zero إذا المجموح اللي
+
+319
+00:24:56,010 --> 00:24:59,490
+هيروح لل zero إذا صارت عند ال x أنه تتقل إلى مين؟
+
+320
+00:24:59,490 --> 00:25:04,390
+إلى ال x weakly، strongly، under the condition x
+
+321
+00:25:04,390 --> 00:25:07,170
+أنه تذهب إلى ال x weakly عند ال dimension لل x
+
+322
+00:25:07,170 --> 00:25:13,350
+بساوة k أو finite example
+
+323
+00:25:18,930 --> 00:25:24,970
+الأول مثلًا الـ Hilbert space الـ Hilbert space Xn
+
+324
+00:25:24,970 --> 00:25:29,150
+تذهب إلى X weekly فان دول F Xn و Z تذهب إلى X و Z
+
+325
+00:25:29,150 --> 00:25:31,410
+for all Z مين in H
+
+326
+00:25:40,280 --> 00:25:44,740
+يكافئ أن نقول أن f of x which هي xn و z بتروح لل x
+
+327
+00:25:44,740 --> 00:25:47,820
+و z for all ليش هذا؟ هذا ما أحنا عارفينه، هذه
+
+328
+00:25:47,820 --> 00:25:54,300
+المعلومة سهلة فشو معناه أن xn بتروح لل x weekly؟
+
+329
+00:25:54,300 --> 00:26:01,650
+معناته هذا يكافئ أن f of xnبتروح لل F of X لكل FY
+
+330
+00:26:01,650 --> 00:26:05,770
+الموجودة في الـ X' صح ولا لأ؟ اللي هي الـ H' في
+
+331
+00:26:05,770 --> 00:26:09,490
+هذا الحالة لكن أنا بعرف من جهة أخرى، من الـ 381
+
+332
+00:26:09,490 --> 00:26:12,390
+الـ Raise Representation Theorem أنه لكل F element
+
+333
+00:26:12,390 --> 00:26:17,610
+في الـ H' اللي هو بقدر ألاجله F of X and can be
+
+334
+00:26:17,610 --> 00:26:23,160
+written as X ومين وZ صح؟ماشي؟ إذا يعني هذا ال
+
+335
+00:26:23,160 --> 00:26:27,820
+condition ماقدر أستبدله بإنه اللي هو xn و z بتروح
+
+336
+00:26:27,820 --> 00:26:31,600
+لل x و z for all z in H و التفاصيل اللي لكم طيب
+
+337
+00:26:31,600 --> 00:26:44,460
+اللي بعده الآن انقل بي .. انقل بي .. انقل بيأنا
+
+338
+00:26:44,460 --> 00:26:47,860
+طبعا بي أكبر واحدة صغيرة من infinity Xn بتروح لل X
+
+339
+00:26:47,860 --> 00:26:51,580
+weekly إذا وفقط إذا الشرطين التاليات يعني الآن
+
+340
+00:26:51,580 --> 00:26:55,860
+عندي شرطين يكافئن Xn بتروح لل X weekly الشرط الأول
+
+341
+00:26:55,860 --> 00:27:02,120
+ال sequence normal Xn أشماله is boundedالشرط
+
+342
+00:27:02,120 --> 00:27:07,440
+الثاني for every prefix j we have alpha jn بتروح
+
+343
+00:27:07,440 --> 00:27:15,280
+للxi j as n goes to infinity اللي هي حيث xn هذه
+
+344
+00:27:15,280 --> 00:27:21,820
+عبارة عن xi jn والx يمين هي xi j يعني هذه بتروحالـ
+
+345
+00:27:21,820 --> 00:27:25,640
+Xn بتروح للـ X weekly إذا كانها bounded والجزء
+
+346
+00:27:25,640 --> 00:27:30,260
+الثاني إنه كل واحدة من ال terms اللي هنا Alpha J
+
+347
+00:27:30,260 --> 00:27:35,880
+يعني Alpha واحد N بتروح للألف واحد Alpha اتنين N
+
+348
+00:27:35,880 --> 00:27:39,380
+بتروح للألف اتنين فاهمين؟ إيه الأخر؟ إيه المعنى
+
+349
+00:27:39,380 --> 00:27:42,800
+النهاية؟ هذا هذولة التانية مع بعض وكافئن هذولة
+
+350
+00:27:42,800 --> 00:27:49,130
+الآن هذه النظرية أو هذه اللي هي الخاصيةحنجيها اللي
+
+351
+00:27:49,130 --> 00:27:53,930
+هي خلّيني أقول automatic تطلع من مين؟ من اللمة بس
+
+352
+00:27:53,930 --> 00:27:57,050
+انت بيصير اللي .. اللي احنا بنحكي عنه ال ال ال ال
+
+353
+00:27:57,050 --> 00:27:57,950
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+354
+00:27:57,950 --> 00:27:58,490
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+355
+00:27:58,490 --> 00:27:58,670
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+356
+00:27:58,670 --> 00:27:59,830
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+357
+00:27:59,830 --> 00:28:03,030
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+358
+00:28:03,030 --> 00:28:10,750
+ال
+
+359
+00:28:14,670 --> 00:28:18,130
+ماشي الحل هو جايلك أصلا في الكتاب هذي left to the
+
+360
+00:28:18,130 --> 00:28:20,790
+reader ب exercise من مين من اللي تحته و بوضح بعض
+
+361
+00:28:20,790 --> 00:28:25,070
+الشغلات طيب خلّيني ان شاء الله اندي أشتغل على لمّة
+
+362
+00:28:25,070 --> 00:28:31,210
+أربعة تمانية سبعة اللي هي in general هذي بتقوللي
+
+363
+00:28:31,210 --> 00:28:36,890
+ان I know the space X in general we have X and
+
+364
+00:28:36,890 --> 00:28:42,900
+بتروح لل X weekly تكافئإنه الـ sequence normal XN
+
+365
+00:28:42,900 --> 00:28:47,920
+is bounded، هاي واحدة، اتنين، for every element of
+
+366
+00:28:47,920 --> 00:28:52,340
+a total M، اللي subset M of X' في اللي فوق الـ
+
+367
+00:28:52,340 --> 00:28:58,260
+total subset، اللي هي الـ An، total subset طيب،
+
+368
+00:28:58,260 --> 00:29:03,000
+for every element F of a total subset M of X'، we
+
+369
+00:29:03,000 --> 00:29:06,020
+have F of XN بتروح لمينال of X as M قصه نفيل
+
+370
+00:29:06,020 --> 00:29:11,650
+تانية، يعني، شوفواالآن لو جينا حللنا النظرية
+
+371
+00:29:11,650 --> 00:29:16,690
+بالمنبرهن Xn بتروح للـ X weekly، إيش معناتها؟ إن F
+
+372
+00:29:16,690 --> 00:29:21,030
+of Xn بتروح لل F of X لكل F element الـ main، الـ
+
+373
+00:29:21,030 --> 00:29:25,850
+X'اللي أنا هذا بقولك أنا هذا الشرط الكثير اللي
+
+374
+00:29:25,850 --> 00:29:31,530
+الهن كلهن بديش لكل أفوال من TX' بيثبت فيني ان يكون
+
+375
+00:29:31,530 --> 00:29:36,290
+لكل أفوال ما لها في total subset يعني جزء من X'
+
+376
+00:29:36,690 --> 00:29:41,130
+لكن بدها زجة شوية عشان تتفل ال weekly ان يكون norm
+
+377
+00:29:41,130 --> 00:29:44,890
+لكسرني إيش ماله is bounded بيعطيني هذا يؤدي إلى
+
+378
+00:29:44,890 --> 00:29:48,410
+هذا وهذا يؤدي لهذا هلاجيه اللي هو أمر سهل من
+
+379
+00:29:48,410 --> 00:29:52,680
+الخواص اللي قبل شوية حصلناهالأنه قبل بشوية قلنا
+
+380
+00:29:52,680 --> 00:29:57,160
+لما Xn تروح لل X weekly Normal Xn bounded برهنها
+
+381
+00:29:57,160 --> 00:30:00,520
+توه، هاي واحد اتنين، شو معناه Xn بتروح لل X
+
+382
+00:30:00,520 --> 00:30:05,140
+weekly؟ فإن F of Xn بتروح ل F of X لكل F من ضمن
+
+383
+00:30:05,140 --> 00:30:09,940
+انها دول، إذا هذا الاتجاهجاهز دل مين اطلع للي
+
+384
+00:30:09,940 --> 00:30:13,420
+اتجاه الثاني اذا if xn بتروح للي x weakly then a
+
+385
+00:30:13,420 --> 00:30:16,540
+follows from لما كذا and b follows from the
+
+386
+00:30:16,540 --> 00:30:18,860
+definition of weak convergence اللي حكيته قبل قليل
+
+387
+00:30:18,860 --> 00:30:23,620
+شوية اذا نطلع فوق وبدنا نثبت مين conversely طيب
+
+388
+00:30:23,620 --> 00:30:27,280
+نيجي الان conversely ونعني بعض الشغلات هيك الحلوة
+
+389
+00:30:27,280 --> 00:30:35,620
+بنعملها و بنصل للي بدنايالأن شو معناته أن total
+
+390
+00:30:35,620 --> 00:30:43,520
+set أن total set in X' معناته أن ال span للأم
+
+391
+00:30:43,520 --> 00:30:49,340
+أقل جاب بساومين X' هذا الان اللي هو ال bridge اللي
+
+392
+00:30:49,340 --> 00:30:54,960
+بدصل من خلاله لالمطلوب conversely suppose that A
+
+393
+00:30:54,960 --> 00:30:59,630
+and B holdو بدنا نتبط ان Xn بتروح للـ X weekly By
+
+394
+00:30:59,630 --> 00:31:06,580
+A مدام Xn bounded لنوم Xn أصغر سوى C لكل Nوالنورم
+
+395
+00:31:06,580 --> 00:31:10,840
+ال X أصغر أو يساوي C for sufficiently large mean
+
+396
+00:31:10,840 --> 00:31:15,520
+اللي هو mean C مدام ال XN بتروح ال N، النورم ال XN
+
+397
+00:31:15,520 --> 00:31:21,200
+أصغر أو يساوي C for all N، إذن automatically اللي
+
+398
+00:31:21,200 --> 00:31:25,580
+هي النورمها، اللي هو النورم ال X، هيكون ماله أصغر
+
+399
+00:31:25,580 --> 00:31:31,540
+أو يساوي Cاللي هو هذي طبعا أصغر يساوي C for all n
+
+400
+00:31:31,540 --> 00:31:35,880
+جارس نصف شالد ليه لاعيش C انك تختار C أشمالها
+
+401
+00:31:35,880 --> 00:31:39,780
+كبيرة كفاية انها تكفل ال .. ال .. ال .. since M is
+
+402
+00:31:39,780 --> 00:31:45,830
+total in X primeما دام total in X'، then for every
+
+403
+00:31:45,830 --> 00:31:49,530
+F in X'، there exists a sequence Fi in span لـM،
+
+404
+00:31:49,530 --> 00:31:54,710
+such that Fi بتروح لمن؟ لـF، dense، مش الآن هذه
+
+405
+00:31:54,710 --> 00:31:59,670
+dense في هذه A، إذا أي element هنا، بلاقي ال
+
+406
+00:31:59,670 --> 00:32:03,310
+sequence في اللي جوا، كون ذالك له،ماشي، تعريف ال
+
+407
+00:32:03,310 --> 00:32:08,600
+densityطيب الآن since M is total إذا ال span لـ M
+
+408
+00:32:08,600 --> 00:32:13,560
+بساوي X' then لكل F element in X' there exist a
+
+409
+00:32:13,560 --> 00:32:17,700
+sequence of I in span M such that F I بتروح لمين؟
+
+410
+00:32:17,700 --> 00:32:22,660
+لل F هايو since span ل M is dense in X' إذا مدام F
+
+411
+00:32:22,660 --> 00:32:26,900
+I بتروح لل F إذا بقدر أسغر المسافة جد ما بديThen,
+
+412
+00:32:27,100 --> 00:32:31,100
+for every Y أكبر من 0, there exists J such that
+
+413
+00:32:31,100 --> 00:32:39,810
+normal Fi-F أصغر من مين من Y على 3Cراحظوا ال
+
+414
+00:32:39,810 --> 00:32:43,790
+convergence في العالم
+
+415
+00:32:43,790 --> 00:32:49,050
+تبع x' يعني in the norm تبع x' يعني أصلا كل ال
+
+416
+00:32:49,050 --> 00:32:52,450
+convergence لما كنا نقول convergence في x زمان ال
+
+417
+00:32:52,450 --> 00:32:54,990
+convergence في ال x لما نحكي عليه with respect to
+
+418
+00:32:54,990 --> 00:32:59,050
+the norm يعني ال strong convergenceطيب إذا الأن
+
+419
+00:32:59,050 --> 00:33:02,790
+صار عندي normal fi ناقص f أصغر من أي إبسلون في
+
+420
+00:33:02,790 --> 00:33:05,970
+الدنيا من ضمنها y على تلاتة c ده استخدمها للحسابات
+
+421
+00:33:05,970 --> 00:33:09,810
+بعد شوية زي ما أنتوا عارفين لأن moreover since fi
+
+422
+00:33:09,810 --> 00:33:15,290
+element مسبان لل M then by B there is n such that
+
+423
+00:33:15,290 --> 00:33:21,310
+fi of x n ناقص fi of x أصغر من y على تلاتة for all
+
+424
+00:33:21,310 --> 00:33:27,420
+n أكبر من مين من اللي هي مين من n عنديFI of XN
+
+425
+00:33:27,420 --> 00:33:32,460
+ناقص FI of X التي أصغر من Y على 3 لكل N أكبر من
+
+426
+00:33:32,460 --> 00:33:40,420
+100 من N طيب أطلع لفوق then for all N أكبر من N we
+
+427
+00:33:40,420 --> 00:33:45,840
+have أحسب لـ FI of XN ناقص F of X هذه بالـ
+
+428
+00:33:45,840 --> 00:33:49,200
+Triangling Quality بدي أضيف ترم وأطرح ترم أصغر أو
+
+429
+00:33:49,200 --> 00:33:53,140
+يساوي اللي هو norm أو absolute value للـ FI of XN
+
+430
+00:33:53,140 --> 00:33:59,800
+ناقص FI of XN هي اللي ضفتهاوهنا طرحت او ضفت a5x
+
+431
+00:33:59,800 --> 00:34:05,420
+انا ناقص مين a5x زاد a5x ناقص a5x طرحت مين تنتين
+
+432
+00:34:05,420 --> 00:34:09,940
+ضفت تنتين اه ماشي الحل الان صار عندى الان الاولى
+
+433
+00:34:09,940 --> 00:34:16,450
+هذه اللى هو اصغر او شوية normal FI ناقص F وهذه X
+
+434
+00:34:16,450 --> 00:34:24,210
+زائد المفهومة هذه أصغر من مين من Y ع تلاتة وهذه FI
+
+435
+00:34:24,210 --> 00:34:27,590
+of X ناقص نفس اللي عملته في اللي فوق Normal FI
+
+436
+00:34:27,590 --> 00:34:32,870
+ناقص F في Normal مين ال X هذه الواحدة فيها اللي هو
+
+437
+00:34:32,870 --> 00:34:37,650
+FI ناقص F أصغر من Y ع تلاتة C وهذه أصغر أو شوه C
+
+438
+00:34:38,610 --> 00:34:42,370
+هذه زي ما هي وهذه نفس الاشي أصغر يساوي y ع تلاتة c
+
+439
+00:34:42,370 --> 00:34:46,510
+وهذه أصغر من c إذا اللي هو صارت عندي y ع تلاتة y ع
+
+440
+00:34:46,510 --> 00:34:49,970
+تلاتة y ع تلاتة أو يساوي إبسلون الآن صار عندي الآن
+
+441
+00:34:49,970 --> 00:34:54,130
+ال absolute value لل F of X نقص F of X أصغر أو
+
+442
+00:34:54,130 --> 00:34:59,130
+يساوي إبسلون و F كانت arbitrary إذا هذا معناته إنه
+
+443
+00:34:59,130 --> 00:35:03,130
+F of X هان بتروح لل F of X ك number إذا معناته X
+
+444
+00:35:03,130 --> 00:35:07,870
+هان بتروح لل X إيش ماله weekly و هيك بيكون احنا
+
+445
+00:35:08,660 --> 00:35:15,700
+خلصنا اللي هو المحاضرة نزل المحاضرة وان شاء الله
+
+446
+00:35:15,700 --> 00:35:18,920
+إلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Z5xeo5Xjt84_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Z5xeo5Xjt84_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..aa973b208f72fa750cb5e7603aa778ecb71b5fd0
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Z5xeo5Xjt84_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2224, "start": 5.06, "end": 22.24, "text": "بسم الله الرحمن الرحيم الحمد لله رب العالمين والصلاة والسلام على سيد المسلمين سيدنا محمد وعلى أهله وصحبه أجمعين هذه هي المحاضرة رقم 32 مساق تحليل اقتراني أو تحليل دالي طلاب طالبات الجامعة الإسلامية ماجستير الرياضيات", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21542, 2304, 3215, 24976, 3224, 12602, 3555, 18863, 45340, 9957, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 8608, 25708, 9673, 3794, 19528, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 5551, 3224, 43761, 4032, 9381, 5016, 3555, 3224, 5551, 7435, 2304, 3615, 9957, 29538, 39896, 9673, 5016, 46958, 25720, 12602, 4587, 2304, 8858, 47524, 995, 4587, 6055, 5016, 20292, 1211, 1975, 38149, 2288, 7649, 1829, 34051, 6055, 5016, 20292, 1211, 11778, 6027, 1829, 23032, 15040, 3555, 23032, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 3714, 26108, 14851, 13546, 2423, 16572, 46958, 1829, 9307], "avg_logprob": -0.10966169970844863, "compression_ratio": 1.9455445544554455, "no_speech_prob": 1.6629695892333984e-05, "words": [{"start": 5.06, "end": 5.38, "word": "بسم", "probability": 0.842041015625}, {"start": 5.38, "end": 5.58, "word": " الله", "probability": 0.96435546875}, {"start": 5.58, "end": 5.94, "word": " الرحمن", "probability": 0.9677734375}, {"start": 5.94, "end": 6.4, "word": " الرحيم", "probability": 0.9943033854166666}, {"start": 6.4, "end": 6.78, "word": " الحمد", "probability": 0.8655598958333334}, {"start": 6.78, "end": 7.04, "word": " لله", "probability": 0.9482421875}, {"start": 7.04, "end": 7.22, "word": " رب", "probability": 0.963134765625}, {"start": 7.22, "end": 7.8, "word": " العالمين", "probability": 0.994140625}, {"start": 7.8, "end": 8.24, "word": " والصلاة", "probability": 0.85711669921875}, {"start": 8.24, "end": 8.66, "word": " والسلام", "probability": 0.9591471354166666}, {"start": 8.66, "end": 8.88, "word": " على", "probability": 0.72265625}, {"start": 8.88, "end": 9.2, "word": " سيد", "probability": 0.960205078125}, {"start": 9.2, "end": 9.76, "word": " المسلمين", "probability": 0.78045654296875}, {"start": 9.76, "end": 10.08, "word": " سيدنا", "probability": 0.9679361979166666}, {"start": 10.08, "end": 10.52, "word": " محمد", "probability": 0.9895833333333334}, {"start": 10.52, "end": 10.8, "word": " وعلى", "probability": 0.8977864583333334}, {"start": 10.8, "end": 11.02, "word": " أهله", "probability": 0.8020833333333334}, {"start": 11.02, "end": 11.52, "word": " وصحبه", "probability": 0.831591796875}, {"start": 11.52, "end": 12.08, "word": " أجمعين", "probability": 0.89365234375}, {"start": 12.08, "end": 12.94, "word": " هذه", "probability": 0.88525390625}, {"start": 12.94, "end": 13.12, "word": " هي", "probability": 0.5244140625}, {"start": 13.12, "end": 13.64, "word": " المحاضرة", "probability": 0.98486328125}, {"start": 13.64, "end": 13.9, "word": " رقم", "probability": 0.93505859375}, {"start": 13.9, "end": 14.64, "word": " 32", "probability": 0.80029296875}, {"start": 14.64, "end": 15.46, "word": " مساق", "probability": 0.9324544270833334}, {"start": 15.46, "end": 17.14, "word": " تحليل", "probability": 0.986083984375}, {"start": 17.14, "end": 17.82, "word": " اقتراني", "probability": 0.8955078125}, {"start": 17.82, "end": 18.02, "word": " أو", "probability": 0.5673828125}, {"start": 18.02, "end": 18.48, "word": " تحليل", "probability": 0.990234375}, {"start": 18.48, "end": 19.0, "word": " دالي", "probability": 0.9842122395833334}, {"start": 19.0, "end": 19.48, "word": " طلاب", "probability": 0.8095703125}, {"start": 19.48, "end": 19.98, "word": " طالبات", "probability": 0.964111328125}, {"start": 19.98, "end": 20.34, "word": " الجامعة", "probability": 0.990234375}, {"start": 20.34, "end": 20.98, "word": " الإسلامية", "probability": 0.94921875}, {"start": 20.98, "end": 21.6, "word": " ماجستير", "probability": 0.876220703125}, {"start": 21.6, "end": 22.24, "word": " الرياضيات", "probability": 0.87607421875}], "temperature": 1.0}, {"id": 2, "seek": 4296, "start": 23.56, "end": 42.96, "text": "وصلنا لعند اللي هو اربعة تمانية strong and weak convergence نشوف ايش اللي هو نقصد اللي هو strong و weak convergence طبعا احنا اللي هنحكي عن اللي هو norm this base نحكي عن ال convergence في داخل norm this base", "tokens": [2407, 36520, 8315, 5296, 3615, 41260, 13672, 1829, 31439, 1975, 25513, 27884, 46811, 7649, 10632, 2068, 293, 5336, 32181, 8717, 8592, 38688, 1975, 1829, 8592, 13672, 1829, 31439, 8717, 4587, 9381, 3215, 13672, 1829, 31439, 2068, 4032, 5336, 32181, 23032, 3555, 3615, 995, 1975, 5016, 8315, 13672, 1829, 8032, 1863, 5016, 4117, 1829, 18871, 13672, 1829, 31439, 2026, 341, 3096, 8717, 5016, 4117, 1829, 18871, 2423, 32181, 8978, 11778, 47283, 1211, 2026, 341, 3096], "avg_logprob": -0.2362500043710073, "compression_ratio": 1.84472049689441, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 23.56, "end": 24.14, "word": "وصلنا", "probability": 0.9173177083333334}, {"start": 24.14, "end": 24.58, "word": " لعند", "probability": 0.7211100260416666}, {"start": 24.58, "end": 24.9, "word": " اللي", "probability": 0.68310546875}, {"start": 24.9, "end": 25.2, "word": " هو", "probability": 0.91845703125}, {"start": 25.2, "end": 25.74, "word": " اربعة", "probability": 0.68011474609375}, {"start": 25.74, "end": 26.4, "word": " تمانية", "probability": 0.974609375}, {"start": 26.4, "end": 27.12, "word": " strong", "probability": 0.400390625}, {"start": 27.12, "end": 27.38, "word": " and", "probability": 0.90576171875}, {"start": 27.38, "end": 27.58, "word": " weak", "probability": 0.98388671875}, {"start": 27.58, "end": 28.28, "word": " convergence", "probability": 0.9541015625}, {"start": 28.28, "end": 29.16, "word": " نشوف", "probability": 0.7281087239583334}, {"start": 29.16, "end": 29.46, "word": " ايش", "probability": 0.7704264322916666}, {"start": 29.46, "end": 29.64, "word": " اللي", "probability": 0.967529296875}, {"start": 29.64, "end": 30.08, "word": " هو", "probability": 0.98974609375}, {"start": 30.08, "end": 32.12, "word": " نقصد", "probability": 0.791748046875}, {"start": 32.12, "end": 32.36, "word": " اللي", "probability": 0.89697265625}, {"start": 32.36, "end": 32.86, "word": " هو", "probability": 0.9765625}, {"start": 32.86, "end": 34.46, "word": " strong", "probability": 0.81689453125}, {"start": 34.46, "end": 34.66, "word": " و", "probability": 0.494140625}, {"start": 34.66, "end": 34.82, "word": " weak", "probability": 0.93212890625}, {"start": 34.82, "end": 35.26, "word": " convergence", "probability": 0.9638671875}, {"start": 35.26, "end": 35.58, "word": " طبعا", "probability": 0.9093017578125}, {"start": 35.58, "end": 35.96, "word": " احنا", "probability": 0.9567057291666666}, {"start": 35.96, "end": 36.52, "word": " اللي", "probability": 0.763671875}, {"start": 36.52, "end": 37.24, "word": " هنحكي", "probability": 0.7303466796875}, {"start": 37.24, "end": 37.54, "word": " عن", "probability": 0.9736328125}, {"start": 37.54, "end": 38.0, "word": " اللي", "probability": 0.94921875}, {"start": 38.0, "end": 38.28, "word": " هو", "probability": 0.9853515625}, {"start": 38.28, "end": 38.66, "word": " norm", "probability": 0.83203125}, {"start": 38.66, "end": 38.94, "word": " this", "probability": 0.428466796875}, {"start": 38.94, "end": 39.38, "word": " base", "probability": 0.74365234375}, {"start": 39.38, "end": 40.42, "word": " نحكي", "probability": 0.8310546875}, {"start": 40.42, "end": 40.58, "word": " عن", "probability": 0.9873046875}, {"start": 40.58, "end": 40.72, "word": " ال", "probability": 0.9580078125}, {"start": 40.72, "end": 41.32, "word": " convergence", "probability": 0.9541015625}, {"start": 41.32, "end": 41.76, "word": " في", "probability": 0.77783203125}, {"start": 41.76, "end": 42.16, "word": " داخل", "probability": 0.97607421875}, {"start": 42.16, "end": 42.42, "word": " norm", "probability": 0.8046875}, {"start": 42.42, "end": 42.64, "word": " this", "probability": 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x", "probability": 0.673828125}, {"start": 56.59, "end": 56.75, "word": " is", "probability": 0.7158203125}, {"start": 56.75, "end": 56.95, "word": " said", "probability": 0.86328125}, {"start": 56.95, "end": 57.13, "word": " to", "probability": 0.98193359375}, {"start": 57.13, "end": 57.73, "word": " be", "probability": 0.93994140625}, {"start": 57.73, "end": 58.39, "word": " strongly", "probability": 0.8955078125}, {"start": 58.39, "end": 59.31, "word": " convergent", "probability": 0.957763671875}, {"start": 59.31, "end": 59.61, "word": " or", "probability": 0.79833984375}, {"start": 59.61, "end": 60.53, "word": " convergent", "probability": 0.97216796875}, {"start": 60.53, "end": 60.79, "word": " in", "probability": 0.857421875}, {"start": 60.79, "end": 60.93, "word": " the", "probability": 0.88671875}, {"start": 60.93, "end": 61.23, "word": " norm", "probability": 0.9697265625}, {"start": 61.23, "end": 61.97, "word": " يعني", "probability": 0.7119140625}, {"start": 61.97, "end": 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75.68, "end": 76.0, "word": " xn", "probability": 0.860107421875}, {"start": 76.0, "end": 76.42, "word": " converges", "probability": 0.409423828125}, {"start": 76.42, "end": 76.54, "word": " to", "probability": 0.95751953125}, {"start": 76.54, "end": 76.8, "word": " x", "probability": 0.97021484375}], "temperature": 1.0}, {"id": 5, "seek": 9819, "start": 83.73, "end": 98.19, "text": "لذلك عندما نكتب xn converges للـ x بالشكل هذا اللي نقصد فيها هو xn is strongly convergence to main to x مايعنيها؟ معناته أن ال limit للـ xn ناقص x", "tokens": [1211, 8848, 23275, 43242, 15042, 8717, 4117, 2655, 3555, 2031, 77, 9652, 2880, 24976, 39184, 2031, 20666, 8592, 28820, 23758, 13672, 1829, 8717, 4587, 9381, 3215, 8978, 11296, 31439, 2031, 77, 307, 10613, 32181, 281, 2135, 281, 2031, 19446, 40228, 22653, 11296, 22807, 20449, 8315, 47395, 14739, 2423, 4948, 24976, 39184, 2031, 77, 8717, 995, 4587, 9381, 2031], "avg_logprob": -0.5958686258833287, "compression_ratio": 1.3790849673202614, 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0.95947265625}, {"start": 234.67, "end": 234.85, "word": " من", "probability": 0.77783203125}, {"start": 234.85, "end": 235.07, "word": " ثم", "probability": 0.9931640625}, {"start": 235.07, "end": 235.41, "word": " نشوف", "probability": 0.8743489583333334}, {"start": 235.41, "end": 235.73, "word": " ايش", "probability": 0.7776692708333334}, {"start": 235.73, "end": 235.91, "word": " في", "probability": 0.91650390625}, {"start": 235.91, "end": 236.87, "word": " condition", "probability": 0.60986328125}, {"start": 236.87, "end": 238.45, "word": " بنحطه", "probability": 0.9532470703125}, {"start": 238.45, "end": 238.75, "word": " على", "probability": 0.87939453125}, {"start": 238.75, "end": 239.11, "word": " اللي", "probability": 0.970458984375}, {"start": 239.11, "end": 239.37, "word": " هو", "probability": 0.98876953125}, {"start": 239.37, "end": 239.69, "word": " non", "probability": 0.7216796875}, {"start": 239.69, "end": 240.19, "word": " displaced", "probability": 0.326904296875}, {"start": 240.19, "end": 240.57, "word": " عشان", "probability": 0.9658203125}, {"start": 240.57, "end": 240.95, "word": " يصير", "probability": 0.9073893229166666}, {"start": 240.95, "end": 241.09, "word": " اللي", "probability": 0.9248046875}, {"start": 241.09, "end": 241.29, "word": " هو", "probability": 0.9765625}, {"start": 241.29, "end": 241.43, "word": " ال", "probability": 0.83154296875}, {"start": 241.43, "end": 241.59, "word": " weak", "probability": 0.89306640625}, {"start": 241.59, "end": 242.09, "word": " convergence", "probability": 0.96044921875}, {"start": 242.09, "end": 242.27, "word": " و", "probability": 0.6064453125}, {"start": 242.27, "end": 242.35, "word": " ال", "probability": 0.763671875}, {"start": 242.35, "end": 242.63, "word": " strong", "probability": 0.85400390625}, {"start": 242.63, "end": 243.47, "word": " يشمله", "probability": 0.7144012451171875}, {"start": 243.47, "end": 244.15, "word": " زي", "probability": 0.979248046875}, {"start": 244.15, "end": 244.53, "word": " بعض", "probability": 0.993408203125}], "temperature": 1.0}, {"id": 12, "seek": 25355, "start": 245.73, "end": 253.55, "text": "لاحظوا في الـ R كنا نحكي عن weak convergence و strong convergence كنا نحكي عنه في الـ sequences", "tokens": [1211, 39319, 19913, 14407, 8978, 2423, 39184, 497, 9122, 8315, 8717, 5016, 4117, 1829, 18871, 5336, 32181, 4032, 2068, 32181, 9122, 8315, 8717, 5016, 4117, 1829, 18871, 3224, 8978, 2423, 39184, 22978], "avg_logprob": -0.3697916666666667, "compression_ratio": 1.3645833333333333, "no_speech_prob": 0.0, "words": [{"start": 245.73, "end": 246.29, "word": "لاحظوا", "probability": 0.4791259765625}, {"start": 246.29, "end": 246.39, "word": " في", "probability": 0.58251953125}, {"start": 246.39, "end": 246.61, "word": " الـ", "probability": 0.67236328125}, {"start": 246.61, "end": 246.81, "word": " R", "probability": 0.432861328125}, {"start": 246.81, "end": 247.83, "word": " كنا", "probability": 0.61224365234375}, {"start": 247.83, "end": 248.29, "word": " نحكي", "probability": 0.910400390625}, {"start": 248.29, "end": 248.41, "word": " عن", "probability": 0.89453125}, {"start": 248.41, "end": 248.59, "word": " weak", "probability": 0.50927734375}, {"start": 248.59, "end": 250.61, "word": " convergence", "probability": 0.912109375}, {"start": 250.61, "end": 250.75, "word": " و", "probability": 0.89599609375}, {"start": 250.75, "end": 250.99, "word": " strong", "probability": 0.40673828125}, {"start": 250.99, "end": 251.69, "word": " convergence", "probability": 0.947265625}, {"start": 251.69, "end": 251.97, "word": " كنا", "probability": 0.6514892578125}, {"start": 251.97, "end": 252.37, "word": " نحكي", "probability": 0.983642578125}, {"start": 252.37, "end": 252.65, "word": " عنه", "probability": 0.8798828125}, {"start": 252.65, "end": 253.03, "word": " في", "probability": 0.9365234375}, {"start": 253.03, "end": 253.17, "word": " الـ", "probability": 0.766845703125}, {"start": 253.17, "end": 253.55, "word": " sequences", "probability": 0.51318359375}], "temperature": 1.0}, {"id": 13, "seek": 27570, "start": 254.82, "end": 275.7, "text": "سنجد أن في الـ R و في الـ C و في الحاجات اللي زي .. في كل الـ finite dimensional spaces سيكون اللي هو الـ weak convergence و الـ strong Gاش مالهين are the same خلّينا الأن نشوف أول لمّة لمّة الأولى let Xn be a weakly اللي هو convergence sequence around space X سي Xn بتروح للـ X مالها weakly", "tokens": [3794, 1863, 7435, 3215, 14739, 8978, 2423, 39184, 497, 4032, 8978, 2423, 39184, 383, 4032, 8978, 21542, 26108, 9307, 13672, 1829, 30767, 1829, 4386, 8978, 28242, 2423, 39184, 19362, 18795, 7673, 8608, 1829, 30544, 13672, 1829, 31439, 2423, 39184, 5336, 32181, 4032, 2423, 39184, 2068, 460, 33599, 3714, 6027, 3224, 9957, 366, 264, 912, 16490, 1211, 11703, 9957, 995, 16247, 1863, 8717, 8592, 38688, 5551, 12610, 32767, 11703, 3660, 32767, 11703, 3660, 16247, 12610, 7578, 718, 1783, 77, 312, 257, 5336, 356, 13672, 1829, 31439, 32181, 8310, 926, 1901, 1783, 8608, 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{"start": 261.12, "end": 261.28, "word": " اللي", "probability": 0.705322265625}, {"start": 261.28, "end": 261.46, "word": " هو", "probability": 0.95458984375}, {"start": 261.46, "end": 261.6, "word": " الـ", "probability": 0.6923828125}, {"start": 261.6, "end": 261.76, "word": " weak", "probability": 0.9765625}, {"start": 261.76, "end": 262.36, "word": " convergence", "probability": 0.9716796875}, {"start": 262.36, "end": 262.66, "word": " و", "probability": 0.5009765625}, {"start": 262.66, "end": 263.42, "word": " الـ", "probability": 0.748779296875}, {"start": 263.42, "end": 263.42, "word": " strong", "probability": 0.748046875}, {"start": 263.42, "end": 263.72, "word": " Gاش", "probability": 0.1959228515625}, {"start": 263.72, "end": 264.26, "word": " مالهين", "probability": 0.762451171875}, {"start": 264.26, "end": 264.76, "word": " are", "probability": 0.51708984375}, {"start": 264.76, "end": 265.0, "word": " the", "probability": 0.88134765625}, {"start": 265.0, "end": 265.2, "word": " same", "probability": 0.90087890625}, {"start": 265.2, "end": 265.64, "word": " خلّينا", "probability": 0.68115234375}, {"start": 265.64, "end": 265.86, "word": " الأن", "probability": 0.644287109375}, {"start": 265.86, "end": 266.12, "word": " نشوف", "probability": 0.99365234375}, {"start": 266.12, "end": 266.4, "word": " أول", "probability": 0.976318359375}, {"start": 266.4, "end": 266.82, "word": " لمّة", "probability": 0.7841796875}, {"start": 266.82, "end": 268.02, "word": " لمّة", "probability": 0.6505940755208334}, {"start": 268.02, "end": 268.3, "word": " الأولى", "probability": 0.978515625}, {"start": 268.3, "end": 268.48, "word": " let", "probability": 0.47216796875}, {"start": 268.48, "end": 268.82, "word": " Xn", "probability": 0.5216064453125}, {"start": 268.82, "end": 269.0, "word": " be", "probability": 0.81103515625}, {"start": 269.0, "end": 269.18, "word": " a", "probability": 0.98193359375}, {"start": 269.18, "end": 269.68, "word": " weakly", "probability": 0.814697265625}, {"start": 269.68, "end": 270.34, "word": " اللي", "probability": 0.9052734375}, {"start": 270.34, "end": 270.48, "word": " هو", "probability": 0.96728515625}, {"start": 270.48, "end": 270.98, "word": " convergence", "probability": 0.958984375}, {"start": 270.98, "end": 271.46, "word": " sequence", "probability": 0.5908203125}, {"start": 271.46, "end": 271.76, "word": " around", "probability": 0.5654296875}, {"start": 271.76, "end": 272.28, "word": " space", "probability": 0.69482421875}, {"start": 272.28, "end": 272.7, "word": " X", "probability": 0.970703125}, {"start": 272.7, "end": 273.44, "word": " سي", "probability": 0.61328125}, {"start": 273.44, "end": 273.78, "word": " Xn", "probability": 0.65380859375}, {"start": 273.78, "end": 274.06, "word": " بتروح", "probability": 0.9248046875}, {"start": 274.06, "end": 274.3, "word": " للـ", "probability": 0.5601806640625}, {"start": 274.3, "end": 274.42, "word": " X", "probability": 0.9326171875}, {"start": 274.42, "end": 274.92, "word": " مالها", "probability": 0.9493815104166666}, {"start": 274.92, "end": 275.7, "word": " weakly", "probability": 0.955810546875}], "temperature": 1.0}, {"id": 14, "seek": 29583, "start": 276.06, "end": 295.84, "text": "أثناء ذلك، قيمة الـ weak X of Xn هي محدودة، وهي أشمالها وحيدة، إذن قيمة، في حالة، احنا بنحكي عن أهم حالة مين؟ حالة الـ weak convergence قيمة اللي هي وحيدة، اتنين، every subsequence of Xn converges أشماله weakly to X", "tokens": [10721, 12984, 1863, 16606, 29910, 23275, 12399, 12174, 32640, 3660, 2423, 39184, 5336, 1783, 295, 1783, 77, 39896, 3714, 24401, 23328, 3660, 12399, 37037, 1829, 5551, 8592, 2304, 6027, 11296, 4032, 5016, 25708, 3660, 12399, 11933, 8848, 1863, 12174, 32640, 3660, 12399, 8978, 11331, 6027, 3660, 12399, 1975, 5016, 8315, 44945, 5016, 4117, 1829, 18871, 5551, 16095, 11331, 6027, 3660, 3714, 9957, 22807, 11331, 6027, 3660, 2423, 39184, 5336, 32181, 12174, 32640, 3660, 13672, 1829, 39896, 4032, 5016, 25708, 3660, 12399, 1975, 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"end": 280.5, "word": " محدودة،", "probability": 0.47060546875}, {"start": 280.5, "end": 280.76, "word": " وهي", "probability": 0.55352783203125}, {"start": 280.76, "end": 281.28, "word": " أشمالها", "probability": 0.88876953125}, {"start": 281.28, "end": 282.32, "word": " وحيدة،", "probability": 0.835546875}, {"start": 282.32, "end": 282.58, "word": " إذن", "probability": 0.5094401041666666}, {"start": 282.58, "end": 283.4, "word": " قيمة،", "probability": 0.7158203125}, {"start": 283.4, "end": 283.68, "word": " في", "probability": 0.56689453125}, {"start": 283.68, "end": 284.02, "word": " حالة،", "probability": 0.7279052734375}, {"start": 284.02, "end": 284.2, "word": " احنا", "probability": 0.7451171875}, {"start": 284.2, "end": 284.54, "word": " بنحكي", "probability": 0.904052734375}, {"start": 284.54, "end": 284.7, "word": " عن", "probability": 0.462158203125}, {"start": 284.7, "end": 285.12, "word": " أهم", "probability": 0.36474609375}, {"start": 285.12, "end": 285.44, "word": " حالة", "probability": 0.9803059895833334}, {"start": 285.44, "end": 286.14, "word": " مين؟", "probability": 0.7552083333333334}, {"start": 286.14, "end": 286.52, "word": " حالة", "probability": 0.9791666666666666}, {"start": 286.52, "end": 286.66, "word": " الـ", "probability": 0.873779296875}, {"start": 286.66, "end": 286.82, "word": " weak", "probability": 0.89892578125}, {"start": 286.82, "end": 287.48, "word": " convergence", "probability": 0.96337890625}, {"start": 287.48, "end": 288.64, "word": " قيمة", "probability": 0.8024088541666666}, {"start": 288.64, "end": 288.94, "word": " اللي", "probability": 0.759765625}, {"start": 288.94, "end": 289.38, "word": " هي", "probability": 0.94287109375}, {"start": 289.38, "end": 290.34, "word": " وحيدة،", "probability": 0.86376953125}, {"start": 290.34, "end": 291.3, "word": " اتنين،", "probability": 0.82578125}, {"start": 291.3, "end": 291.52, "word": " every", "probability": 0.1324462890625}, {"start": 291.52, "end": 292.26, "word": " 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"end": 374.72, "word": " مين", "probability": 0.7587890625}, {"start": 374.72, "end": 375.28, "word": " إذا", "probability": 0.84375}, {"start": 375.28, "end": 375.58, "word": " ال", "probability": 0.787109375}, {"start": 375.58, "end": 375.9, "word": " X", "probability": 0.9208984375}, {"start": 375.9, "end": 376.28, "word": " minus", "probability": 0.9501953125}, {"start": 376.28, "end": 376.68, "word": " Y", "probability": 0.9951171875}, {"start": 376.68, "end": 377.28, "word": " هتساوي", "probability": 0.966015625}, {"start": 377.28, "end": 378.0, "word": " سفر", "probability": 0.9734700520833334}, {"start": 378.0, "end": 378.38, "word": " إذا", "probability": 0.84326171875}, {"start": 378.38, "end": 378.88, "word": " معناته", "probability": 0.9542643229166666}, {"start": 378.88, "end": 379.24, "word": " X", "probability": 0.955078125}, {"start": 379.24, "end": 379.94, "word": " هتساوي", "probability": 0.9642578125}, {"start": 379.94, "end": 380.3, "word": " Y", "probability": 0.99072265625}, {"start": 380.3, "end": 381.08, "word": " معناته", "probability": 0.9816080729166666}, {"start": 381.08, "end": 381.54, "word": " إنه", "probability": 0.539794921875}, {"start": 381.54, "end": 382.0, "word": " ال", "probability": 0.80029296875}, {"start": 382.0, "end": 382.38, "word": " limit", "probability": 0.88671875}, {"start": 382.38, "end": 382.7, "word": " ما", "probability": 0.77490234375}, {"start": 382.7, "end": 382.98, "word": " لها", "probability": 0.892578125}, {"start": 382.98, "end": 383.48, "word": " is", "probability": 0.9423828125}, {"start": 383.48, "end": 383.86, "word": " unique", "probability": 0.8828125}, {"start": 383.86, "end": 384.32, "word": " under", "probability": 0.90380859375}, {"start": 384.32, "end": 384.62, "word": " the", "probability": 0.8994140625}, {"start": 384.62, "end": 384.86, "word": " weak", "probability": 0.345703125}, {"start": 384.86, "end": 385.56, "word": " convergence", "probability": 0.94775390625}], "temperature": 1.0}, {"id": 19, "seek": 40555, "start": 386.03, "end": 405.55, "text": "هذا بالنسبة لمن؟ لـ B برضه نفس الأشياء إعتمادا على خواص الـ sequence of numbers سنحصل على خواص الـ convergence للـ sequence لو جيت الآن قلت", "tokens": [3224, 15730, 20666, 1863, 35457, 3660, 5296, 27842, 22807, 5296, 39184, 363, 4724, 43042, 3224, 8717, 36178, 16247, 8592, 1829, 16606, 11933, 34268, 15042, 28259, 15844, 16490, 2407, 33546, 2423, 39184, 8310, 295, 3547, 8608, 1863, 5016, 36520, 15844, 16490, 2407, 33546, 2423, 39184, 32181, 24976, 39184, 8310, 45164, 10874, 36081, 6024, 48506, 12174, 1211, 2655], "avg_logprob": -0.4089912197046113, "compression_ratio": 1.4210526315789473, "no_speech_prob": 2.682209014892578e-06, "words": [{"start": 386.03, "end": 386.35, "word": "هذا", "probability": 0.714599609375}, {"start": 386.35, "end": 386.77, "word": " بالنسبة", "probability": 0.9598388671875}, {"start": 386.77, "end": 387.45, "word": " لمن؟", "probability": 0.5581868489583334}, {"start": 387.45, "end": 388.05, "word": " لـ", "probability": 0.635498046875}, {"start": 388.05, "end": 388.59, "word": " B", "probability": 0.1424560546875}, {"start": 388.59, "end": 392.93, "word": " برضه", "probability": 0.6522216796875}, {"start": 392.93, "end": 393.35, "word": " نفس", "probability": 0.8984375}, {"start": 393.35, "end": 393.81, "word": " الأشياء", "probability": 0.75030517578125}, {"start": 393.81, "end": 394.39, "word": " إعتمادا", "probability": 0.64166259765625}, {"start": 394.39, "end": 394.69, "word": " على", "probability": 0.458984375}, {"start": 394.69, "end": 395.43, "word": " خواص", "probability": 0.9436848958333334}, {"start": 395.43, "end": 395.91, "word": " الـ", "probability": 0.648193359375}, {"start": 395.91, "end": 396.51, "word": " sequence", "probability": 0.447998046875}, {"start": 396.51, "end": 396.89, "word": " of", "probability": 0.904296875}, {"start": 396.89, "end": 397.35, "word": " numbers", "probability": 0.8115234375}, {"start": 397.35, "end": 397.97, "word": " سنحصل", "probability": 0.7989501953125}, {"start": 397.97, "end": 398.33, "word": " على", "probability": 0.83544921875}, {"start": 398.33, "end": 399.87, "word": " خواص", "probability": 0.798583984375}, {"start": 399.87, "end": 400.37, "word": " الـ", "probability": 0.815673828125}, {"start": 400.37, "end": 401.97, "word": " convergence", "probability": 0.546875}, {"start": 401.97, "end": 402.51, "word": " للـ", "probability": 0.4312744140625}, {"start": 402.51, "end": 402.93, "word": " sequence", "probability": 0.95458984375}, {"start": 402.93, "end": 403.63, "word": " لو", "probability": 0.572265625}, {"start": 403.63, "end": 404.19, "word": " جيت", "probability": 0.5706787109375}, {"start": 404.19, "end": 405.05, "word": " الآن", "probability": 0.636474609375}, {"start": 405.05, "end": 405.55, "word": " قلت", "probability": 0.8134765625}], "temperature": 1.0}, {"id": 20, "seek": 43341, "start": 407.31, "end": 433.41, "text": "خلّينا نفترض إن Xn مرتبط بالـ X ما لها weekly بتاخد الآن أي subsequence منها و اكتبت برضه انها مرتبط بالـ X ما لها weekly بدي أقول let Xnk be any subsequence of Xn ماشي الحال؟ الآن مدام Xn بتروح للـ X weekly then", "tokens": [9778, 1211, 11703, 9957, 995, 8717, 5172, 2655, 43042, 36145, 1783, 77, 3714, 43500, 3555, 9566, 20666, 39184, 1783, 19446, 5296, 11296, 12460, 39894, 47283, 3215, 6024, 48506, 36632, 13924, 655, 9154, 11296, 4032, 1975, 4117, 2655, 3555, 2655, 4724, 43042, 3224, 16472, 11296, 3714, 43500, 3555, 9566, 20666, 39184, 1783, 19446, 5296, 11296, 12460, 4724, 16254, 5551, 39648, 718, 1783, 77, 74, 312, 604, 13924, 655, 295, 1783, 77, 3714, 33599, 1829, 21542, 6027, 22807, 6024, 48506, 3714, 3215, 10943, 1783, 77, 39894, 32887, 5016, 24976, 39184, 1783, 12460, 550], "avg_logprob": -0.371603271883467, "compression_ratio": 1.675531914893617, "no_speech_prob": 8.940696716308594e-07, "words": [{"start": 407.31, "end": 407.79, "word": "خلّينا", "probability": 0.8751953125}, {"start": 407.79, "end": 408.27, "word": " نفترض", 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0.82763671875}, {"start": 413.99, "end": 414.29, "word": " منها", "probability": 0.98291015625}, {"start": 414.29, "end": 414.41, "word": " و", "probability": 0.73583984375}, {"start": 414.41, "end": 414.77, "word": " اكتبت", "probability": 0.598291015625}, {"start": 414.77, "end": 414.97, "word": " برضه", "probability": 0.9645182291666666}, {"start": 414.97, "end": 415.19, "word": " انها", "probability": 0.7159423828125}, {"start": 415.19, "end": 415.49, "word": " مرتبط", "probability": 0.89208984375}, {"start": 415.49, "end": 415.69, "word": " بالـ", "probability": 0.6376953125}, {"start": 415.69, "end": 415.69, "word": " X", "probability": 0.9111328125}, {"start": 415.69, "end": 415.77, "word": " ما", "probability": 0.93505859375}, {"start": 415.77, "end": 416.31, "word": " لها", "probability": 0.960205078125}, {"start": 416.31, "end": 416.83, "word": " weekly", "probability": 0.98193359375}, {"start": 416.83, "end": 417.43, "word": " بدي", "probability": 0.4185791015625}, {"start": 417.43, "end": 417.73, "word": " أقول", "probability": 0.7430419921875}, {"start": 417.73, "end": 418.15, "word": " let", "probability": 0.47607421875}, {"start": 418.15, "end": 420.19, "word": " Xnk", "probability": 0.5616455078125}, {"start": 420.19, "end": 421.39, "word": " be", "probability": 0.3984375}, {"start": 421.39, "end": 422.43, "word": " any", "probability": 0.8916015625}, {"start": 422.43, "end": 425.13, "word": " subsequence", "probability": 0.997314453125}, {"start": 425.13, "end": 426.25, "word": " of", "probability": 0.97607421875}, {"start": 426.25, "end": 427.29, "word": " Xn", "probability": 0.973388671875}, {"start": 427.29, "end": 427.93, "word": " ماشي", "probability": 0.6004638671875}, {"start": 427.93, "end": 429.19, "word": " الحال؟", "probability": 0.7616373697916666}, {"start": 429.19, "end": 429.51, "word": " الآن", "probability": 0.60772705078125}, {"start": 429.51, "end": 431.01, "word": " مدام", "probability": 0.7980143229166666}, {"start": 431.01, "end": 431.41, "word": " Xn", "probability": 0.924072265625}, {"start": 431.41, "end": 431.73, "word": " بتروح", "probability": 0.9459635416666666}, {"start": 431.73, "end": 431.95, "word": " للـ", "probability": 0.5482177734375}, {"start": 431.95, "end": 432.11, "word": " X", "probability": 0.9208984375}, {"start": 432.11, "end": 432.53, "word": " weekly", "probability": 0.9755859375}, {"start": 432.53, "end": 433.41, "word": " then", "probability": 0.64697265625}], "temperature": 1.0}, {"id": 21, "seek": 45578, "start": 434.24, "end": 455.78, "text": "أكيد الـ f of xn هتروح للـ f of x لكل الأثوين الموجودة في الـ x' الان سارة تقدر عبارة عن sequence of numbers ال sequence of numbers أي subsequence منها هتكون في ال virtue of the same limit إذا ال subsequence f of xnk", "tokens": [10721, 4117, 25708, 2423, 39184, 283, 295, 2031, 77, 8032, 2655, 32887, 5016, 24976, 39184, 283, 295, 2031, 5296, 28820, 2423, 10721, 12984, 2407, 9957, 9673, 29245, 23328, 3660, 8978, 2423, 39184, 2031, 6, 2423, 7649, 8608, 9640, 3660, 6055, 28543, 2288, 6225, 3555, 9640, 3660, 18871, 8310, 295, 3547, 2423, 8310, 295, 3547, 36632, 13924, 655, 9154, 11296, 8032, 2655, 30544, 8978, 2423, 20816, 295, 264, 912, 4948, 11933, 15730, 2423, 13924, 655, 283, 295, 2031, 77, 74], "avg_logprob": -0.28925781659781935, "compression_ratio": 1.6032608695652173, "no_speech_prob": 9.5367431640625e-07, "words": [{"start": 434.24, "end": 434.78, "word": "أكيد", "probability": 0.94091796875}, {"start": 434.78, "end": 435.04, "word": " الـ", "probability": 0.5516357421875}, {"start": 435.04, "end": 435.2, "word": " f", "probability": 0.314208984375}, {"start": 435.2, "end": 435.38, "word": " of", "probability": 0.339599609375}, {"start": 435.38, "end": 435.88, "word": " xn", "probability": 0.6199951171875}, {"start": 435.88, "end": 437.12, "word": " هتروح", "probability": 0.8887939453125}, {"start": 437.12, "end": 437.38, "word": " للـ", "probability": 0.762939453125}, {"start": 437.38, "end": 437.5, "word": " f", "probability": 0.833984375}, {"start": 437.5, "end": 437.66, "word": " of", "probability": 0.9462890625}, {"start": 437.66, "end": 438.06, "word": " x", "probability": 0.9931640625}, {"start": 438.06, "end": 439.1, "word": " لكل", "probability": 0.919677734375}, {"start": 439.1, "end": 439.64, "word": " الأثوين", "probability": 0.577685546875}, {"start": 439.64, "end": 440.38, "word": " الموجودة", "probability": 0.9298095703125}, {"start": 440.38, "end": 441.38, "word": " في", "probability": 0.91748046875}, {"start": 441.38, "end": 441.52, "word": " الـ", "probability": 0.87841796875}, {"start": 441.52, "end": 441.66, "word": " x'", "probability": 0.71484375}, {"start": 442.02, "end": 443.54, "word": " الان", "probability": 0.5546875}, {"start": 443.54, "end": 443.86, "word": " سارة", "probability": 0.77587890625}, {"start": 443.86, "end": 444.1, "word": " تقدر", "probability": 0.6454874674479166}, {"start": 444.1, "end": 444.46, "word": " عبارة", "probability": 0.987548828125}, {"start": 444.46, "end": 444.66, "word": " عن", "probability": 0.990234375}, {"start": 444.66, "end": 445.38, "word": " sequence", "probability": 0.880859375}, {"start": 445.38, "end": 445.96, "word": " of", "probability": 0.9814453125}, {"start": 445.96, "end": 446.82, "word": " numbers", "probability": 0.88720703125}, {"start": 446.82, "end": 447.62, "word": " ال", "probability": 0.69677734375}, {"start": 447.62, "end": 448.02, "word": " sequence", "probability": 0.79248046875}, {"start": 448.02, "end": 448.22, "word": " of", "probability": 0.97607421875}, {"start": 448.22, "end": 448.78, "word": " numbers", "probability": 0.91943359375}, {"start": 448.78, "end": 449.22, "word": " أي", "probability": 0.46240234375}, {"start": 449.22, "end": 450.46, "word": " subsequence", "probability": 0.90478515625}, {"start": 450.46, "end": 451.04, "word": " منها", "probability": 0.994873046875}, {"start": 451.04, "end": 451.68, "word": " هتكون", "probability": 0.8196614583333334}, {"start": 451.68, "end": 451.84, "word": " في", "probability": 0.6982421875}, {"start": 451.84, "end": 451.9, "word": " ال", "probability": 0.50634765625}, {"start": 451.9, "end": 452.08, "word": " virtue", "probability": 0.4052734375}, {"start": 452.08, "end": 452.22, "word": " of", "probability": 0.4599609375}, {"start": 452.22, "end": 452.3, "word": " the", "probability": 0.9072265625}, {"start": 452.3, "end": 452.48, "word": " same", "probability": 0.9072265625}, {"start": 452.48, "end": 452.82, "word": " limit", "probability": 0.96044921875}, {"start": 452.82, "end": 453.38, "word": " إذا", "probability": 0.608154296875}, {"start": 453.38, "end": 453.58, "word": " ال", "probability": 0.494140625}, {"start": 453.58, "end": 454.36, "word": " subsequence", "probability": 0.988525390625}, {"start": 454.36, "end": 454.7, "word": " f", "probability": 0.83154296875}, {"start": 454.7, "end": 454.96, "word": " of", "probability": 0.88720703125}, {"start": 454.96, "end": 455.78, "word": " xnk", "probability": 0.7520345052083334}], "temperature": 1.0}, {"id": 22, "seek": 47631, "start": 456.69, "end": 476.31, "text": "اللي هو conveys لمين لل F of X لكل FY موجودة برضه في الـ X' وهذا معناته هو تعريف إن X and K بتروح لل X weekly إذا أي subsequence conveys weekly to the same limit as الsequence الأصلية", "tokens": [6027, 20292, 31439, 18053, 749, 32767, 9957, 24976, 479, 295, 1783, 5296, 28820, 479, 56, 3714, 29245, 23328, 3660, 4724, 43042, 3224, 8978, 2423, 39184, 1783, 6, 37037, 15730, 20449, 8315, 47395, 31439, 37279, 16572, 5172, 36145, 1783, 293, 591, 39894, 32887, 5016, 24976, 1783, 12460, 11933, 15730, 36632, 13924, 655, 18053, 749, 12460, 281, 264, 912, 4948, 382, 2423, 11834, 655, 16247, 9381, 20292, 3660], "avg_logprob": -0.3736007569441155, "compression_ratio": 1.3457446808510638, "no_speech_prob": 2.4437904357910156e-06, "words": [{"start": 456.69, "end": 456.93, "word": "اللي", "probability": 0.486328125}, {"start": 456.93, "end": 457.13, "word": " هو", 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{"start": 462.67, "end": 462.79, "word": " X'", "probability": 0.83447265625}, {"start": 463.17, "end": 464.13, "word": " وهذا", "probability": 0.88818359375}, {"start": 464.13, "end": 464.87, "word": " معناته", "probability": 0.93212890625}, {"start": 464.87, "end": 466.15, "word": " هو", "probability": 0.95068359375}, {"start": 466.15, "end": 466.69, "word": " تعريف", "probability": 0.98779296875}, {"start": 466.69, "end": 466.81, "word": " إن", "probability": 0.33056640625}, {"start": 466.81, "end": 467.05, "word": " X", "probability": 0.9423828125}, {"start": 467.05, "end": 467.31, "word": " and", "probability": 0.0869140625}, {"start": 467.31, "end": 467.61, "word": " K", "probability": 0.95458984375}, {"start": 467.61, "end": 468.65, "word": " بتروح", "probability": 0.8883463541666666}, {"start": 468.65, "end": 468.81, "word": " لل", "probability": 0.62548828125}, {"start": 468.81, "end": 469.29, "word": " X", "probability": 0.80859375}, {"start": 469.29, "end": 470.19, "word": " 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"probability": 0.771484375}], "temperature": 1.0}, {"id": 23, "seek": 50754, "start": 479.32, "end": 507.54, "text": "اللي هو الـ sequence اللي هو ما لها norm لـ Xn إيش ما لها is اللي هي bounded ال sequence norm لـ Xn is bounded عند Xn بتروح لل X weekly ماشي الحال لل X then F of Xn بتروح لل F of X لكل F الموجودة في ال X' هذا صار تعريف فهمنا الان so that the sequence of numbers F of Xn is bounded أكيد", "tokens": [6027, 20292, 31439, 2423, 39184, 8310, 13672, 1829, 31439, 19446, 5296, 11296, 2026, 5296, 39184, 1783, 77, 11933, 1829, 8592, 19446, 5296, 11296, 307, 13672, 1829, 39896, 37498, 2423, 8310, 2026, 5296, 39184, 1783, 77, 307, 37498, 43242, 1783, 77, 39894, 32887, 5016, 24976, 1783, 12460, 3714, 33599, 1829, 21542, 6027, 24976, 1783, 550, 479, 295, 1783, 77, 39894, 32887, 5016, 24976, 479, 295, 1783, 5296, 28820, 479, 9673, 29245, 23328, 3660, 8978, 2423, 1783, 6, 23758, 20328, 9640, 37279, 16572, 5172, 6156, 16095, 8315, 2423, 7649, 370, 300, 264, 8310, 295, 3547, 479, 295, 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"word": " Xn", "probability": 0.4588623046875}, {"start": 484.02, "end": 484.4, "word": " إيش", "probability": 0.7767740885416666}, {"start": 484.4, "end": 484.58, "word": " ما", "probability": 0.96728515625}, {"start": 484.58, "end": 484.96, "word": " لها", "probability": 0.93994140625}, {"start": 484.96, "end": 485.8, "word": " is", "probability": 0.49609375}, {"start": 485.8, "end": 486.2, "word": " اللي", "probability": 0.919921875}, {"start": 486.2, "end": 486.64, "word": " هي", "probability": 0.916015625}, {"start": 486.64, "end": 487.48, "word": " bounded", "probability": 0.8515625}, {"start": 487.48, "end": 488.16, "word": " ال", "probability": 0.86328125}, {"start": 488.16, "end": 488.6, "word": " sequence", "probability": 0.71826171875}, {"start": 488.6, "end": 489.02, "word": " norm", "probability": 0.361572265625}, {"start": 489.02, "end": 489.26, "word": " لـ", "probability": 0.79150390625}, {"start": 489.26, "end": 489.68, "word": " Xn", "probability": 0.96484375}, 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"probability": 0.72314453125}, {"start": 495.68, "end": 496.02, "word": " F", "probability": 0.447998046875}, {"start": 496.02, "end": 496.12, "word": " of", "probability": 0.3662109375}, {"start": 496.12, "end": 496.42, "word": " Xn", "probability": 0.96533203125}, {"start": 496.42, "end": 496.74, "word": " بتروح", "probability": 0.9700520833333334}, {"start": 496.74, "end": 496.9, "word": " لل", "probability": 0.90185546875}, {"start": 496.9, "end": 497.06, "word": " F", "probability": 0.90185546875}, {"start": 497.06, "end": 497.2, "word": " of", "probability": 0.74169921875}, {"start": 497.2, "end": 497.36, "word": " X", "probability": 0.99755859375}, {"start": 497.36, "end": 497.66, "word": " لكل", "probability": 0.84619140625}, {"start": 497.66, "end": 497.86, "word": " F", "probability": 0.63818359375}, {"start": 497.86, "end": 498.56, "word": " الموجودة", "probability": 0.82720947265625}, {"start": 498.56, "end": 499.06, "word": " في", "probability": 0.85400390625}, {"start": 499.06, "end": 499.22, "word": " ال", "probability": 0.537109375}, {"start": 499.22, "end": 499.4, "word": " X'", "probability": 0.8349609375}, {"start": 499.74, "end": 500.32, "word": " هذا", "probability": 0.68359375}, {"start": 500.32, "end": 500.58, "word": " صار", "probability": 0.97900390625}, {"start": 500.58, "end": 501.12, "word": " تعريف", "probability": 0.9632161458333334}, {"start": 501.12, "end": 502.24, "word": " فهمنا", "probability": 0.95947265625}, {"start": 502.24, "end": 503.14, "word": " الان", "probability": 0.45794677734375}, {"start": 503.14, "end": 503.42, "word": " so", "probability": 0.5419921875}, {"start": 503.42, "end": 503.7, "word": " that", "probability": 0.9384765625}, {"start": 503.7, "end": 503.9, "word": " the", "probability": 0.8095703125}, {"start": 503.9, "end": 504.52, "word": " sequence", "probability": 0.978515625}, {"start": 504.52, "end": 504.88, "word": " of", "probability": 0.9716796875}, {"start": 504.88, "end": 505.42, "word": " numbers", "probability": 0.8701171875}, {"start": 505.42, "end": 505.64, "word": " F", "probability": 0.78857421875}, {"start": 505.64, "end": 505.8, "word": " of", "probability": 0.92578125}, {"start": 505.8, "end": 506.14, "word": " Xn", "probability": 0.98095703125}, {"start": 506.14, "end": 506.36, "word": " is", "probability": 0.96484375}, {"start": 506.36, "end": 506.76, "word": " bounded", "probability": 0.943359375}, {"start": 506.76, "end": 507.54, "word": " أكيد", "probability": 0.9597981770833334}], "temperature": 1.0}, {"id": 24, "seek": 52790, "start": 508.12, "end": 527.9, "text": "لاحظوا كل اعتمادي تحويل اللي هو convergence in the norm اللي هو x as if convergence weekly in the norm ل convergence of mean of numbers اللي صارتها debounded that is there exists cf اللي هي constant depending on mean on f", "tokens": [15040, 5016, 19913, 14407, 28242, 1975, 34268, 15042, 16254, 6055, 5016, 2407, 26895, 13672, 1829, 31439, 32181, 294, 264, 2026, 13672, 1829, 31439, 2031, 382, 498, 32181, 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"word": " the", "probability": 0.86279296875}, {"start": 512.2, "end": 512.62, "word": " norm", "probability": 0.96240234375}, {"start": 512.62, "end": 513.08, "word": " اللي", "probability": 0.7398681640625}, {"start": 513.08, "end": 513.18, "word": " هو", "probability": 0.888671875}, {"start": 513.18, "end": 513.34, "word": " x", "probability": 0.1309814453125}, {"start": 513.34, "end": 513.6, "word": " as", "probability": 0.260986328125}, {"start": 513.6, "end": 513.72, "word": " if", "probability": 0.8212890625}, {"start": 513.72, "end": 514.16, "word": " convergence", "probability": 0.85888671875}, {"start": 514.16, "end": 514.64, "word": " weekly", "probability": 0.485107421875}, {"start": 514.64, "end": 514.82, "word": " in", "probability": 0.93798828125}, {"start": 514.82, "end": 514.92, "word": " the", "probability": 0.9150390625}, {"start": 514.92, "end": 515.26, "word": " norm", "probability": 0.9609375}, {"start": 515.26, "end": 515.7, "word": " ل", "probability": 0.890625}, {"start": 515.7, "end": 516.28, "word": " convergence", "probability": 0.8466796875}, {"start": 516.28, "end": 516.84, "word": " of", "probability": 0.97021484375}, {"start": 516.84, "end": 517.18, "word": " mean", "probability": 0.7294921875}, {"start": 517.18, "end": 517.56, "word": " of", "probability": 0.93701171875}, {"start": 517.56, "end": 518.2, "word": " numbers", "probability": 0.87744140625}, {"start": 518.2, "end": 519.6, "word": " اللي", "probability": 0.58221435546875}, {"start": 519.6, "end": 521.18, "word": " صارتها", "probability": 0.883056640625}, {"start": 521.18, "end": 521.66, "word": " debounded", "probability": 0.554443359375}, {"start": 521.66, "end": 522.12, "word": " that", "probability": 0.66455078125}, {"start": 522.12, "end": 522.38, "word": " is", "probability": 0.93603515625}, {"start": 522.38, "end": 522.62, "word": " there", "probability": 0.8447265625}, {"start": 522.62, "end": 523.02, "word": " exists", "probability": 0.54833984375}, {"start": 523.02, "end": 523.68, "word": " cf", "probability": 0.65576171875}, {"start": 523.68, "end": 525.04, "word": " اللي", "probability": 0.6326904296875}, {"start": 525.04, "end": 525.2, "word": " هي", "probability": 0.92138671875}, {"start": 525.2, "end": 525.74, "word": " constant", "probability": 0.95703125}, {"start": 525.74, "end": 526.26, "word": " depending", "probability": 0.8994140625}, {"start": 526.26, "end": 526.7, "word": " on", "probability": 0.9521484375}, {"start": 526.7, "end": 527.08, "word": " mean", "probability": 0.71728515625}, {"start": 527.08, "end": 527.62, "word": " on", "probability": 0.4833984375}, {"start": 527.62, "end": 527.9, "word": " f", "probability": 0.72607421875}], "temperature": 1.0}, {"id": 25, "seek": 54641, "start": 528.54, "end": 546.42, "text": "لأن هذا الكلام هذه تطلع على فوق هذه ال sequence f of xn is bounded لمين؟ لل f اللي بحكي عنها إذا أكيد ال c تبعتها بتعتمد على مين؟ على ال f إذا بصير عند ال absolute value أو ال modulus لل f of xn أصغر يستوي cf لكل n", "tokens": [1211, 33456, 23758, 2423, 28820, 10943, 29538, 6055, 9566, 1211, 3615, 15844, 6156, 30543, 29538, 2423, 8310, 283, 295, 2031, 77, 307, 37498, 5296, 2304, 9957, 22807, 24976, 283, 13672, 1829, 4724, 5016, 4117, 1829, 18871, 11296, 11933, 15730, 5551, 4117, 25708, 2423, 269, 6055, 3555, 34268, 11296, 39894, 34268, 2304, 3215, 15844, 3714, 9957, 22807, 15844, 2423, 283, 11933, 15730, 4724, 9381, 13546, 43242, 2423, 8236, 2158, 34051, 2423, 42287, 24976, 283, 295, 2031, 77, 5551, 9381, 17082, 2288, 7251, 14851, 45865, 269, 69, 5296, 28820, 297], "avg_logprob": -0.29441713215260024, "compression_ratio": 1.5825242718446602, "no_speech_prob": 5.543231964111328e-06, "words": [{"start": 528.54, "end": 528.8, "word": "لأن", "probability": 0.73974609375}, {"start": 528.8, "end": 528.98, "word": " هذا", "probability": 0.6376953125}, {"start": 528.98, "end": 529.36, "word": " الكلام", "probability": 0.9208984375}, {"start": 529.36, "end": 529.92, "word": " هذه", "probability": 0.16845703125}, {"start": 529.92, "end": 530.96, "word": " تطلع", "probability": 0.77734375}, {"start": 530.96, "end": 531.06, "word": " على", "probability": 0.369384765625}, {"start": 531.06, "end": 531.34, "word": " فوق", "probability": 0.942626953125}, {"start": 531.34, "end": 532.0, "word": " هذه", "probability": 0.51953125}, {"start": 532.0, "end": 532.18, "word": " ال", "probability": 0.80615234375}, {"start": 532.18, "end": 532.76, "word": " sequence", "probability": 0.66845703125}, {"start": 532.76, "end": 533.46, "word": " f", "probability": 0.290283203125}, {"start": 533.46, "end": 533.62, "word": " of", "probability": 0.481201171875}, {"start": 533.62, "end": 534.0, "word": " xn", "probability": 0.665771484375}, {"start": 534.0, "end": 534.2, "word": " is", "probability": 0.77490234375}, {"start": 534.2, "end": 534.68, "word": " bounded", "probability": 0.919921875}, {"start": 534.68, "end": 535.88, "word": " لمين؟", "probability": 0.6839599609375}, {"start": 535.88, "end": 536.12, "word": " لل", "probability": 0.6337890625}, {"start": 536.12, "end": 536.4, "word": " f", "probability": 0.3447265625}, {"start": 536.4, "end": 536.52, "word": " اللي", "probability": 0.9345703125}, {"start": 536.52, "end": 536.76, "word": " بحكي", "probability": 0.9444580078125}, {"start": 536.76, "end": 537.18, "word": " عنها", "probability": 0.99658203125}, {"start": 537.18, "end": 537.78, "word": " إذا", "probability": 0.7578125}, {"start": 537.78, "end": 538.2, "word": " أكيد", "probability": 0.8660481770833334}, {"start": 538.2, "end": 538.34, "word": " ال", "probability": 0.916015625}, {"start": 538.34, "end": 538.5, "word": " c", "probability": 0.46826171875}, {"start": 538.5, "end": 538.98, "word": " تبعتها", "probability": 0.750732421875}, {"start": 538.98, "end": 539.42, "word": " بتعتمد", "probability": 0.882080078125}, {"start": 539.42, "end": 539.56, "word": " على", "probability": 0.82373046875}, {"start": 539.56, "end": 540.1, "word": " مين؟", "probability": 0.9423828125}, {"start": 540.1, "end": 540.26, "word": " على", "probability": 0.845703125}, {"start": 540.26, "end": 540.44, "word": " ال", "probability": 0.65087890625}, {"start": 540.44, "end": 540.44, "word": " f", "probability": 0.6591796875}, {"start": 540.44, "end": 540.68, "word": " إذا", "probability": 0.880859375}, {"start": 540.68, "end": 541.1, "word": " بصير", "probability": 0.6114095052083334}, {"start": 541.1, "end": 541.24, "word": " عند", "probability": 0.72802734375}, {"start": 541.24, "end": 541.36, "word": " ال", "probability": 0.79345703125}, {"start": 541.36, "end": 541.62, "word": " absolute", "probability": 0.9375}, {"start": 541.62, "end": 542.06, "word": " value", "probability": 0.9912109375}, {"start": 542.06, "end": 542.2, "word": " أو", "probability": 0.76953125}, {"start": 542.2, "end": 542.3, "word": " ال", "probability": 0.82470703125}, {"start": 542.3, "end": 542.68, "word": " modulus", "probability": 0.97607421875}, {"start": 542.68, "end": 543.36, "word": " لل", "probability": 0.5361328125}, {"start": 543.36, "end": 543.56, "word": " f", "probability": 0.767578125}, {"start": 543.56, "end": 543.68, "word": " of", "probability": 0.9482421875}, {"start": 543.68, "end": 544.04, "word": " xn", "probability": 0.986083984375}, {"start": 544.04, "end": 544.42, "word": " أصغر", "probability": 0.985595703125}, {"start": 544.42, "end": 544.7, "word": " يستوي", "probability": 0.3792317708333333}, {"start": 544.7, "end": 545.52, "word": " cf", "probability": 0.63623046875}, {"start": 545.52, "end": 546.1, "word": " لكل", "probability": 0.97509765625}, {"start": 546.1, "end": 546.42, "word": " n", "probability": 0.65283203125}], "temperature": 1.0}, {"id": 26, "seek": 56852, "start": 546.9, "end": 568.52, "text": "الآن using the canonical mapping C إذا بتذكره من X لعين X double prime هذا ال canonical mapping كيف كنا عارفينه where ناخد اللي هو can define GN element in X double prime by حكيناه المرة السابقة تفصيله المرة السابقة 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معناها is bounded وهذا is bounded for all f element in x' لكن x' is complete", "tokens": [1211, 28820, 283, 9673, 29245, 23328, 3660, 8978, 2423, 39184, 2031, 6, 16490, 10859, 3215, 6024, 48506, 2423, 39184, 8236, 2158, 29538, 5296, 11296, 2423, 8236, 2158, 295, 290, 295, 283, 4724, 3794, 2407, 38207, 2423, 8236, 2158, 295, 283, 295, 2031, 77, 13672, 1829, 31439, 5551, 9381, 17082, 2288, 34051, 13412, 20498, 9957, 269, 69, 11933, 15730, 20328, 9640, 43242, 3224, 6024, 48506, 29538, 8717, 36178, 11296, 307, 37498, 29538, 8717, 36178, 11296, 307, 37498, 5296, 28814, 1863, 29538, 37498, 11933, 15730, 29538, 1975, 1829, 8592, 20449, 8315, 11296, 307, 37498, 37037, 15730, 307, 37498, 337, 439, 283, 4478, 294, 2031, 6, 44381, 2031, 6, 307, 3566], "avg_logprob": -0.37098624071943653, "compression_ratio": 1.8170212765957447, "no_speech_prob": 7.152557373046875e-07, "words": [{"start": 569.02, "end": 569.44, "word": "لكل", "probability": 0.67578125}, {"start": 569.44, "end": 569.66, "word": " 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"word": " ايش", "probability": 0.4462076822916667}, {"start": 590.32, "end": 590.74, "word": " معناها", "probability": 0.607666015625}, {"start": 590.74, "end": 591.14, "word": " is", "probability": 0.50146484375}, {"start": 591.14, "end": 591.5, "word": " bounded", "probability": 0.8642578125}, {"start": 591.5, "end": 592.34, "word": " وهذا", "probability": 0.752685546875}, {"start": 592.34, "end": 592.62, "word": " is", "probability": 0.9462890625}, {"start": 592.62, "end": 593.02, "word": " bounded", "probability": 0.92431640625}, {"start": 593.02, "end": 593.36, "word": " for", "probability": 0.84375}, {"start": 593.36, "end": 593.64, "word": " all", "probability": 0.92724609375}, {"start": 593.64, "end": 593.84, "word": " f", "probability": 0.6669921875}, {"start": 593.84, "end": 594.14, "word": " element", "probability": 0.51904296875}, {"start": 594.14, "end": 594.32, "word": " in", "probability": 0.8701171875}, {"start": 594.32, "end": 594.52, "word": " x'", "probability": 0.92138671875}, {"start": 594.88, "end": 595.62, "word": " لكن", "probability": 0.9306640625}, {"start": 595.62, "end": 595.96, "word": " x'", "probability": 0.9404296875}, {"start": 596.38, "end": 597.08, "word": " is", "probability": 0.853515625}, {"start": 597.08, "end": 597.7, "word": " complete", "probability": 0.88720703125}], "temperature": 1.0}, {"id": 28, "seek": 61786, "start": 598.64, "end": 617.86, "text": "إذا باى اللي هي uniform boundedness اللي ناخدناها المرة الماضية نورمها هيكون bounded مظبوط ولا لأ حكيناه المرة الفاتة مدام أنها bounded إذا و ال X' is complete اللي عليها معرفة اللي هي اللي عنده GN", "tokens": [28814, 15730, 4724, 995, 7578, 13672, 1829, 39896, 9452, 37498, 1287, 13672, 1829, 8717, 47283, 3215, 8315, 11296, 9673, 25720, 9673, 46958, 10632, 8717, 13063, 2304, 11296, 39896, 30544, 37498, 3714, 19913, 3555, 2407, 9566, 49429, 5296, 10721, 11331, 4117, 1829, 8315, 3224, 9673, 25720, 27188, 9307, 3660, 3714, 3215, 10943, 14739, 11296, 37498, 11933, 15730, 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ناخد واحدة واحدة ديجي ناخد الأولة الآن", "tokens": [6027, 33456, 2423, 39184, 2656, 4308, 295, 316, 643, 406, 281, 312, 2074, 294, 2674, 37495, 22653, 8978, 3224, 13672, 1829, 31439, 5336, 32181, 37893, 2068, 32181, 4032, 5016, 1863, 47283, 3215, 50113, 6027, 25124, 17082, 1211, 6024, 104, 6027, 12984, 3660, 47525, 8315, 8717, 11622, 25708, 13412, 2288, 9566, 13412, 2407, 10632, 15844, 2423, 5336, 32181, 13672, 1829, 7251, 9778, 1211, 11703, 1829, 3224, 2068, 13672, 1829, 12174, 1211, 8315, 3224, 12174, 36150, 13412, 2407, 10632, 3714, 15040, 5016, 19913, 3660, 16472, 3224, 45164, 25961, 2423, 10139, 2423, 1783, 19362, 8032, 1829, 30544, 2423, 5336, 32181, 11933, 1829, 8592, 3714, 6027, 3224, 4032, 21292, 3615, 9566, 1829, 13672, 1829, 31439, 2423, 2068, 32181, 11778, 1829, 7435, 1829, 8717, 47283, 3215, 36764, 24401, 3660, 36764, 24401, 3660, 11778, 1829, 7435, 1829, 8717, 47283, 3215, 16247, 12610, 3660, 6024, 48506], "avg_logprob": -0.2128348181290286, "compression_ratio": 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"probability": 0.9658203125}, {"start": 1714.91, "end": 1716.65, "word": " X", "probability": 0.75927734375}, {"start": 1716.65, "end": 1716.89, "word": " and", "probability": 0.327392578125}, {"start": 1716.89, "end": 1717.39, "word": " بتروح", "probability": 0.9747721354166666}, {"start": 1717.39, "end": 1717.63, "word": " لل", "probability": 0.8466796875}, {"start": 1717.63, "end": 1717.97, "word": " X", "probability": 0.9072265625}, {"start": 1717.97, "end": 1718.61, "word": " weekly", "probability": 0.72900390625}, {"start": 1718.61, "end": 1719.83, "word": " تكافئ", "probability": 0.9212646484375}], "temperature": 1.0}, {"id": 78, "seek": 174810, "start": 1720.66, "end": 1748.1, "text": "إنه الـ sequence normal XN is bounded، هاي واحدة، اتنين، for every element of a total M، اللي subset M of X' في اللي فوق الـ total subset، اللي هي الـ An، total subset طيب، for every element F of a total subset M of X'، we have F of XN بتروح لمينال of X as M قصه نفيل تانية، يعني، شوفوا", 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" XN", "probability": 0.891845703125}, {"start": 1743.96, "end": 1744.28, "word": " بتروح", "probability": 0.9322916666666666}, {"start": 1744.28, "end": 1744.8, "word": " لمينال", "probability": 0.656494140625}, {"start": 1744.8, "end": 1744.94, "word": " of", "probability": 0.66015625}, {"start": 1744.94, "end": 1745.22, "word": " X", "probability": 0.99365234375}, {"start": 1745.22, "end": 1745.42, "word": " as", "probability": 0.6943359375}, {"start": 1745.42, "end": 1745.6, "word": " M", "probability": 0.740234375}, {"start": 1745.6, "end": 1745.84, "word": " قصه", "probability": 0.381591796875}, {"start": 1745.84, "end": 1746.02, "word": " نفيل", "probability": 0.476318359375}, {"start": 1746.02, "end": 1746.64, "word": " تانية،", "probability": 0.661376953125}, {"start": 1746.64, "end": 1747.64, "word": " يعني،", "probability": 0.88525390625}, {"start": 1747.64, "end": 1748.1, "word": " شوفوا", "probability": 0.9596354166666666}], "temperature": 1.0}, {"id": 79, "seek": 176117, "start": 1749.07, "end": 1761.17, "text": "الآن لو جينا حللنا النظرية بالمنبرهن Xn بتروح للـ X weekly، إيش معناتها؟ إن F of Xn بتروح لل F of X لكل F element الـ main، الـ X'", "tokens": [6027, 148, 48506, 45164, 10874, 1829, 8315, 11331, 1211, 1211, 8315, 28239, 19913, 2288, 10632, 20666, 27842, 26890, 3224, 1863, 1783, 77, 39894, 32887, 5016, 24976, 39184, 1783, 12460, 12399, 11933, 1829, 8592, 20449, 8315, 2655, 11296, 22807, 36145, 479, 295, 1783, 77, 39894, 32887, 5016, 24976, 479, 295, 1783, 5296, 28820, 479, 4478, 2423, 39184, 2135, 12399, 2423, 39184, 1783, 6], "avg_logprob": -0.3244047751502385, "compression_ratio": 1.3888888888888888, "no_speech_prob": 0.0, "words": [{"start": 1749.0700000000002, "end": 1749.67, "word": "الآن", "probability": 0.5861002604166666}, {"start": 1749.67, "end": 1750.27, "word": " لو", "probability": 0.8046875}, {"start": 1750.27, "end": 1750.67, "word": " جينا", "probability": 0.7140299479166666}, {"start": 1750.67, "end": 1751.17, "word": " حللنا", "probability": 0.9041748046875}, {"start": 1751.17, "end": 1751.65, "word": " النظرية", "probability": 0.86669921875}, {"start": 1751.65, "end": 1752.51, "word": " بالمنبرهن", "probability": 0.75615234375}, {"start": 1752.51, "end": 1753.37, "word": " Xn", "probability": 0.30572509765625}, {"start": 1753.37, "end": 1753.67, "word": " بتروح", "probability": 0.9109700520833334}, {"start": 1753.67, "end": 1753.91, "word": " للـ", "probability": 0.5498046875}, {"start": 1753.91, "end": 1754.03, "word": " X", "probability": 0.64892578125}, {"start": 1754.03, "end": 1755.05, "word": " weekly،", "probability": 0.5958251953125}, {"start": 1755.05, "end": 1755.25, "word": " إيش", "probability": 0.83447265625}, {"start": 1755.25, "end": 1756.31, "word": " معناتها؟", "probability": 0.91142578125}, {"start": 1756.31, "end": 1756.45, "word": " إن", "probability": 0.62109375}, {"start": 1756.45, "end": 1756.69, "word": " F", "probability": 0.495361328125}, {"start": 1756.69, "end": 1756.89, "word": " of", "probability": 0.293701171875}, {"start": 1756.89, "end": 1757.31, "word": " Xn", "probability": 0.92529296875}, {"start": 1757.31, "end": 1757.83, "word": " بتروح", "probability": 0.9453125}, {"start": 1757.83, "end": 1757.99, "word": " لل", "probability": 0.87548828125}, {"start": 1757.99, "end": 1758.17, "word": " F", "probability": 0.51904296875}, {"start": 1758.17, "end": 1758.35, "word": " of", "probability": 0.89599609375}, {"start": 1758.35, "end": 1758.65, "word": " X", "probability": 0.9970703125}, {"start": 1758.65, "end": 1759.41, "word": " لكل", "probability": 0.94873046875}, {"start": 1759.41, "end": 1759.63, "word": " F", "probability": 0.8671875}, {"start": 1759.63, "end": 1759.93, "word": " element", "probability": 0.544921875}, {"start": 1759.93, "end": 1760.23, "word": " الـ", "probability": 0.78076171875}, {"start": 1760.23, "end": 1760.85, "word": " main،", "probability": 0.4337158203125}, {"start": 1760.85, "end": 1761.03, "word": " الـ", "probability": 0.729736328125}, {"start": 1761.03, "end": 1761.17, "word": " X'", "probability": 0.888671875}], "temperature": 1.0}, {"id": 80, "seek": 179093, "start": 1762.81, "end": 1790.93, "text": "اللي أنا هذا بقولك أنا هذا الشرط الكثير اللي الهن كلهن بديش لكل أفوال من TX' بيثبت فيني ان يكون لكل أفوال ما لها في total subset يعني جزء من X' لكن بدها زجة شوية عشان تتفل ال weekly ان يكون norm لكسرني إيش ماله is bounded بيعطيني هذا يؤدي إلى هذا وهذا يؤدي لهذا هلاجيه اللي هو أمر سهل من الخواص اللي قبل شوية حصلناها", "tokens": [6027, 20292, 41850, 23758, 4724, 39648, 4117, 41850, 23758, 25124, 2288, 9566, 33251, 12984, 13546, 13672, 1829, 2423, 3224, 1863, 28242, 3224, 1863, 4724, 16254, 8592, 5296, 28820, 5551, 5172, 2407, 6027, 9154, 314, 55, 6, 4724, 1829, 12984, 3555, 2655, 8978, 22653, 16472, 7251, 30544, 5296, 28820, 5551, 5172, 2407, 6027, 19446, 5296, 11296, 8978, 3217, 25993, 37495, 22653, 10874, 11622, 38207, 9154, 1783, 6, 44381, 47525, 11296, 30767, 7435, 3660, 13412, 2407, 10632, 6225, 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mean اللي هو mean C مدام ال XN بتروح ال N، النورم ال XN أصغر أو يساوي C for all N، إذن automatically اللي هي النورمها، اللي هو النورم ال X، هيكون ماله أصغر أو يساوي C", "tokens": [2407, 6027, 1863, 13063, 2304, 2423, 1783, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 383, 337, 31868, 2416, 914, 13672, 1829, 31439, 914, 383, 3714, 3215, 10943, 2423, 1783, 45, 39894, 32887, 5016, 2423, 426, 12399, 28239, 13063, 2304, 2423, 1783, 45, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 383, 337, 439, 426, 12399, 11933, 8848, 1863, 6772, 13672, 1829, 39896, 28239, 13063, 2304, 11296, 12399, 13672, 1829, 31439, 28239, 13063, 2304, 2423, 1783, 12399, 39896, 30544, 3714, 6027, 3224, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 383], "avg_logprob": -0.32927631892656023, "compression_ratio": 1.8806818181818181, "no_speech_prob": 6.079673767089844e-06, "words": [{"start": 1865.8999999999999, "end": 1866.58, "word": "والنورم", "probability": 0.54072265625}, {"start": 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1924.58, "end": 1945.76, "text": "طيب الآن since M is total إذا ال span لـ M بساوي X' then لكل F element in X' there exist a sequence of I in span M such that F I بتروح لمين؟ لل F هايو since span ل M is dense in X' إذا مدام F I بتروح لل F إذا بقدر أسغر المسافة جد ما بدي", "tokens": [9566, 1829, 3555, 6024, 48506, 1670, 376, 307, 3217, 11933, 15730, 2423, 16174, 5296, 39184, 376, 4724, 3794, 995, 45865, 1783, 6, 550, 5296, 28820, 479, 4478, 294, 1783, 6, 456, 2514, 257, 8310, 295, 286, 294, 16174, 376, 1270, 300, 479, 286, 39894, 32887, 5016, 32767, 9957, 22807, 24976, 479, 8032, 47302, 2407, 1670, 16174, 5296, 376, 307, 18011, 294, 1783, 6, 11933, 15730, 3714, 3215, 10943, 479, 286, 39894, 32887, 5016, 24976, 479, 11933, 15730, 4724, 28543, 2288, 5551, 3794, 17082, 2288, 9673, 3794, 31845, 3660, 10874, 3215, 19446, 4724, 16254], "avg_logprob": -0.2932180708393137, "compression_ratio": 1.4741784037558685, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 1924.58, "end": 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2099.91, "word": " هان", "probability": 0.249664306640625}, {"start": 2099.91, "end": 2100.21, "word": " بتروح", "probability": 0.9324544270833334}, {"start": 2100.21, "end": 2100.39, "word": " لل", "probability": 0.75927734375}, {"start": 2100.39, "end": 2100.55, "word": " F", "probability": 0.8388671875}, {"start": 2100.55, "end": 2100.73, "word": " of", "probability": 0.95751953125}, {"start": 2100.73, "end": 2101.05, "word": " X", "probability": 0.998046875}, {"start": 2101.05, "end": 2101.49, "word": " ك", "probability": 0.8037109375}, {"start": 2101.49, "end": 2101.73, "word": " number", "probability": 0.3798828125}, {"start": 2101.73, "end": 2102.55, "word": " إذا", "probability": 0.90087890625}, {"start": 2102.55, "end": 2102.95, "word": " معناته", "probability": 0.9630533854166666}, {"start": 2102.95, "end": 2103.13, "word": " X", "probability": 0.86474609375}, {"start": 2103.13, "end": 2103.25, "word": " هان", "probability": 0.878173828125}, {"start": 2103.25, "end": 2103.53, 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1829, 31439, 9673, 5016, 46958, 25720, 8717, 11622, 1211, 9673, 5016, 46958, 25720, 4032, 7649, 13412, 16606, 21984, 30731, 5296, 4587, 16606, 19753, 34740], "avg_logprob": -0.16875000049670538, "compression_ratio": 1.3703703703703705, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2108.66, "end": 2110.0, "word": "خلصنا", "probability": 0.955322265625}, {"start": 2110.0, "end": 2110.26, "word": " اللي", "probability": 0.72314453125}, {"start": 2110.26, "end": 2110.78, "word": " هو", "probability": 0.98046875}, {"start": 2110.78, "end": 2112.68, "word": " المحاضرة", "probability": 0.973876953125}, {"start": 2112.68, "end": 2113.24, "word": " نزل", "probability": 0.6970621744791666}, {"start": 2113.24, "end": 2114.36, "word": " المحاضرة", "probability": 0.918701171875}, {"start": 2114.36, "end": 2114.8, "word": " وان", "probability": 0.87353515625}, {"start": 2114.8, "end": 2115.04, "word": " شاء", "probability": 0.9755859375}, {"start": 2115.04, "end": 2115.7, "word": " الله", "probability": 0.9501953125}, {"start": 2115.7, "end": 2116.56, "word": " إلى", "probability": 0.47509765625}, {"start": 2116.56, "end": 2117.82, "word": " لقاء", "probability": 0.9685872395833334}, {"start": 2117.82, "end": 2118.92, "word": " آخر", "probability": 0.875244140625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2119.3085, "duration_after_vad": 2078.8981249999956}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Z5xeo5Xjt84_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Z5xeo5Xjt84_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8cf6e573fb0e5e248adb5722db792574c1ea98c8
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Z5xeo5Xjt84_raw.srt
@@ -0,0 +1,1804 @@
+1
+00:00:05,060 --> 00:00:07,800
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,800 --> 00:00:10,800
+والصلاة والسلام على سيد المسلمين سيدنا محمد وعلى
+
+3
+00:00:10,800 --> 00:00:15,460
+أهله وصحبه أجمعين هذه هي المحاضرة رقم 32 مساق
+
+4
+00:00:15,460 --> 00:00:20,340
+تحليل اقتراني أو تحليل دالي طلاب طالبات الجامعة
+
+5
+00:00:20,340 --> 00:00:25,200
+الإسلامية ماجستير الرياضياتوصلنا لعند اللي هو
+
+6
+00:00:25,200 --> 00:00:29,460
+اربعة تمانية strong and weak convergence نشوف ايش
+
+7
+00:00:29,460 --> 00:00:35,260
+اللي هو نقصد اللي هو strong و weak convergence
+
+8
+00:00:35,260 --> 00:00:39,380
+طبعا احنا اللي هنحكي عن اللي هو norm this base
+
+9
+00:00:39,380 --> 00:00:42,960
+نحكي عن ال convergence في داخل norm this base
+
+10
+00:00:44,590 --> 00:00:48,030
+بنتعرف على نوعين من أنواع ال convergence في ال
+
+11
+00:00:48,030 --> 00:00:53,110
+node space ونشوف أيش معنات كل نوع من النوعين a
+
+12
+00:00:53,110 --> 00:00:57,730
+sequence xn in a node space x is said to be
+
+13
+00:00:57,730 --> 00:01:01,970
+strongly convergent or convergent in the norm يعني
+
+14
+00:01:01,970 --> 00:01:04,290
+ال convergence with respect to mean to the norm
+
+15
+00:01:11,440 --> 00:01:15,680
+وهذا الكلام احنا بنرمزله باسم limit xn بساوة x او
+
+16
+00:01:15,680 --> 00:01:16,800
+xn converges to x
+
+17
+00:01:23,730 --> 00:01:28,990
+لذلك عندما نكتب xn converges للـ x بالشكل هذا اللي
+
+18
+00:01:28,990 --> 00:01:33,310
+نقصد فيها هو xn is strongly convergence to main to
+
+19
+00:01:33,310 --> 00:01:39,030
+x مايعنيها؟ معناته أن ال limit للـ xn ناقص xبروح
+
+20
+00:01:39,030 --> 00:01:42,990
+للـ 0 as N goes from mean to infinity في هذه
+
+21
+00:01:42,990 --> 00:01:46,590
+الحالة بنسمي الـ X the limit اللي هو the strong
+
+22
+00:01:46,590 --> 00:01:50,790
+limit of mean of the sequence XN الآن في
+
+23
+00:01:50,790 --> 00:01:54,550
+convergence آخر اللي هو سنتعرف عليه اللي هو
+
+24
+00:01:54,550 --> 00:02:00,950
+sequence بنقول عنه XN converts ل X weekly طبعا الـ
+
+25
+00:02:00,950 --> 00:02:06,210
+XN والـ X برضه الموجودات الـ XNوالـ x elements in
+
+26
+00:02:06,210 --> 00:02:11,230
+the non-dospace is x هذا الأولاني اللي هو الـ
+
+27
+00:02:11,230 --> 00:02:13,610
+strong convergence والآن بدنا نعرف الـ weak
+
+28
+00:02:13,610 --> 00:02:16,590
+convergence إيش معناته اللي هو xₙ تروح للـ x
+
+29
+00:02:16,590 --> 00:02:23,650
+weekly إذا كان اللي هو لكل f element اللي هو x برا
+
+30
+00:02:23,650 --> 00:02:26,270
+يعني bounded linear operator bounded linear
+
+31
+00:02:26,270 --> 00:02:26,590
+function
+
+32
+00:02:30,120 --> 00:02:34,720
+Converging to the off of X هذا معناته ان Xn
+
+33
+00:02:34,720 --> 00:02:39,300
+Converges لإكسية شمال و weekly لحظه اللي هو احنا
+
+34
+00:02:39,300 --> 00:02:44,240
+حولنا الحدير من Xn ل X اللي هي في الـ non spaces
+
+35
+00:02:44,240 --> 00:02:48,420
+إلى convergence في الواقع في الـ scalar field لأن
+
+36
+00:02:48,420 --> 00:02:52,480
+off of Xn و off of X شمالها عبارة عن number يعني
+
+37
+00:02:52,480 --> 00:02:54,980
+complex أو real حسب اللي هو ال complex field عشان
+
+38
+00:02:54,980 --> 00:03:01,110
+هيك بنسمي weekly convergence يعني باختصاربالنسبة
+
+39
+00:03:01,110 --> 00:03:08,550
+لـ Xn في الوضع X قد يكون مرتبطاً يومياً إذا كان
+
+40
+00:03:08,550 --> 00:03:11,850
+هناك X أقل من X كما لو كان هناك X أقل من X كما لو
+
+41
+00:03:11,850 --> 00:03:19,290
+كان هناك X أقل من X كما لو كان هناك X أقل من X
+
+42
+00:03:22,940 --> 00:03:26,280
+لأن أكيد في علاقة بين الـ weak convergence وبين
+
+43
+00:03:26,280 --> 00:03:29,640
+mean وبين ال strong convergence يعني انتبه عن
+
+44
+00:03:29,640 --> 00:03:32,900
+الواحد هيقول أكيد ال strong convergence إيش هيقدر
+
+45
+00:03:32,900 --> 00:03:35,680
+لل weak convergence لكن the convergence need not
+
+46
+00:03:35,680 --> 00:03:41,390
+to be true in general هنشوف اللي هوكيف نثبت الـ Xn
+
+47
+00:03:41,390 --> 00:03:47,810
+بتروح للـ X weakly بيؤدي لـ weakly و كيف اللي هو
+
+48
+00:03:47,810 --> 00:03:52,330
+انه احنا نثبت انه اللي هو ال converts need not to
+
+49
+00:03:52,330 --> 00:03:55,910
+be true عن طريق example و من ثم نشوف ايش في
+
+50
+00:03:55,910 --> 00:04:00,570
+condition بنحطه على اللي هو non displaced عشان
+
+51
+00:04:00,570 --> 00:04:03,470
+يصير اللي هو ال weak convergence و ال strong يشمله
+
+52
+00:04:03,470 --> 00:04:10,610
+زي بعضلاحظوا في الـ R كنا نحكي عن weak convergence
+
+53
+00:04:10,610 --> 00:04:13,550
+و strong convergence كنا نحكي عنه في الـ sequences
+
+54
+00:04:14,820 --> 00:04:17,620
+سنجد أن في الـ R و في الـ C و في الحاجات اللي زي
+
+55
+00:04:17,620 --> 00:04:21,280
+.. في كل الـ finite dimensional spaces سيكون اللي
+
+56
+00:04:21,280 --> 00:04:24,260
+هو الـ weak convergence و الـ strong Gاش مالهين
+
+57
+00:04:24,260 --> 00:04:28,300
+are the same خلّينا الأن نشوف أول لمّة لمّة الأولى
+
+58
+00:04:28,300 --> 00:04:31,460
+let Xn be a weakly اللي هو convergence sequence
+
+59
+00:04:31,460 --> 00:04:36,620
+around space X سي Xn بتروح للـ X مالها weaklyأثناء
+
+60
+00:04:36,620 --> 00:04:41,280
+ذلك، قيمة الـ weak X of Xn هي محدودة، وهي أشمالها
+
+61
+00:04:41,280 --> 00:04:45,440
+وحيدة، إذن قيمة، في حالة، احنا بنحكي عن أهم حالة
+
+62
+00:04:45,440 --> 00:04:50,340
+مين؟ حالة الـ weak convergence قيمة اللي هي وحيدة،
+
+63
+00:04:50,340 --> 00:04:53,920
+اتنين، every subsequence of Xn converges أشماله
+
+64
+00:04:53,920 --> 00:04:59,010
+weakly to Xالحالة في الـ sequence الـ norm لـ Xn
+
+65
+00:04:59,010 --> 00:05:03,330
+أشمالها is bounded إذا كل هذه الأمور اللي هو من
+
+66
+00:05:03,330 --> 00:05:06,050
+خواص الـ weak convergence يعني لو بدنا نيدي
+
+67
+00:05:06,050 --> 00:05:11,090
+نعطيكوا sketch للبرهان نفترض إن Xn بتروح لـ X
+
+68
+00:05:11,090 --> 00:05:16,450
+weekly و Xn بتروح لـ Y أيش برضه weekly يعني بروح
+
+69
+00:05:16,450 --> 00:05:19,790
+إني أشمال إلى different limits و في الآخر نثبت إنه
+
+70
+00:05:19,790 --> 00:05:24,120
+أشمال و X و Y هي نفس الأشياءالان شو معنات xn بتروح
+
+71
+00:05:24,120 --> 00:05:28,600
+لل x weekly لان لكل f element in x prime هيكون عند
+
+72
+00:05:28,600 --> 00:05:35,000
+ال f of xn بتروح لمين لل f of x معايا نفس الاشي
+
+73
+00:05:35,000 --> 00:05:39,620
+مدام xn بتروح لل y weekly لكل f element in x prime
+
+74
+00:05:39,620 --> 00:05:47,170
+هتطلع f of xn برضه هتروح لمين لل fهذه سيكوينس نمبر
+
+75
+00:05:47,170 --> 00:05:50,610
+و هذه سيكوينس نمبر و احنا نعرف ان سيكوينس نمبر
+
+76
+00:05:50,610 --> 00:05:53,510
+عندما يكون مرتبط مع مرتبط مع نفس المقالة إلى نفس
+
+77
+00:05:53,510 --> 00:05:54,150
+المقالة
+
+78
+00:05:59,080 --> 00:06:04,280
+هي ساوي F of Y هذا الكلام لكل مين لكل F element in
+
+79
+00:06:04,280 --> 00:06:10,440
+X' هذا معناته أن F of X minus Y هتساوي سفر لكل F
+
+80
+00:06:10,440 --> 00:06:14,720
+element in X' واحنا أخدنا نتيجة قبل هيك هتطلع مين
+
+81
+00:06:14,720 --> 00:06:20,300
+إذا ال X minus Y هتساوي سفر إذا معناته X هتساوي Y
+
+82
+00:06:20,300 --> 00:06:24,620
+معناته إنه ال limit ما لها is unique under the
+
+83
+00:06:24,620 --> 00:06:32,930
+weak convergenceهذا بالنسبة لمن؟ لـ B برضه
+
+84
+00:06:32,930 --> 00:06:36,890
+نفس الأشياء إعتمادا على خواص الـ sequence of
+
+85
+00:06:36,890 --> 00:06:42,510
+numbers سنحصل على خواص الـ convergence للـ
+
+86
+00:06:42,510 --> 00:06:49,330
+sequence لو جيت الآن قلتخلّينا نفترض إن Xn مرتبط
+
+87
+00:06:49,330 --> 00:06:53,990
+بالـ X ما لها weekly بتاخد الآن أي subsequence
+
+88
+00:06:53,990 --> 00:06:56,830
+منها و اكتبت برضه انها مرتبط بالـ X ما لها weekly
+
+89
+00:06:56,830 --> 00:07:07,930
+بدي أقول let Xnk be any subsequence of Xn ماشي
+
+90
+00:07:07,930 --> 00:07:14,780
+الحال؟ الآن مدام Xn بتروح للـ X weekly thenأكيد
+
+91
+00:07:14,780 --> 00:07:20,380
+الـ f of xn هتروح للـ f of x لكل الأثوين الموجودة
+
+92
+00:07:20,380 --> 00:07:25,960
+في الـ x' الان سارة تقدر عبارة عن sequence of
+
+93
+00:07:25,960 --> 00:07:31,040
+numbers ال sequence of numbers أي subsequence منها
+
+94
+00:07:31,040 --> 00:07:33,580
+هتكون في ال virtue of the same limit إذا ال
+
+95
+00:07:33,580 --> 00:07:39,910
+subsequence f of xnkاللي هو conveys لمين لل F of X
+
+96
+00:07:39,910 --> 00:07:46,690
+لكل FY موجودة برضه في الـ X' وهذا معناته هو تعريف
+
+97
+00:07:46,690 --> 00:07:51,990
+إن X and K بتروح لل X weekly إذا أي subsequence
+
+98
+00:07:51,990 --> 00:07:55,610
+conveys weekly to the same limit as الsequence
+
+99
+00:07:55,610 --> 00:07:56,310
+الأصلية
+
+100
+00:07:59,320 --> 00:08:04,400
+اللي هو الـ sequence اللي هو ما لها norm لـ Xn إيش
+
+101
+00:08:04,400 --> 00:08:09,680
+ما لها is اللي هي bounded ال sequence norm لـ Xn
+
+102
+00:08:09,680 --> 00:08:14,460
+is bounded عند Xn بتروح لل X weekly ماشي الحال لل
+
+103
+00:08:14,460 --> 00:08:19,060
+X then F of Xn بتروح لل F of X لكل F الموجودة في
+
+104
+00:08:19,060 --> 00:08:23,900
+ال X' هذا صار تعريف فهمنا الان so that the
+
+105
+00:08:23,900 --> 00:08:28,580
+sequence of numbers F of Xn is bounded أكيدلاحظوا
+
+106
+00:08:28,580 --> 00:08:32,620
+كل اعتمادي تحويل اللي هو convergence in the norm
+
+107
+00:08:32,620 --> 00:08:35,700
+اللي هو x as if convergence weekly in the norm ل
+
+108
+00:08:35,700 --> 00:08:41,180
+convergence of mean of numbers اللي صارتها
+
+109
+00:08:41,180 --> 00:08:45,740
+debounded that is there exists cf اللي هي constant
+
+110
+00:08:45,740 --> 00:08:51,060
+depending on mean on fلأن هذا الكلام هذه تطلع على
+
+111
+00:08:51,060 --> 00:08:56,400
+فوق هذه ال sequence f of xn is bounded لمين؟ لل f
+
+112
+00:08:56,400 --> 00:08:59,560
+اللي بحكي عنها إذا أكيد ال c تبعتها بتعتمد على
+
+113
+00:08:59,560 --> 00:09:02,300
+مين؟ على ال f إذا بصير عند ال absolute value أو ال
+
+114
+00:09:02,300 --> 00:09:07,980
+modulus لل f of xn أصغر يستوي cf لكل nالآن using
+
+115
+00:09:07,980 --> 00:09:11,580
+the canonical mapping C إذا بتذكره من X لعين X
+
+116
+00:09:11,580 --> 00:09:13,700
+double prime هذا ال canonical mapping كيف كنا
+
+117
+00:09:13,700 --> 00:09:20,880
+عارفينه where ناخد اللي هو can define GN element
+
+118
+00:09:20,880 --> 00:09:23,900
+in X double prime by حكيناه المرة السابقة تفصيله
+
+119
+00:09:23,900 --> 00:09:28,520
+المرة السابقة تاخدناه GN of F ايش متساوي F of XN
+
+120
+00:09:29,020 --> 00:09:32,460
+لكل f الموجودة في الـ x' خُد الآن الـ absolute
+
+121
+00:09:32,460 --> 00:09:37,560
+value هذه لها ال absolute value of g of f بسوء ال
+
+122
+00:09:37,560 --> 00:09:42,060
+absolute value of f of xn اللي هو أصغر أو شومين cf
+
+123
+00:09:42,060 --> 00:09:47,460
+إذا صار عنده الآن هذه نفسها is bounded هذه نفسها
+
+124
+00:09:47,460 --> 00:09:51,140
+is bounded لإن هذه bounded إذا هذه ايش معناها is
+
+125
+00:09:51,140 --> 00:09:54,520
+bounded وهذا is bounded for all f element in x'
+
+126
+00:09:54,880 --> 00:10:02,660
+لكن x' is completeإذا باى اللي هي uniform
+
+127
+00:10:02,660 --> 00:10:06,160
+boundedness اللي ناخدناها المرة الماضية نورمها
+
+128
+00:10:06,160 --> 00:10:09,860
+هيكون bounded مظبوط ولا لأ حكيناه المرة الفاتة
+
+129
+00:10:09,860 --> 00:10:15,060
+مدام أنها bounded إذا و ال X' is complete اللي
+
+130
+00:10:15,060 --> 00:10:22,000
+عليها معرفة اللي هي اللي عنده GNمعرفة على Complete
+
+131
+00:10:22,000 --> 00:10:26,560
+Space إذا بالـ Uniform Boundedness Theorem شروطها
+
+132
+00:10:26,560 --> 00:10:30,760
+مطبقة حيكون الـ Normal GN is bounded معناته Normal
+
+133
+00:10:30,760 --> 00:10:33,820
+GN is bounded معناته اللي هو Normal XN bounded
+
+134
+00:10:33,820 --> 00:10:38,700
+لإنه أثبتنا في أربعة، ستة، واحد إن Normal XN هو
+
+135
+00:10:38,700 --> 00:10:45,480
+Normal GN ومن ثم أثبتنا Normal XN is bounded طيب،
+
+136
+00:10:45,480 --> 00:10:46,720
+الـtheorem اللي بعدها
+
+137
+00:10:50,820 --> 00:10:56,160
+اللي وعدناكم فيه let Xn be a sequence in unknown
+
+138
+00:10:56,160 --> 00:11:01,260
+space X then
+
+139
+00:11:01,260 --> 00:11:06,940
+a strong convergence implies ما له weak
+
+140
+00:11:06,940 --> 00:11:10,160
+convergence with the same limit يعني لو الآن Xn
+
+141
+00:11:10,160 --> 00:11:14,900
+بتروح لل X strongly هتروح لل X أش ما لها weakly
+
+142
+00:11:15,620 --> 00:11:19,120
+الأن الـ Converse of A need not to be true in
+
+143
+00:11:19,120 --> 00:11:23,380
+general يعني فيه اللي هو weak convergence مش
+
+144
+00:11:23,380 --> 00:11:27,860
+strong convergence وحناخد مثال الشغل الثالثة بدنا
+
+145
+00:11:27,860 --> 00:11:30,740
+نزيد شرط شوية على ال weak convergence اللي يخلّيه
+
+146
+00:11:30,740 --> 00:11:34,100
+strong اللي قلناه قبل شوية ملاحظة انه لو كان ال
+
+147
+00:11:34,100 --> 00:11:36,460
+dimension ال X finite هيكون ال weak convergence
+
+148
+00:11:36,460 --> 00:11:40,360
+إيش ماله وبيعطي اللي هو ال strong convergence ديجي
+
+149
+00:11:40,360 --> 00:11:43,840
+ناخد واحدة واحدة ديجي ناخد الأولة الآنالان لو
+
+150
+00:11:43,840 --> 00:11:50,340
+فرضنا ان xn بتروح لل x اللي هو strongly ماشي؟ ايش
+
+151
+00:11:50,340 --> 00:11:56,280
+معناته هذا؟ اذا then norm ال xn ناقص x بروح لمين؟
+
+152
+00:11:56,280 --> 00:12:01,030
+لصفرالان بيثبتلك ان ال XN بتروح لل XA شمالها
+
+153
+00:12:01,030 --> 00:12:05,970
+weekly ايش يعني بيثبتلك بيثبتلك ان لكل F element
+
+154
+00:12:05,970 --> 00:12:11,870
+in X' يطلع F of XN بيروح لمين لل F of X ماشي الحال
+
+155
+00:12:11,870 --> 00:12:19,050
+هاي اللي بيثبتهإيش يعني؟ يعني بمعنى بدي أثبتلك بدي
+
+156
+00:12:19,050 --> 00:12:23,010
+أثبتلك إنه لو أخدت ال absolute value of f of x n
+
+157
+00:12:23,010 --> 00:12:27,510
+ماقص f of x بدي أثبتلك إن هذا بروح للسفر as n goes
+
+158
+00:12:27,510 --> 00:12:32,110
+to infinity معايا يا جماعة؟ الآن شوفوا هذا هذا
+
+159
+00:12:32,110 --> 00:12:38,310
+طبعا أصغر اللي بيساوي ال f of x n ماقص x صح ولا
+
+160
+00:12:38,310 --> 00:12:42,950
+لأ؟ لأن f is linear وهذا أصغر أو يساوي normal f
+
+161
+00:12:44,140 --> 00:12:49,150
+فنورمين الـ x أهم ناقص x لأن f is boundedالـ N as
+
+162
+00:12:49,150 --> 00:12:53,410
+N goes to infinity هذا بيروح لمين؟ للـ Zero إذاً و
+
+163
+00:12:53,410 --> 00:12:59,850
+هذا أكبر و سوء سفر إذاً F of X N هتروح لل F of X و
+
+164
+00:12:59,850 --> 00:13:04,470
+كانت F arbitrary قلمة X Prime إذاً هذا معناته إذا
+
+165
+00:13:04,470 --> 00:13:09,190
+X N بتروح لل X weekly إذا اللي هو ال strong
+
+166
+00:13:09,190 --> 00:13:12,770
+convergence واضح أنه بيعطي مين؟ اللي هو ال weak
+
+167
+00:13:12,770 --> 00:13:16,610
+convergenceيجي الآن بقول لك if the converse of A
+
+168
+00:13:16,610 --> 00:13:20,570
+is not true in general وخلّينا نشوف المثال أو ال
+
+169
+00:13:20,570 --> 00:13:25,750
+counter example اللي معطينيه اطلع لفوق شوية الان
+
+170
+00:13:25,750 --> 00:13:30,830
+let E N let E N be an orthonormal sequence in
+
+171
+00:13:30,830 --> 00:13:34,650
+Hilbert space mean H وقولنا ان ال ال ال ال ال
+
+172
+00:13:34,650 --> 00:13:38,110
+Hilbert space has an orthonormal اللي هو بنقدر
+
+173
+00:13:38,110 --> 00:13:41,350
+ناخد فيه an orthonormal sequenceBy Ray's
+
+174
+00:13:41,350 --> 00:13:44,450
+Representation Theorem اللي استخدمناها كثير تلاتة
+
+175
+00:13:44,450 --> 00:13:48,030
+تمانية واحد لدرجة ان احنا حافظنا رقمها By Ray's
+
+176
+00:13:48,030 --> 00:13:51,970
+Representation Theorem Any F المتنقطش برايم has a
+
+177
+00:13:51,970 --> 00:13:55,010
+representation F of X مش بيساوي X و Z و الـ Z ده
+
+178
+00:13:55,010 --> 00:13:59,590
+unique زي ما اتفجنا ماشي الحال طيب hence الان مدام
+
+179
+00:13:59,590 --> 00:14:02,270
+F of X بيساوي X و Z أكيد ال F of En تبع
+
+180
+00:14:02,270 --> 00:14:07,300
+الورتنورمال بيساوي En و 100 و Zماشي هذا الكلام
+
+181
+00:14:07,300 --> 00:14:12,380
+طبعا الان اي F element الـ H' له Z اللي هي بقدر
+
+182
+00:14:12,380 --> 00:14:19,180
+اكتب ال F بدللتها اتفقنا؟ طيب الان F of E N بساول
+
+183
+00:14:19,180 --> 00:14:24,270
+ال inner product بين E N و Zالان انا بتثبتلكم انه
+
+184
+00:14:24,270 --> 00:14:29,350
+اللي هو عند ال EN هذه converts to zero weekly لكن
+
+185
+00:14:29,350 --> 00:14:33,890
+مش strongly ماشي ال EN هذه ال orthonormal sequence
+
+186
+00:14:33,890 --> 00:14:36,510
+اللي هو اللي ماخدها في ال H بتثبتلكم انها تروح
+
+187
+00:14:36,510 --> 00:14:41,940
+weekly لل zero لكن مش strongly ده نشوف كدهالان
+
+188
+00:14:41,940 --> 00:14:45,240
+بالـ Bessel Inquality عشان أصل اللي .. اللي بديها
+
+189
+00:14:45,240 --> 00:14:48,460
+لو جيت أخدت اللي هو ال .. الـ Bessel Inquality
+
+190
+00:14:48,460 --> 00:14:51,260
+اللي مش ذاكرينها لقينا الربروضاكت بين الـ E ان
+
+191
+00:14:51,260 --> 00:14:55,360
+والـ Z تربيع من ان و نحد إلى مالة نهاية هذا أصغر و
+
+192
+00:14:55,360 --> 00:14:58,280
+ساوي من نور من Z التربيع، هذه اللي هي الـ Bessel
+
+193
+00:14:58,280 --> 00:15:03,580
+Inquality اللي أخدناها طيبالان معناته انه صارت هذه
+
+194
+00:15:03,580 --> 00:15:07,840
+ال series converge مزامها محدودة بمين بالقيمة اللي
+
+195
+00:15:07,840 --> 00:15:11,240
+هي norm of z مدام انها مرتبطت اذا ال limit اللي
+
+196
+00:15:11,240 --> 00:15:14,880
+جوا ايه شماله سفر انا بحكي عن number صرت هذا
+
+197
+00:15:14,880 --> 00:15:17,800
+absolute value معناه صرت number الان limit اللي
+
+198
+00:15:17,800 --> 00:15:20,740
+جوا ايه شماله سفر اذا هذا المقدار بروح ل zero as n
+
+199
+00:15:20,740 --> 00:15:26,040
+goes to infinityالان و هذا بيعطيني هذا صار اللي هو
+
+200
+00:15:26,040 --> 00:15:29,560
+ال absolute value له يروح لل zero برضه اذا اكيد
+
+201
+00:15:29,560 --> 00:15:32,180
+اللي هو ال F of EN اللي هو سوء EN و Z برضه هيروح
+
+202
+00:15:32,180 --> 00:15:37,800
+لمين لل zero واضح الان هذا المقدار راح لل صفر و
+
+203
+00:15:37,800 --> 00:15:42,260
+انا بعرف ان هذا المقدار تربيع ال FEN يعني صارت FEN
+
+204
+00:15:42,260 --> 00:15:45,600
+تربيع بتروح لل صفر اذا ال FEN نفسها هتروح لمين لل
+
+205
+00:15:45,600 --> 00:15:51,080
+zeroالـ 0 اللي هو عبارة عن الـ F of إيه عش؟ of 0
+
+206
+00:15:51,080 --> 00:15:58,420
+ماشي اللي هي as n goes since F المتنقضش prime هذا
+
+207
+00:15:58,420 --> 00:16:01,320
+اللي هو بيروح للـ 0 اللي هو بسوء إيه عش؟ F of 0
+
+208
+00:16:01,320 --> 00:16:06,540
+لأن F of 0 بسوء 0 لكل F linear functional عارفين
+
+209
+00:16:06,540 --> 00:16:09,440
+هذا المعلومة؟ since F المتنقضش prime was arbitrary
+
+210
+00:16:09,440 --> 00:16:16,070
+إذا EN هذه الـ EN هتروح لمين؟ للي هويعني الأن
+
+211
+00:16:16,070 --> 00:16:23,410
+أثبتتلكم F of E N بتروح لل F of Zero لكل F element
+
+212
+00:16:23,410 --> 00:16:27,810
+in H' هذا اللي أثبته هذا أيش معناته أن E N بتروح
+
+213
+00:16:27,810 --> 00:16:35,390
+لل Zero weekly إذا أثبتنا أن E N بتروح للصفر
+
+214
+00:16:35,390 --> 00:16:45,200
+weekly بل أثبت أن E N مستحيل تروحللسفر يعني مستحيل
+
+215
+00:16:45,200 --> 00:16:50,960
+ان يكون عندي Normal EN ناقص السفر ويساوي Normal EN
+
+216
+00:16:50,960 --> 00:16:58,280
+يروح لمين للسفر هذا الكلام مستحيل لسبب بسيط الان
+
+217
+00:16:58,280 --> 00:17:08,300
+اطلع لفوق احسبلي الانخُد أي N لا تساوى M وحسب
+
+218
+00:17:08,300 --> 00:17:13,280
+المسافة بين E M وE N ال E M إيش هي صفار صفار صفار
+
+219
+00:17:13,280 --> 00:17:17,420
+معدى عند ال Nth term واحد وال E N صفار صفار صفار
+
+220
+00:17:17,420 --> 00:17:21,640
+معدى عند ال Nth term بساوى واحدأذا سأقرا هذا الـ a
+
+221
+00:17:21,640 --> 00:17:25,360
+المقصي يعني عبارة عن كل هن أسفار معادة جزئين فيه
+
+222
+00:17:25,360 --> 00:17:29,180
+هن أش بيساوي واحد واحد فال summation الهن تربيع
+
+223
+00:17:29,180 --> 00:17:32,420
+لكل واحد الكل أص نص اللي هو عبارة عن واحد وكمان
+
+224
+00:17:32,420 --> 00:17:35,460
+واحد اتنين الكل أص نص مايصير جدياش اللي هو جدر
+
+225
+00:17:35,460 --> 00:17:38,340
+التنين إذا هذا اللي جوا نور مجدر التنين يعني
+
+226
+00:17:38,340 --> 00:17:42,880
+تربيعه أش بيساوي اتنين فاهمين اللي بحكيه؟أو إذا
+
+227
+00:17:42,880 --> 00:17:46,800
+حسبته بالشكل هذا E M و E N و E N و E N هذا ال E M
+
+228
+00:17:46,800 --> 00:17:51,760
+وال E M اللي هو norm واحد وهذا norm واحد اللي هو
+
+229
+00:17:51,760 --> 00:17:54,540
+بيصير norm اتنين وطبعا وال E M من علي ال E N لما
+
+230
+00:17:54,540 --> 00:17:59,880
+تفكه بيطلع سفر لإنهم orthonormal اتنين عامدين على
+
+231
+00:17:59,880 --> 00:18:03,440
+بعض وال E M وال E N برضه أيش بيساوي بيساوي سفرإذن
+
+232
+00:18:03,440 --> 00:18:09,360
+الـ N صارت هذه الـ Sequence E N مش كوشي لإن البعد
+
+233
+00:18:09,360 --> 00:18:12,360
+بينه نشمل و بساوي و بساوي و اتنين راحت N إلى مالة
+
+234
+00:18:12,360 --> 00:18:16,140
+نهاية و لا ال M إلى مالة نهاية لن يتغير الأبعاد
+
+235
+00:18:16,140 --> 00:18:20,560
+المسافات بين كل عنصر و الثاني ابعد عن بعض ففيش إيش
+
+236
+00:18:20,560 --> 00:18:24,380
+يروحه باتجاهه يعني بمعنى آخر E N صارت is not
+
+237
+00:18:24,380 --> 00:18:27,460
+cauchy إيش معنات is not cauchy و في إحنا في
+
+238
+00:18:27,460 --> 00:18:31,580
+complete space يعني معناها is not convergentإذا
+
+239
+00:18:31,580 --> 00:18:36,880
+الان EN is not .. does not converge مثلا does not
+
+240
+00:18:36,880 --> 00:18:41,760
+converge إذا normal EN هذا does not converge to
+
+241
+00:18:41,760 --> 00:18:47,340
+zero يعني بمعنى أخر EN does not converge strongly
+
+242
+00:18:47,340 --> 00:18:53,840
+to zero هاي مثلا نيجي الآن للي بعده اللي بعده في
+
+243
+00:18:53,840 --> 00:18:55,460
+حالة ال dimension
+
+244
+00:18:58,000 --> 00:19:02,080
+للـ X بيساوي مثلا ال K زي ما هو مسميها اللي هو
+
+245
+00:19:02,080 --> 00:19:07,860
+finite هيكون عند ال XM بتروح لل X weekly if and
+
+246
+00:19:07,860 --> 00:19:12,220
+only if XM بتروح لل X إشمالها strongly
+
+247
+00:19:15,220 --> 00:19:20,380
+الاتجاه هذا أثبتناه إذا نظل على يثبت أنه لما ال
+
+248
+00:19:20,380 --> 00:19:23,940
+dimension لل X بيساوي كده و كائنة Xn بتروح لل X
+
+249
+00:19:23,940 --> 00:19:29,320
+weekly يعطيني إن Normal Xn ناطس ال X بيروح لمين؟
+
+250
+00:19:29,320 --> 00:19:33,220
+لل Zero أو بمعنى آخر Xn بتروح لل X strongly واضح
+
+251
+00:19:33,220 --> 00:19:38,800
+الكلام، هي اللي بدي أثبته طيب شوفوا الآن كيف بدي
+
+252
+00:19:38,800 --> 00:19:44,780
+أكيد استعمل اللي هو ال dimension لل X is finiteلما
+
+253
+00:19:44,780 --> 00:19:47,860
+الـ dimension للـ X is finite إذن فيه bases صحيح
+
+254
+00:19:47,860 --> 00:19:52,280
+طيب إذا الأن suppose that XM بتروح ل X weakly and
+
+255
+00:19:52,280 --> 00:19:55,260
+dimension ل X بالساوة K وبيتثبت إن XM بتروح ل X
+
+256
+00:19:55,260 --> 00:19:59,240
+strongly لأن مدام الـ finite dimensional واسمه K
+
+257
+00:19:59,240 --> 00:20:03,460
+إذا بقدر أجرأ و أقول let E1 و E2 لعند الـ E كي بيه
+
+258
+00:20:03,460 --> 00:20:07,500
+أي basis of مين of X مدام basis ل X إذا أي
+
+259
+00:20:07,500 --> 00:20:12,730
+sequenceXn عناصرها X واحد في الـ X والـ X اتنين في
+
+260
+00:20:12,730 --> 00:20:15,910
+الـ X والـ Xn in general في الـ X إذا بقدر اكتبها
+
+261
+00:20:15,910 --> 00:20:19,090
+على صورة linear combination من مين؟ من عناصر ال
+
+262
+00:20:19,090 --> 00:20:24,310
+bases إذا صار عندي الـ Xn بيساوي Alpha J N يعني EJ
+
+263
+00:20:24,310 --> 00:20:28,490
+J من واحد عند K وAlpha J N هذي أشملها عبارة عن ال
+
+264
+00:20:28,490 --> 00:20:34,400
+scalars يعني الآن X واحداللي بيصير Alpha 1 1 Alpha
+
+265
+00:20:34,400 --> 00:20:41,980
+2 1 Alpha 3 1 Alpha 4 1 Alpha 5 K Alpha 1 Alpha K
+
+266
+00:20:41,980 --> 00:20:47,590
+1الأن X2 نفس الشيء X3 نفس الشيء إذا صارت عندي هذه
+
+267
+00:20:47,590 --> 00:20:51,030
+sequence of elements in mean in X الان برضه نفس
+
+268
+00:20:51,030 --> 00:20:56,830
+الشيء خد X بتساوي اللي هو summation لألف ج أيه جه
+
+269
+00:20:56,830 --> 00:20:59,710
+جه من عند واحد لعند مين لعند كيه برضه ليه ال
+
+270
+00:20:59,710 --> 00:21:03,370
+compilation من مين من العناصر الان by assumption
+
+271
+00:21:03,370 --> 00:21:06,430
+احنا ما احنا قولنا X ان بتروح لمين لل X weekly
+
+272
+00:21:06,430 --> 00:21:10,130
+كترت ال X ان بصورة هذه و كترت ال X بصورة هذه بناء
+
+273
+00:21:10,130 --> 00:21:13,510
+على ال dimension لل X بساوة K و هذا هو ال basisطيب
+
+274
+00:21:13,510 --> 00:21:16,770
+by assumption مدام x1 بتروح إلى x weekly إذا أنا
+
+275
+00:21:16,770 --> 00:21:19,270
+هيطلع عندي f of x2 بتروح إلى ال f of x لكل mean
+
+276
+00:21:19,270 --> 00:21:24,550
+لكل f element in x prime in particular ما هو ال x
+
+277
+00:21:24,550 --> 00:21:29,310
+prime اللي هو برضه ال dimension ياله k إذا فيه
+
+278
+00:21:29,310 --> 00:21:35,670
+باسيس باسيس تبعه اللي هو مثلا نسموه f1, f2أف تلاتة
+
+279
+00:21:35,670 --> 00:21:39,450
+لأنه functions لعند أف كي مظبوط ولا لأ نحن لا نعرف
+
+280
+00:21:39,450 --> 00:21:43,510
+ان ال dimension لل X كي ال X برايم برضه دايما مش
+
+281
+00:21:43,510 --> 00:21:47,710
+نقوله إيش بساوي بساوة كي إذن الآن in particular
+
+282
+00:21:47,710 --> 00:21:51,810
+مدام هذا الصحيح لكل العناصر تبعات الأف ال X برايم
+
+283
+00:21:51,810 --> 00:21:55,710
+إذا صحيحة برضه العناصر من ال bases اللي هى النمو
+
+284
+00:21:55,710 --> 00:21:58,590
+اللي من هنا مظبوط هذا اللي هو ال bases اللي هو
+
+285
+00:21:58,590 --> 00:21:59,610
+basis of
+
+286
+00:22:02,200 --> 00:22:07,520
+معايا؟ طيب شوفوا صارت عندي fj of xn بتروح لل fj of
+
+287
+00:22:07,520 --> 00:22:14,560
+x يعني f1 و f2 و f3 و f4 لكل اللي عند مين لعند ال
+
+288
+00:22:14,560 --> 00:22:20,440
+kطيب where fg of j من عناصر ال basis هذوله بيكون
+
+289
+00:22:20,440 --> 00:22:23,580
+fg of ej أشبه ساوي و ساوي واحد كل هذا مر علينا
+
+290
+00:22:23,580 --> 00:22:28,460
+سابقا and fj of m إيش هتساوي اك سفر لكل أملة تساوي
+
+291
+00:22:28,460 --> 00:22:33,260
+j إذا صار عندى الآن بناء على هذا الكلام لو أجيت
+
+292
+00:22:33,260 --> 00:22:38,790
+دخلت ال fj على ال xnكلن هيتصفرن بس هيدلل مين عندى
+
+293
+00:22:38,790 --> 00:22:45,250
+Alpha J اللي هي ال N معايا كلن هيتصفرن فبصير F J
+
+294
+00:22:45,250 --> 00:22:50,850
+of X N بسوا Alpha J مين N و F J of X هيتلع مين هو
+
+295
+00:22:50,850 --> 00:22:58,790
+ال Alpha J لأن F عملها
+
+296
+00:22:58,790 --> 00:23:09,330
+.. انتبهوالأن أحسبه Fj of xn بساوية Fj of الوه ال
+
+297
+00:23:09,330 --> 00:23:18,010
+summation Alpha 1n E1 زائد لما أصل لآخر واحدة
+
+298
+00:23:18,010 --> 00:23:24,710
+Alpha الوه KN EK ماشي
+
+299
+00:23:27,700 --> 00:23:37,740
+كل حيتصفر للجوا معدنين لرقمها Alpha J N E J حيصير
+
+300
+00:23:37,740 --> 00:23:41,040
+عنده هذا سفر و هذا سفر لأنه Linear تدخل عليها كل
+
+301
+00:23:41,040 --> 00:23:46,540
+زمان عند هدولة كلها نصفار معدنين لـ FJ of Alpha J
+
+302
+00:23:46,540 --> 00:23:51,040
+N E J و هد قيمتها إيش بتساوي هد بتطلع برا و هد
+
+303
+00:23:51,040 --> 00:23:56,860
+قيمتها واحد فبصير Alpha J NSimilarly, Fj of X
+
+304
+00:23:56,860 --> 00:24:01,340
+هتطلع مين؟ Alpha J بناء عليه مادام قولنا أن Fj of
+
+305
+00:24:01,340 --> 00:24:06,060
+X هتطلع Fj of X معناته أصبحت عندي Fj أن بدل هذه
+
+306
+00:24:06,060 --> 00:24:08,540
+بتروح لمين؟ للـ Alpha J
+
+307
+00:24:12,070 --> 00:24:17,330
+ألفا جي أن هتروح للألفا جي as n goes to infinity
+
+308
+00:24:17,330 --> 00:24:21,730
+وهذا لكل جي جي بتساوي واحد واثنين لعين جمين لعين
+
+309
+00:24:21,730 --> 00:24:26,310
+كي كل هنا دول أشمالي الصحيحة اطلع then خلصنا then
+
+310
+00:24:26,310 --> 00:24:31,190
+احسب للان normal xn ناقص normal x ايش بيساوي ال xn
+
+311
+00:24:31,190 --> 00:24:35,350
+هيقبلتهاوالـ X هي قيمتها طرحناها من بعض طلعت هذا
+
+312
+00:24:35,350 --> 00:24:39,030
+القيمة هذا اللي هو أصغر أو ساوي لل triangle
+
+313
+00:24:39,030 --> 00:24:41,990
+inequality ال absolute value هذا في ال norm هذا
+
+314
+00:24:41,990 --> 00:24:45,710
+هذا ايش معنى هذا الان الان الان الان الان الان
+
+315
+00:24:45,710 --> 00:24:46,150
+الان الان الان الان الان الان الان الان الان الان
+
+316
+00:24:46,150 --> 00:24:49,650
+الان الان الان الانإنه هذا as n goes to infinity
+
+317
+00:24:49,650 --> 00:24:52,490
+منها أنا alpha j ومن هنا ال alpha j تذهب إلى مين؟
+
+318
+00:24:52,490 --> 00:24:56,010
+إذن كل واحد منهم اللي جوه ال zero إذا المجموح اللي
+
+319
+00:24:56,010 --> 00:24:59,490
+هيروح لل zero إذا صارت عند ال x أنه تتقل إلى مين؟
+
+320
+00:24:59,490 --> 00:25:04,390
+إلى ال x weakly، strongly، under the condition x
+
+321
+00:25:04,390 --> 00:25:07,170
+أنه تذهب إلى ال x weakly عند ال dimension لل x
+
+322
+00:25:07,170 --> 00:25:13,350
+بساوة k أو finite example
+
+323
+00:25:18,930 --> 00:25:24,970
+الأول مثلًا الـ Hilbert space الـ Hilbert space Xn
+
+324
+00:25:24,970 --> 00:25:29,150
+تذهب إلى X weekly فان دول F Xn و Z تذهب إلى X و Z
+
+325
+00:25:29,150 --> 00:25:31,410
+for all Z مين in H
+
+326
+00:25:40,280 --> 00:25:44,740
+يكافئ أن نقول أن f of x which هي xn و z بتروح لل x
+
+327
+00:25:44,740 --> 00:25:47,820
+و z for all ليش هذا؟ هذا ما أحنا عارفينه، هذه
+
+328
+00:25:47,820 --> 00:25:54,300
+المعلومة سهلة فشو معناه أن xn بتروح لل x weekly؟
+
+329
+00:25:54,300 --> 00:26:01,650
+معناته هذا يكافئ أن f of xnبتروح لل F of X لكل FY
+
+330
+00:26:01,650 --> 00:26:05,770
+الموجودة في الـ X' صح ولا لأ؟ اللي هي الـ H' في
+
+331
+00:26:05,770 --> 00:26:09,490
+هذا الحالة لكن أنا بعرف من جهة أخرى، من الـ 381
+
+332
+00:26:09,490 --> 00:26:12,390
+الـ Raise Representation Theorem أنه لكل F element
+
+333
+00:26:12,390 --> 00:26:17,610
+في الـ H' اللي هو بقدر ألاجله F of X and can be
+
+334
+00:26:17,610 --> 00:26:23,160
+written as X ومين وZ صح؟ماشي؟ إذا يعني هذا ال
+
+335
+00:26:23,160 --> 00:26:27,820
+condition ماقدر أستبدله بإنه اللي هو xn و z بتروح
+
+336
+00:26:27,820 --> 00:26:31,600
+لل x و z for all z in H و التفاصيل اللي لكم طيب
+
+337
+00:26:31,600 --> 00:26:44,460
+اللي بعده الآن انقل بي .. انقل بي .. انقل بيأنا
+
+338
+00:26:44,460 --> 00:26:47,860
+طبعا بي أكبر واحدة صغيرة من infinity Xn بتروح لل X
+
+339
+00:26:47,860 --> 00:26:51,580
+weekly إذا وفقط إذا الشرطين التاليات يعني الآن
+
+340
+00:26:51,580 --> 00:26:55,860
+عندي شرطين يكافئن Xn بتروح لل X weekly الشرط الأول
+
+341
+00:26:55,860 --> 00:27:02,120
+ال sequence normal Xn أشماله is boundedالشرط
+
+342
+00:27:02,120 --> 00:27:07,440
+الثاني for every prefix j we have alpha jn بتروح
+
+343
+00:27:07,440 --> 00:27:15,280
+للxi j as n goes to infinity اللي هي حيث xn هذه
+
+344
+00:27:15,280 --> 00:27:21,820
+عبارة عن xi jn والx يمين هي xi j يعني هذه بتروحالـ
+
+345
+00:27:21,820 --> 00:27:25,640
+Xn بتروح للـ X weekly إذا كانها bounded والجزء
+
+346
+00:27:25,640 --> 00:27:30,260
+الثاني إنه كل واحدة من ال terms اللي هنا Alpha J
+
+347
+00:27:30,260 --> 00:27:35,880
+يعني Alpha واحد N بتروح للألف واحد Alpha اتنين N
+
+348
+00:27:35,880 --> 00:27:39,380
+بتروح للألف اتنين فاهمين؟ إيه الأخر؟ إيه المعنى
+
+349
+00:27:39,380 --> 00:27:42,800
+النهاية؟ هذا هذولة التانية مع بعض وكافئن هذولة
+
+350
+00:27:42,800 --> 00:27:49,130
+الآن هذه النظرية أو هذه اللي هي الخاصيةحنجيها اللي
+
+351
+00:27:49,130 --> 00:27:53,930
+هي خلّيني أقول automatic تطلع من مين؟ من اللمة بس
+
+352
+00:27:53,930 --> 00:27:57,050
+انت بيصير اللي .. اللي احنا بنحكي عنه ال ال ال ال
+
+353
+00:27:57,050 --> 00:27:57,950
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+354
+00:27:57,950 --> 00:27:58,490
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+355
+00:27:58,490 --> 00:27:58,670
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+356
+00:27:58,670 --> 00:27:59,830
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+357
+00:27:59,830 --> 00:28:03,030
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+358
+00:28:03,030 --> 00:28:03,030
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+359
+00:28:03,030 --> 00:28:10,750
+ال
+
+360
+00:28:10,750 --> 00:28:10,750
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+361
+00:28:10,750 --> 00:28:10,750
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+362
+00:28:10,750 --> 00:28:10,750
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+363
+00:28:10,750 --> 00:28:10,750
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+364
+00:28:14,670 --> 00:28:18,130
+ماشي الحل هو جايلك أصلا في الكتاب هذي left to the
+
+365
+00:28:18,130 --> 00:28:20,790
+reader ب exercise من مين من اللي تحته و بوضح بعض
+
+366
+00:28:20,790 --> 00:28:25,070
+الشغلات طيب خلّيني ان شاء الله اندي أشتغل على لمّة
+
+367
+00:28:25,070 --> 00:28:31,210
+أربعة تمانية سبعة اللي هي in general هذي بتقوللي
+
+368
+00:28:31,210 --> 00:28:36,890
+ان I know the space X in general we have X and
+
+369
+00:28:36,890 --> 00:28:42,900
+بتروح لل X weekly تكافئإنه الـ sequence normal XN
+
+370
+00:28:42,900 --> 00:28:47,920
+is bounded، هاي واحدة، اتنين، for every element of
+
+371
+00:28:47,920 --> 00:28:52,340
+a total M، اللي subset M of X' في اللي فوق الـ
+
+372
+00:28:52,340 --> 00:28:58,260
+total subset، اللي هي الـ An، total subset طيب،
+
+373
+00:28:58,260 --> 00:29:03,000
+for every element F of a total subset M of X'، we
+
+374
+00:29:03,000 --> 00:29:06,020
+have F of XN بتروح لمينال of X as M قصه نفيل
+
+375
+00:29:06,020 --> 00:29:11,650
+تانية، يعني، شوفواالآن لو جينا حللنا النظرية
+
+376
+00:29:11,650 --> 00:29:16,690
+بالمنبرهن Xn بتروح للـ X weekly، إيش معناتها؟ إن F
+
+377
+00:29:16,690 --> 00:29:21,030
+of Xn بتروح لل F of X لكل F element الـ main، الـ
+
+378
+00:29:21,030 --> 00:29:25,850
+X'اللي أنا هذا بقولك أنا هذا الشرط الكثير اللي
+
+379
+00:29:25,850 --> 00:29:31,530
+الهن كلهن بديش لكل أفوال من TX' بيثبت فيني ان يكون
+
+380
+00:29:31,530 --> 00:29:36,290
+لكل أفوال ما لها في total subset يعني جزء من X'
+
+381
+00:29:36,690 --> 00:29:41,130
+لكن بدها زجة شوية عشان تتفل ال weekly ان يكون norm
+
+382
+00:29:41,130 --> 00:29:44,890
+لكسرني إيش ماله is bounded بيعطيني هذا يؤدي إلى
+
+383
+00:29:44,890 --> 00:29:48,410
+هذا وهذا يؤدي لهذا هلاجيه اللي هو أمر سهل من
+
+384
+00:29:48,410 --> 00:29:52,680
+الخواص اللي قبل شوية حصلناهالأنه قبل بشوية قلنا
+
+385
+00:29:52,680 --> 00:29:57,160
+لما Xn تروح لل X weekly Normal Xn bounded برهنها
+
+386
+00:29:57,160 --> 00:30:00,520
+توه، هاي واحد اتنين، شو معناه Xn بتروح لل X
+
+387
+00:30:00,520 --> 00:30:05,140
+weekly؟ فإن F of Xn بتروح ل F of X لكل F من ضمن
+
+388
+00:30:05,140 --> 00:30:09,940
+انها دول، إذا هذا الاتجاهجاهز دل مين اطلع للي
+
+389
+00:30:09,940 --> 00:30:13,420
+اتجاه الثاني اذا if xn بتروح للي x weakly then a
+
+390
+00:30:13,420 --> 00:30:16,540
+follows from لما كذا and b follows from the
+
+391
+00:30:16,540 --> 00:30:18,860
+definition of weak convergence اللي حكيته قبل قليل
+
+392
+00:30:18,860 --> 00:30:23,620
+شوية اذا نطلع فوق وبدنا نثبت مين conversely طيب
+
+393
+00:30:23,620 --> 00:30:27,280
+نيجي الان conversely ونعني بعض الشغلات هيك الحلوة
+
+394
+00:30:27,280 --> 00:30:35,620
+بنعملها و بنصل للي بدنايالأن شو معناته أن total
+
+395
+00:30:35,620 --> 00:30:43,520
+set أن total set in X' معناته أن ال span للأم
+
+396
+00:30:43,520 --> 00:30:49,340
+أقل جاب بساومين X' هذا الان اللي هو ال bridge اللي
+
+397
+00:30:49,340 --> 00:30:54,960
+بدصل من خلاله لالمطلوب conversely suppose that A
+
+398
+00:30:54,960 --> 00:30:59,630
+and B holdو بدنا نتبط ان Xn بتروح للـ X weekly By
+
+399
+00:30:59,630 --> 00:31:06,580
+A مدام Xn bounded لنوم Xn أصغر سوى C لكل Nوالنورم
+
+400
+00:31:06,580 --> 00:31:10,840
+ال X أصغر أو يساوي C for sufficiently large mean
+
+401
+00:31:10,840 --> 00:31:15,520
+اللي هو mean C مدام ال XN بتروح ال N، النورم ال XN
+
+402
+00:31:15,520 --> 00:31:21,200
+أصغر أو يساوي C for all N، إذن automatically اللي
+
+403
+00:31:21,200 --> 00:31:25,580
+هي النورمها، اللي هو النورم ال X، هيكون ماله أصغر
+
+404
+00:31:25,580 --> 00:31:31,540
+أو يساوي Cاللي هو هذي طبعا أصغر يساوي C for all n
+
+405
+00:31:31,540 --> 00:31:35,880
+جارس نصف شالد ليه لاعيش C انك تختار C أشمالها
+
+406
+00:31:35,880 --> 00:31:39,780
+كبيرة كفاية انها تكفل ال .. ال .. ال .. since M is
+
+407
+00:31:39,780 --> 00:31:45,830
+total in X primeما دام total in X'، then for every
+
+408
+00:31:45,830 --> 00:31:49,530
+F in X'، there exists a sequence Fi in span لـM،
+
+409
+00:31:49,530 --> 00:31:54,710
+such that Fi بتروح لمن؟ لـF، dense، مش الآن هذه
+
+410
+00:31:54,710 --> 00:31:59,670
+dense في هذه A، إذا أي element هنا، بلاقي ال
+
+411
+00:31:59,670 --> 00:32:03,310
+sequence في اللي جوا، كون ذالك له،ماشي، تعريف ال
+
+412
+00:32:03,310 --> 00:32:08,600
+densityطيب الآن since M is total إذا ال span لـ M
+
+413
+00:32:08,600 --> 00:32:13,560
+بساوي X' then لكل F element in X' there exist a
+
+414
+00:32:13,560 --> 00:32:17,700
+sequence of I in span M such that F I بتروح لمين؟
+
+415
+00:32:17,700 --> 00:32:22,660
+لل F هايو since span ل M is dense in X' إذا مدام F
+
+416
+00:32:22,660 --> 00:32:26,900
+I بتروح لل F إذا بقدر أسغر المسافة جد ما بديThen,
+
+417
+00:32:27,100 --> 00:32:31,100
+for every Y أكبر من 0, there exists J such that
+
+418
+00:32:31,100 --> 00:32:39,810
+normal Fi-F أصغر من مين من Y على 3Cراحظوا ال
+
+419
+00:32:39,810 --> 00:32:43,790
+convergence في العالم
+
+420
+00:32:43,790 --> 00:32:49,050
+تبع x' يعني in the norm تبع x' يعني أصلا كل ال
+
+421
+00:32:49,050 --> 00:32:52,450
+convergence لما كنا نقول convergence في x زمان ال
+
+422
+00:32:52,450 --> 00:32:54,990
+convergence في ال x لما نحكي عليه with respect to
+
+423
+00:32:54,990 --> 00:32:59,050
+the norm يعني ال strong convergenceطيب إذا الأن
+
+424
+00:32:59,050 --> 00:33:02,790
+صار عندي normal fi ناقص f أصغر من أي إبسلون في
+
+425
+00:33:02,790 --> 00:33:05,970
+الدنيا من ضمنها y على تلاتة c ده استخدمها للحسابات
+
+426
+00:33:05,970 --> 00:33:09,810
+بعد شوية زي ما أنتوا عارفين لأن moreover since fi
+
+427
+00:33:09,810 --> 00:33:15,290
+element مسبان لل M then by B there is n such that
+
+428
+00:33:15,290 --> 00:33:21,310
+fi of x n ناقص fi of x أصغر من y على تلاتة for all
+
+429
+00:33:21,310 --> 00:33:27,420
+n أكبر من مين من اللي هي مين من n عنديFI of XN
+
+430
+00:33:27,420 --> 00:33:32,460
+ناقص FI of X التي أصغر من Y على 3 لكل N أكبر من
+
+431
+00:33:32,460 --> 00:33:40,420
+100 من N طيب أطلع لفوق then for all N أكبر من N we
+
+432
+00:33:40,420 --> 00:33:45,840
+have أحسب لـ FI of XN ناقص F of X هذه بالـ
+
+433
+00:33:45,840 --> 00:33:49,200
+Triangling Quality بدي أضيف ترم وأطرح ترم أصغر أو
+
+434
+00:33:49,200 --> 00:33:53,140
+يساوي اللي هو norm أو absolute value للـ FI of XN
+
+435
+00:33:53,140 --> 00:33:59,800
+ناقص FI of XN هي اللي ضفتهاوهنا طرحت او ضفت a5x
+
+436
+00:33:59,800 --> 00:34:05,420
+انا ناقص مين a5x زاد a5x ناقص a5x طرحت مين تنتين
+
+437
+00:34:05,420 --> 00:34:09,940
+ضفت تنتين اه ماشي الحل الان صار عندى الان الاولى
+
+438
+00:34:09,940 --> 00:34:16,450
+هذه اللى هو اصغر او شوية normal FI ناقص F وهذه X
+
+439
+00:34:16,450 --> 00:34:24,210
+زائد المفهومة هذه أصغر من مين من Y ع تلاتة وهذه FI
+
+440
+00:34:24,210 --> 00:34:27,590
+of X ناقص نفس اللي عملته في اللي فوق Normal FI
+
+441
+00:34:27,590 --> 00:34:32,870
+ناقص F في Normal مين ال X هذه الواحدة فيها اللي هو
+
+442
+00:34:32,870 --> 00:34:37,650
+FI ناقص F أصغر من Y ع تلاتة C وهذه أصغر أو شوه C
+
+443
+00:34:38,610 --> 00:34:42,370
+هذه زي ما هي وهذه نفس الاشي أصغر يساوي y ع تلاتة c
+
+444
+00:34:42,370 --> 00:34:46,510
+وهذه أصغر من c إذا اللي هو صارت عندي y ع تلاتة y ع
+
+445
+00:34:46,510 --> 00:34:49,970
+تلاتة y ع تلاتة أو يساوي إبسلون الآن صار عندي الآن
+
+446
+00:34:49,970 --> 00:34:54,130
+ال absolute value لل F of X نقص F of X أصغر أو
+
+447
+00:34:54,130 --> 00:34:59,130
+يساوي إبسلون و F كانت arbitrary إذا هذا معناته إنه
+
+448
+00:34:59,130 --> 00:35:03,130
+F of X هان بتروح لل F of X ك number إذا معناته X
+
+449
+00:35:03,130 --> 00:35:07,870
+هان بتروح لل X إيش ماله weekly و هيك بيكون احنا
+
+450
+00:35:08,660 --> 00:35:15,700
+خلصنا اللي هو المحاضرة نزل المحاضرة وان شاء الله
+
+451
+00:35:15,700 --> 00:35:18,920
+إلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/c4_dQ90VN3U_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/c4_dQ90VN3U_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c7ccd3a348bfb59ff7f24d2aa8d4af35fb26cb41
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/c4_dQ90VN3U_postprocess.srt
@@ -0,0 +1,2588 @@
+1
+00:00:05,260 --> 00:00:07,600
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,600 --> 00:00:10,240
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,240 --> 00:00:13,700
+آله والصحابي أجمعين هذه المحاضرة رقم تلاتة وتلاتين
+
+4
+00:00:13,700 --> 00:00:19,300
+مساق تحليل اقتراني أو تحليل دالي طلاب طالبات
+
+5
+00:00:19,300 --> 00:00:22,620
+الجامعة الإسلامية ماجستير وصلنا هنا عند أربعة تسعة
+
+6
+00:00:22,620 --> 00:00:25,460
+اللي هو convergence of sequences of operators and
+
+7
+00:00:25,460 --> 00:00:30,050
+functionalsاللي هان المرة الفاتة احنا حكينا طبعا
+
+8
+00:00:30,050 --> 00:00:32,910
+احنا حكينا عن اللي هو ال convergence في ال normed
+
+9
+00:00:32,910 --> 00:00:37,230
+space بالنسبة لل sequences في ال normed space قلنا
+
+10
+00:00:37,230 --> 00:00:39,570
+لو كان في عند ال sequence في ال normed space xn
+
+11
+00:00:39,570 --> 00:00:44,250
+بتروح لل x strongly و xn بتروح لل x اللي هو mean
+
+12
+00:00:44,250 --> 00:00:47,470
+weekly وعرفله شو معناته strongly وشو معناته weakly
+
+13
+00:00:48,150 --> 00:00:52,250
+لحظوا احنا ال .. ال .. ال .. عادة لما كنا نحكي لما
+
+14
+00:00:52,250 --> 00:00:55,270
+نشتغل في الـ Real Analysis أو في ال Complex لما
+
+15
+00:00:55,270 --> 00:00:57,770
+نحكي عن Convergence كنا نحكي عن Convergence واحد
+
+16
+00:00:57,770 --> 00:01:00,790
+اللي هو الـ X بتروح للـ X اللي هو مانحكيش لا
+
+17
+00:01:00,790 --> 00:01:04,790
+Weekly ولا Convergence ولا .. ولا Strongly تبع
+
+18
+00:01:04,790 --> 00:01:08,570
+للحديث، ركزوا في الكلمتين تبع للحديث إنه احنا في
+
+19
+00:01:08,570 --> 00:01:13,570
+الـ Rأو في الـ C الـ dimension للـ R أو للـ C is
+
+20
+00:01:13,570 --> 00:01:16,910
+finite فبما أنه is finite إذا بيكون ال weak و ال
+
+21
+00:01:16,910 --> 00:01:22,090
+strong إيش ما له اللي هو are the same الآن بأيضا
+
+22
+00:01:22,090 --> 00:01:25,770
+في لما كنا نحكي في التحليل في التحليل اللي هو
+
+23
+00:01:25,770 --> 00:01:30,190
+الحقيقي كنا لما نيجي نحكي عن sequence of functions
+
+24
+00:01:30,750 --> 00:01:34,850
+كنا نحكي عن نوعين من الـ convergence FN بتروح للـ
+
+25
+00:01:34,850 --> 00:01:38,290
+F اللي هو بنسكت، شو معناه F ان كنا نسميها
+
+26
+00:01:38,290 --> 00:01:41,710
+pointwise convergence وكنا نحكي عن convergence
+
+27
+00:01:41,710 --> 00:01:46,610
+تاني اللي هو FN بتروح uniformly لمين؟ للـ Fالآن
+
+28
+00:01:46,610 --> 00:01:51,370
+العالم الجديد هذا مشابه هحكي عن convergence لـ
+
+29
+00:01:51,370 --> 00:01:54,890
+functions هنا هحكي عن convergence ل operators اللي
+
+30
+00:01:54,890 --> 00:01:59,770
+هي دول برضه في النهاية الآن تبعاً للمنطق اللي
+
+31
+00:01:59,770 --> 00:02:03,170
+استشغلناه هنا برضه هيكون في عندى بدل اتنين من
+
+32
+00:02:03,170 --> 00:02:07,030
+انواع ال convergence هيكون في عندى اللي هو three
+
+33
+00:02:07,030 --> 00:02:12,320
+من ال convergenceطبعاً لأني أنا بحكي عن اللي هو
+
+34
+00:02:12,320 --> 00:02:16,460
+normed spaces in general أما الحديث في الـ real أو
+
+35
+00:02:16,460 --> 00:02:19,920
+كده كل حديث في number أو في finite dimensional
+
+36
+00:02:19,920 --> 00:02:24,940
+space خلينا نشوف كيف بدنا نحكي عن اللي هو ال
+
+37
+00:02:24,940 --> 00:02:29,280
+sequence of operators إيش الأنواع ال convergence
+
+38
+00:02:29,280 --> 00:02:33,160
+بالنسبة إليها اللي هندرسها let x and y be normed
+
+39
+00:02:33,160 --> 00:02:38,140
+space أو spaces a sequence TN of operators هذه T1
+
+40
+00:02:38,890 --> 00:02:41,990
+bounded linear operator T2 bounded linear operator
+
+41
+00:02:41,990 --> 00:02:45,450
+إلى آخر هي دي sequence من العناصر اللي هي من ال
+
+42
+00:02:45,450 --> 00:02:48,530
+bounded linear operators اللي في B X Y ده set of
+
+43
+00:02:48,530 --> 00:02:52,430
+all bounded linear operators من X لعندي M لعندي I
+
+44
+00:02:52,430 --> 00:02:56,270
+إذا عرفنا العالم اللي بنشتغل فيه اللي هو عبارة عن
+
+45
+00:02:56,270 --> 00:03:01,830
+B of X وY وعناصره اللي هي عناصر ال sequence TN من
+
+46
+00:03:01,830 --> 00:03:06,370
+هذا اللي هو ال space اللي هم بده يبدأ يعرفكم إيش
+
+47
+00:03:06,370 --> 00:03:11,320
+ال convergence واحدuniformly convergent if TN
+
+48
+00:03:11,320 --> 00:03:18,780
+converges in the norm of B X Y مجرد
+
+49
+00:03:18,780 --> 00:03:23,340
+اللي هي مين بنحكي في ال norm تبع مين تبع ال B نفسه
+
+50
+00:03:23,340 --> 00:03:27,040
+اللي هو that is there is T من X لعند Y such that
+
+51
+00:03:27,040 --> 00:03:30,120
+norm TN نقص T بتروح ل 0 as N goes from mean to
+
+52
+00:03:30,120 --> 00:03:34,810
+infinityإذن وكان إنه شبيه بالـ Strongly بس هنا الـ
+
+53
+00:03:34,810 --> 00:03:39,270
+Strongly كان جاعد في الـ X هذا جاعد في مين؟ في الـ
+
+54
+00:03:39,270 --> 00:03:45,570
+Bxy لإن الـ X عناصره Xn بتروح للـ X Strongly
+
+55
+00:03:45,570 --> 00:03:49,450
+معناته Normal Xn نقص الـ X بتروح لـ Zero هنا الآن
+
+56
+00:03:49,450 --> 00:03:55,610
+العناصر هنا دوالTn بتروح للـT اللي هو with respect
+
+57
+00:03:55,610 --> 00:03:59,610
+to space هذا strongly اسمه لكن عشان نميزه عن
+
+58
+00:03:59,610 --> 00:04:04,670
+strongly اللي بعد شوية هنقول عنه uniformly يعني Tn
+
+59
+00:04:04,670 --> 00:04:13,310
+بتروح للـT uniformly معنى بإن نورم الـTn ناقص T هو
+
+60
+00:04:13,310 --> 00:04:17,450
+اللي بيروح لمين للـ0 والنورم هذا هو النورم تبع مين
+
+61
+00:04:17,450 --> 00:04:23,730
+تبع الـP X أو Yفي convergence آخر اللي هو بنقول
+
+62
+00:04:23,730 --> 00:04:27,390
+strongly convergence شبيه بال pointwise
+
+63
+00:04:27,390 --> 00:04:33,410
+convergence تبع زمان اللي هو إيش بقول اطلع لفوق if
+
+64
+00:04:33,410 --> 00:04:37,870
+TN X converge strongly in Y for every mean X
+
+65
+00:04:37,870 --> 00:04:43,270
+element in X إذا الآن بنيجي عندى في عندى sequence
+
+66
+00:04:43,270 --> 00:04:51,510
+TN في الـP XY في الـ BX و Y TN في الـ BX و Y عند
+
+67
+00:04:51,510 --> 00:04:56,590
+TN في الـ BX و Y و بناخد أي X وين موجودة في الـ X
+
+68
+00:04:56,590 --> 00:05:03,710
+أي X وين موجودة في الـ X بدي أحكي عن اللي هو TNX
+
+69
+00:05:03,710 --> 00:05:08,490
+converged لمين لـ TX هذه الـ sequence صارت of
+
+70
+00:05:08,490 --> 00:05:12,270
+elements وين موجودة في الـ Y بس بحكي عن X محددة
+
+71
+00:05:12,270 --> 00:05:19,730
+وين موجودة في الـ X بقول TNXبتروح للـ TX strongly
+
+72
+00:05:19,730 --> 00:05:27,710
+إذا كان نورم الـ TNX ناقص TX بروح للـ 0 as N goes
+
+73
+00:05:27,710 --> 00:05:30,810
+from mean to infinity لحظة أنا شغلي هذا نورم الـ
+
+74
+00:05:30,810 --> 00:05:34,090
+TNX والـ TX وين موجود في الـ Y وكأن عالم اللي
+
+75
+00:05:34,090 --> 00:05:38,210
+بشتغل فيه مين هو اللي هو الـ Y اطلع لفوق
+
+76
+00:05:42,260 --> 00:05:46,360
+وإذا كانت تتعامل بشكل قوى إذا كانت T و X تتعامل
+
+77
+00:05:46,360 --> 00:05:52,480
+بشكل قوى بشكل Y لكل X في أقل X، هذا يعني أن هناك T
+
+78
+00:05:52,480 --> 00:05:56,660
+في أقل X و Y مثل ذلك، نورم T و X يذهب إلى T و X
+
+79
+00:05:56,660 --> 00:06:01,560
+نقص T و X يذهب إلى Zero كما أن N يذهب إلى أقل لكل
+
+80
+00:06:01,560 --> 00:06:05,880
+X في أقل من من في X هو لو تعمقت في القمر و في
+
+81
+00:06:05,880 --> 00:06:09,980
+الواقع اللي هو T و X تذهب إلى T و X بشكل قوى في
+
+82
+00:06:09,980 --> 00:06:16,990
+من؟في النوم تبع ال Yوهذه Tn بتروح للـ T strongly
+
+83
+00:06:16,990 --> 00:06:22,050
+برضه بس في الـ norm تبع ال B هذه بنسميها اللي هي
+
+84
+00:06:22,050 --> 00:06:26,190
+uniform convergence لأهمية ال convergence هذا اللي
+
+85
+00:06:26,190 --> 00:06:31,330
+هو .. او لعدم اعتماد Tn-T في ال convergence على ال
+
+86
+00:06:31,330 --> 00:06:36,250
+X المحددة هنا اللي كنا نسميه زمان ال uniform
+
+87
+00:06:36,250 --> 00:06:39,150
+convergence في ال functions العادية وهذه كنا
+
+88
+00:06:39,150 --> 00:06:43,590
+نسميها pointwise convergenceالان هذولا النوعين ما
+
+89
+00:06:43,590 --> 00:06:47,430
+كانوا نوعين قديمات الان النوع الثالث الجديد اللي
+
+90
+00:06:47,430 --> 00:06:50,550
+هو الـ weakly convergent اللي هو الـ weakly
+
+91
+00:06:50,550 --> 00:06:54,630
+convergent ان الـ TNX converge اللي هو ايه اش ماله
+
+92
+00:06:54,630 --> 00:07:03,150
+weakly to some T ماشي الحال الان TNX شو معناه TN
+
+93
+00:07:03,150 --> 00:07:07,690
+TN X
+
+94
+00:07:09,460 --> 00:07:15,880
+converges weakly to TX نفس اللي قدلنا المرة اللي
+
+95
+00:07:15,880 --> 00:07:19,600
+فاتت يعني مش ليش جديد نفس اللي حكينا عنه في
+
+96
+00:07:19,600 --> 00:07:25,080
+المحاضرة اللي فاتت for every F element اللي هو N
+
+97
+00:07:25,080 --> 00:07:33,120
+اللي هي الـY' عندي يجب أن يكون F of T and X ناقص F
+
+98
+00:07:33,120 --> 00:07:40,560
+of T Xconverge to zero as n goes to infinity الان
+
+99
+00:07:40,560 --> 00:07:44,220
+واحده انه هذا وهذا هيصير زي بعض في حالة الـ finite
+
+100
+00:07:44,220 --> 00:07:48,640
+dimensional space عشان هيك احنا مابنحكيش عنه في ال
+
+101
+00:07:48,640 --> 00:07:50,880
+.. في ال .. في الـ real العادى ولا في ال complex
+
+102
+00:07:50,880 --> 00:07:54,640
+العادى بنحكي عن نوعين من ال convergence لل
+
+103
+00:07:54,640 --> 00:07:58,340
+functions او لل operators واحد اسمه uniformly واحد
+
+104
+00:07:58,340 --> 00:08:02,780
+اسمه pointwiseالآن هذا عنا هنا هنسميه uniformly
+
+105
+00:08:02,780 --> 00:08:07,440
+uniformly هنسمي ال point wise strongly و هنسمي ال
+
+106
+00:08:07,440 --> 00:08:11,680
+weakly اللي هو بالتسمياء و بالمفهوم اللي حكيناه
+
+107
+00:08:11,680 --> 00:08:16,340
+المرة اللي فاتت في المحاضرة السابقة نيجي الآن واضح
+
+108
+00:08:16,340 --> 00:08:22,600
+واضح أنه من خلال التعريف اللي حكيناها أنه ال TN
+
+109
+00:08:22,600 --> 00:08:27,660
+أنه
+
+110
+00:08:27,660 --> 00:08:31,590
+لما نقول TNالـ Uniform Convergence، الـ Operator
+
+111
+00:08:31,590 --> 00:08:34,930
+Convergence، يعني قوة قوة قوة قوة قوة قوة قوة قوة
+
+112
+00:08:34,930 --> 00:08:38,110
+قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة
+
+113
+00:08:38,110 --> 00:08:38,570
+قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة
+
+114
+00:08:38,570 --> 00:08:39,550
+قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة
+
+115
+00:08:39,550 --> 00:08:40,650
+قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة
+
+116
+00:08:40,650 --> 00:08:48,150
+قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة
+
+117
+00:08:48,150 --> 00:08:54,050
+قو
+
+118
+00:08:55,430 --> 00:09:00,010
+شو معناته اللي هو اللي هو عندي طبعا الـ TN عجبه عن
+
+119
+00:09:00,010 --> 00:09:06,090
+sequence element in B X Y و الـ T برضه element in
+
+120
+00:09:06,090 --> 00:09:15,150
+B X Y اللي هو شو معناته انه uniformly ال norm TN
+
+121
+00:09:15,150 --> 00:09:22,150
+نقص T تروح للـ 0 as N goes to infinity لان letاللي
+
+122
+00:09:22,150 --> 00:09:32,450
+هو TN X هالجي تاخد for every X element in X let TN
+
+123
+00:09:32,450 --> 00:09:38,050
+X converge لمين لـ TX strongly إيش معناته معناته
+
+124
+00:09:38,050 --> 00:09:43,130
+norm الـ TN X نقص TX اللي هو إيش مهلا بروح لصفر
+
+125
+00:09:43,130 --> 00:09:47,670
+هذا اللي بدأ تبته صح؟ الآن بدأ أثبت هذه مانعش أقول
+
+126
+00:09:47,670 --> 00:09:52,490
+it بدأ أثبت هذهأخذت X أشمالها arbitrarily وحسبني
+
+127
+00:09:52,490 --> 00:09:58,090
+الآن norm of TN X ناقص مين TX هذا بتساوي norm of
+
+128
+00:09:58,090 --> 00:10:03,870
+TN ناقص T X وهذه اللي هي أصغر تساوي norm of TN
+
+129
+00:10:03,870 --> 00:10:09,170
+ناقص T في norm X مدام strongly إذا هذا بيروح لـ0
+
+130
+00:10:09,170 --> 00:10:16,120
+إذا هذا بيروح لـ0 إذا صارت TN Xهتروح للـ TX
+
+131
+00:10:16,120 --> 00:10:20,700
+strongly وهو المطلوب التاني سهل نفس الأسلوب الآن
+
+132
+00:10:20,700 --> 00:10:27,500
+بتاخد let X element in X و F element in main in Y'
+
+133
+00:10:27,780 --> 00:10:30,700
+عشان أثبت main ال weekly
+
+134
+00:10:33,690 --> 00:10:38,870
+وبنفسي نفسي نفسي الأسلوب حتتاني أه الآن احنا
+
+135
+00:10:38,870 --> 00:10:41,950
+أثبتنا في ال .. في ال .. في ال .. في خلينا نقول في
+
+136
+00:10:41,950 --> 00:10:44,110
+ال normed space العادى الآن ده أثبتها لمي لل
+
+137
+00:10:44,110 --> 00:10:48,530
+operators برضه هيكون مشابه مشابه خالص الان norm
+
+138
+00:10:48,530 --> 00:10:58,610
+norm الحسبولي F of TN X ناقص F of TX فاهمين أه هذا
+
+139
+00:10:58,610 --> 00:11:04,290
+أصغر بسبب نورم ال F في norm ال TN ناقص Tفي نور
+
+140
+00:11:04,290 --> 00:11:08,550
+مين؟ الـ X هذا دستور مباشر أنه الـ uniform اللي
+
+141
+00:11:08,550 --> 00:11:13,650
+بيقدي ل مين؟ لل strongly هذا اللي هو بيبقى بيروح
+
+142
+00:11:13,650 --> 00:11:19,730
+لل zero as n goes to infinity إذاً F of T and X
+
+143
+00:11:19,730 --> 00:11:27,570
+بتروح لل F of T Xهذا أثبت لكم مين الـ uniformly
+
+144
+00:11:27,570 --> 00:11:34,810
+أدى إلى مين إلى الـ weekly يعني TNX
+
+145
+00:11:34,810 --> 00:11:39,470
+بتروح لTX
+
+146
+00:11:39,470 --> 00:11:42,750
+تقولوا معايا TNX بتروح لTX weekly
+
+147
+00:11:47,050 --> 00:11:50,310
+أثبتت أن F of T and X نقص F of T X بروح للـ Zero
+
+148
+00:11:50,310 --> 00:11:54,270
+As N goes to infinity لكل F element in Y' و X
+
+149
+00:11:54,270 --> 00:11:56,890
+element in X' هذا يعني أن T and X بتروح للـ T X
+
+150
+00:11:56,890 --> 00:12:00,930
+أشمالها Weekly هذا أثبته من وين؟ من الـ Uniform
+
+151
+00:12:00,930 --> 00:12:04,390
+يؤدي إلى الـ Weekly مباشرة Strong يؤدي إلى الـ
+
+152
+00:12:04,390 --> 00:12:09,070
+Weekly ما أثبته قبل بشوية أي سؤال؟ طيب يلّا لبعده
+
+153
+00:12:14,430 --> 00:12:17,570
+الأن الـ Converse لا يجب أن يكون عاملًا يعني فيه
+
+154
+00:12:17,570 --> 00:12:22,370
+في عندك اللي هو strong operator convergence لا يجب
+
+155
+00:12:22,370 --> 00:12:26,070
+أن يكون من ال uniform يعني بقدر أجيبلك اللي هو
+
+156
+00:12:26,070 --> 00:12:30,130
+strong convergence لكن ماله مش uniform convergence
+
+157
+00:12:30,130 --> 00:12:36,530
+خد الآن let TN be a sequence of operators where TN
+
+158
+00:12:36,530 --> 00:12:41,420
+من L2 لعند ما L2 is defined byانت عارفين طبعا ايش
+
+159
+00:12:41,420 --> 00:12:46,060
+الـ Normal على الـ L2 وكيف بنحسم وكيف كده المفروض
+
+160
+00:12:46,060 --> 00:12:51,080
+هذا كله يعني معلوم لنا من خلال اللي هي اللي هي
+
+161
+00:12:51,080 --> 00:12:56,800
+معلوماتنا في المادة سابقا نيجي الآن نشوف ايش اللي
+
+162
+00:12:56,800 --> 00:13:02,250
+بدنا نسويه بالظبطبدنا نجيب operator الآن أو
+
+163
+00:13:02,250 --> 00:13:07,430
+sequence of operators إنها الـ T and X بتروح للـ
+
+164
+00:13:07,430 --> 00:13:11,330
+TX هذا forever X اللي منتقلته الـ T and X بتروح
+
+165
+00:13:11,330 --> 00:13:18,080
+للـ TX strongly طبعا ولكن butنورم الـ TN ناقص الـ
+
+166
+00:13:18,080 --> 00:13:22,740
+T does not converge to 0 يعني الـ TN بتروحش لمن؟
+
+167
+00:13:22,740 --> 00:13:26,500
+للـ T uniformly يعني بدنا نثبت أن الـ TN does not
+
+168
+00:13:26,500 --> 00:13:32,060
+converge uniformly لمن؟ للـ T لمّا نجيب الـ
+
+169
+00:13:32,060 --> 00:13:35,080
+Sequence T نجيب الـ T إيش الـ space اللي اختارنا
+
+170
+00:13:35,080 --> 00:13:40,160
+اللي نشتغل عليه؟ الـ L2 مين هو ال operator؟ اللي
+
+171
+00:13:40,160 --> 00:13:46,870
+هو ال operator التالي TNمن الـ 2 عند الـ 2 كيف بدي
+
+172
+00:13:46,870 --> 00:13:50,950
+أعرفه ال element اللي في ال ال 2 ال X بيساوي كصي
+
+173
+00:13:50,950 --> 00:13:56,910
+واحد كصي اتنين كصي تلاتة كصي N كصي N زائد واحد إلى
+
+174
+00:13:56,910 --> 00:14:01,050
+مال نهاية ماشي هذا عنصر مين ال ال 2 الأن بدي
+
+175
+00:14:01,050 --> 00:14:05,810
+أعرفلكم ال TN إيش ال TN بتسوي بتيجي بتاخد لك ال X
+
+176
+00:14:05,810 --> 00:14:10,550
+هذا TN X بتيجي بت .. بت .. بت .. كل اللي قالها
+
+177
+00:14:10,550 --> 00:14:17,190
+هدولة بتسفرهابترسله هنا مين؟ لـ Zero Zero Zero
+
+178
+00:14:17,190 --> 00:14:22,390
+Zero عن طبعا هذا الـ N لهذه اللي هو Zn زائد واحد
+
+179
+00:14:22,390 --> 00:14:26,390
+او Xn زائد واحد Xn زائد اتنين و بيظل ماشي إلى ماله
+
+180
+00:14:26,390 --> 00:14:35,040
+نهاية يعني و كأنه بيقولي T1 X بساوي Zero X2T2X
+
+181
+00:14:35,040 --> 00:14:46,920
+بيساوي 0 0 X3 و بكمل T3X بيساوي 0 0 0 X4 X5 و بكمل
+
+182
+00:14:46,920 --> 00:14:50,340
+ماشي الحال إذا نوضح إيش ال sequence of operators
+
+183
+00:14:50,340 --> 00:14:55,470
+اللي عندى معاياهذه اللي هي الـ sequence of
+
+184
+00:14:55,470 --> 00:14:58,590
+operators where x اللي هي زي ما قلنا size J اللي
+
+185
+00:14:58,590 --> 00:15:02,770
+قلته it is easy to see that TN is linear for any N
+
+186
+00:15:02,770 --> 00:15:08,090
+Linear فهي سهل اثباتها خدوا الـ N X هيها خدوا Y
+
+187
+00:15:08,090 --> 00:15:13,450
+بساوي جامعة واحد جامعة اتنين لما لا نهاية الان T
+
+188
+00:15:13,450 --> 00:15:20,050
+Alpha X زائد Y فمين هو في ده اعملها TN بساوية TN
+
+189
+00:15:21,090 --> 00:15:26,510
+أيش α X زائد Y؟ اللي هي Alpha Xi 1 زائد Gamma 1
+
+190
+00:15:26,510 --> 00:15:32,030
+Alpha Xi 2 زائد Gamma 2 وبتظلها ماشية، ماشي؟ أيش
+
+191
+00:15:32,030 --> 00:15:35,530
+بتعمل ال Tn هذه؟ بتقول هي سفر، سفر و بيظل الأسافر
+
+192
+00:15:35,530 --> 00:15:41,510
+عند مين؟ Alpha N زائد 1 Alpha Xi N زائد 1 زائد
+
+193
+00:15:41,510 --> 00:15:45,550
+Gamma N زائد 1 و بتكمل، ماشي؟ اللي أنا بفصلها
+
+194
+00:15:45,550 --> 00:15:51,870
+الأجزاء، بسهولاللي هو Alpha في Zero Zero Zero و
+
+195
+00:15:51,870 --> 00:15:56,370
+Exide N زائد واحد و Exide N زائد اتنين و بنكمل
+
+196
+00:15:56,370 --> 00:16:03,510
+زائد Zero Zero Zero Gamma N زائد واحد و لما لا
+
+197
+00:16:03,510 --> 00:16:07,670
+نهاية و يساوي هذه Alpha هذه كلها مين هي عبارة عن
+
+198
+00:16:07,670 --> 00:16:13,710
+TN X و هذه مين هي TN Y إذا TN إزلينا و طول ما
+
+199
+00:16:13,710 --> 00:16:18,410
+تكتشف TN إيش معناها إزليناAlso for any n sense
+
+200
+00:16:18,410 --> 00:16:23,490
+norm of TNX بيحسبوا الـ TNX مين ال TNX اللي هي
+
+201
+00:16:23,490 --> 00:16:29,710
+هذولة هي هنا ال TNX هيها summation هذا تربيع زائد
+
+202
+00:16:29,710 --> 00:16:31,290
+هذا تربيع زائد هذا تربيع زائد هذا تربيع زائد هذا
+
+203
+00:16:31,290 --> 00:16:32,270
+تربيع زائد هذا تربيع زائد هذا تربيع زائد هذا تربيع
+
+204
+00:16:32,270 --> 00:16:32,630
+زائد هذا تربيع زائد هذا تربيع زائد هذا تربيع زائد
+
+205
+00:16:32,630 --> 00:16:32,790
+هذا تربيع زائد هذا تربيع زائد هذا تربيع زائد هذا
+
+206
+00:16:32,790 --> 00:16:32,810
+تربيع زائد هذا تربيع زائد هذا تربيع زائد هذا تربيع
+
+207
+00:16:32,810 --> 00:16:32,930
+زائد هذا تربيع زائد هذا تربيع زائد هذا تربيع زائد
+
+208
+00:16:32,930 --> 00:16:38,060
+هذا تربيع زائد هذا تربيعصار عندي طبعا الأول هدول
+
+209
+00:16:38,060 --> 00:16:41,800
+الأن أسفار فهيبدأ العد من وين؟ من n زاد واحد إلى
+
+210
+00:16:41,800 --> 00:16:45,720
+مال النهاية أكيد هو هذا أصغر أو شاوي العد من واحد
+
+211
+00:16:45,720 --> 00:16:48,060
+إلى مال النهاية هذا العد من واحد إلى مال نهاية هو
+
+212
+00:16:48,060 --> 00:16:52,380
+نورم ال X إذا صار نورم ال TL X أصغر أو شاوي مين؟
+
+213
+00:16:52,600 --> 00:16:56,800
+نورم الـ X اطلع لفوق الان اخدوا الان ال supermom
+
+214
+00:16:56,800 --> 00:17:01,080
+على نورم ال X بيصير ال supermom ايه؟ نورم ال TN
+
+215
+00:17:01,080 --> 00:17:06,260
+أكبر أو يسوى واحد اخلقوا معناه، ماشي؟ الان لو
+
+216
+00:17:06,260 --> 00:17:08,720
+اجينا .. بدي اثبتلك ان نورم ال TN أكبر أو يسوى
+
+217
+00:17:08,720 --> 00:17:12,220
+واحد بيصير نورم ال TN أيش بيسوى؟ بيسوى واحد و هذا
+
+218
+00:17:12,220 --> 00:17:14,960
+اللي هيخليني انه .. يعني أستحين انه .. ان النورم
+
+219
+00:17:14,960 --> 00:17:19,700
+يروح لمين؟ للسفر؟ نورم ال TN نقصتي؟ شوفوا moreover
+
+220
+00:17:19,700 --> 00:17:24,720
+if we choose X0بساوة صفر صفر صفر يعني هنرسلها
+
+221
+00:17:24,720 --> 00:17:30,320
+نفسها اه فبصير يعني اخدت هذه هي ال X note عساس انه
+
+222
+00:17:30,320 --> 00:17:33,780
+يصير TN X note ايش الساوية لإنه هيسفر المهمة
+
+223
+00:17:33,780 --> 00:17:37,890
+بصفرات مراسل فبتطلع TN X note بساوية X noteاللي
+
+224
+00:17:37,890 --> 00:17:41,070
+هنأنصره نورم الـ TN اللي هو الـ suprem of ما هين
+
+225
+00:17:41,070 --> 00:17:44,970
+كلين أكيد أكبر و سوى نورم ال specific value ال
+
+226
+00:17:44,970 --> 00:17:50,350
+specific function هذه أو specific computation عند
+
+227
+00:17:50,350 --> 00:17:53,550
+X0 يعني بمعنى آخر عن نورم الـ X0 هدي زي هدي بيطلع
+
+228
+00:17:53,550 --> 00:17:56,610
+أشمال واحد إذا نورم الـ TN أكبر سوى واحد إذا نصر
+
+229
+00:17:56,610 --> 00:18:00,040
+من التنتين مع بعض نورم الـ TN بيسوى واحدومنه
+
+230
+00:18:00,040 --> 00:18:04,760
+احسبوله الان norm of TN نقص Zero اللي احنا متوقعين
+
+231
+00:18:04,760 --> 00:18:09,020
+يروح عليه point اللي هو strong convergence ال TN
+
+232
+00:18:09,020 --> 00:18:12,960
+نقص Zero Zero operator بيساوي norm of TN ايش اللي
+
+233
+00:18:12,960 --> 00:18:17,220
+بيساوي؟ بيساوي واحد اذا هذا يستحيل يروح لمين؟
+
+234
+00:18:17,220 --> 00:18:23,270
+للصفرأذا T يعني غير الـ T1 و T2 و T3 و مش هيروح لا
+
+235
+00:18:23,270 --> 00:18:27,830
+إشي مش هيروح للصفر هيضلوا إش ما لواحد إذا which
+
+236
+00:18:27,830 --> 00:18:31,630
+implies that Tn is not uniformly convergent to
+
+237
+00:18:31,630 --> 00:18:35,350
+mean to the zero operator أنا بدأ أثبتلك الآن but
+
+238
+00:18:35,350 --> 00:18:40,350
+it converges strongly to the zero operator يعني
+
+239
+00:18:40,350 --> 00:18:44,850
+but it is clear that for all x element in L2 we
+
+240
+00:18:44,850 --> 00:18:50,810
+haveخد TNX احسب في موقع 4X معادل هي TNX as N goes
+
+241
+00:18:50,810 --> 00:18:54,930
+to infinity بسفر بسفر بسفر بسفر بسفر بسفر بسفر
+
+242
+00:18:54,930 --> 00:18:55,530
+بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر
+
+243
+00:18:55,530 --> 00:18:57,330
+بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر
+
+244
+00:18:57,330 --> 00:19:00,810
+بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر
+
+245
+00:19:00,810 --> 00:19:06,370
+بسفر بسفر بسللـ Zero operator إذا صار عندي هذا TN
+
+246
+00:19:06,370 --> 00:19:09,810
+converts strongly to اللي هو Zero operator إذا صار
+
+247
+00:19:09,810 --> 00:19:13,330
+عندي مثال uniformly convergent ب .. ب .. ب .. ب
+
+248
+00:19:13,330 --> 00:19:16,250
+strongly convergent which is not uniformly
+
+249
+00:19:16,250 --> 00:19:20,970
+convergent الآن بدنا ناخد مثال تاني اللي هو ال
+
+250
+00:19:20,970 --> 00:19:23,870
+weak operator convergence need not imply mean
+
+251
+00:19:23,870 --> 00:19:30,370
+strong operator إيش convergence الآن مثال .. مثال
+
+252
+00:19:30,370 --> 00:19:31,450
+برضه على دوال
+
+253
+00:19:36,310 --> 00:19:42,310
+الآن برضه عديالة نشوف الآن تشغلوش بالكم خلوكم
+
+254
+00:19:42,310 --> 00:19:45,630
+معايا الامتحان ينسوا الامتحان الـ weak operator
+
+255
+00:19:45,630 --> 00:19:48,310
+convergence لا يجب أن يمثل الـ strong operator
+
+256
+00:19:48,310 --> 00:19:52,870
+convergence ناخد الـ sequence اللي بتلبي هذا الغرض
+
+257
+00:19:52,870 --> 00:19:58,590
+شوفوا اللي هي برضه أنا هشتغل ع مين على الـ Hilbert
+
+258
+00:19:58,590 --> 00:20:02,470
+space أو الـ L2 أو الـ Hilbert sequence space
+
+259
+00:20:12,990 --> 00:20:22,930
+خدلي الان TN من الـ 2 لعند الـ L2 و خدلي طبعا اللي
+
+260
+00:20:22,930 --> 00:20:28,150
+هي معهودة X بتساوي XI I I من واحد إلى ملا نهاية
+
+261
+00:20:28,150 --> 00:20:36,570
+خدلي ال TN X بساوي الان سفرلي N مرة سفرها لكن لو
+
+262
+00:20:36,570 --> 00:20:40,880
+سمحت خليلي الباقي زي ما هو يعني اعملي shiftلأ الـ
+
+263
+00:20:40,880 --> 00:20:45,280
+operator هيك shift للـ X ارميها صفار صفار صفار N
+
+264
+00:20:45,280 --> 00:20:49,480
+من المرات و بعدين ابدأ اقول XI 1 XI 2 إلى ما
+
+265
+00:20:49,480 --> 00:20:53,880
+لنهاية هذا الآن ال operator برضه اللي هو هتلاقيه
+
+266
+00:20:53,880 --> 00:20:57,720
+bounded linear operator من اللي جابه مثل اللي جابه
+
+267
+00:20:57,720 --> 00:21:00,780
+قبل بشوية حليته مافيش داعي داعي دو where the
+
+268
+00:21:00,780 --> 00:21:04,540
+number of zeros is N and X بيستوي XI IIt is easy
+
+269
+00:21:04,540 --> 00:21:08,400
+to see that Tn is linear and bounded for any n الـ
+
+270
+00:21:08,400 --> 00:21:11,540
+boundedness سهل الـ linear تعملته الـ boundedness
+
+271
+00:21:11,540 --> 00:21:18,200
+خد Tn X إيش حيساوي ال summation of xi I تربيع I من
+
+272
+00:21:18,200 --> 00:21:21,460
+واحد إلى ملاها، صح ولا لأ؟ لإن هو .. بالحسب إن هو
+
+273
+00:21:21,460 --> 00:21:25,440
+أسفل و بعدين و بعدين و هو عبارة عن مين؟ norm أص
+
+274
+00:21:25,440 --> 00:21:29,940
+نص، هذا norm الـ Xبالظبط ولا لأ؟ إذا أكيد bounded
+
+275
+00:21:29,940 --> 00:21:34,340
+Tn X هو نورم واحد كمان مش bounded بس و نورم Tn
+
+276
+00:21:34,340 --> 00:21:42,040
+بسوء واحد بالظبط طيب اطلع على فوق since L2 is a
+
+277
+00:21:42,040 --> 00:21:44,900
+Hilbert space then every linear functional F
+
+278
+00:21:44,900 --> 00:21:49,520
+element in L2أسهل ليه في الـ L2 على طول بعمله الـ
+
+279
+00:21:49,520 --> 00:21:52,420
+Representation بالـ Ray's Representation الـ
+
+280
+00:21:52,420 --> 00:21:55,800
+theorem has Ray's Representation F of X بيساوي X و
+
+281
+00:21:55,800 --> 00:22:00,080
+Z و يساوي كالـ inner product بينهم اللي هو تبعات
+
+282
+00:22:00,080 --> 00:22:03,480
+هدف تبعات هدف بس كواحدة عادية واحدة conjugate XII
+
+283
+00:22:03,480 --> 00:22:07,000
+أو XIJ Gamma J conjugate J من واحد إلى ما ننهيها
+
+284
+00:22:07,000 --> 00:22:11,420
+حيث الـ Z هي تبعات Gamma J والـ X هي من XIIواضح
+
+285
+00:22:11,420 --> 00:22:15,180
+هذا الـ Z اللي لاجناها for every F element in L2
+
+286
+00:22:15,180 --> 00:22:22,040
+there exists Z such that F of X بيساومين X O Z لكن
+
+287
+00:22:22,040 --> 00:22:25,720
+من جهة أخرى أحسب للـ F of T X N بدي أثبت ليه
+
+288
+00:22:25,720 --> 00:22:32,400
+convergence لأن أنا بدي أثبتلك أن F of T X N بتروح
+
+289
+00:22:32,400 --> 00:22:39,180
+إلى F of something X N نشوف إيش هو الـ something
+
+290
+00:22:39,180 --> 00:22:39,500
+هنا
+
+291
+00:22:44,930 --> 00:22:49,590
+صلى على النبي عليه الصلاة والسلام احسب لي F of T N
+
+292
+00:22:49,590 --> 00:22:54,710
+X اللي هي بالساوي حسب اللي هي ال rule اللي عندى T
+
+293
+00:22:54,710 --> 00:22:59,990
+N X و Z و هذه اللي هي بالساوي T N X H هي اللي هي
+
+294
+00:22:59,990 --> 00:23:08,030
+طيب شوفوا كيف هدول السفر هياخدوا مينهيخدم مين هي
+
+295
+00:23:08,030 --> 00:23:12,610
+الـ Z جامعة واحد جامعة اتنين جامعة N جامعة N زائد
+
+296
+00:23:12,610 --> 00:23:16,650
+واحد الاخره الان ادول الاسفار هيخدم في طريقهم
+
+297
+00:23:16,650 --> 00:23:22,470
+هذوله لما نضرب من فيهم اذا هيبدأ العد ل XI واحد هو
+
+298
+00:23:22,470 --> 00:23:28,550
+XI N او جامعة N زائد واحد فطبيعي بساول هو XIJ
+
+299
+00:23:28,550 --> 00:23:32,210
+minus N Gamma J J من عند N زائد واحد إلى مين إلى
+
+300
+00:23:32,210 --> 00:23:35,550
+ما لا نهاية و اللي بده يبدأ بهدف J هدف الساقين هي
+
+301
+00:23:35,550 --> 00:23:44,310
+J زائد N و بده يبدأ يشتغل أو J من واحد فاهمين؟ هذا
+
+302
+00:23:44,310 --> 00:23:47,630
+اللي هو نفسه عبارة عن K من واحد إلى ما لا نهاية X
+
+303
+00:23:47,630 --> 00:23:52,520
+I K Gamma N K زائد واحد فاهمين؟كيف اللي هو غيرنا
+
+304
+00:23:52,520 --> 00:23:56,180
+ال index من هاللهان طيب الان by Cauchy Schwarzen
+
+305
+00:23:56,180 --> 00:24:01,180
+quality خد لهذه f of TNX اللي هو absolute value
+
+306
+00:24:01,180 --> 00:24:04,040
+لها وهذا ال absolute value وستخدم ال Cauchy
+
+307
+00:24:04,040 --> 00:24:09,060
+Schwarzen quality فبصير absolute value تربيع بساوي
+
+308
+00:24:09,060 --> 00:24:13,480
+هذه تربيع اللي هي أصغر أو اللي هي بساوي هذه نورم
+
+309
+00:24:13,480 --> 00:24:17,910
+هذه ماشي اللي هو تربيع أصغر أو .. فاهمين؟مسير أصغر
+
+310
+00:24:17,910 --> 00:24:21,770
+أو يساوي اللي هو summation هذا تربيع اللي جوا فال
+
+311
+00:24:21,770 --> 00:24:25,430
+summation هذا تربيع اللي جوا ال N هذا as N goes to
+
+312
+00:24:25,430 --> 00:24:29,590
+infinity هذا من وين بيبدأ ال K من M من N زائد واحد
+
+313
+00:24:29,590 --> 00:24:33,370
+إلى مانا النهاية هذا as N goes to infinity بتروح
+
+314
+00:24:33,370 --> 00:24:38,010
+لمين لل zeroفاهمين اللي بحكيه أخدت أنا اشتغلت على
+
+315
+00:24:38,010 --> 00:24:44,150
+هذه أو على اللي هي والأولى من عند واحد فصلت
+
+316
+00:24:44,150 --> 00:24:49,130
+التنتين هذه بديتها اللي هي من عند زائد واحد اللي
+
+317
+00:24:49,130 --> 00:24:53,010
+هي اللي بتبدأ عندها وهذه بتبدأ من واحد وتظل ماشية
+
+318
+00:24:53,620 --> 00:24:57,320
+مفهوم هذا بتروح إلى الـ Zero إذاً هذا كله هيروح
+
+319
+00:24:57,320 --> 00:25:00,700
+للـ Zero إذا صار معناته F of TN X لكل تربيع
+
+320
+00:25:00,700 --> 00:25:04,660
+بيروحنا منين للـ Zero اللي هو في الواقع F of Zero
+
+321
+00:25:04,660 --> 00:25:10,280
+Operator منين X يعني اللي أثبتته أنه الـ TN الـ TN
+
+322
+00:25:10,280 --> 00:25:14,320
+اللي هو Weekly Operator converges to the Zero
+
+323
+00:25:14,320 --> 00:25:19,760
+Operator يعني الـ TN X بتروح للـ Zero X لكل X
+
+324
+00:25:19,760 --> 00:25:22,440
+element in X ماله
+
+325
+00:25:25,010 --> 00:25:30,290
+بالنسبة لـ Tn هو كذلك، لكن Tn ليس عمليًا عمليًا
+
+326
+00:25:30,290 --> 00:25:41,990
+عمليًا عمليًا عمليًا عمليًا عمليًا عمليًا
+
+327
+00:25:42,250 --> 00:25:46,810
+الـ TNX ناقص Zero X اللي هو بيروح للـ Zero for
+
+328
+00:25:46,810 --> 00:25:52,330
+every X المنتج من هنا NX لو لجيت X واحدة بس بحيث
+
+329
+00:25:52,330 --> 00:25:57,450
+انه نورم الـ TNX ناقص Zero X بيروحش للـ Zero
+
+330
+00:25:57,450 --> 00:26:02,170
+معناته الـ TNX does not converge this strongly to
+
+331
+00:26:02,170 --> 00:26:07,170
+Zero X هاي X خد X إيش بتساوي واحد سفر سفر سفر
+
+332
+00:26:07,170 --> 00:26:15,690
+وحسبلي الآن TNX وTNXهتطلع اللي هي عبارة عن T M نقص
+
+333
+00:26:15,690 --> 00:26:19,050
+T N of X اللي هو هيطلع إيه أشماله جدر التنين
+
+334
+00:26:19,050 --> 00:26:23,290
+بتعرفوا تحسبوها اللي هي for all M لا تساوي N
+
+335
+00:26:23,290 --> 00:26:26,710
+معناته إنه is not Cauchy sequence مدام is not
+
+336
+00:26:26,710 --> 00:26:30,350
+Cauchy sequence is not converge إذا صار عندي اللي
+
+337
+00:26:30,350 --> 00:26:37,370
+هو norm T N X نقص T N is not converge strongly ل 0
+
+338
+00:26:40,760 --> 00:26:48,940
+طيب Note الان ال functionals
+
+339
+00:26:49,600 --> 00:26:52,740
+الـ Functionals، لو واحد .. الآن احنا بنحكي عن
+
+340
+00:26:52,740 --> 00:26:56,000
+Operators اللي هي الـ T أن و ان موجودة، انتبهوا
+
+341
+00:26:56,000 --> 00:27:00,660
+للمراحة ده، بين X و بين مين؟ بين Y، من normed
+
+342
+00:27:00,660 --> 00:27:05,680
+space ل normed space طيب لو بدينا بدنا نحكي بـ X و
+
+343
+00:27:05,680 --> 00:27:08,760
+ال scalar field تبعها، يعني بمعنى أخر، بدنا نحكي
+
+344
+00:27:08,760 --> 00:27:13,540
+عن مين؟ عن الـ X'أه يعني الأن ال operators اللي
+
+345
+00:27:13,540 --> 00:27:17,080
+أنا بدأ أخدها من وين من X لعند مين لـ scalar فيه
+
+346
+00:27:17,080 --> 00:27:19,540
+التباحة يعني بدأ أحكي عن ال functionality F
+
+347
+00:27:19,540 --> 00:27:24,560
+element من مين ل X' F N element in X' لما أحكي عن
+
+348
+00:27:24,560 --> 00:27:31,780
+ال F N element in X' معناته أنا صرت اللي هو اللي
+
+349
+00:27:31,780 --> 00:27:35,940
+.. اللي .. اللي هنا finite dimensional يعني بيصير
+
+350
+00:27:35,940 --> 00:27:41,890
+ال F N Xعبارة عن مش فنون انتسبيس عادي صار في
+
+351
+00:27:41,890 --> 00:27:44,970
+finite dimensional فبصير ال strongly و ال weak ليه
+
+352
+00:27:44,970 --> 00:27:50,970
+ايش ماله زي بعض فعشان هيك بحكيش لما احكي عن ال
+
+353
+00:27:50,970 --> 00:27:55,680
+functional بصير احكي بنوعية اخرىالان بيصير عندي
+
+354
+00:27:55,680 --> 00:27:59,580
+نوعين since the real and complex field are finite
+
+355
+00:27:59,580 --> 00:28:04,880
+dimensional then by theorem 48C the weak and
+
+356
+00:28:04,880 --> 00:28:08,660
+strong convergence of any sequence of bounded
+
+357
+00:28:08,660 --> 00:28:15,160
+linear functionals are the same يعني ال weak و ال
+
+358
+00:28:15,160 --> 00:28:19,820
+strong أيش بيصيرن؟ بيصيرن زي بعضالان definition
+
+359
+00:28:19,820 --> 00:28:24,720
+بناء عليه الان احنا لما بدنا نحكي let FN be a
+
+360
+00:28:24,720 --> 00:28:27,220
+sequence of bounded linear functions on and among
+
+361
+00:28:27,220 --> 00:28:31,300
+the space X then في عين دي بدأ احكي عن لان معين من
+
+362
+00:28:31,300 --> 00:28:35,620
+ال operators من ال convergence strong convergence
+
+363
+00:28:35,620 --> 00:28:43,580
+of FN الان اذا بدأ احكي عن نوعيات تخصنين اللي هو
+
+364
+00:28:43,580 --> 00:28:48,330
+ال convergence لل FNStrongly convergence of FN
+
+365
+00:28:48,330 --> 00:28:52,310
+means that there is F element in X prime Such that
+
+366
+00:28:52,310 --> 00:28:55,570
+norm of FN minus F بتروح لمين للزيرو as N goes to
+
+367
+00:28:55,570 --> 00:29:00,650
+infinity وكأنه بحكي عن اللي هو مين هنا اللي هو ال
+
+368
+00:29:00,650 --> 00:29:04,090
+uniform convergence هناك مكافئ لمين ال uniform
+
+369
+00:29:04,090 --> 00:29:07,230
+convergence إذا لما الآن بدي أحكي في ال functional
+
+370
+00:29:07,230 --> 00:29:10,870
+ركزوا الآن بدي أحكي في ال functional وكأن زي ما
+
+371
+00:29:10,870 --> 00:29:13,490
+كنت أحكي في الأول في المحاضرة اللي فاتت في ال X في
+
+372
+00:29:13,490 --> 00:29:17,770
+نورمهاوهنا بتحكي في norm منين؟ في norm الـ X' لأن
+
+373
+00:29:17,770 --> 00:29:22,530
+الآن سيرة الـ Fn وين موجودة؟ في الـ X' فالآن ما
+
+374
+00:29:22,530 --> 00:29:27,770
+بتحكي عن اللي هو strong ل convergence فيها Fn ناقص
+
+375
+00:29:27,770 --> 00:29:32,250
+F اللي بتروحلها بروح للـ 0 as N goes to infinity
+
+376
+00:29:32,250 --> 00:29:35,210
+هذا اللي في حالة ال operators كنت سميه uniform
+
+377
+00:29:35,210 --> 00:29:39,330
+convergence وهنا بده أسميه إيش ماله؟ strong
+
+378
+00:29:39,330 --> 00:29:43,850
+convergence لمين؟لـ Sequence of Functions عشان ما
+
+379
+00:29:43,850 --> 00:29:47,790
+اتخربتوش في الواقع هذا اللي كنا نسميه Uniform
+
+380
+00:29:47,790 --> 00:29:51,170
+Convergence وحتى أيام الباكاليوروس كنا نسميه
+
+381
+00:29:51,170 --> 00:29:54,990
+Uniform Convergence اللي هي في حالة اللي هي Area
+
+382
+00:29:54,990 --> 00:29:58,130
+اللي هنا نسميه Strong Convergence طيب، اللي هنا في
+
+383
+00:29:58,130 --> 00:30:01,590
+حاجة اسمها Weak Star Convergence الـWeak Star
+
+384
+00:30:01,590 --> 00:30:06,290
+لمين؟ With respect to F طيب الـWeak Convergence
+
+385
+00:30:06,290 --> 00:30:09,730
+كنا ناخد اللي هو For Every F Element ان كنا نقول
+
+386
+00:30:09,730 --> 00:30:16,760
+ان XNعشان ما تتربطوش Xn بتروح لل X weekly ناخد
+
+387
+00:30:16,760 --> 00:30:21,840
+مين؟ ناخد every F element in X prime ونقول F of Xn
+
+388
+00:30:21,840 --> 00:30:25,940
+بتروح لل F of X إيه شماله؟ اذا نقصده في التبسيه
+
+389
+00:30:25,940 --> 00:30:28,830
+sequence of numbersطب إحنا الآن .. طب هي عندنا
+
+390
+00:30:28,830 --> 00:30:33,510
+جاهزة أصلا لما .. عندنا الـ Fn هي .. هي أصلا
+
+391
+00:30:33,510 --> 00:30:37,330
+functional نفسها فإيش اللي بدي أسوي؟ بدي أسوي ..
+
+392
+00:30:37,330 --> 00:30:41,150
+أسمي حاجة اسم weak star convergence و بكتبها
+
+393
+00:30:41,150 --> 00:30:47,050
+convergence of Fn means that there is a prime such
+
+394
+00:30:47,050 --> 00:30:51,360
+that الآنبدخلش F عليها على الـ sequence لأ بقول
+
+395
+00:30:51,360 --> 00:30:54,840
+such that F N of X بتروح لل F of X as N goes to
+
+396
+00:30:54,840 --> 00:30:58,140
+infinity لكل X هو element in X وهذا معناته F N
+
+397
+00:30:58,140 --> 00:31:04,860
+بتروح لل F مين weekly بس
+
+398
+00:31:04,860 --> 00:31:11,400
+طلعونها للفرق بس
+
+399
+00:31:11,400 --> 00:31:18,420
+انتبهوا وصلة لمن؟ هي في عندي Xهذا ما يسمى كـ
+
+400
+00:31:18,420 --> 00:31:23,560
+Normed Space وفي عند X' اللي هو الـ Dual Space
+
+401
+00:31:23,560 --> 00:31:27,800
+اللي لها هذا بتحكي عن weak convergence وهذا weak
+
+402
+00:31:27,800 --> 00:31:32,960
+star convergence و Xاللي هي norm of the space و X'
+
+403
+00:31:33,300 --> 00:31:37,740
+أشماله اللي هو dual space لها طيب، شوفوا، صلى الله
+
+404
+00:31:37,740 --> 00:31:41,140
+عني، بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس،
+
+405
+00:31:41,140 --> 00:31:42,640
+بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس،
+
+406
+00:31:42,640 --> 00:31:44,400
+بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس،
+
+407
+00:31:44,400 --> 00:31:52,260
+بلس، بلس، بلس، بلس، بلس، بلس، بلس،
+
+408
+00:31:52,260 --> 00:31:56,320
+بلس،
+
+409
+00:31:57,020 --> 00:32:00,060
+هي هي هي هي هي ال sequence أه ال N ال sequence
+
+410
+00:32:00,060 --> 00:32:04,420
+بينما هنا لما بحكي عن weak star بحكي عن sequence
+
+411
+00:32:04,420 --> 00:32:09,620
+وين موجودة في ال X' مش sequence في ال X فبصير عندي
+
+412
+00:32:09,620 --> 00:32:14,080
+FN هي ال sequence وين في ال X' و ال F اللي
+
+413
+00:32:14,080 --> 00:32:18,640
+بتروحلها برضه وين موجودة في ال X' فبقول FN بتروح
+
+414
+00:32:18,640 --> 00:32:25,070
+لل F weak star معناتهإن الـ N بسير لأن لكل مين ال
+
+415
+00:32:25,070 --> 00:32:30,770
+N بعكسها لكل X في ال X بطلع عند أف N of X بتروح لل
+
+416
+00:32:30,770 --> 00:32:35,450
+أف of مين of X يعني الآن ال sequence هذه لمين لل
+
+417
+00:32:35,450 --> 00:32:39,390
+أف N اللي في وين في ال X' بينما ال XN هذه ال
+
+418
+00:32:39,390 --> 00:32:44,730
+sequence في وين في ال X نفسهاالطول هنا لتحقيق الـ
+
+419
+00:32:44,730 --> 00:32:48,490
+weak star هي الـ F اللي في الـ X' بينما الطول هنا
+
+420
+00:32:48,490 --> 00:32:52,750
+لتحقيق الـ W star اللي يمين الـ Xات اللي في الـ L
+
+421
+00:32:52,750 --> 00:33:00,810
+في الـ X يلّا نبعدها إلى أن نرمحك let X and Y be
+
+422
+00:33:00,810 --> 00:33:05,330
+normed this basis and T and B a sequence of
+
+423
+00:33:05,330 --> 00:33:12,500
+elements in B X or Yإذا Tن تتعامل بشكل عام لـ T،
+
+424
+00:33:12,500 --> 00:33:17,020
+فإن T تتعامل بشكل عام لـ T، فإن T تتعامل بشكل عام
+
+425
+00:33:17,020 --> 00:33:26,360
+ل T، فإن T تتعامل
+
+426
+00:33:26,360 --> 00:33:34,520
+بشكل
+
+427
+00:33:34,520 --> 00:33:37,490
+عام ل T، فإنلكن كنا نقول أن الـ Pointwise لا
+
+428
+00:33:37,490 --> 00:33:41,730
+يستطيع أن المقدرة عنده Fn converge للـF اللي هو
+
+429
+00:33:41,730 --> 00:33:44,970
+زمان، تبع زمان، تبع الـReal أو تبع الـC إذا كانت
+
+430
+00:33:44,970 --> 00:33:48,610
+Fn بتروح للـF pointwise وكانت Fn sequence of
+
+431
+00:33:48,610 --> 00:33:51,210
+continuous functions ليس شرط أن الـF تكون
+
+432
+00:33:51,210 --> 00:33:54,510
+continuous وكنا لما نحكي عن الـintegrable ونحكي عن
+
+433
+00:33:54,510 --> 00:33:56,530
+الـdifferentiability برضه كان لهم conditions كان
+
+434
+00:33:56,530 --> 00:33:59,650
+يمكن الـdifferentiability بتهزج تاني غير اللي هو
+
+435
+00:33:59,650 --> 00:34:06,600
+الـUFO طيبالآن Strongly or weakly convergence of
+
+436
+00:34:06,600 --> 00:34:11,260
+TN to some T إلى كده need not imply أيش معلوه زي
+
+437
+00:34:11,260 --> 00:34:14,240
+اللي قلته قبل شوية إنه الـ weakly و الـ strongly
+
+438
+00:34:14,240 --> 00:34:19,160
+convergence للـ TN غير مؤهل إنه ياخد ال sequence
+
+439
+00:34:19,160 --> 00:34:23,120
+of continuous bounded functions أو continuous
+
+440
+00:34:23,120 --> 00:34:26,980
+linear functions أو bounded linear functions
+
+441
+00:34:26,980 --> 00:34:30,720
+لbounded linear functionإذا الموهّل مين بس اللي
+
+442
+00:34:30,720 --> 00:34:34,620
+بقدر يودّهيه اللي هو بس اللي هو مين ال uniform
+
+443
+00:34:34,620 --> 00:34:42,480
+convergence الان الواحد البرهان لكم مش صعب نيجي
+
+444
+00:34:42,480 --> 00:34:44,680
+نبرهن مين اتنين يعني بدي اجيب مثال
+
+445
+00:34:48,960 --> 00:34:54,240
+بـ strong أو weak convergence من continuous
+
+446
+00:34:54,240 --> 00:34:57,640
+functions أو bounded linear operators التي مش
+
+447
+00:34:57,640 --> 00:35:03,820
+موجودة في Bxy لأ يمكنها تكون تشوفوا اطلع لفوق to
+
+448
+00:35:03,820 --> 00:35:09,220
+verify two اللي هاد اتنين consider the subspace X
+
+449
+00:35:09,220 --> 00:35:15,030
+ايش بتساوي اطلع لفوقبيساوي x بيساوي xij الامتنان 2
+
+450
+00:35:15,030 --> 00:35:19,090
+such that x has many finitely many zeros of L2
+
+451
+00:35:19,090 --> 00:35:23,890
+اشمالها اللي هي ال non zero finite بس و البعدي
+
+452
+00:35:23,890 --> 00:35:30,630
+اشماله أصفر let Tn من x لعند x be defined by Tn x
+
+453
+00:35:30,630 --> 00:35:35,590
+ايش بتساوي اللي هو هدول بس اشماله في عندك finite
+
+454
+00:35:35,590 --> 00:35:41,250
+number of elements مش zeroX has finitely many non
+
+455
+00:35:41,250 --> 00:35:44,490
+-zero numbers هذا اللي هو ال space اللي عندي هذا
+
+456
+00:35:44,490 --> 00:35:50,150
+ال subspace من مين؟ من ال L2 نفسه طيب يعني تقولي
+
+457
+00:35:50,150 --> 00:35:59,030
+ال element اللي هو اللي في ال L2 نص؟ ربع؟ تسع؟
+
+458
+00:35:59,030 --> 00:36:02,570
+واحد ع ستاش؟ إلى ما لا نهاية؟ هذا مش موجود في ال X
+
+459
+00:36:02,570 --> 00:36:10,080
+هذه لكن موجود في ال L2لأن الـ summation له finite
+
+460
+00:36:10,080 --> 00:36:13,520
+طيب
+
+461
+00:36:13,520 --> 00:36:17,120
+لكن .. لكن مش كل ال terms كل ال terms بيبقى
+
+462
+00:36:17,120 --> 00:36:19,240
+لانهاية مش zero طيب
+
+463
+00:36:21,410 --> 00:36:28,370
+طيب أخدنا T ان Xاش بتساوي T واحد X بتساوي ال .. ال
+
+464
+00:36:28,370 --> 00:36:29,150
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+465
+00:36:29,150 --> 00:36:29,430
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+466
+00:36:29,430 --> 00:36:29,610
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+467
+00:36:29,610 --> 00:36:30,950
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+468
+00:36:30,950 --> 00:36:32,290
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+469
+00:36:32,290 --> 00:36:32,530
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+470
+00:36:32,530 --> 00:36:33,010
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+471
+00:36:33,010 --> 00:36:35,890
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+472
+00:36:35,890 --> 00:36:36,170
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+473
+00:36:36,170 --> 00:36:36,190
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+474
+00:36:36,190 --> 00:36:43,370
+ال .. ال .. ال .. ال .. ال .. ال
+
+475
+00:36:44,750 --> 00:36:49,410
+T3 نفس الشيء الـ TN التي تضرب 1×2×3×4 لما تصل لـ N
+
+476
+00:36:49,410 --> 00:36:54,590
+و بعدها تبقى كما هي هذه التي هي TNX و خد TX
+
+477
+00:36:54,590 --> 00:37:02,470
+defined by TX ايش بتساوي GXiJ هذي لاحظ لما N تروح
+
+478
+00:37:02,470 --> 00:37:04,930
+إلى ما على النهاية يضرب و يضرب و يضرب و يضرب و
+
+479
+00:37:04,930 --> 00:37:11,290
+يضرب و يضرب و يضربمشكلة مكبرة N بزيادة ضرب عند N
+
+480
+00:37:11,290 --> 00:37:13,670
+زيادة واحد بيصير ضربان فما بالكم اللي مروحوا
+
+481
+00:37:13,670 --> 00:37:16,190
+البلد؟ هذا بيصير كل المضروبات وكأنهم هذا roughly
+
+482
+00:37:16,190 --> 00:37:19,270
+الكلام طيب it is left to the reader to show that
+
+483
+00:37:19,270 --> 00:37:23,810
+for unfixed N TN is linear and bounded برضه نفس
+
+484
+00:37:23,810 --> 00:37:26,230
+الأشياء ال linearity و ال boundedness مشابه اللي
+
+485
+00:37:26,230 --> 00:37:30,310
+حكيناه قبل و شوية ال unboundedness سهل ال bounded
+
+486
+00:37:30,310 --> 00:37:34,570
+norm TN هذا بيساوي norm هذا و هذا أصغر أو ساوي
+
+487
+00:37:34,570 --> 00:37:40,500
+اللي هو Nفى Normal X على اعتبار ان كله واضربات
+
+488
+00:37:40,500 --> 00:37:49,300
+عندك انا لان انا اكبر واحدة مش فاهمين؟
+
+489
+00:37:49,300 --> 00:37:50,780
+طيب لأ
+
+490
+00:38:03,150 --> 00:38:08,630
+TNX بساوية اللي هو عبارة عن مين اللي هو norm TNX
+
+491
+00:38:08,630 --> 00:38:14,030
+بساوية norm اللي هو XI واحد XI اتنين XI اتنين لعند
+
+492
+00:38:14,030 --> 00:38:19,310
+ان ان XI ان والباب المضروب الاخر هنا هذا أصغر أوي
+
+493
+00:38:19,310 --> 00:38:25,570
+ساوياللي هو اعتبر ان هذا اللي هو norm هنا اللي هو
+
+494
+00:38:25,570 --> 00:38:27,610
+عبارة عن ال summation لهذا و لهذا و لهذا ال
+
+495
+00:38:27,610 --> 00:38:32,570
+summation أصغر و أصغر ال summation ان في xii I من
+
+496
+00:38:32,570 --> 00:38:39,010
+عند واحد إلى ما لنهاية تربيع الكل أص نص norm تربيع
+
+497
+00:38:39,010 --> 00:38:42,970
+نحسب norm تربيع مش مشكلة كأني سحبت الان هذول لإن
+
+498
+00:38:42,970 --> 00:38:47,750
+هذول بس الان هنا أنا ضربت انفين كله طيب
+
+499
+00:38:50,470 --> 00:38:53,450
+It is left to infix TN is bound linear or
+
+500
+00:38:53,450 --> 00:38:57,770
+unbounded Moreover T is linear but is not bounded
+
+501
+00:38:57,770 --> 00:39:01,710
+T هذه هذه T is linear لكن أشمالها is not bounded
+
+502
+00:39:01,710 --> 00:39:06,890
+الآن T X بتساوي J في مين كساية واحد في كساية اتنين
+
+503
+00:39:06,890 --> 00:39:11,510
+في كساية تلاتة is not boundedإنها متعبرة وليس
+
+504
+00:39:11,510 --> 00:39:15,730
+متعبرة ثم T هو إيش معناه element in B وليس element
+
+505
+00:39:15,730 --> 00:39:23,670
+in B of X إذا مش مستحيل أن الـTن تكون مرتبط لمن؟
+
+506
+00:39:23,670 --> 00:39:31,630
+لـT أه الـTن مستحيل تروح لمن؟ لـT أخيراً واضح أن
+
+507
+00:39:31,630 --> 00:39:36,080
+الـTن مرتبط بشكل قوي لمن؟ لـTاللي قلته في الأول،
+
+508
+00:39:36,080 --> 00:39:39,900
+أول ما حكيت، الـTN، شو معناه الـTN؟ شو معناه الـTN
+
+509
+00:39:39,900 --> 00:39:45,260
+strongly تروح convergence to T؟ إنه، اللي هو TN X
+
+510
+00:39:45,260 --> 00:39:51,200
+معقص TX يروح نمين للسفر، TN as N goes to infinity،
+
+511
+00:39:51,200 --> 00:39:56,410
+هذه اللي هي هيهاهو as n goes to infinity بيصير كل
+
+512
+00:39:56,410 --> 00:40:01,750
+هنا إشمع من XI J التي عرفناها
+
+513
+00:40:01,750 --> 00:40:06,250
+TX XI J في J هذا as n goes to infinity بيصير هيلية
+
+514
+00:40:06,250 --> 00:40:11,900
+فهو بيصير هذا النقص هذا تقوله أحلاميين للزيرولكن
+
+515
+00:40:11,900 --> 00:40:16,260
+الـ Tn اللي هو a conversion where norm of Tn X
+
+516
+00:40:16,260 --> 00:40:19,080
+بتروح لـ 0 as N goes to infinity لجبته لكن قبل
+
+517
+00:40:19,080 --> 00:40:25,340
+بشوية الـ Tn does not converge uniformly does not
+
+518
+00:40:25,340 --> 00:40:29,260
+converge T can't be element in B of X فهذا اللي هو
+
+519
+00:40:29,260 --> 00:40:32,360
+بيعطيني اللي هو strongly or weakly conversion of
+
+520
+00:40:32,360 --> 00:40:37,420
+Tn so it need not imply that T element in B of X
+
+521
+00:40:37,420 --> 00:40:47,040
+or Y يعني رغم هيك كان عنديالـ TN عشان ابعدنا طبعا
+
+522
+00:40:47,040 --> 00:40:51,900
+مش هيكون uniformly أكيد مش هيكون uniformly أه مش
+
+523
+00:40:51,900 --> 00:40:56,340
+هيكون uniformly لإن شو معناته uniformly أنك تقدر
+
+524
+00:40:56,340 --> 00:41:00,200
+تحسب ان norm الـ TN ناقص الـ T لكن أنا ماقدرش
+
+525
+00:41:00,200 --> 00:41:03,480
+أحسبه أصلا لإن الـ T أشمال has not bounded باشي
+
+526
+00:41:03,480 --> 00:41:09,640
+الحال فالأن أثبتنا أن TN X بتروح للـ TX strongly
+
+527
+00:41:11,650 --> 00:41:18,230
+الـ T is not in between B of X أو Y يعني الآن اللي
+
+528
+00:41:18,230 --> 00:41:21,230
+هو الـ strong convergence طبعا مادام الـ strong
+
+529
+00:41:21,230 --> 00:41:25,570
+convergence ده أكيد أشمل weak convergence إذن سواء
+
+530
+00:41:25,570 --> 00:41:28,790
+strong أو weak مش هيقدر يكون مؤهل يودّي الـ T في
+
+531
+00:41:28,790 --> 00:41:32,970
+الـ B L of X نيجي
+
+532
+00:41:32,970 --> 00:41:39,610
+نشوف كده إجتماعيل يلّا
+
+533
+00:41:39,610 --> 00:41:46,850
+ما بنخلصين تفكّر علىلما let X be أبلغ space وY
+
+534
+00:41:46,850 --> 00:41:49,550
+along the space and T and B a sequence of elements
+
+535
+00:41:49,550 --> 00:41:53,910
+in B X Y that converge strongly to a limit T
+
+536
+00:41:53,910 --> 00:41:57,910
+element in B X Y then T أشملها element in B X Y
+
+537
+00:41:57,910 --> 00:42:03,570
+إذا أنا بقولك انت
+
+538
+00:42:03,570 --> 00:42:07,870
+ممكن تكون في ذكية بسيطة تخلي اللي هو الـ strongly
+
+539
+00:42:07,870 --> 00:42:13,050
+convergentأه يخلّي الـ Limit وإن موجودة في الـ P X
+
+540
+00:42:13,050 --> 00:42:17,290
+وY بس اللي مطلوب أن الـ X وY يكونوا إيه الشمالين
+
+541
+00:42:17,290 --> 00:42:24,770
+بنخس Basis ماشي لإنه هيحولك اللي هو هيحصل على ال
+
+542
+00:42:24,770 --> 00:42:28,450
+boundedness المفقود أو اللي هو ال boundedness
+
+543
+00:42:28,450 --> 00:42:35,970
+لميلة T نشوف كيف أو حتى ال sequence نفسها تصير الـ
+
+544
+00:42:35,970 --> 00:42:40,290
+T أن تروح خلّيني أقول Roughlyبالـ TN uniformly it
+
+545
+00:42:40,290 --> 00:42:43,190
+is left to the reader to prove that T is linear
+
+546
+00:42:43,190 --> 00:42:48,090
+سيبها لكم الان since TN X بتروح لل TX لكل X
+
+547
+00:42:48,090 --> 00:42:53,130
+element in X by لمّة 1 4 2 A the sequence TN X is
+
+548
+00:42:53,130 --> 00:42:57,070
+bounded اتفاقنا عليه اه عارفين هو هذا TN X بتروح
+
+549
+00:42:57,070 --> 00:43:01,970
+لل TX في ال norm تبع مين؟ تبع ال X تبع ال Y و ال Y
+
+550
+00:43:01,970 --> 00:43:05,430
+إذا بنخس بي اس إذا TN X الشمال هتكون is bounded
+
+551
+00:43:05,430 --> 00:43:11,650
+however X is completeصارت هذه bounded و الـ X is
+
+552
+00:43:11,650 --> 00:43:14,550
+complete إذا بالـ Uniform Boundedness Theorem
+
+553
+00:43:14,550 --> 00:43:19,290
+هتحولك الـ boundedness لهذه لـ boundedness لميه
+
+554
+00:43:19,290 --> 00:43:22,830
+للـ TN هتصير اللي هي نوم الـ TN أصغر شهر و C for
+
+555
+00:43:22,830 --> 00:43:27,650
+all N يعني independent of X بتصير هذا الـ Uniform
+
+556
+00:43:27,650 --> 00:43:33,170
+Boundedness وهذه بتطلب الـ X إيش تكون completeهنا
+
+557
+00:43:33,170 --> 00:43:36,030
+Hence خدوا نورم الـ TN X هيكون أصغر أو ساوى نورم
+
+558
+00:43:36,030 --> 00:43:40,130
+الـ TN في نورم الـ X وهذه أصغر أو ساوى C في نورم
+
+559
+00:43:40,130 --> 00:43:43,770
+الـ X الآن دخلوا ال limit علي الجهد التاني
+
+560
+00:43:43,770 --> 00:43:46,470
+وستستخدموا ال continuity لل TN و ال continuity لل
+
+561
+00:43:46,470 --> 00:43:50,840
+normهذا صار أصغر أشهر و C في X دخلوا ال limit هنا
+
+562
+00:43:50,840 --> 00:43:54,100
+واستخدوا ال continuity لل TN و ال continuity نميين
+
+563
+00:43:54,100 --> 00:43:59,640
+لل norm بس يوم norm limit ال TN ال X هو TX وهذا
+
+564
+00:43:59,640 --> 00:44:02,760
+limit اللي هو norm TN X أصغر أشهر و C في norm X
+
+565
+00:44:02,760 --> 00:44:06,840
+hence اللي هي صارت عند T is bounded then T element
+
+566
+00:44:06,840 --> 00:44:14,000
+in B X أو Y اطلع للفوق البعدها let Xدع X و Y يكون
+
+567
+00:44:14,000 --> 00:44:19,140
+بانخسباسي و TN يكون سيكوانس من الأشياء الميانة في
+
+568
+00:44:19,140 --> 00:44:24,320
+B X و Y إذا X و Y أشمل بانخسباسي و TN سيكوانس في B
+
+569
+00:44:24,320 --> 00:44:30,900
+X و Y ثم TN تتعامل بشكل قوى إذا كانت تتعامل بشكل
+
+570
+00:44:30,900 --> 00:44:33,500
+قوى إذا كانت تتعامل بشكل قوى إذا كانت تتعامل بشكل
+
+571
+00:44:33,500 --> 00:44:38,290
+قوىاللي هو الـ sequence TNX is Cauchy in Y for
+
+572
+00:44:38,290 --> 00:44:42,670
+every X in a total subset M of mean of X ما هي الـ
+
+573
+00:44:42,670 --> 00:44:47,750
+TNX مزام converge إذا Cauchy ماياشي الحال Cauchy
+
+574
+00:44:47,750 --> 00:44:51,730
+إذا سواء Cauchy كانت الـ X في الـ Y نفسها أو في
+
+575
+00:44:51,730 --> 00:44:54,790
+الـ X نفسها أو في subset منها إذا الـ automatic
+
+576
+00:44:54,790 --> 00:44:58,150
+هذا جزء منها زي ما حكينا في الجبل طيب
+
+577
+00:45:00,170 --> 00:45:04,890
+بالتدريج if TN X بتروح ل TX لكل X element in X
+
+578
+00:45:04,890 --> 00:45:09,590
+يعني strongly هذا إيش معلوق strongly then TN X is
+
+579
+00:45:09,590 --> 00:45:14,990
+bounded ماشي الحال أخدناها and so بقى uniform
+
+580
+00:45:14,990 --> 00:45:18,810
+bounded نص فيهم إيش هتطلع norm TN is bounded إذن
+
+581
+00:45:18,810 --> 00:45:22,850
+هذه automatic طلعتفي حالة تسأل هي مين فردت اللي هو
+
+582
+00:45:22,850 --> 00:45:26,110
+الـ strongly convergence الان بيه from the
+
+583
+00:45:26,110 --> 00:45:29,850
+definition of strongly operator convergence and
+
+584
+00:45:29,850 --> 00:45:33,840
+the fact every convergence sequence is Cauchyاللي
+
+585
+00:45:33,840 --> 00:45:36,340
+هو ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+586
+00:45:36,340 --> 00:45:36,460
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+587
+00:45:36,460 --> 00:45:36,520
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+588
+00:45:36,520 --> 00:45:36,560
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+589
+00:45:36,560 --> 00:45:36,800
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+590
+00:45:36,800 --> 00:45:37,320
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+591
+00:45:37,320 --> 00:45:37,380
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+592
+00:45:37,380 --> 00:45:42,680
+ال .. ال .. ال .. ال ..
+
+593
+00:45:42,680 --> 00:45:47,360
+ال
+
+594
+00:45:47,360 --> 00:45:48,280
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+595
+00:45:48,280 --> 00:45:48,360
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+596
+00:45:48,360 --> 00:45:56,920
+ال .. ال .. ال .. ال .. ال
+
+597
+00:46:03,400 --> 00:46:06,960
+أطلع لفوق مشابه للي حكينا قبل بشوية suppose that a
+
+598
+00:46:06,960 --> 00:46:09,860
+and b holds then there exists c أكبر من صفر such
+
+599
+00:46:09,860 --> 00:46:12,880
+that more than t أن اش ماله أصغر أو ساوسين من
+
+600
+00:46:12,880 --> 00:46:17,680
+المعطى for all n since m is totally in x فزي ما
+
+601
+00:46:17,680 --> 00:46:21,480
+عملنا قبل بشوية ال span ل ال m اش ماله then is في
+
+602
+00:46:21,480 --> 00:46:25,900
+ال xما دام span لـ M دنس في الـ X إذا لكل X في الـ
+
+603
+00:46:25,900 --> 00:46:29,280
+X بقدر ألاقي sequence من هنا اللي هو Converge إلها
+
+604
+00:46:29,280 --> 00:46:35,000
+أو بقدر أقول لكل X هنا بقدر أخد المسافة بينها وبين
+
+605
+00:46:35,000 --> 00:46:38,620
+اللي هو elements من هنا صغيرة صغيرة صغيرة جدا زي
+
+606
+00:46:38,620 --> 00:46:47,360
+ما بدي فاهمين؟ الآن يا جماعة ال span لـ M دنس في
+
+607
+00:46:47,360 --> 00:46:54,950
+من؟ في الـ X إذا لكل X في الـ Xاللي هو بقدر ألاقي
+
+608
+00:46:54,950 --> 00:47:01,130
+element في الـ M يكون very close إليه لأن هي أصلا
+
+609
+00:47:01,130 --> 00:47:04,870
+dense فيه فبكون عندي for every Y أكبر من 0 there
+
+610
+00:47:04,870 --> 00:47:08,190
+exists Y element اسمها للـ M such that normal X
+
+611
+00:47:08,190 --> 00:47:14,880
+minus Y أشمل أصغر من تلت عالمين على Cلأن الـ M
+
+612
+00:47:14,880 --> 00:47:22,420
+dense في الـ X، أي X هنا can be .. we can find M Y
+
+613
+00:47:22,420 --> 00:47:26,580
+في الـ span تكون very close له، نفس منطقة الـ
+
+614
+00:47:26,580 --> 00:47:30,560
+sequence، وبرمجانه سهل، الـ norm X minus Y أصغر من
+
+615
+00:47:30,560 --> 00:47:33,300
+Y على مين؟ على تلاتة C، يعني زغرت المسافة زي ما
+
+616
+00:47:33,300 --> 00:47:38,320
+بديالان من B اللي هو Tny is Cauchy مدام Cauchy
+
+617
+00:47:38,320 --> 00:47:44,320
+بقدر عليها K بحيث أن Tny نقص Tmy أصغر من أي أبسلون
+
+618
+00:47:44,320 --> 00:47:46,580
+في الدنيا من ضمن هذه الأبسلون على تلاتة اللي بديها
+
+619
+00:47:46,580 --> 00:47:52,620
+الان therefore لكل M و N أكبر من K اللي لجيت هنا
+
+620
+00:47:53,810 --> 00:47:59,530
+بحصل معالي وانا fixed x we have احسبلي Tnx نقص Tmx
+
+621
+00:47:59,530 --> 00:48:03,690
+اللي هو اصغر او شاوي ضيفوا الtermين واطرحوهن
+
+622
+00:48:03,690 --> 00:48:07,310
+واستخدموا ال triangle inequality اصغر او شاوي Tnx
+
+623
+00:48:07,310 --> 00:48:15,320
+نقص Tny زي Tmy نقص Tmxالأن نفس اللي عملته قبل
+
+624
+00:48:15,320 --> 00:48:19,760
+بشوية هذي بيصير أصغر TN of X minus Y إذا أصغر يسوي
+
+625
+00:48:19,760 --> 00:48:25,100
+نورم TN في نورم X minus Y وهذه التانية أصغر من مين
+
+626
+00:48:25,100 --> 00:48:29,900
+من Y على 3 حكيناها وهذه نفس اللي عملته قبل بشوية
+
+627
+00:48:29,900 --> 00:48:33,900
+في البرهان اللي في المحاضرة اللي فاتت نورم TN في
+
+628
+00:48:33,900 --> 00:48:39,510
+نورم Y minus Xالأن هذا أصغر أو ساوى C وهذا أصغر من
+
+629
+00:48:39,510 --> 00:48:44,990
+Y ع تلاتة C وهذه Y ع تلاتة وهذا أصغر من C وهذا
+
+630
+00:48:44,990 --> 00:48:48,610
+أصغر من Y ع تلاتة C وكل معلومات أصغر من مين من Y
+
+631
+00:48:48,610 --> 00:48:52,510
+وإذا صار عندي ال TNX نقص TNX أصغر من أي Y في
+
+632
+00:48:52,510 --> 00:48:56,130
+الدنيا ماشي الحال إذا صارت ال TNX عبارة عن إيه
+
+633
+00:48:56,130 --> 00:48:59,550
+شكوشي sequenceكوشي سيكوينس وفيه complete إذا
+
+634
+00:48:59,550 --> 00:49:03,010
+converges إذا صارت عند T and X converges in B and
+
+635
+00:49:03,010 --> 00:49:07,350
+Y وهذا يعني T and X converges strongly آخر
+
+636
+00:49:07,350 --> 00:49:12,210
+corollary منها اللي هي a sequence of N of bounded
+
+637
+00:49:12,210 --> 00:49:17,810
+linear functionals on a بنخ space X is weak star
+
+638
+00:49:17,810 --> 00:49:22,680
+convergenceالقاعدة تكون عبارة عن عبارة عالية على X
+
+639
+00:49:22,680 --> 00:49:25,240
+إذا كانت عبارة عنها عبارة عنها عبارة عنها عبارة
+
+640
+00:49:25,240 --> 00:49:25,940
+عنها عبارة عنها عبارة عنها عبارة عنها عبارة عنها
+
+641
+00:49:25,940 --> 00:49:26,640
+عبارة عنها عبارة عنها عبارة عنها عبارة عنها عبارة
+
+642
+00:49:26,640 --> 00:49:26,780
+عنها عبارة عنها عبارة عنها عبارة عنها عبارة عنها
+
+643
+00:49:26,780 --> 00:49:28,460
+عبارة عنها عبارة عنها عبارة عنها عبارة عنها عبارة
+
+644
+00:49:28,460 --> 00:49:29,300
+عنها عبارة عنها عبارة عنها عبارة عنها عبارة عنها
+
+645
+00:49:29,300 --> 00:49:30,640
+عبارة عنها عبارة عنها عبارة عنها عبارة عنها عبارة
+
+646
+00:49:30,640 --> 00:49:34,260
+عنها عبارة عنها عبارة
+
+647
+00:49:34,260 --> 00:49:34,760
+عنها ع
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/c4_dQ90VN3U_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/c4_dQ90VN3U_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..8e9244da6a91bbb4b6cb8556bd307c64642849c4
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/c4_dQ90VN3U_raw.json
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+{"segments": [{"id": 1, "seek": 2610, "start": 5.26, "end": 26.1, "text": "بسم الله الرحمن الرحيم الحمد لله رب العالمين والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى آله والصحابي أجمعين هذه المحاضرة رقم تلاتة وتلاتين مساق تحليل اقتراني أو تحليل دالي طلاب طالبات الجامعة الإسلامية ماجستير وصلنا هنا عند أربعة تسعة اللي هو convergence of sequences of operators and functionals", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21542, 2304, 3215, 24976, 3224, 12602, 3555, 18863, 45340, 9957, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 8608, 25708, 9673, 2288, 3794, 1211, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 19753, 43761, 16070, 9381, 5016, 16758, 1829, 5551, 7435, 2304, 3615, 9957, 29538, 9673, 5016, 46958, 25720, 12602, 4587, 2304, 6055, 1211, 9307, 3660, 34683, 1211, 9307, 9957, 47524, 995, 4587, 6055, 5016, 20292, 1211, 1975, 38149, 2288, 7649, 1829, 34051, 6055, 5016, 20292, 1211, 11778, 6027, 1829, 23032, 15040, 3555, 23032, 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"end": 94.85, "word": " للـ", "probability": 0.7509765625}, {"start": 94.85, "end": 95.13, "word": " F", "probability": 0.78125}, {"start": 95.13, "end": 95.69, "word": " اللي", "probability": 0.7470703125}, {"start": 95.69, "end": 95.87, "word": " هو", "probability": 0.97998046875}, {"start": 95.87, "end": 96.77, "word": " بنسكت،", "probability": 0.6982421875}, {"start": 96.77, "end": 97.09, "word": " شو", "probability": 0.699951171875}, {"start": 97.09, "end": 97.33, "word": " معناه", "probability": 0.765869140625}, {"start": 97.33, "end": 97.49, "word": " F", "probability": 0.556640625}, {"start": 97.49, "end": 97.63, "word": " ان", "probability": 0.24365234375}, {"start": 97.63, "end": 97.89, "word": " كنا", "probability": 0.7398681640625}, {"start": 97.89, "end": 98.29, "word": " نسميها", "probability": 0.972412109375}, {"start": 98.29, "end": 98.97, "word": " pointwise", "probability": 0.598388671875}, {"start": 98.97, "end": 99.73, "word": " convergence", "probability": 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" X", "probability": 0.9404296875}, {"start": 226.99, "end": 227.27, "word": " بتروح", "probability": 0.9646809895833334}, {"start": 227.27, "end": 227.75, "word": " لـ", "probability": 0.87939453125}, {"start": 227.75, "end": 228.25, "word": " Zero", "probability": 0.60986328125}, {"start": 228.25, "end": 228.93, "word": " هنا", "probability": 0.81103515625}, {"start": 228.93, "end": 229.45, "word": " الآن", "probability": 0.827392578125}, {"start": 229.45, "end": 230.43, "word": " العناصر", "probability": 0.8316650390625}, {"start": 230.43, "end": 230.71, "word": " هنا", "probability": 0.7392578125}, {"start": 230.71, "end": 231.63, "word": " دوال", "probability": 0.8123372395833334}], "temperature": 1.0}, {"id": 11, "seek": 25920, "start": 232.13, "end": 259.21, "text": "Tn بتروح للـT اللي هو with respect to space هذا strongly اسمه لكن عشان نميزه عن strongly اللي بعد شوية هنقول عنه uniformly يعني Tn بتروح للـT uniformly معنى بإن نورم الـTn ناقص T هو اللي بيروح لمين للـ0 والنورم هذا 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0.54931640625}, {"start": 711.93, "end": 712.35, "word": " لكل", "probability": 0.906494140625}, {"start": 712.35, "end": 712.63, "word": " F", "probability": 0.96484375}, {"start": 712.63, "end": 712.97, "word": " element", "probability": 0.505859375}, {"start": 712.97, "end": 713.21, "word": " in", "probability": 0.60693359375}, {"start": 713.21, "end": 713.33, "word": " Y'", "probability": 0.9775390625}, {"start": 713.67, "end": 714.11, "word": " و", "probability": 0.92626953125}, {"start": 714.11, "end": 714.27, "word": " X", "probability": 0.66015625}, {"start": 714.27, "end": 714.47, "word": " element", "probability": 0.8759765625}, {"start": 714.47, "end": 714.69, "word": " in", "probability": 0.9443359375}, {"start": 714.69, "end": 714.79, "word": " X'", "probability": 0.99462890625}, {"start": 715.03, "end": 715.23, "word": " هذا", "probability": 0.62744140625}, {"start": 715.23, "end": 715.55, "word": " يعني", "probability": 0.66943359375}, {"start": 715.55, "end": 715.67, "word": " أن", "probability": 0.66943359375}, {"start": 715.67, "end": 715.77, "word": " T", "probability": 0.79736328125}, {"start": 715.77, "end": 715.93, "word": " and", "probability": 0.77294921875}, {"start": 715.93, "end": 716.15, "word": " X", "probability": 0.99609375}, {"start": 716.15, "end": 716.47, "word": " بتروح", "probability": 0.8740234375}, {"start": 716.47, "end": 716.65, "word": " للـ", "probability": 0.4990234375}, {"start": 716.65, "end": 716.73, "word": " T", "probability": 0.84375}, {"start": 716.73, "end": 716.89, "word": " X", "probability": 0.4794921875}, {"start": 716.89, "end": 717.47, "word": " أشمالها", "probability": 0.8578125}, {"start": 717.47, "end": 718.17, "word": " Weekly", "probability": 0.6826171875}, {"start": 718.17, "end": 718.65, "word": " هذا", "probability": 0.7392578125}, {"start": 718.65, "end": 719.19, "word": " أثبته", "probability": 0.8785400390625}, {"start": 719.19, "end": 719.39, "word": " من", "probability": 0.98046875}, {"start": 719.39, "end": 720.05, "word": " وين؟", "probability": 0.58447265625}, {"start": 720.05, "end": 720.23, "word": " من", "probability": 0.984375}, {"start": 720.23, "end": 720.45, "word": " الـ", "probability": 0.76953125}, {"start": 720.45, "end": 720.93, "word": " Uniform", "probability": 0.679931640625}, {"start": 720.93, "end": 721.43, "word": " يؤدي", "probability": 0.90087890625}, {"start": 721.43, "end": 721.67, "word": " إلى", "probability": 0.93115234375}, {"start": 721.67, "end": 721.81, "word": " الـ", "probability": 0.770263671875}, {"start": 721.81, "end": 721.99, "word": " Weekly", "probability": 0.93896484375}, {"start": 721.99, "end": 722.65, "word": " مباشرة", "probability": 0.9942626953125}, {"start": 722.65, "end": 723.61, "word": " Strong", "probability": 0.38232421875}, {"start": 723.61, "end": 724.13, "word": " يؤدي", "probability": 0.7939453125}, {"start": 724.13, "end": 724.27, "word": " إلى", "probability": 0.87451171875}, {"start": 724.27, "end": 724.39, "word": " الـ", "probability": 0.93505859375}, {"start": 724.39, "end": 724.57, "word": " Weekly", "probability": 0.9697265625}, {"start": 724.57, "end": 724.75, "word": " ما", "probability": 0.342529296875}, {"start": 724.75, "end": 725.13, "word": " أثبته", "probability": 0.863525390625}, {"start": 725.13, "end": 725.37, "word": " قبل", "probability": 0.97509765625}, {"start": 725.37, "end": 726.37, "word": " بشوية", "probability": 0.74462890625}, {"start": 726.37, "end": 727.37, "word": " أي", "probability": 0.6123046875}, {"start": 727.37, "end": 728.09, "word": " سؤال؟", "probability": 0.95166015625}, {"start": 728.09, "end": 728.37, "word": " طيب", "probability": 0.9228515625}, {"start": 728.37, "end": 728.57, "word": " يلّا", "probability": 0.7437744140625}, {"start": 728.57, "end": 729.07, "word": " لبعده", "probability": 0.72491455078125}], "temperature": 1.0}, {"id": 31, "seek": 75909, "start": 734.43, "end": 759.09, "text": "الأن الـ Converse لا يجب أن يكون عاملًا يعني فيه في عندك اللي هو strong operator convergence لا يجب أن يكون من ال uniform يعني بقدر أجيبلك اللي هو strong convergence لكن ماله مش uniform convergence خد الآن let TN be a sequence of operators where TN من L2 لعند ما L2 is defined by", "tokens": [6027, 33456, 2423, 39184, 2656, 4308, 20193, 7251, 7435, 3555, 14739, 7251, 30544, 6225, 10943, 1211, 14111, 995, 37495, 22653, 8978, 3224, 8978, 43242, 4117, 13672, 1829, 31439, 2068, 12973, 32181, 20193, 7251, 7435, 3555, 14739, 7251, 30544, 9154, 2423, 9452, 37495, 22653, 4724, 28543, 2288, 5551, 7435, 1829, 3555, 23275, 13672, 1829, 31439, 2068, 32181, 44381, 19446, 43761, 37893, 9452, 32181, 16490, 3215, 6024, 48506, 718, 314, 45, 312, 257, 8310, 295, 19077, 689, 314, 45, 9154, 441, 17, 5296, 3615, 41260, 19446, 441, 17, 307, 7642, 538], "avg_logprob": -0.39583332737286886, "compression_ratio": 1.7117117117117118, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 734.43, "end": 734.87, "word": "الأن", "probability": 0.701904296875}, {"start": 734.87, "end": 735.03, "word": " الـ", "probability": 0.636962890625}, {"start": 735.03, "end": 735.41, "word": " Converse", "probability": 0.4417724609375}, {"start": 735.41, "end": 735.61, "word": " لا", "probability": 0.490966796875}, {"start": 735.61, "end": 735.67, "word": " يجب", "probability": 0.8704427083333334}, {"start": 735.67, "end": 735.73, "word": " أن", "probability": 0.69580078125}, {"start": 735.73, "end": 735.97, "word": " يكون", "probability": 0.85595703125}, {"start": 735.97, "end": 736.65, "word": " عاملًا", "probability": 0.49298095703125}, {"start": 736.65, "end": 737.15, "word": " يعني", "probability": 0.5211181640625}, {"start": 737.15, "end": 737.57, "word": " فيه", "probability": 0.41748046875}, {"start": 737.57, "end": 738.65, "word": " في", "probability": 0.2462158203125}, {"start": 738.65, "end": 739.13, "word": " عندك", "probability": 0.93505859375}, {"start": 739.13, "end": 739.35, "word": " اللي", "probability": 0.812255859375}, {"start": 739.35, "end": 739.65, "word": " هو", "probability": 0.98876953125}, {"start": 739.65, "end": 740.53, "word": " strong", "probability": 0.10406494140625}, {"start": 740.53, "end": 740.91, "word": " operator", "probability": 0.56591796875}, {"start": 740.91, "end": 741.69, "word": " convergence", "probability": 0.96923828125}, {"start": 741.69, "end": 742.25, "word": " لا", "probability": 0.63525390625}, {"start": 742.25, "end": 742.37, "word": " يجب", "probability": 0.951171875}, {"start": 742.37, "end": 742.41, "word": " أن", "probability": 0.7578125}, {"start": 742.41, "end": 742.67, "word": " يكون", "probability": 0.540771484375}, {"start": 742.67, "end": 743.11, "word": " من", "probability": 0.206787109375}, {"start": 743.11, "end": 743.63, "word": " ال", "probability": 0.5087890625}, {"start": 743.63, "end": 743.95, "word": " uniform", "probability": 0.1953125}, {"start": 743.95, "end": 744.71, "word": " يعني", "probability": 0.891845703125}, {"start": 744.71, "end": 745.05, "word": " بقدر", "probability": 0.96923828125}, {"start": 745.05, "end": 745.55, "word": " أجيبلك", "probability": 0.90830078125}, {"start": 745.55, "end": 745.77, "word": " اللي", "probability": 0.968994140625}, {"start": 745.77, "end": 746.07, "word": " هو", "probability": 0.98974609375}, {"start": 746.07, "end": 747.05, "word": " strong", "probability": 0.82568359375}, {"start": 747.05, "end": 747.57, "word": " convergence", "probability": 0.9658203125}, {"start": 747.57, "end": 747.95, "word": " لكن", "probability": 0.91162109375}, {"start": 747.95, "end": 748.37, "word": " ماله", "probability": 0.474853515625}, {"start": 748.37, "end": 748.73, "word": " مش", "probability": 0.94873046875}, {"start": 748.73, "end": 749.31, "word": " uniform", "probability": 0.94140625}, {"start": 749.31, "end": 750.13, "word": " convergence", "probability": 0.97998046875}, {"start": 750.13, "end": 751.59, "word": " خد", "probability": 0.838134765625}, {"start": 751.59, "end": 751.85, "word": " الآن", "probability": 0.80224609375}, {"start": 751.85, "end": 752.07, "word": " let", "probability": 0.36083984375}, {"start": 752.07, "end": 752.39, "word": " TN", "probability": 0.839111328125}, {"start": 752.39, "end": 752.59, "word": " be", "probability": 0.310302734375}, {"start": 752.59, "end": 754.01, "word": " a", "probability": 0.75927734375}, {"start": 754.01, "end": 754.35, "word": " sequence", "probability": 0.9248046875}, {"start": 754.35, "end": 754.57, "word": " of", "probability": 0.97412109375}, {"start": 754.57, "end": 755.13, "word": " operators", "probability": 0.939453125}, {"start": 755.13, "end": 756.15, "word": " where", "probability": 0.7724609375}, {"start": 756.15, "end": 756.53, "word": " TN", "probability": 0.943603515625}, {"start": 756.53, "end": 756.67, "word": " من", "probability": 0.96630859375}, {"start": 756.67, "end": 756.95, "word": " L2", "probability": 0.899658203125}, {"start": 756.95, "end": 757.23, "word": " لعند", "probability": 0.7547200520833334}, {"start": 757.23, "end": 757.35, "word": " ما", "probability": 0.44189453125}, {"start": 757.35, "end": 758.17, "word": " L2", "probability": 0.6832275390625}, {"start": 758.17, "end": 758.37, "word": " is", "probability": 0.78173828125}, {"start": 758.37, "end": 758.75, "word": " defined", "probability": 0.9130859375}, {"start": 758.75, "end": 759.09, "word": " by", "probability": 0.9873046875}], "temperature": 1.0}, {"id": 32, "seek": 77824, "start": 760.3, "end": 778.24, "text": "انت عارفين طبعا ايش الـ Normal على الـ L2 وكيف بنحسم وكيف كده المفروض هذا كله يعني معلوم لنا من خلال اللي هي اللي هي معلوماتنا في المادة سابقا نيجي الآن نشوف ايش اللي بدنا نسويه بالظبط", "tokens": [7649, 2655, 6225, 9640, 5172, 9957, 23032, 3555, 3615, 995, 1975, 1829, 8592, 2423, 39184, 21277, 15844, 2423, 39184, 441, 17, 4032, 4117, 33911, 44945, 5016, 38251, 4032, 4117, 33911, 9122, 3215, 3224, 9673, 5172, 32887, 11242, 23758, 28242, 3224, 37495, 22653, 20449, 1211, 20498, 5296, 8315, 9154, 16490, 1211, 6027, 13672, 1829, 39896, 13672, 1829, 39896, 20449, 1211, 20498, 9307, 8315, 8978, 9673, 18513, 3660, 8608, 16758, 4587, 995, 8717, 1829, 7435, 1829, 6024, 48506, 8717, 8592, 38688, 1975, 1829, 8592, 13672, 1829, 47525, 8315, 8717, 3794, 45865, 3224, 20666, 19913, 3555, 9566], "avg_logprob": -0.15476973590097928, "compression_ratio": 1.7052631578947368, "no_speech_prob": 2.2530555725097656e-05, "words": [{"start": 760.3, "end": 760.56, "word": "انت", "probability": 0.597900390625}, {"start": 760.56, "end": 760.9, "word": " عارفين", "probability": 0.83453369140625}, {"start": 760.9, "end": 761.2, "word": " طبعا", "probability": 0.9371337890625}, {"start": 761.2, "end": 761.42, "word": " ايش", "probability": 0.8162434895833334}, {"start": 761.42, "end": 761.66, "word": " الـ", "probability": 0.5675048828125}, {"start": 761.66, "end": 761.8, "word": " Normal", "probability": 0.533203125}, {"start": 761.8, "end": 762.56, "word": " على", "probability": 0.3701171875}, {"start": 762.56, "end": 763.3, "word": " الـ", "probability": 0.8212890625}, {"start": 763.3, "end": 763.72, "word": " L2", "probability": 0.790283203125}, {"start": 763.72, "end": 764.54, "word": " وكيف", "probability": 0.7879231770833334}, {"start": 764.54, "end": 765.02, "word": " بنحسم", "probability": 0.796875}, {"start": 765.02, "end": 765.32, "word": " وكيف", "probability": 0.798828125}, {"start": 765.32, "end": 765.56, "word": " كده", "probability": 0.8826497395833334}, {"start": 765.56, "end": 766.06, "word": " المفروض", "probability": 0.9476318359375}, {"start": 766.06, "end": 766.18, "word": " هذا", "probability": 0.775390625}, {"start": 766.18, "end": 766.92, "word": " كله", "probability": 0.99267578125}, {"start": 766.92, "end": 767.26, "word": " يعني", "probability": 0.93212890625}, {"start": 767.26, "end": 767.84, "word": " معلوم", "probability": 0.99072265625}, {"start": 767.84, "end": 768.4, "word": " لنا", "probability": 0.795166015625}, {"start": 768.4, "end": 768.6, "word": " من", "probability": 0.99560546875}, {"start": 768.6, "end": 769.24, "word": " خلال", "probability": 0.99609375}, {"start": 769.24, "end": 769.58, "word": " اللي", "probability": 0.9013671875}, {"start": 769.58, "end": 769.94, "word": " هي", "probability": 0.94384765625}, {"start": 769.94, "end": 770.9, "word": " اللي", "probability": 0.76953125}, {"start": 770.9, "end": 771.08, "word": " هي", "probability": 0.91796875}, {"start": 771.08, "end": 771.9, "word": " معلوماتنا", "probability": 0.9798828125}, {"start": 771.9, "end": 772.26, "word": " في", "probability": 0.96875}, {"start": 772.26, "end": 772.96, "word": " المادة", "probability": 0.9817708333333334}, {"start": 772.96, "end": 773.64, "word": " سابقا", "probability": 0.9818115234375}, {"start": 773.64, "end": 774.42, "word": " نيجي", "probability": 0.79083251953125}, {"start": 774.42, "end": 774.8, "word": " الآن", "probability": 0.7144775390625}, {"start": 774.8, "end": 775.6, "word": " نشوف", "probability": 0.97216796875}, {"start": 775.6, "end": 776.64, "word": " ايش", "probability": 0.8439127604166666}, {"start": 776.64, "end": 776.8, "word": " اللي", "probability": 0.990966796875}, {"start": 776.8, "end": 777.06, "word": " بدنا", "probability": 0.967529296875}, {"start": 777.06, "end": 777.62, "word": " نسويه", "probability": 0.98681640625}, {"start": 777.62, "end": 778.24, "word": " بالظبط", "probability": 0.991455078125}], "temperature": 1.0}, {"id": 33, "seek": 79547, "start": 778.95, "end": 795.47, "text": "بدنا نجيب operator الآن أو sequence of operators إنها الـ T and X بتروح للـ TX هذا forever X اللي منتقلته الـ T and X بتروح للـ TX strongly طبعا ولكن but", "tokens": [44510, 8315, 8717, 7435, 1829, 3555, 12973, 6024, 48506, 34051, 8310, 295, 19077, 36145, 11296, 2423, 39184, 314, 293, 1783, 39894, 32887, 5016, 24976, 39184, 314, 55, 23758, 5680, 1783, 13672, 1829, 9154, 2655, 4587, 1211, 47395, 2423, 39184, 314, 293, 1783, 39894, 32887, 5016, 24976, 39184, 314, 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1072.23, "word": " X0", "probability": 0.923095703125}, {"start": 1072.23, "end": 1072.83, "word": " هدي", "probability": 0.4241943359375}, {"start": 1072.83, "end": 1073.05, "word": " زي", "probability": 0.994873046875}, {"start": 1073.05, "end": 1073.27, "word": " هدي", "probability": 0.934814453125}, {"start": 1073.27, "end": 1073.55, "word": " بيطلع", "probability": 0.92255859375}, {"start": 1073.55, "end": 1073.89, "word": " أشمال", "probability": 0.72015380859375}, {"start": 1073.89, "end": 1074.17, "word": " واحد", "probability": 0.910888671875}, {"start": 1074.17, "end": 1074.37, "word": " إذا", "probability": 0.88134765625}, {"start": 1074.37, "end": 1074.63, "word": " نورم", "probability": 0.96435546875}, {"start": 1074.63, "end": 1074.77, "word": " الـ", "probability": 0.727294921875}, {"start": 1074.77, "end": 1074.93, "word": " TN", "probability": 0.925048828125}, {"start": 1074.93, "end": 1075.15, "word": " أكبر", "probability": 0.9873046875}, {"start": 1075.15, "end": 1075.37, "word": " سوى", "probability": 0.7789713541666666}, {"start": 1075.37, "end": 1075.75, "word": " واحد", "probability": 0.949462890625}, {"start": 1075.75, "end": 1076.37, "word": " إذا", "probability": 0.952880859375}, {"start": 1076.37, "end": 1076.61, "word": " نصر", "probability": 0.6212565104166666}, {"start": 1076.61, "end": 1076.73, "word": " من", "probability": 0.68896484375}, {"start": 1076.73, "end": 1077.07, "word": " التنتين", "probability": 0.7024739583333334}, {"start": 1077.07, "end": 1077.23, "word": " مع", "probability": 0.9970703125}, {"start": 1077.23, "end": 1077.49, "word": " بعض", "probability": 0.996337890625}, {"start": 1077.49, "end": 1077.77, "word": " نورم", "probability": 0.9716796875}, {"start": 1077.77, "end": 1077.93, "word": " الـ", "probability": 0.8759765625}, {"start": 1077.93, "end": 1078.09, "word": " TN", "probability": 0.94482421875}, {"start": 1078.09, "end": 1078.37, "word": " بيسوى", "probability": 0.754931640625}, {"start": 1078.37, 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{"start": 1084.76, "end": 1085.32, "word": " يروح", "probability": 0.97900390625}, {"start": 1085.32, "end": 1085.7, "word": " عليه", "probability": 0.96728515625}, {"start": 1085.7, "end": 1086.14, "word": " point", "probability": 0.7958984375}, {"start": 1086.14, "end": 1086.52, "word": " اللي", "probability": 0.91748046875}, {"start": 1086.52, "end": 1086.66, "word": " هو", "probability": 0.96484375}, {"start": 1086.66, "end": 1086.94, "word": " strong", "probability": 0.465087890625}, {"start": 1086.94, "end": 1087.5, "word": " convergence", "probability": 0.9462890625}, {"start": 1087.5, "end": 1088.54, "word": " ال", "probability": 0.6298828125}, {"start": 1088.54, "end": 1089.02, "word": " TN", "probability": 0.848388671875}, {"start": 1089.02, "end": 1089.38, "word": " نقص", "probability": 0.97900390625}, {"start": 1089.38, "end": 1089.74, "word": " Zero", "probability": 0.95654296875}, {"start": 1089.74, "end": 1090.54, "word": " Zero", "probability": 0.1695556640625}, 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"probability": 0.9814453125}, {"start": 1684.62, "end": 1684.88, "word": " and", "probability": 0.96484375}, {"start": 1684.88, "end": 1685.3, "word": " strong", "probability": 0.80224609375}, {"start": 1685.3, "end": 1686.04, "word": " convergence", "probability": 0.94873046875}, {"start": 1686.04, "end": 1686.3, "word": " of", "probability": 0.974609375}, {"start": 1686.3, "end": 1686.56, "word": " any", "probability": 0.9150390625}, {"start": 1686.56, "end": 1687.32, "word": " sequence", "probability": 0.96484375}, {"start": 1687.32, "end": 1688.0, "word": " of", "probability": 0.97216796875}, {"start": 1688.0, "end": 1688.66, "word": " bounded", "probability": 0.9423828125}, {"start": 1688.66, "end": 1689.28, "word": " linear", "probability": 0.9091796875}, {"start": 1689.28, "end": 1691.68, "word": " functionals", "probability": 0.83544921875}, {"start": 1691.68, "end": 1693.1, "word": " are", "probability": 0.203125}, {"start": 1693.1, "end": 1693.36, "word": " the", "probability": 0.90087890625}, {"start": 1693.36, "end": 1693.66, "word": " same", "probability": 0.908203125}, {"start": 1693.66, "end": 1694.42, "word": " يعني", "probability": 0.8896484375}, {"start": 1694.42, "end": 1694.56, "word": " ال", "probability": 0.892578125}, {"start": 1694.56, "end": 1694.88, "word": " weak", "probability": 0.951171875}, {"start": 1694.88, "end": 1695.06, "word": " و", "probability": 0.70263671875}, {"start": 1695.06, "end": 1695.16, "word": " ال", "probability": 0.80419921875}, {"start": 1695.16, "end": 1695.44, "word": " strong", "probability": 0.94921875}, {"start": 1695.44, "end": 1695.6, "word": " أيش", "probability": 0.6068115234375}, {"start": 1695.6, "end": 1696.46, "word": " بيصيرن؟", "probability": 0.7251790364583334}, {"start": 1696.46, "end": 1697.14, "word": " بيصيرن", "probability": 0.9806640625}, {"start": 1697.14, "end": 1697.44, "word": " زي", "probability": 0.96728515625}, {"start": 1697.44, "end": 1697.86, "word": " بعض", "probability": 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{"start": 1739.09, "end": 1739.51, "word": " هنا", "probability": 0.921875}, {"start": 1739.51, "end": 1740.21, "word": " اللي", "probability": 0.951416015625}, {"start": 1740.21, "end": 1740.43, "word": " هو", "probability": 0.9833984375}, {"start": 1740.43, "end": 1740.65, "word": " ال", "probability": 0.94091796875}, {"start": 1740.65, "end": 1741.09, "word": " uniform", "probability": 0.638671875}, {"start": 1741.09, "end": 1742.01, "word": " convergence", "probability": 0.96337890625}, {"start": 1742.01, "end": 1742.67, "word": " هناك", "probability": 0.9892578125}, {"start": 1742.67, "end": 1743.37, "word": " مكافئ", "probability": 0.949462890625}, {"start": 1743.37, "end": 1743.65, "word": " لمين", "probability": 0.6845703125}, {"start": 1743.65, "end": 1743.81, "word": " ال", "probability": 0.44921875}, {"start": 1743.81, "end": 1744.09, "word": " uniform", "probability": 0.87939453125}, {"start": 1744.09, "end": 1744.69, "word": " convergence", "probability": 0.95263671875}, {"start": 1744.69, "end": 1745.27, "word": " إذا", "probability": 0.694091796875}, {"start": 1745.27, "end": 1745.49, "word": " لما", "probability": 0.830810546875}, {"start": 1745.49, "end": 1745.81, "word": " الآن", "probability": 0.730224609375}, {"start": 1745.81, "end": 1746.17, "word": " بدي", "probability": 0.6357421875}, {"start": 1746.17, "end": 1746.49, "word": " أحكي", "probability": 0.95751953125}, {"start": 1746.49, "end": 1746.63, "word": " في", "probability": 0.953125}, {"start": 1746.63, "end": 1746.75, "word": " ال", "probability": 0.96728515625}, {"start": 1746.75, "end": 1747.23, "word": " functional", "probability": 0.496826171875}, {"start": 1747.23, "end": 1747.89, "word": " ركزوا", "probability": 0.8985595703125}, {"start": 1747.89, "end": 1748.19, "word": " الآن", "probability": 0.77587890625}, {"start": 1748.19, "end": 1749.09, "word": " بدي", "probability": 0.893798828125}, {"start": 1749.09, "end": 1749.33, "word": " أحكي", "probability": 0.9908447265625}, 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"probability": 0.9578450520833334}, {"start": 1998.66, "end": 1998.66, "word": " T", "probability": 0.89892578125}, {"start": 1998.66, "end": 2006.36, "word": " تتعامل", "probability": 0.98876953125}, {"start": 2006.36, "end": 2014.52, "word": " بشكل", "probability": 0.9661458333333334}, {"start": 2014.52, "end": 2014.96, "word": " عام", "probability": 0.994873046875}, {"start": 2014.96, "end": 2015.04, "word": " ل", "probability": 0.9111328125}, {"start": 2015.04, "end": 2015.26, "word": " T،", "probability": 0.779052734375}, {"start": 2015.26, "end": 2015.52, "word": " فإن", "probability": 0.9583333333333334}], "temperature": 1.0}, {"id": 85, "seek": 204139, "start": 2015.55, "end": 2041.39, "text": "لكن كنا نقول أن الـ Pointwise لا يستطيع أن المقدرة عنده Fn converge للـF اللي هو زمان، تبع زمان، تبع الـReal أو تبع الـC إذا كانت Fn بتروح للـF pointwise وكانت Fn sequence of continuous functions ليس شرط أن الـF تكون continuous وكنا لما نحكي عن الـintegrable ونحكي عن الـdifferentiability 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"end": 2033.31, "word": " عن", "probability": 0.9794921875}, {"start": 2033.31, "end": 2033.99, "word": " الـintegrable", "probability": 0.67138671875}, {"start": 2033.99, "end": 2034.35, "word": " ونحكي", "probability": 0.88037109375}, {"start": 2034.35, "end": 2034.51, "word": " عن", "probability": 0.9951171875}, {"start": 2034.51, "end": 2035.19, "word": " الـdifferentiability", "probability": 0.85107421875}, {"start": 2035.19, "end": 2035.43, "word": " برضه", "probability": 0.9296875}, {"start": 2035.43, "end": 2035.61, "word": " كان", "probability": 0.98876953125}, {"start": 2035.61, "end": 2035.77, "word": " لهم", "probability": 0.3712158203125}, {"start": 2035.77, "end": 2036.25, "word": " conditions", "probability": 0.85400390625}, {"start": 2036.25, "end": 2036.53, "word": " كان", "probability": 0.9609375}, {"start": 2036.53, "end": 2036.79, "word": " يمكن", "probability": 0.685546875}, {"start": 2036.79, "end": 2037.61, "word": " الـdifferentiability", "probability": 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2578.33, "word": " في", "probability": 0.53515625}, {"start": 2578.33, "end": 2578.47, "word": " ال", "probability": 0.52294921875}, {"start": 2578.47, "end": 2578.85, "word": " norm", "probability": 0.5908203125}, {"start": 2578.85, "end": 2579.27, "word": " تبع", "probability": 0.95361328125}, {"start": 2579.27, "end": 2579.59, "word": " مين؟", "probability": 0.7032877604166666}, {"start": 2579.59, "end": 2579.79, "word": " تبع", "probability": 0.9739583333333334}, {"start": 2579.79, "end": 2579.93, "word": " ال", "probability": 0.93017578125}, {"start": 2579.93, "end": 2580.21, "word": " X", "probability": 0.95947265625}, {"start": 2580.21, "end": 2580.59, "word": " تبع", "probability": 0.84716796875}, {"start": 2580.59, "end": 2580.71, "word": " ال", "probability": 0.9833984375}, {"start": 2580.71, "end": 2580.93, "word": " Y", "probability": 0.9755859375}, {"start": 2580.93, "end": 2581.61, "word": " و", "probability": 0.87451171875}, {"start": 2581.61, "end": 2581.75, "word": " ال", "probability": 0.5517578125}, {"start": 2581.75, "end": 2581.97, "word": " Y", "probability": 0.978515625}, {"start": 2581.97, "end": 2582.19, "word": " إذا", "probability": 0.830322265625}, {"start": 2582.19, "end": 2582.61, "word": " بنخس", "probability": 0.7305501302083334}, {"start": 2582.61, "end": 2582.81, "word": " بي", "probability": 0.77490234375}, {"start": 2582.81, "end": 2582.89, "word": " اس", "probability": 0.232177734375}, {"start": 2582.89, "end": 2583.07, "word": " إذا", "probability": 0.6865234375}, {"start": 2583.07, "end": 2583.47, "word": " TN", "probability": 0.7183837890625}, {"start": 2583.47, "end": 2583.65, "word": " X", "probability": 0.96728515625}, {"start": 2583.65, "end": 2583.99, "word": " الشمال", "probability": 0.8902994791666666}, {"start": 2583.99, "end": 2584.49, "word": " هتكون", "probability": 0.8561197916666666}, {"start": 2584.49, "end": 2585.03, "word": " is", "probability": 0.88525390625}, {"start": 2585.03, "end": 2585.43, "word": " bounded", "probability": 0.951171875}, {"start": 2585.43, "end": 2586.31, "word": " however", "probability": 0.84375}, {"start": 2586.31, "end": 2586.73, "word": " X", "probability": 0.95947265625}, {"start": 2586.73, "end": 2586.95, "word": " is", "probability": 0.9677734375}, {"start": 2586.95, "end": 2587.63, "word": " complete", "probability": 0.84521484375}], "temperature": 1.0}, {"id": 108, "seek": 261133, "start": 2589.05, "end": 2611.33, "text": "صارت هذه bounded و الـ X is complete إذا بالـ Uniform Boundedness Theorem هتحولك الـ boundedness لهذه لـ boundedness لميه للـ TN هتصير اللي هي نوم الـ TN أصغر شهر و C for all N يعني independent of X بتصير هذا الـ Uniform Boundedness وهذه بتطلب الـ X إيش تكون complete", "tokens": [9381, 9640, 2655, 29538, 37498, 4032, 2423, 39184, 1783, 307, 3566, 11933, 15730, 20666, 39184, 1156, 8629, 363, 37706, 1287, 440, 37956, 8032, 2655, 5016, 12610, 4117, 2423, 39184, 37498, 1287, 46740, 24192, 5296, 39184, 37498, 1287, 32767, 1829, 3224, 24976, 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"end": 2591.65, "word": " is", "probability": 0.85986328125}, {"start": 2591.65, "end": 2592.19, "word": " complete", "probability": 0.8525390625}, {"start": 2592.19, "end": 2592.71, "word": " إذا", "probability": 0.70947265625}, {"start": 2592.71, "end": 2593.05, "word": " بالـ", "probability": 0.86083984375}, {"start": 2593.05, "end": 2593.33, "word": " Uniform", "probability": 0.805419921875}, {"start": 2593.33, "end": 2593.99, "word": " Boundedness", "probability": 0.8211263020833334}, {"start": 2593.99, "end": 2594.55, "word": " Theorem", "probability": 0.797119140625}, {"start": 2594.55, "end": 2596.15, "word": " هتحولك", "probability": 0.74677734375}, {"start": 2596.15, "end": 2596.41, "word": " الـ", "probability": 0.72216796875}, {"start": 2596.41, "end": 2597.15, "word": " boundedness", "probability": 0.867431640625}, {"start": 2597.15, "end": 2597.77, "word": " لهذه", "probability": 0.97802734375}, {"start": 2597.77, "end": 2598.29, "word": " لـ", "probability": 0.446533203125}, {"start": 2598.29, "end": 2598.97, "word": " boundedness", "probability": 0.788818359375}, {"start": 2598.97, "end": 2599.29, "word": " لميه", "probability": 0.582275390625}, {"start": 2599.29, "end": 2599.57, "word": " للـ", "probability": 0.676513671875}, {"start": 2599.57, "end": 2599.85, "word": " TN", "probability": 0.79443359375}, {"start": 2599.85, "end": 2600.37, "word": " هتصير", "probability": 0.888671875}, {"start": 2600.37, "end": 2600.49, "word": " اللي", "probability": 0.60699462890625}, {"start": 2600.49, "end": 2600.63, "word": " هي", "probability": 0.72021484375}, {"start": 2600.63, "end": 2600.89, "word": " نوم", "probability": 0.68359375}, {"start": 2600.89, "end": 2601.05, "word": " الـ", "probability": 0.853515625}, {"start": 2601.05, "end": 2601.29, "word": " TN", "probability": 0.836181640625}, {"start": 2601.29, "end": 2601.51, "word": " أصغر", "probability": 0.91259765625}, {"start": 2601.51, "end": 2601.77, "word": " شهر", "probability": 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0.736328125}, {"start": 2607.21, "end": 2607.65, "word": " Uniform", "probability": 0.926025390625}, {"start": 2607.65, "end": 2608.51, "word": " Boundedness", "probability": 0.890625}, {"start": 2608.51, "end": 2608.81, "word": " وهذه", "probability": 0.698974609375}, {"start": 2608.81, "end": 2609.49, "word": " بتطلب", "probability": 0.8224283854166666}, {"start": 2609.49, "end": 2609.77, "word": " الـ", "probability": 0.806640625}, {"start": 2609.77, "end": 2609.97, "word": " X", "probability": 0.974609375}, {"start": 2609.97, "end": 2610.19, "word": " إيش", "probability": 0.7509765625}, {"start": 2610.19, "end": 2610.67, "word": " تكون", "probability": 0.9853515625}, {"start": 2610.67, "end": 2611.33, "word": " complete", "probability": 0.56982421875}], "temperature": 1.0}, {"id": 109, "seek": 262679, "start": 2612.81, "end": 2626.79, "text": "هنا Hence خدوا نورم الـ TN X هيكون أصغر أو ساوى نورم الـ TN في نورم الـ X وهذه أصغر أو ساوى C في نورم الـ X الآن دخلوا ال limit علي الجهد التاني وستستخدموا ال continuity لل TN و ال continuity لل norm", "tokens": [3224, 8315, 22229, 16490, 3215, 14407, 8717, 13063, 2304, 2423, 39184, 314, 45, 1783, 39896, 30544, 5551, 9381, 17082, 2288, 34051, 8608, 995, 2407, 7578, 8717, 13063, 2304, 2423, 39184, 314, 45, 8978, 8717, 13063, 2304, 2423, 39184, 1783, 37037, 24192, 5551, 9381, 17082, 2288, 34051, 8608, 995, 2407, 7578, 383, 8978, 8717, 13063, 2304, 2423, 39184, 1783, 6024, 48506, 11778, 9778, 1211, 14407, 2423, 4948, 25894, 25724, 3224, 3215, 16712, 7649, 1829, 4032, 14851, 14851, 9778, 40448, 14407, 2423, 23807, 24976, 314, 45, 4032, 2423, 23807, 24976, 2026], "avg_logprob": -0.3562499887413449, "compression_ratio": 1.808139534883721, "no_speech_prob": 3.337860107421875e-06, "words": [{"start": 2612.81, "end": 2613.17, "word": "هنا", "probability": 0.26287841796875}, {"start": 2613.17, "end": 2613.61, "word": " Hence", "probability": 0.279052734375}, {"start": 2613.61, "end": 2614.01, "word": " خدوا", "probability": 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TN", "probability": 0.714599609375}, {"start": 2625.67, "end": 2625.75, "word": " و", "probability": 0.5234375}, {"start": 2625.75, "end": 2625.83, "word": " ال", "probability": 0.377197265625}, {"start": 2625.83, "end": 2626.21, "word": " continuity", "probability": 0.638671875}, {"start": 2626.21, "end": 2626.47, "word": " لل", "probability": 0.8525390625}, {"start": 2626.47, "end": 2626.79, "word": " norm", "probability": 0.56396484375}], "temperature": 1.0}, {"id": 110, "seek": 265194, "start": 2627.96, "end": 2651.94, "text": "هذا صار أصغر أشهر و C في X دخلوا ال limit هنا واستخدوا ال continuity لل TN و ال continuity نميين لل norm بس يوم norm limit ال TN ال X هو TX وهذا limit اللي هو norm TN X أصغر أشهر و C في norm X hence اللي هي صارت عند T is bounded then T element in B X أو Y اطلع للفوق البعدها let X", "tokens": [3224, 15730, 20328, 9640, 5551, 9381, 17082, 2288, 5551, 8592, 3224, 2288, 4032, 383, 8978, 1783, 11778, 9778, 1211, 14407, 2423, 4948, 34105, 36764, 14851, 9778, 3215, 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ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال", "tokens": [6027, 20292, 31439, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 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2873.81, "end": 2874.61, "word": "بحصل", "probability": 0.6121419270833334}, {"start": 2874.61, "end": 2875.33, "word": " معالي", "probability": 0.6769205729166666}, {"start": 2875.33, "end": 2875.85, "word": " وانا", "probability": 0.8351236979166666}, {"start": 2875.85, "end": 2876.07, "word": " fixed", "probability": 0.619140625}, {"start": 2876.07, "end": 2876.37, "word": " x", "probability": 0.8251953125}, {"start": 2876.37, "end": 2876.53, "word": " we", "probability": 0.409912109375}, {"start": 2876.53, "end": 2876.87, "word": " have", "probability": 0.95849609375}, {"start": 2876.87, "end": 2877.79, "word": " احسبلي", "probability": 0.8524169921875}, {"start": 2877.79, "end": 2878.45, "word": " Tnx", "probability": 0.4095052083333333}, {"start": 2878.45, "end": 2878.85, "word": " نقص", "probability": 0.6551106770833334}, {"start": 2878.85, "end": 2879.53, "word": " Tmx", "probability": 0.9358723958333334}, {"start": 2879.53, "end": 2880.37, "word": " اللي", "probability": 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diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/dAhzu2_CB2I_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/dAhzu2_CB2I_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..18b0862b6fe66a5cd217b03bc9f4154723ffc458
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/dAhzu2_CB2I_raw.srt
@@ -0,0 +1,724 @@
+1
+00:00:05,470 --> 00:00:08,230
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,230 --> 00:00:11,930
+والصلاة والسلام على سيد المرسلين سيدنا محمد على
+
+3
+00:00:11,930 --> 00:00:15,690
+آله وصحبه أجمعين هذه المحاضرة رقم اربع وتلاتين
+
+4
+00:00:15,690 --> 00:00:20,310
+مساق تحليل daily او تحليل اقتراني طلاب وطالبات
+
+5
+00:00:20,310 --> 00:00:27,030
+الجامعة الإسلامية ماجستير رياضية وصلنا لعند اربع
+
+6
+00:00:27,030 --> 00:00:31,250
+اتناش اللي هي ال open mapping theorem اللي هي عشر
+
+7
+00:00:31,250 --> 00:00:32,490
+او واحداش مش مقلبات
+
+8
+00:00:35,050 --> 00:00:39,410
+النظرية الثالثة في من النظريات الأساسية بعد ال
+
+9
+00:00:39,410 --> 00:00:47,350
+uniform boundedness theorem هو أخدناها المرة
+
+10
+00:00:47,350 --> 00:00:50,310
+الماضية وهذه الثالثة وقبلها أخدنا لها البنغ
+
+11
+00:00:50,310 --> 00:00:54,990
+theorem فبكون هذه الثالث نظرية أساسية ونظريات اللي
+
+12
+00:00:54,990 --> 00:01:00,090
+اللي بنعتبرها أساسية في مساق اللي هو أو في تحليل
+
+13
+00:01:00,090 --> 00:01:07,130
+في التحليل الداليالدفينيشن اللي أخدناها قبل هيك
+
+14
+00:01:07,130 --> 00:01:12,270
+بعتقد اللي هو شو معناته open mapping let
+
+15
+00:01:12,270 --> 00:01:15,870
+X be and Y be metric spaces then T من domain of T
+
+16
+00:01:15,870 --> 00:01:20,390
+لعند Y with domain of T جزء من ال metric space X
+
+17
+00:01:20,390 --> 00:01:23,690
+is called an open mapping هذا اللي هو open mapping
+
+18
+00:01:23,690 --> 00:01:27,830
+ده كان بيرسل ال open ل openباختصار الان ال
+
+19
+00:01:27,830 --> 00:01:32,170
+continuous برجع ورجوع بياخد اللي هو the inverse
+
+20
+00:01:32,170 --> 00:01:36,490
+image of open event is open إذا هاي اللي هو معناته
+
+21
+00:01:36,490 --> 00:01:39,390
+ال open mapping نيجي الآن لللمة اللي عندها دي اللي
+
+22
+00:01:39,390 --> 00:01:44,010
+ما بنقش و رهنها اللي هي بتقول مع أنه قبل ذلك احنا
+
+23
+00:01:44,010 --> 00:01:49,490
+رهنناها يعني اربعة اتنين اتنين اللي اما bounded
+
+24
+00:01:49,490 --> 00:01:55,760
+linear operator T from أبنخ space XX on to a
+
+25
+00:01:55,760 --> 00:01:59,880
+banach space Y has the property that the image T
+
+26
+00:01:59,880 --> 00:02:05,400
+of B of the open unit ball B اللي هو contains an
+
+27
+00:02:05,400 --> 00:02:11,120
+open ball about zero element in Y يعني الآن لو كان
+
+28
+00:02:11,120 --> 00:02:19,220
+عندي ال T عبارة عن bounded linear operator بس من
+
+29
+00:02:19,220 --> 00:02:28,340
+وين لوينمن بنخس Base X لبنخس Base Yبقول اللي هو
+
+30
+00:02:28,340 --> 00:02:31,580
+bounded linear operator T يعني زي على لغتنا اللي
+
+31
+00:02:31,580 --> 00:02:35,820
+كنا نحكي فيها المرة الماضية T element in B L أو B
+
+32
+00:02:35,820 --> 00:02:41,280
+of X أو Y أو B L of X Y حالها السابقة ال .. ال ..
+
+33
+00:02:41,280 --> 00:02:46,260
+ال .. ال .. الرمز اللي احنا بنستخدمه اللي هو the
+
+34
+00:02:46,260 --> 00:02:48,820
+space of all bounded linear operators لو كان T is
+
+35
+00:02:48,820 --> 00:02:52,220
+a bounded linear operator then it has البرمجة
+
+36
+00:02:52,220 --> 00:03:00,650
+التالية أنه لو أجينا أخدنا أي أبنUnit ball B 0 و 1
+
+37
+00:03:00,650 --> 00:03:13,450
+المركز 0 و نصف القطر 1 من الـ X هذه ترسلها تي أوف
+
+38
+00:03:13,450 --> 00:03:21,690
+بي إلى تي أوف بي اللي بتحتوي في داخلها على open
+
+39
+00:03:21,690 --> 00:03:31,120
+ball B primeاللي هو with center 0 ووركز R for some
+
+40
+00:03:31,120 --> 00:03:36,880
+R أكبر من 0إذا اللي هي الـ bounded linear operator
+
+41
+00:03:36,880 --> 00:03:40,360
+from أبناء في space into أبناء في space أو into
+
+42
+00:03:40,360 --> 00:03:45,460
+أبناء في space has the property that it اللي هو
+
+43
+00:03:45,460 --> 00:03:52,700
+any ball ال unit ball في ال X هيكون T of B يحتوي
+
+44
+00:03:52,700 --> 00:03:59,830
+في داخلها open ball يعني open circleالان .. الان
+
+45
+00:03:59,830 --> 00:04:03,850
+.. هذه الخاصية على الـ B نفسها الان في النظرية
+
+46
+00:04:03,850 --> 00:04:05,910
+اللي هو بالما بين فيه اللي بدأت تنجل الخاصية على
+
+47
+00:04:05,910 --> 00:04:08,850
+كل ال .. ال .. ال .. ال sets يعني مش بدأت هي تنجل
+
+48
+00:04:08,850 --> 00:04:12,330
+ال open .. ال .. نجلة اللي هو ال .. ال .. ال .. ال
+
+49
+00:04:12,330 --> 00:04:15,870
+.. ال open unit ball إلى open set لأ بدت تنجل أي
+
+50
+00:04:15,870 --> 00:04:19,210
+open set إلى مين إلى open set يعني صارت اللي هو
+
+51
+00:04:19,210 --> 00:04:23,410
+برهان النظرية سهل اعتمادا على مين؟ على اللي ماء
+
+52
+00:04:23,410 --> 00:04:28,230
+اللي فوقفي بعض الكتب ممكن يبدأ لك من الصفر من هنا
+
+53
+00:04:28,230 --> 00:04:31,490
+و يبدأ يبرهن في داخله اللمّة في الواقع بياخد أولا
+
+54
+00:04:31,490 --> 00:04:34,770
+حالة الهادي وبعدين منها بنتقل إلى الحالة العامة
+
+55
+00:04:34,770 --> 00:04:39,110
+الان احنا بدنا اللي هو طبعا ضيق الوقت وعنا يعني
+
+56
+00:04:39,110 --> 00:04:45,620
+خليني أقول صارت الكمية شوية يعني كبيرة يعنيفبدنا
+
+57
+00:04:45,620 --> 00:04:49,820
+ناخد اللي هو ال open mapping theorem اللي نسميها
+
+58
+00:04:49,820 --> 00:04:55,060
+bounded inverse theorem هو الاسم هذا ال open
+
+59
+00:04:55,060 --> 00:04:57,660
+mapping theorem لإنه هي بترسل open إلى open هي
+
+60
+00:04:57,660 --> 00:05:01,840
+واحد اللي هي ال bounded operator الشغل الثاني لو
+
+61
+00:05:01,840 --> 00:05:05,040
+كانت one to one و one to two بيصير اللي هو ال
+
+62
+00:05:05,040 --> 00:05:09,830
+inverseماله is a bounded linear operator لانه
+
+63
+00:05:09,830 --> 00:05:13,270
+بيصير اللي هو continuous وماكن continuous وlinear
+
+64
+00:05:13,270 --> 00:05:17,030
+لذا راح يصير اشماله اللي هو bounded لان انتوا
+
+65
+00:05:17,030 --> 00:05:19,490
+عارفين ان ال continuity تكافئ ال boundedness في
+
+66
+00:05:19,490 --> 00:05:22,890
+حالة من ال linear operators اتفجنا عليها هذا زمان
+
+67
+00:05:23,880 --> 00:05:28,440
+طيب a bounded linear operator from a بنخس base x
+
+68
+00:05:28,440 --> 00:05:35,040
+onto a بنخس base y is an open mapping هذه الإعلان
+
+69
+00:05:35,040 --> 00:05:40,060
+اللي هو الآن any bounded linear operator يعني أنت
+
+70
+00:05:40,060 --> 00:05:43,120
+بتعطيني وقت إيش بيكون ال bounded linear operator
+
+71
+00:05:43,120 --> 00:05:47,420
+أو ال continuous operator وقت إيش بيكون open إذا
+
+72
+00:05:47,420 --> 00:05:54,030
+كان ال T من بنخس base لبنخس baseوكان الـ T عبارة
+
+73
+00:05:54,030 --> 00:06:00,870
+عن bounded linear operator هذا بيقوللي أكيد هيطلع
+
+74
+00:06:00,870 --> 00:06:06,540
+طبعا on toأكيد حيطلع عندي إيش ماله الـ T is an
+
+75
+00:06:06,540 --> 00:06:10,620
+open mapping أو الـ T is open هذه النظرية خلّيني
+
+76
+00:06:10,620 --> 00:06:14,480
+أتبرهن لأن الجزء الثاني اللي بيظل hence if T is
+
+77
+00:06:14,480 --> 00:06:19,280
+bijective مثلا تي بيجيكتف صارت إيش مالها one to
+
+78
+00:06:19,280 --> 00:06:22,180
+one و one to two إذا ال inverse صارت موجودة و ال
+
+79
+00:06:22,180 --> 00:06:26,200
+inverse ما هي من خاصية ال open هياخد ال open و
+
+80
+00:06:26,200 --> 00:06:30,810
+يرجع لمن؟ ل open و يكون احناالـ T inverse طبعاً هو
+
+81
+00:06:30,810 --> 00:06:32,890
+الـ T بودّي الـ open لـ open صارت الـ T inverse هي
+
+82
+00:06:32,890 --> 00:06:35,610
+ترجع الـ open لـ open إذا صارت الـ T inverse is
+
+83
+00:06:35,610 --> 00:06:38,290
+continuous is then bounded لأنها تكون linear
+
+84
+00:06:38,290 --> 00:06:42,510
+automatic إذا من الجزء الثاني إذا أثبتنا الأول
+
+85
+00:06:42,510 --> 00:06:47,530
+خلصنا خلّينا عشان ما أطولش عليكم لأن let E عشان
+
+86
+00:06:47,530 --> 00:06:51,590
+أثبتوا أن T is open بتاخد open ست هنا و أثبتلك إن
+
+87
+00:06:51,590 --> 00:06:57,260
+هي أشمالها open في مين؟ في ال Y خلّينا ناخد الآنهي
+
+88
+00:06:57,260 --> 00:07:05,000
+عندي الان T من X لعند Y onto function خد الان let
+
+89
+00:07:05,000 --> 00:07:10,360
+A subset من مين من X ماشي الحال الان و ال A
+
+90
+00:07:10,360 --> 00:07:13,840
+مااخدها انا A شمالها open set بدي اثبتلكم ال T of
+
+91
+00:07:13,840 --> 00:07:20,000
+A is open بدي اثبت ال T of A is open كيف اثبتها
+
+92
+00:07:20,000 --> 00:07:23,860
+باخد اي نقطة هنا و بلاقي بقى كل مكان ماله جوا ت ال
+
+93
+00:07:23,860 --> 00:07:30,820
+T of A طيبالان لت Y بتساوي TX طبعا اكيد TX هتكون
+
+94
+00:07:30,820 --> 00:07:36,220
+بأي element منين in T of A عشان ألاجي ball حوالها
+
+95
+00:07:36,220 --> 00:07:39,640
+تكون في داخل ال team في A طيب صارت الان ال Y
+
+96
+00:07:39,640 --> 00:07:41,780
+بتساوي Y element in T of A
+
+97
+00:07:45,360 --> 00:07:48,820
+إذاً صار معناه y element in T of A إذاً صار there
+
+98
+00:07:48,820 --> 00:07:53,600
+exist x element in A such that Tx هي مين ال Y
+
+99
+00:07:53,600 --> 00:07:57,940
+مظبوط ولا لأ؟ هيت معناه يهو y element in T of A
+
+100
+00:07:57,940 --> 00:08:03,920
+إذاً ما هي A open since A is open then A contains
+
+101
+00:08:03,920 --> 00:08:08,660
+an open ball with center مين X إذاً صارت مادام A
+
+102
+00:08:08,660 --> 00:08:15,180
+is open إذا عندي فيه ballwith center X و Radius R
+
+103
+00:08:15,180 --> 00:08:22,960
+جزئية من الـ Min من الـ A Hence,
+
+104
+00:08:23,080 --> 00:08:28,260
+A minus XX contains an open ball with center Min 0
+
+105
+00:08:28,260 --> 00:08:37,780
+بتكون A minus X تحتوي ball with center Min 0 و
+
+106
+00:08:37,780 --> 00:08:43,450
+some radius اللي هو R طيب كيف هذه؟خدوا الـ Element
+
+107
+00:08:43,450 --> 00:08:47,030
+هنا وبدأ أوصلكم إيه وإيه موجودها اعتمادًا على هذه
+
+108
+00:08:47,030 --> 00:08:51,030
+الـ Element هذه الان اتفجنا انه متحقق هذي بيقولك
+
+109
+00:08:51,030 --> 00:08:57,830
+انت اعطيها هذي خدوا الان Y element بي Zero R ايش
+
+110
+00:08:57,830 --> 00:09:03,210
+معناته ان المسافة بين هذي و هذي أصغر من R ماشي
+
+111
+00:09:03,210 --> 00:09:08,530
+الحال الان عندك المسافةعشان بتثبت أنه .. بتثبت أنه
+
+112
+00:09:08,530 --> 00:09:12,170
+ال .. ال .. ال .. ال .. ال element المهانة element
+
+113
+00:09:12,170 --> 00:09:18,630
+هنا ماشي الحال الان عندك ال Y يعني و ك .. و كأنه
+
+114
+00:09:18,630 --> 00:09:22,670
+بتثبت ال Y هنا يعني و كأنه بتثبت ال Y زياد X اللي
+
+115
+00:09:22,670 --> 00:09:26,950
+هو وين موجودة في هذه ده نشوف كيف عندى لو جيت أخدت
+
+116
+00:09:26,950 --> 00:09:35,090
+ال Y زياد X Y زياد X ماقص ال X صح؟ اللي هي إيش
+
+117
+00:09:35,090 --> 00:09:40,910
+بتساوي؟الـY ما هي الـY هنا إذا أنا هتكون أصغر من
+
+118
+00:09:40,910 --> 00:09:46,730
+مين يعني ساعة الـY زيادة X وين موجودة؟ في هذه، صح؟
+
+119
+00:09:46,730 --> 00:09:49,430
+مادة ما صارت في هنا إذا الـY زيادة X فين؟ في الـA
+
+120
+00:09:49,430 --> 00:09:53,430
+إذا صارت الـY زيادة X في الـA إيش معناه الـY زيادة
+
+121
+00:09:53,430 --> 00:09:58,230
+X في الـA؟ يعني الـY element الـA minus من؟ minus
+
+122
+00:09:58,230 --> 00:10:02,890
+الـXيعني بدأت الآن Y في الـ Heavy وانتهيت Y موجودة
+
+123
+00:10:02,890 --> 00:10:06,590
+في الـ A-X إذاً اعتمادًا على هذه بما أن الـ A
+
+124
+00:10:06,590 --> 00:10:11,530
+تحتوي على الـ ball X و R أكيد الـ A-X هتحتوي على
+
+125
+00:10:11,530 --> 00:10:16,910
+مين؟ على الـ B, 0, H, R وهذا يعني أن A-X نفسها is
+
+126
+00:10:16,910 --> 00:10:22,670
+open خلّيني هذا خطوة الـ Hence A-X contains an
+
+127
+00:10:22,670 --> 00:10:27,900
+open ball with center 0اللي هنلق ال radius of the
+
+128
+00:10:27,900 --> 00:10:31,300
+ball ايش ماله؟ R، احنا مسميه R ال radius of the
+
+129
+00:10:31,300 --> 00:10:36,140
+ball بساوي R لأن end K بساوي هذا ال R، then K في A
+
+130
+00:10:36,140 --> 00:10:41,360
+minus X، اللي هنهيعنى اتفجنا عشان تكون واضحة لكم
+
+131
+00:10:42,210 --> 00:10:47,470
+إتفجنا إن الـ a-x تحتوي على هذه، لو الآن أخدنا
+
+132
+00:10:47,470 --> 00:10:52,130
+الواحد على R في هذه، هتكون بتحتوي على مين؟ الـ
+
+133
+00:10:52,130 --> 00:10:57,010
+ball، zero و مين و واحد، و أثبتها سهل كمان يعني،
+
+134
+00:10:57,010 --> 00:10:59,910
+زي هذه، مجرد إن الواحد ده لكيد تدخل، تدخل في الـ
+
+135
+00:10:59,910 --> 00:11:03,910
+norm و تدخل في تعريف الـ a-x إذا صار عندي يا
+
+136
+00:11:03,910 --> 00:11:11,060
+جماعة، الآن زي ما اتفجناالـ A أخدت الـ K بصيحة 1
+
+137
+00:11:11,060 --> 00:11:14,000
+على 4 ثم اللي هي الـ 1 على R اللي هي الـ K في A
+
+138
+00:11:14,000 --> 00:11:16,960
+minus X زي ما قلنا هنا Contains the open ball mean
+
+139
+00:11:16,960 --> 00:11:22,540
+B01 الآن إيش بتستخدم؟ اللمّة Then by لمّة أربعة و
+
+140
+00:11:22,540 --> 00:11:26,300
+أتناش اتنين اتنين اتنين بيكون الـ T لهذه الست اللي
+
+141
+00:11:26,300 --> 00:11:30,580
+هو بحتوي بيصير الـ T لهذه الست الآن هذه الست اللي
+
+142
+00:11:30,580 --> 00:11:38,730
+هي K اتفجنا الآن أوصلنا إلى إنه الـ Kاللي هي الـ 1
+
+143
+00:11:38,730 --> 00:11:42,630
+على R أو الـ K زي ما بيبقى بيحسبوا في A minus X
+
+144
+00:11:42,630 --> 00:11:52,410
+هذه contains an open ball with center 0 ماشي
+
+145
+00:11:52,410 --> 00:12:00,030
+الحال؟ طيب الآن هذه اللي هي الـ K A minus X الـ T
+
+146
+00:12:00,030 --> 00:12:06,020
+لها هي اللي بتحتوي Aمن اللمّة اللي جوه احتواط الـ
+
+147
+00:12:06,020 --> 00:12:09,360
+open vol هي هتحتوى من مين open vol about مين اللي
+
+148
+00:12:09,360 --> 00:12:15,680
+هو الـ zero هذه نفسها عبارة عنطبعا الـ T Linear
+
+149
+00:12:15,680 --> 00:12:18,780
+الـ K لما يدخل على أي element بتطلع بتعرفوا تثبتوا
+
+150
+00:12:18,780 --> 00:12:25,240
+هذا بتاخدوا ال element هنا تاخدوا ال T of K a
+
+151
+00:12:25,240 --> 00:12:28,740
+small نقص X و بعدين تطلعوه برا او الاخر تطلع نفس
+
+152
+00:12:28,740 --> 00:12:34,060
+الشيء بسوء K of T of A نقص mean T of X هذي
+
+153
+00:12:34,060 --> 00:12:39,490
+contains a ball about mean zeroالآن unthought T of
+
+154
+00:12:39,490 --> 00:12:44,810
+A نقص T X بتحتوي اللي هو برضه open المؤمن يعني
+
+155
+00:12:44,810 --> 00:12:55,650
+الآن K T of A minus X contains اللي هو سمناها
+
+156
+00:12:55,650 --> 00:13:03,130
+عبارة عن K T of A نقص T X، مظبوط؟ هذه كلها على بعض
+
+157
+00:13:03,130 --> 00:13:15,950
+بتحتوي ballزيرو و ريدس إبشلون الان عندي ك مش هتفرق
+
+158
+00:13:15,950 --> 00:13:19,790
+معاها بس هتفرق في ريدس تبع حاجة بيصير T of A minus
+
+159
+00:13:19,790 --> 00:13:26,070
+T of X بتحتوي على ball بيزيرو و بيصير إبشلون في
+
+160
+00:13:26,070 --> 00:13:33,240
+مين في ك نصف القطر بس بتتغير أو على كلأن هذا
+
+161
+00:13:33,240 --> 00:13:37,320
+بيحتوي هذا إذا نزلنا عاملنا قبل بشوية هيصير T of A
+
+162
+00:13:37,320 --> 00:13:45,580
+يحتوي ball إذا قشنطت دي صراحة TX وY صح؟ اللي هو
+
+163
+00:13:45,580 --> 00:13:50,580
+مين؟ ball Y اللي سميناها من رأس الدور Y و some
+
+164
+00:13:50,580 --> 00:13:56,300
+radius اللي هو R إذا صرت T of A contains a ball
+
+165
+00:13:56,300 --> 00:14:02,590
+about مين؟ اللي هو TX بالساوي Yالان اخدنا احنا اذا
+
+166
+00:14:02,590 --> 00:14:07,970
+ايش اللي صار في كل الجثة انه اخدت a open set واخدت
+
+167
+00:14:07,970 --> 00:14:12,490
+اللي هي arbitrary y عند T of a لجأتي اللي هو T of
+
+168
+00:14:12,490 --> 00:14:17,170
+a بتحتوي open بولة about مين ال Y وهذا معنى ايش
+
+169
+00:14:17,170 --> 00:14:21,770
+انه but Y was arbitrary then T of a is open
+
+170
+00:14:21,770 --> 00:14:28,490
+therefore T is an open mapping اي سؤال؟ طيب اخر
+
+171
+00:14:28,490 --> 00:14:28,950
+نقطة
+
+172
+00:14:35,020 --> 00:14:41,240
+خلّيني بس نكمل Therefore
+
+173
+00:14:41,240 --> 00:14:45,600
+T is an open mapping ماشي الحال finally if T is
+
+174
+00:14:45,600 --> 00:14:51,420
+bijective then T inverse exist and linear by
+
+175
+00:14:51,420 --> 00:14:56,760
+theorem 2,6,10 طبعا هذا الكلام مفهوم however T is
+
+176
+00:14:56,760 --> 00:15:03,300
+open by open mapping theorem by theorem 1,3,4إذاً
+
+177
+00:15:03,300 --> 00:15:07,260
+T is إيش مالها؟ continuous كل هذا خدناتنا بهذه
+
+178
+00:15:07,260 --> 00:15:10,820
+الطريقة الآن and so by theorem إتنين سبعة تسعة
+
+179
+00:15:10,820 --> 00:15:13,760
+مدام تكون continuous هذا كل كل اللي قلته في أول
+
+180
+00:15:13,760 --> 00:15:17,900
+محاضرة إذاً is bounded وهيك بيكون الله يعطيك
+
+181
+00:15:17,900 --> 00:15:19,420
+العافية وإلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/fs3UcYAAOXg_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/fs3UcYAAOXg_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..0ae6d2c1bb98975bd012e75374a6db9a1864d722
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/fs3UcYAAOXg_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 1955, "start": 5.04, "end": 19.56, "text": "بسم الله الرحمن الرحيم الحمد لله رب العالمين والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى آله وصحابي أجمعين هذه المحاضرة رقم 18 مساق تحليل دالي أو تحليل إقتراني طلاب وطالبات الجامعة الإسلامية ماجستير رياضية", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21542, 2304, 3215, 24976, 3224, 12602, 3555, 18863, 45340, 9957, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 8608, 25708, 9673, 2288, 3794, 1211, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 19753, 43761, 4032, 9381, 5016, 16758, 1829, 5551, 7435, 2304, 3615, 9957, 29538, 9673, 5016, 46958, 25720, 12602, 4587, 2304, 2443, 47524, 995, 4587, 6055, 5016, 20292, 1211, 11778, 6027, 1829, 34051, 6055, 5016, 20292, 1211, 11933, 38149, 2288, 7649, 1829, 23032, 15040, 3555, 4032, 9566, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 3714, 26108, 14851, 13546, 12602, 1829, 46958, 10632], "avg_logprob": -0.11458333547192591, "compression_ratio": 1.92964824120603, "no_speech_prob": 0.0004711151123046875, "words": [{"start": 5.04, "end": 5.42, "word": "بسم", "probability": 0.81689453125}, {"start": 5.42, "end": 5.58, "word": " الله", "probability": 0.9541015625}, {"start": 5.58, "end": 5.92, "word": " الرحمن", "probability": 0.95947265625}, {"start": 5.92, "end": 6.32, "word": " الرحيم", "probability": 0.994140625}, {"start": 6.32, "end": 6.66, "word": " الحمد", "probability": 0.88037109375}, {"start": 6.66, "end": 6.94, "word": " لله", "probability": 0.955078125}, {"start": 6.94, "end": 7.16, "word": " رب", "probability": 0.964111328125}, {"start": 7.16, "end": 7.66, "word": " العالمين", "probability": 0.9934895833333334}, {"start": 7.66, "end": 8.06, "word": " والصلاة", "probability": 0.81884765625}, {"start": 8.06, "end": 8.44, "word": " والسلام", "probability": 0.96728515625}, {"start": 8.44, "end": 8.64, "word": " على", "probability": 0.58056640625}, {"start": 8.64, "end": 8.92, "word": " سيد", "probability": 0.96630859375}, {"start": 8.92, "end": 9.42, "word": " المرسلين", "probability": 0.98779296875}, {"start": 9.42, "end": 9.8, "word": " سيدنا", "probability": 0.9671223958333334}, {"start": 9.8, "end": 10.16, "word": " محمد", "probability": 0.9814453125}, {"start": 10.16, "end": 10.38, "word": " وعلى", "probability": 0.87890625}, {"start": 10.38, "end": 10.6, "word": " آله", "probability": 0.748779296875}, {"start": 10.6, "end": 11.0, "word": " وصحابي", "probability": 0.79072265625}, {"start": 11.0, "end": 11.48, "word": " أجمعين", "probability": 0.83720703125}, {"start": 11.48, "end": 12.16, "word": " هذه", "probability": 0.8232421875}, {"start": 12.16, "end": 12.66, "word": " المحاضرة", "probability": 0.9833984375}, {"start": 12.66, "end": 12.94, "word": " رقم", "probability": 0.9264322916666666}, {"start": 12.94, "end": 13.56, "word": " 18", "probability": 0.80322265625}, {"start": 13.56, "end": 14.2, "word": " مساق", "probability": 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"text": "ووصلنا لعند اليوم عند section 3-2 further properties of inner product spaces اللي هي خواص أخرى لل inner product spaces والمحاضرة ليه قصيرة وسهلة على السري ان شاء الله اللي هي لمّة الأولى 3-2-1 اللي هم تسميها Schwarz Inquality و Triangle Inquality", "tokens": [2407, 2407, 36520, 8315, 5296, 3615, 41260, 45595, 20498, 43242, 3541, 805, 12, 17, 3052, 7221, 295, 7284, 1674, 7673, 13672, 1829, 39896, 16490, 14407, 9381, 5551, 34740, 7578, 24976, 7284, 1674, 7673, 4032, 45340, 5016, 46958, 25720, 32239, 3224, 12174, 9381, 48923, 46952, 3224, 37977, 15844, 21136, 16572, 16472, 13412, 16606, 21984, 13672, 1829, 39896, 32767, 11703, 3660, 16247, 12610, 7578, 805, 12, 17, 12, 16, 13672, 1829, 8032, 2304, 6055, 38251, 1829, 11296, 2065, 31991, 682, 11286, 4032, 10931, 7846, 682, 11286], "avg_logprob": -0.2621323543436387, "compression_ratio": 1.5130434782608695, "no_speech_prob": 1.8477439880371094e-05, "words": [{"start": 20.37, "end": 21.17, "word": "ووصلنا", "probability": 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{"start": 78.03, "end": 78.29, "word": " في", "probability": 0.9306640625}, {"start": 78.29, "end": 79.75, "word": " حالة", "probability": 0.8326822916666666}, {"start": 79.75, "end": 79.89, "word": " الـ", "probability": 0.60107421875}, {"start": 79.89, "end": 80.11, "word": " inner", "probability": 0.650390625}, {"start": 80.11, "end": 80.35, "word": " و", "probability": 0.34033203125}, {"start": 80.35, "end": 80.83, "word": " product", "probability": 0.88525390625}, {"start": 80.83, "end": 81.77, "word": " الآن", "probability": 0.5972900390625}, {"start": 81.77, "end": 82.41, "word": " where", "probability": 0.6767578125}, {"start": 82.41, "end": 82.63, "word": " the", "probability": 0.72119140625}, {"start": 82.63, "end": 83.15, "word": " equality", "probability": 0.9267578125}, {"start": 83.15, "end": 83.63, "word": " sign", "probability": 0.90380859375}, {"start": 83.63, "end": 83.85, "word": " هذا", "probability": 0.59375}, {"start": 83.85, "end": 84.15, "word": " طبعا", 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"word": " و", "probability": 0.73095703125}, {"start": 1030.28, "end": 1030.4, "word": " Y", "probability": 0.91064453125}, {"start": 1030.4, "end": 1030.7, "word": " بضل", "probability": 0.5779622395833334}, {"start": 1030.7, "end": 1031.22, "word": " التفاصيل", "probability": 0.9700927734375}, {"start": 1031.22, "end": 1031.66, "word": " لكم", "probability": 0.6544189453125}, {"start": 1031.66, "end": 1032.38, "word": " لإنها", "probability": 0.6650390625}, {"start": 1032.38, "end": 1032.74, "word": " تفاصيل", "probability": 0.9857177734375}, {"start": 1032.74, "end": 1033.24, "word": " حسابات", "probability": 0.8363037109375}, {"start": 1033.24, "end": 1033.42, "word": " و", "probability": 0.9658203125}, {"start": 1033.42, "end": 1033.68, "word": " إلى", "probability": 0.68994140625}, {"start": 1033.68, "end": 1034.0, "word": " لقاء", "probability": 0.83154296875}, {"start": 1034.0, "end": 1034.3, "word": " الآخر", "probability": 0.820556640625}, {"start": 1034.3, "end": 1034.64, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/g1UMuLpn1XM.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/g1UMuLpn1XM.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f68fe5e2bee1083585041b48b1d92c668c4396dd
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/g1UMuLpn1XM.srt
@@ -0,0 +1,2699 @@
+1
+00:00:05,130 --> 00:00:07,790
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,790 --> 00:00:10,810
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:10,810 --> 00:00:14,850
+آله وصحبه أجمعين هذه هي المحاضرة الخامسة مساق 
+
+4
+00:00:14,850 --> 00:00:19,890
+تحليل اقتراني أو تحليل دالي لطلاب وطالبات الجامعة
+
+5
+00:00:19,890 --> 00:00:27,820
+الإسلامية طلبة الـ master أو Master رياضيات، وصلنا أو
+
+6
+00:00:27,820 --> 00:00:32,020
+نهينا Section 1-3، حكينا عن اللي هو الـ open
+
+7
+00:00:32,020 --> 00:00:35,240
+sets والـ neighborhoods والـ closed sets وحكينا 
+
+8
+00:00:35,240 --> 00:00:40,780
+عن أيضًا اللي هو الـ dense sets وعرفنا اللي هو الـ
+
+9
+00:00:40,780 --> 00:00:43,880
+spaces اللي الـ infinity اللي قال الـ infinity مثلًا
+
+10
+00:00:43,880 --> 00:00:47,420
+مش separable بينما قال  لكل بي بأنه أكبر سوى
+
+11
+00:00:47,420 --> 00:00:50,410
+واحد، أصغر من الـ infinity، R-Separable Spaces والـ
+
+12
+00:00:50,410 --> 00:00:54,170
+Spaces التابعة لنا اللي عايشين فيها في الـ Calculus
+
+13
+00:00:54,170 --> 00:00:58,050
+وباقي موادنا اللي هو الـ R والـ C عبارة عن Separable
+
+14
+00:00:58,050 --> 00:01:03,030
+Spaces، الآن بدنا نحكي عن مفاهيم أخرى توبولوجية ولكن 
+
+15
+00:01:03,030 --> 00:01:06,410
+خلينا نقول هذه لا يمكن نستغني عنها أيضًا في اللي هو
+
+16
+00:01:06,410 --> 00:01:10,160
+التحليل، اللي هي convergence، معنى الـ convergence
+
+17
+00:01:10,160 --> 00:01:14,580
+اللي احنا بنعرفه أصلًا بس بنعممه على metric space
+
+18
+00:01:14,580 --> 00:01:17,120
+in general، إيش معنى الـ Cauchy sequences اللي
+
+19
+00:01:17,120 --> 00:01:19,260
+انتوا عارفينها في الـ .. في الـ .. اللي خدناها في
+
+20
+00:01:19,260 --> 00:01:23,340
+الـ real ولكن برضه بنعممها على أي metric space و
+
+21
+00:01:23,340 --> 00:01:26,820
+الـ completeness، بروبرتي دي يعني شغلة جديدة علينا
+
+22
+00:01:26,820 --> 00:01:32,780
+اللي هي الـ space اللي يختص بخاصية الاكتمال أن يكون 
+
+23
+00:01:32,780 --> 00:01:36,060
+الـ space مكتمل، وهذا الـ spaces المكتملة هي spaces
+
+24
+00:01:36,060 --> 00:01:39,760
+خلينا نقول كثير كثير محترمة وبتريحنا، وهنشوف إيش 
+
+25
+00:01:39,760 --> 00:01:43,580
+اللي هو معناه الاكتمال، وهيكون رحلتنا معه شوية
+
+26
+00:01:43,580 --> 00:01:46,900
+طويلة لأنه هيلزمنا في الـ section اللي بعده واللي
+
+27
+00:01:46,900 --> 00:01:52,330
+بعده هنشوف معنى الـ Sequence إنها Convergent، بنقول 
+
+28
+00:01:52,330 --> 00:01:56,190
+a sequence xn in a metric space x و d، إذا جاعد أنا 
+
+29
+00:01:56,190 --> 00:02:00,390
+وان في metric space is said to be convergent ونقول
+
+30
+00:02:00,390 --> 00:02:03,710
+هذا الـ sequence convergent إذا بنلاقي x element 
+
+31
+00:02:03,710 --> 00:02:06,810
+in x، نفس المفهوم اللي احنا بنحكي فيه زمان في الـ
+
+32
+00:02:06,810 --> 00:02:12,470
+real، such that، الآن بنقولش limit xn بتروح لل x لأ
+
+33
+00:02:12,470 --> 00:02:16,370
+الآن صار عندي اللي هو في metric، الـ metric اللي
+
+34
+00:02:16,370 --> 00:02:20,390
+بتحكي عنه اللي هو دي، فبنقول عنه limit d xn و x إيش
+
+35
+00:02:20,390 --> 00:02:25,650
+بيساوي، بيساوي صفر، as n goes to infinity، لاحظوا أنا 
+
+36
+00:02:25,650 --> 00:02:32,890
+بقول الآن إن xn sequence في ال x، بقول xn converts 
+
+37
+00:02:32,890 --> 00:02:36,740
+لل x، convergence ده الـ X، بس وين هذا في الـ metric
+
+38
+00:02:36,740 --> 00:02:40,840
+space اللي هو X و D، يعني الدنيا تبعت الـ convergence
+
+39
+00:02:40,840 --> 00:02:44,540
+هذا اللي هي الـ X و D، بدي أعرف هذا الـ convergence
+
+40
+00:02:44,540 --> 00:02:49,160
+بإيش أنا أصلًا بعرفه من الأصل؟ فحولت الحديث كله من
+
+41
+00:02:49,160 --> 00:02:53,580
+عناصر في داخل الـ X، الـ metric space اللي عندي إلى
+
+42
+00:02:53,580 --> 00:03:00,870
+limit DXN و X as N goes to infinity، بيساوي اللي هو 
+
+43
+00:03:00,870 --> 00:03:05,530
+صفر اللي هو number اللي هو الـ zero بالظبط، الـ
+
+44
+00:03:05,530 --> 00:03:10,590
+number اللي بنحكي عنه مين الـ zero؟ في الواقع أنا هذا
+
+45
+00:03:10,590 --> 00:03:13,810
+الحديث أنا بعرفه لأن الـ distance بين X و N أو X
+
+46
+00:03:13,810 --> 00:03:17,330
+أبريل آلاف أو أرقام، إذا هذه أرقام وكأنه sequence 
+
+47
+00:03:17,330 --> 00:03:20,790
+من أرقام بتديها تروح لمين؟ للصفر، فعرفت الـ 
+
+48
+00:03:20,790 --> 00:03:24,210
+convergence الـ XN في اللي بيروح للـ X في الـ metric
+
+49
+00:03:24,210 --> 00:03:31,370
+space X بدلالة مين؟ بدلالة اللي هو الـ sequence of
+
+50
+00:03:31,370 --> 00:03:36,190
+numbers اللي عندي خلفية عنها من خلال الـ real الأصلي
+
+51
+00:03:36,640 --> 00:03:41,520
+هذا معناه الـ convergence in this case X is called
+
+52
+00:03:41,520 --> 00:03:45,520
+the limit of Xn يعني X اللي هي X هي limit لل Xn or
+
+53
+00:03:45,520 --> 00:03:49,380
+Xn converge to X and we write limit Xn بيساوي X or
+
+54
+00:03:49,380 --> 00:03:53,100
+Xn goes to infinity أو simply زي ما كتبت Xn بتروح
+
+55
+00:03:53,100 --> 00:03:58,750
+للـ X، واضح هذا معناه اللي هو الـ convergence، الآن if 
+
+56
+00:03:58,750 --> 00:04:03,130
+xn is not convergent زي ما احنا متعودين then بنقول 
+
+57
+00:04:03,130 --> 00:04:07,410
+عنها إيش؟ ما لها is a divergent sequence، نيجي
+
+58
+00:04:07,410 --> 00:04:11,350
+للملاحظات اللي بتخلينا نقول بتعمق المفهوم عندنا و
+
+59
+00:04:11,350 --> 00:04:17,380
+بتفهمنا المفهوم بشكل أكبر، حينها لو طلعت لهذا أنا
+
+60
+00:04:17,380 --> 00:04:21,300
+صرت أتعامل وكأنه هذا number، إذا بعرف تعريفه مؤصل 
+
+61
+00:04:21,300 --> 00:04:24,260
+أنا الـ epsilon definition أو الـ epsilon definition
+
+62
+00:04:24,260 --> 00:04:27,620
+تبع اللي هو تبع اللي هو الـ calculus وتبع التحليل
+
+63
+00:04:27,620 --> 00:04:30,560
+بعرفه اللي هو for every epsilon أكبر من 0، there
+
+64
+00:04:30,560 --> 00:04:34,140
+exists k element in n such that for every n أكبر
+
+65
+00:04:34,140 --> 00:04:40,160
+يساوي k، الـ distance بين الـ xn والـ x أصغر من y for
+
+66
+00:04:40,160 --> 00:04:44,660
+every n أي شماله أكبر أو يساوي k، هذا ما طبعًا احنا
+
+67
+00:04:44,660 --> 00:04:48,920
+ممكن نترجمه بشكل آخر إنه اللي هو لكل y أكبر من 0
+
+68
+00:04:48,920 --> 00:04:53,180
+there exists k element in n such that اللي هو عندي 
+
+69
+00:04:53,180 --> 00:05:01,520
+الـ ball اللي مركزه X ونصف قطره Y بتحتوي على كل 
+
+70
+00:05:01,520 --> 00:05:07,820
+الـ X أنات الـ N أكبر أو يساوي واحد، يعني XN element
+
+71
+00:05:07,820 --> 00:05:11,820
+in الـ ball هذه for every N أكبر أو يساوي 100، يمكن
+
+72
+00:05:11,820 --> 00:05:16,520
+أن يحول الحديث من الـ metric هذا إلى الـ ball 
+
+73
+00:05:16,520 --> 00:05:22,300
+المقابلة لها، إذا بيصير عندي الملاحظة الأولى، Limit
+
+74
+00:05:22,300 --> 00:05:26,720
+xn بيساوي x if and only if for every y أكبر من 0
+
+75
+00:05:26,720 --> 00:05:30,400
+there exists k بيساوي k of y in element n، طبعًا الـ k
+
+76
+00:05:30,400 --> 00:05:32,680
+بيساوى k of y على أساس أن الـ k اللي هتطلع عندي 
+
+77
+00:05:32,680 --> 00:05:34,600
+بتاعتها بتمد على مين؟ على الـ epsilon، ما بعرف علاقة
+
+78
+00:05:34,600 --> 00:05:40,960
+بالـ x، such that xn element in ball للـ x و y for
+
+79
+00:05:40,960 --> 00:05:45,580
+all n أكبر أو يساوي k، هذا تعبير آخر عن اللي هو
+
+80
+00:05:45,580 --> 00:05:46,760
+معناه الـ limit
+
+81
+00:05:49,870 --> 00:05:53,350
+الملاحظة الثانية، The limit of a convergent sequence 
+
+82
+00:05:53,350 --> 00:05:56,890
+must be a point of the space XN 4141
+
+83
+00:06:04,250 --> 00:06:07,430
+معناته إن الـ X اللي بتروح لها الـ Xn لازم تكون في
+
+84
+00:06:07,430 --> 00:06:10,890
+مين؟ في الـ space اللي عندي يعني أنا .. هالجد
+
+85
+00:06:10,890 --> 00:06:14,410
+بتفهموه إيش اللي بقصد؟ إنه أنا لما أقول Xn
+
+86
+00:06:14,410 --> 00:06:21,210
+converges in X، معناته limit الـ Xn بتتقارب نحو
+
+87
+00:06:21,210 --> 00:06:27,170
+نقطة اسمها X، والـ X هي الموجودة في الـ x، لكن لو
+
+88
+00:06:27,170 --> 00:06:31,990
+كانت الـ limit xn جاي عبالها رايحة لإشي معين لكن
+
+89
+00:06:31,990 --> 00:06:35,490
+هذا مش موجود في الـ set اللي هي الـ x بنقولش عن الـ
+
+90
+00:06:35,490 --> 00:06:39,770
+sequence إنها converges in this space، لأ، بتكونش
+
+91
+00:06:39,770 --> 00:06:42,710
+converges، إذا اللي بيقوله هنا في الملاحظة 2، الـ the 
+
+92
+00:06:42,710 --> 00:06:46,110
+limit of a convergent sequence must be of the
+
+93
+00:06:46,110 --> 00:06:52,130
+space x اللي مذكور في 4.1.1، otherwise
+
+94
+00:06:52,130 --> 00:06:55,690
+بنقول الـ sequence إيش ما لها؟ is divergent، وماخدوا
+
+95
+00:06:55,690 --> 00:07:02,670
+لكم مثال بقول لكم لو احنا أخذنا الـ X هي عبارة عن 0 1
+
+96
+00:07:02,670 --> 00:07:07,550
+وبس، وأخذنا الـ metric يعني جزء من R أخذته بس
+
+97
+00:07:07,550 --> 00:07:10,470
+المنطقة دي والـ metric هو الـ metric تبع الـ R اللي
+
+98
+00:07:10,470 --> 00:07:13,910
+هو إيش هو؟ الـ metric تبع الـ R الـ distance بين X و Y 
+
+99
+00:07:13,910 --> 00:07:17,910
+بيساوى الـ absolute value X minus Y لكل X و Y اللي
+
+100
+00:07:17,910 --> 00:07:22,760
+موجودة في الـ X اللي فوق، بقول لك الآن بدي أعطيك مثال
+
+101
+00:07:22,760 --> 00:07:25,700
+على الـ sequence دي، هي عبالها تروح لشغلة لكن مش
+
+102
+00:07:25,700 --> 00:07:30,880
+موجودها يعني أخد اللي هو الـ xn إيش بتساوي؟ 1 على n
+
+103
+00:07:30,880 --> 00:07:34,720
+أو n زائد 1، واحدة منكم بجهها n أكبر أو أكبر من مين؟
+
+104
+00:07:34,720 --> 00:07:40,200
+من 1، وإذا بدنا نكون خلينا نقول ألطف، حطها هيك
+
+105
+00:07:40,200 --> 00:07:44,570
+والـ n element in n وخلاص، فاهمين عليها إن أكبر أو يساوي
+
+106
+00:07:44,570 --> 00:07:49,450
+1، أي واحدة منها، لاحظوا هذه الـ Xn سهل لنا نثبتها
+
+107
+00:07:49,450 --> 00:07:54,510
+إن 1 على n زائد 1 لو بدها تروح هتروح لمين؟
+
+108
+00:07:54,510 --> 00:07:59,390
+للصفر لكن الصفر مش موجود في مين؟ عشان هيك بنقول
+
+109
+00:07:59,390 --> 00:08:05,510
+هذه اللي هو الـ sequence does not converge، الين؟ الـ
+
+110
+00:08:05,510 --> 00:08:09,310
+X اللي هو 0 والـ 1 وهي it is clear that 1
+
+111
+00:08:09,310 --> 00:08:12,310
+على n is divergent because 1 على n wants to
+
+112
+00:08:12,310 --> 00:08:16,790
+converge to zero which is not in 0 أو 1، أي 
+
+113
+00:08:16,790 --> 00:08:23,510
+سؤال واضح على الصورة الأمور، طيب نيجي الآن اللي هو
+
+114
+00:08:23,510 --> 00:08:29,430
+بدنا نعرف اللي هو بدأ أروح باتجاه، مدام بدي أحكي عن 
+
+115
+00:08:29,430 --> 00:08:34,310
+convergence، بعد بمشي زي ما كنا نمشي في R بحكي عن
+
+116
+00:08:34,310 --> 00:08:37,710
+convergence، شكلي بدي أحكي عن bounded عشان أحكي عن
+
+117
+00:08:37,710 --> 00:08:42,220
+bounded بدي أشوف حاجة اسمها الـ diameter لمن؟ للـ
+
+118
+00:08:42,220 --> 00:08:46,060
+set، تشوف إيش اللي بنقوله وبدلالتها بدي أعرف الـ
+
+119
+00:08:46,060 --> 00:08:56,920
+boundedness، لو جيت قلت أخدت subset M، a non-empty
+
+120
+00:08:56,920 --> 00:09:00,920
+subset M of a metric space X is said to be bounded
+
+121
+00:09:03,150 --> 00:09:08,430
+rounded if the diameter of M، إيش الـ diameter of M؟
+
+122
+00:09:08,430 --> 00:09:12,030
+الـ diameter of M هو عبارة عن الـ supremum لكل 
+
+123
+00:09:12,030 --> 00:09:17,690
+الأبعاد اللي بيني الموجودة في الـ M، هذا بتسميه
+
+124
+00:09:17,690 --> 00:09:22,410
+إيش ماله؟ الـ diameter لكل الـ M، الآن is finite، لو كان
+
+125
+00:09:22,410 --> 00:09:27,880
+الـ diameter is finite، معناته إنه إن الأ هذا هيكون
+
+126
+00:09:27,880 --> 00:09:32,860
+عدد مظبوط، عدد سموه مثلًا اللي بتكون إيه سموه K مثلًا
+
+127
+00:09:32,860 --> 00:09:40,460
+هذا العدد، عدد الآن بيصير معناته الـ M is finite
+
+128
+00:09:40,460 --> 00:09:48,300
+إن لكل X و Y أو اللي هو there exist KElement in R
+
+129
+00:09:48,300 --> 00:09:53,340
+أو أكبر من صفر، such that المسافة بين X و Y أصغر من
+
+130
+00:09:53,340 --> 00:09:59,800
+K لكل X و Y موجودة في الـ M لأن الـ Supremum نفسه
+
+131
+00:09:59,800 --> 00:10:06,600
+محدود اسمه K، إذا كل المسافات اللي بين العناصر اللي
+
+132
+00:10:06,600 --> 00:10:10,460
+موجودة في هذاك أصغر أو يساوي K، أصغر أو يساوي K هذا
+
+133
+00:10:10,460 --> 00:10:15,080
+مشابه للأصل الـ bounded العادي، احنا لما نقول إن الـ 
+
+134
+00:10:15,080 --> 00:10:18,840
+6 M is bounded، إذا بنلاقي K بحيث إن الـ absolute 
+
+135
+00:10:18,840 --> 00:10:23,340
+value للـ X أصغر أو يساوي K لكل X وين موجودة في الـ
+
+136
+00:10:23,340 --> 00:10:23,500
+M
+
+137
+00:10:27,700 --> 00:10:33,640
+ومنها أصلًا بقدر أقول البسافة بين x و y اللي هي برضه
+
+138
+00:10:33,640 --> 00:10:36,400
+هتكون bargain زي اللي فوق لأنها هتكون أصغر، بحكي عن
+
+139
+00:10:36,400 --> 00:10:40,740
+علامة تبع الـ R أصغر أو يساوي x زائد absolute value لـ y
+
+140
+00:10:40,740 --> 00:10:43,320
+وهذا أصغر من k وأصغر من k لأن هذا أصغر أو يساوي 
+
+141
+00:10:43,320 --> 00:10:49,250
+102k يعني في النهاية اللي هو هذا أو هذا نفس الأشياء
+
+142
+00:10:49,250 --> 00:10:52,030
+بس هذا على الـ metric in general وهذا على mean على 
+
+143
+00:10:52,030 --> 00:10:55,850
+absolute value تبع الزمان إذا تعريفي الجديد يتوافق
+
+144
+00:10:55,850 --> 00:11:00,950
+مع القديم والقديم بيصير حالة خاصة منه إذا الآن
+
+145
+00:11:00,950 --> 00:11:04,470
+ملخص حديثي إن الـ sequence Xm in X is called
+
+146
+00:11:04,470 --> 00:11:07,930
+bounded sequence if the corresponding point set
+
+147
+00:11:07,930 --> 00:11:11,870
+اللي هي X واحدة كل الـ Xات اللي فيها is a bounded
+
+148
+00:11:11,870 --> 00:11:19,130
+subset of mean of X أي سؤال؟ طيب نيجي لللمّة الأولى
+
+149
+00:11:19,130 --> 00:11:24,490
+اللمّة الأولى متوقعينها اللي هي زي اللي .. مش
+
+150
+00:11:24,490 --> 00:11:29,110
+هنحكي .. مش هنحكي وكأنه نصوص جديدة لأ النصوص هي
+
+151
+00:11:29,110 --> 00:11:31,430
+تبعات اللي كنا ناخدها في القارة عن الـ sequences
+
+152
+00:11:31,430 --> 00:11:35,130
+إيش
+
+153
+00:11:35,130 --> 00:11:40,540
+بتقول؟ بتقول لو احنا عندنا let X و D بيه متر كسباس
+
+154
+00:11:40,540 --> 00:11:45,240
+then a convergent sequence in X is bounded هاي هنا
+
+155
+00:11:45,240 --> 00:11:47,200
+كنا نقول زمان أنا convergence sequence is bounded
+
+156
+00:11:47,200 --> 00:11:50,960
+برضه فأي متر كسباس صح والـ limit بقى اللي هي وحيدة
+
+157
+00:11:50,960 --> 00:11:55,980
+برضه نفس الكلام الأولاني برضه بظبط هنا والثانية
+
+158
+00:11:55,980 --> 00:11:59,300
+بقول لك لو كانت الـ XN بتروح للـ X والـ YN بتروح للـ Y
+
+159
+00:11:59,300 --> 00:12:04,600
+أكيد المسافة بين XN و YN برضه هتروح لمين؟ للمسافة
+
+160
+00:12:04,600 --> 00:12:11,100
+بين X و Y ماشي الحال بدنا نثبتها اللي هو التنتين
+
+161
+00:12:11,100 --> 00:12:15,020
+اللي أمامنا الإثبات برضه هتلاقوه مشابه للإثباتات
+
+162
+00:12:15,020 --> 00:12:18,240
+اللي كنا نثبتها في حالة اللي هي الـ Real Numbers
+
+163
+00:12:18,240 --> 00:12:22,220
+بس تشيلواها دي وتحطواها العصيتين اللي زمان كنا
+
+164
+00:12:22,220 --> 00:12:25,880
+ناخدهم العصيتين Absolute Value الآن احنا أيّاشي
+
+165
+00:12:25,880 --> 00:12:29,940
+بنحكي عن الـ Metric دي هتلاقوا الأمور كتير مشابهة
+
+166
+00:12:29,940 --> 00:12:35,160
+تشوفوا نطلع النبي عليه الصلاة والسلام نفترض أن X
+
+167
+00:12:35,160 --> 00:12:39,600
+Unconverges يعني X Un تروح لمين؟ لـ Some X Element in 
+
+168
+00:12:39,600 --> 00:12:45,620
+X Capital الآن برضه لو رجعته برهان اللي هو التحليل
+
+169
+00:12:45,620 --> 00:12:48,360
+هتلاقوا نفس الأشياء إذا لكل أبسلون أكبر من صفر
+
+170
+00:12:48,360 --> 00:12:51,740
+there exist كده كده اللي بتاخد أبسلون تخدمني أخدت 
+
+171
+00:12:51,740 --> 00:12:55,140
+أبسلون أربط إيه؟ يعني أخدت أبسلون محددة سميتها
+
+172
+00:12:55,140 --> 00:12:58,260
+واحد بنفع أخد اتنين، بنفع أخد تلاتة، بنفع أخد 
+
+173
+00:12:58,260 --> 00:13:02,120
+أربع، بنفع أخد ربع، بنفع أخد درجتين، بس ألطف لنفس
+
+174
+00:13:02,120 --> 00:13:06,990
+الواحد، الواحد منيح مازال بتاخد، إذا then for y
+
+175
+00:13:06,990 --> 00:13:09,790
+بيساوي واحد there is k limiting and such that
+
+176
+00:13:09,790 --> 00:13:13,450
+المسافة بين x أن وx أشمالها أصغر من واحد لكل أن 
+
+177
+00:13:13,450 --> 00:13:17,330
+أشمالها أكبر من k هذا التعريف المباشر للـ limit
+
+178
+00:13:17,330 --> 00:13:24,750
+اللي جابناه بشوية حكينا عنه الآن بيقول لي بده الآن
+
+179
+00:13:24,750 --> 00:13:28,590
+أثبت أنها bounded يعني بده أثبت المسافة بين أي
+
+180
+00:13:28,590 --> 00:13:36,560
+مقطعين أصغر من number لجته الآن لاحظوا إن المسافة
+
+181
+00:13:36,560 --> 00:13:42,960
+بين X و N و X أصغر من واحد لكل الانات اللي أكبر من 
+
+182
+00:13:42,960 --> 00:13:46,580
+K لـ XN زيادة واحد و XN زيادة اتنين و XN زيادة
+
+183
+00:13:46,580 --> 00:13:49,820
+تلاتة و XN زيادة أربعة كلهم ضمنتهم اللي أصغر من 
+
+184
+00:13:49,820 --> 00:13:54,260
+واحد ده اللي قبل اللي قبل بتقول خلّي A تساوي الـ
+
+185
+00:13:54,260 --> 00:13:58,180
+maximum بين المسافة X واحد و X و X اتنين و X لعند
+
+186
+00:13:58,180 --> 00:14:04,320
+X K minus واحد ومين؟ و X إذن الآن خلصت من هذه و
+
+187
+00:14:04,320 --> 00:14:10,780
+هذه هيها هخلص اللي بديها أنا اضمنت لكم أن المسافة
+
+188
+00:14:10,780 --> 00:14:18,660
+DXN و X أصلا واحد لكل N أكبر أو يساوي K ودي أخدت
+
+189
+00:14:18,660 --> 00:14:23,120
+الـ A بالساوي الـ maximum للمسافات X واحد مع الـ X
+
+190
+00:14:23,120 --> 00:14:29,440
+اللي ضالن لعند ما أصل لـ D X K minus واحد و X سميت
+
+191
+00:14:29,440 --> 00:14:32,400
+أكبر وروح فيه maximum لأن عددهم عشرة عشرين مية
+
+192
+00:14:32,400 --> 00:14:37,160
+finite إذا فينا الـ maximum ماعشه اسمه M A إذا أكيد
+
+193
+00:14:37,160 --> 00:14:46,130
+أكيد أكيد صار عندي D X M وأي x موجودة اللي هو عندي
+
+194
+00:14:46,130 --> 00:14:50,430
+في الـ sequence اللي هي xm والـ x تبعتي هي اللي بقى
+
+195
+00:14:50,430 --> 00:14:57,890
+بحكي عنها أصغر من الواحد زائد a ليش؟ لأن الآن الـ a
+
+196
+00:14:57,890 --> 00:15:02,930
+هي الـ maximum لمسافاتي ده موجودة أو صفر صح ولا لأ؟
+
+197
+00:15:02,930 --> 00:15:08,190
+الآن الـ .. الـ .. الـ x واحد لعند الـ xk minus واحد
+
+198
+00:15:08,190 --> 00:15:12,290
+أكيد أصغر من الـ a لحالها إذا أكيد أصغر من مين؟ من
+
+199
+00:15:12,290 --> 00:15:15,330
+الواحد زائد إيه؟ البجيات كلها أصغر من واحد لحاله
+
+200
+00:15:15,330 --> 00:15:18,250
+إذا أكيد أصغر من مين؟ واحد زائد a إذا هو ضرب على 
+
+201
+00:15:18,250 --> 00:15:22,510
+صفرين وحجار وقال لك إذا دي Xn و X أصغر من واحد
+
+202
+00:15:22,510 --> 00:15:28,750
+زائد إيه hence for all n and m المسافة بين Xn وXm
+
+203
+00:15:28,750 --> 00:15:31,410
+أصغر أو ساوية تلقى inequality عشان أخلص على اللي
+
+204
+00:15:31,410 --> 00:15:35,240
+بدّوياه وإيش بتثبت؟ بدّه يثبت إنها bounded، إيش الـ
+
+205
+00:15:35,240 --> 00:15:39,380
+bounded؟ إنه المسافات بين أي نقطتين كلهين يكون
+
+206
+00:15:39,380 --> 00:15:44,580
+أصغر من إشي، ماشي؟ لأن خدوا أي نقطتين XN و XM في
+
+207
+00:15:44,580 --> 00:15:47,400
+مين؟ أنا بقى رايح لمين؟ هاي الـ sequence اللي عند
+
+208
+00:15:47,400 --> 00:15:52,220
+الـ XM ونقول عنها bounded إذا كان عناصرها X1 و X2
+
+209
+00:15:52,220 --> 00:15:56,680
+إلى ما لنهاية المسافات بين أي كنتين يكونون أصغر من
+
+210
+00:15:56,680 --> 00:16:00,480
+some number خدت الآن un-arbitrary و un-arbitrary
+
+211
+00:16:00,480 --> 00:16:04,360
+يعني دي X un-arbitrary و X un-arbitrary وحسبت
+
+212
+00:16:04,360 --> 00:16:07,580
+المسافة بينهم بالـ triangling quality أصغر أو سوى
+
+213
+00:16:07,580 --> 00:16:13,000
+دي X un ومين؟ و X أنا هيأت حالي في اللي قبل زائد X
+
+214
+00:16:13,000 --> 00:16:17,440
+un ومين؟ و X الأولى أصغر من واحد زائد إيه أثبتها
+
+215
+00:16:18,160 --> 00:16:21,580
+والتانية أصغر من واحد زاد إيه؟ إذا التنتين أصغر من
+
+216
+00:16:21,580 --> 00:16:25,980
+اتنين زائد مين؟ اتنين إيه؟ إذا المسافة بين أي وقتين
+
+217
+00:16:25,980 --> 00:16:30,440
+الآن في داخل الـ sequence اللي هي أصغر من اتنين زائد 
+
+218
+00:16:30,440 --> 00:16:34,520
+اتنين إيه؟ وهذا معناته أنه صارت عند الـ sequence xn
+
+219
+00:16:34,520 --> 00:16:40,300
+is a bounded sequence طيب صلوا على النبي عليه
+
+220
+00:16:40,300 --> 00:16:42,420
+الصلاة والسلام الآن
+
+221
+00:16:45,850 --> 00:16:49,470
+والـ Limit X مالها؟ واحدة بما أنك تضمن أنك تنتهي من
+
+222
+00:16:49,470 --> 00:16:54,070
+وصول الـ X مالها؟ واحدة بنقول أسيوم ذات Xn بتروح للـ
+
+223
+00:16:54,070 --> 00:16:57,590
+X و Xn بتروح لمين؟ لـ زي الـ two limits وفي الآخر
+
+224
+00:16:57,590 --> 00:17:02,330
+هنطلع X بالساوة زي الـ then المسافة بين X و Z أكيد 
+
+225
+00:17:02,330 --> 00:17:07,070
+مالها؟ أكبر أو ساوة صفر بالنسبة لكم أن هذه 0 أصغر
+
+226
+00:17:07,070 --> 00:17:13,170
+سوى DX وXN زي DXN ومين؟ وZ لكن هذه مش احنا بنقول XN 
+
+227
+00:17:13,170 --> 00:17:17,210
+بتروح لـ X إذا الـ limit هي 0 حسب التعريف ومش بنقول
+
+228
+00:17:17,210 --> 00:17:20,730
+XN بتروح لـ Z إذا الـ limit هي 0 إذا هذول الـ limit
+
+229
+00:17:20,730 --> 00:17:25,070
+هين صفر وهذه صفر إذا اللي في النص قطعنش هتكون صفر
+
+230
+00:17:25,070 --> 00:17:28,650
+ومعناته الـ X أشبتها سوى Z so the limit is unique
+
+231
+00:17:28,650 --> 00:17:36,830
+ماشي الحل نيجي الآن للّي هي بي الآن الـ بي بتقول لك
+
+232
+00:17:36,830 --> 00:17:40,030
+إذا كانت x أن و y أن هذي converge ده الـ x وهذي
+
+233
+00:17:40,030 --> 00:17:42,910
+converge ده الـ y إذا المسافة بين الـ converge ده
+
+234
+00:17:42,910 --> 00:17:48,490
+اللي هو المسافة بين اللي متين طيب برضه البرهان
+
+235
+00:17:48,490 --> 00:17:54,750
+هتجيب بمشي معنى زي الحلاوة وبكل سهولة إيش بقول لنا
+
+236
+00:17:54,750 --> 00:18:01,770
+البرهان بقول التالي بقول نفرض أن Xn بتروح لـ X و Yn
+
+237
+00:18:01,770 --> 00:18:05,170
+بتروح لـ Y إيش معناة Xn بتروح لـ X؟ يعني المسافة بين
+
+238
+00:18:05,170 --> 00:18:10,710
+Xn و Yn هذه المسافة بين Xn و X بيروح للصفر
+
+239
+00:18:10,710 --> 00:18:14,070
+والمسافة بين هذي وهذي بتروح لمين؟ للصفر خلّيها نفل
+
+240
+00:18:14,070 --> 00:18:18,770
+جمال بعد شوية نستخدمها الآن تشوفوا الآن xn و yn
+
+241
+00:18:18,770 --> 00:18:22,990
+المسافة بينهما أصغر أو سوى xn و x و x و mean و y و
+
+242
+00:18:22,990 --> 00:18:27,010
+y و yn استخدمت الـ triangle inequality مرتين طبعا
+
+243
+00:18:27,010 --> 00:18:31,990
+في الي سبب إنه عشان أثبت لكم أن xn و yn ناقص x و y
+
+244
+00:18:31,990 --> 00:18:35,550
+المسافة بينها absolute value أصغر أو سوى هذه
+
+245
+00:18:35,550 --> 00:18:38,330
+المسافة هذه هتروح لصفر وهذه كصفر معناته خلصت
+
+246
+00:18:38,330 --> 00:18:39,190
+دعونا نشوف كده
+
+247
+00:18:42,080 --> 00:18:45,180
+الآن بالـ triangle inequality طلعت عندي هذه hence
+
+248
+00:18:45,180 --> 00:18:51,060
+جي بيها ديها بيصير عند المسافة هيها هيها هيها هيها
+
+249
+00:18:51,060 --> 00:18:53,740
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+250
+00:18:53,740 --> 00:18:53,760
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+251
+00:18:53,760 --> 00:18:53,960
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+252
+00:18:53,960 --> 00:18:56,440
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+253
+00:18:56,440 --> 00:18:58,920
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+254
+00:18:58,920 --> 00:18:58,960
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+255
+00:18:58,960 --> 00:19:00,400
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+256
+00:19:00,400 --> 00:19:00,480
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+257
+00:19:00,480 --> 00:19:07,970
+هيها هيها هيها هيبقدر اللي هو أخد المسافة أثبت أن
+
+258
+00:19:07,970 --> 00:19:13,590
+المسافة بين x و y ناقص xn و yn أصغر من المسافة بين
+
+259
+00:19:13,590 --> 00:19:20,150
+x و xn أو ناقص المسافة عشان أثبت لكم أنا اللي بدي
+
+260
+00:19:20,150 --> 00:19:24,290
+أثبته اللي هو absolute value الـ absolute value
+
+261
+00:19:24,290 --> 00:19:32,170
+distance بين xn و Yn نقص المسافة بين X و Y أصغر أو
+
+262
+00:19:32,170 --> 00:19:35,550
+يساوي هذي طبعا أكبر ويساوي صفر غرضي أثبتها أصغر
+
+263
+00:19:35,550 --> 00:19:43,490
+أو ساوي المسافة بين Xn و X زائد المسافة بين Yn و
+
+264
+00:19:43,490 --> 00:19:49,690
+100 و Y آسف بدون أفسنان أنت فاهم معايا؟ هذي هتروح
+
+265
+00:19:49,690 --> 00:19:52,150
+للسفر وهذي هتروح للسفر إذا هذي هيروح للسفر يكون
+
+266
+00:19:52,150 --> 00:19:57,480
+خلصت اللي أول واحدة عملتها اللي هي المسافة بين XN و
+
+267
+00:19:57,480 --> 00:20:01,880
+YN ناقص هذا أصغر أو ساوي هذه يعني بدي أثبت لكم أن
+
+268
+00:20:01,880 --> 00:20:06,940
+هذه أصغر أو ساوي هذه وبعدين اللي هو مفكوك هيش هذه
+
+269
+00:20:06,940 --> 00:20:10,440
+اللي هو على الجهة الثانية بالسالب بظبط يعني بدي
+
+270
+00:20:10,440 --> 00:20:16,520
+أعكسها بنعكسها بنفس الطريقة بتنعمل سهلة يعني بس الـ
+
+271
+00:20:16,520 --> 00:20:19,720
+triangle inequality بنستخدمها بالشكل الثاني اللي
+
+272
+00:20:19,720 --> 00:20:25,590
+هو similarly DXY ناقص DXN YN اللي هي أصغر أو يساوي
+
+273
+00:20:25,590 --> 00:20:34,510
+دي إكس وإكس أن زائد دي وي أو وي أن إذا بيصير
+
+274
+00:20:34,510 --> 00:20:37,530
+بتدربيها في ناقص عكستها أنا عشان أدرب في ناقص لما
+
+275
+00:20:37,530 --> 00:20:41,070
+أدرب في ناقص بيصير ناقص هذا أصغر أو يساوي إكس أن و
+
+276
+00:20:41,070 --> 00:20:45,090
+وي أن وإكس و.. ومين؟ ووي أنتوا فاهمين إيش
+
+277
+00:20:45,090 --> 00:20:48,450
+بيعمل؟ أنا بدي أجيب هذه بدي مبدأ هذه بدي أبدأ بإكس
+
+278
+00:20:48,450 --> 00:20:55,580
+ووي فاهمين؟ أعملها الآن بدل أن أبدأ بهذه أبدأ بالـ
+
+279
+00:20:55,580 --> 00:20:58,020
+X و Y بحصل على نفسي الاشي هذه بانجله على الجهة
+
+280
+00:20:58,020 --> 00:21:01,000
+التانية بضربه في ناقص بالـ Seer المعقوسة هذه بالظبط 
+
+281
+00:21:01,000 --> 00:21:04,480
+الـSeer عندي اللي هو عبارة عن ناقص هذه أصغر وشاوي
+
+282
+00:21:04,480 --> 00:21:07,900
+هذه وفي الأصل أصغر وشاوي اللي هي الأصلية هذه إذا
+
+283
+00:21:07,900 --> 00:21:11,220
+صار الـ absolute value أكبر وشاوي صفر وأصغر وشاوي
+
+284
+00:21:11,220 --> 00:21:15,960
+هذه الآن هذه راحت للصفر وهذه راحت للصفر إذا هذه
+
+285
+00:21:15,960 --> 00:21:20,000
+راحت للصفر إذا DX عن وY عن بتروح لـ DX وY ماشي
+
+286
+00:21:26,520 --> 00:21:30,900
+إذا نعرف الـ Cauchy Sequence أكيد توقعتوها بس
+
+287
+00:21:30,900 --> 00:21:33,680
+شيلوا absolute ده اللي حطوه بدلها الـD
+
+288
+00:21:37,650 --> 00:21:40,810
+بنقول إن Xn كوشي سيكوينس إذا تحقق اللي التالي for
+
+289
+00:21:40,810 --> 00:21:43,530
+every y أكبر من صفر there exists k element in n
+
+290
+00:21:43,530 --> 00:21:48,010
+such that for every n و m أكبر أو يساوي k عندي
+
+291
+00:21:48,010 --> 00:21:53,290
+بيكون الـ absolute value للـ Xn نقص الـ Xn أصغر من
+
+292
+00:21:53,290 --> 00:21:58,610
+مين؟ من إبسلون، مظبوط ولا لا؟ هذا اللي كنا نحكيه
+
+293
+00:21:58,610 --> 00:22:05,240
+زمان في الريال، بس خيانة، حطوا D و بس دي xn و كده
+
+294
+00:22:05,240 --> 00:22:10,940
+بس هي كل الجثة إذا عشان ما نغلبكم مش بنقول a
+
+295
+00:22:10,940 --> 00:22:14,160
+sequence xn in a metric space xz is said to be
+
+296
+00:22:14,160 --> 00:22:17,260
+Cauchy if for every y أكبر من 0 there exists k
+
+297
+00:22:17,260 --> 00:22:21,080
+such that is مسافة بين xn و xm أصغر من y لكل n و m
+
+298
+00:22:21,080 --> 00:22:25,000
+أكبر من k the space x is called complete ال space
+
+299
+00:22:25,000 --> 00:22:29,380
+بنقول عنه complete space إذا كان every Cauchy
+
+300
+00:22:29,380 --> 00:22:35,980
+sequence converges إذا بتذكروا في تحليل واحد لما
+
+301
+00:22:35,980 --> 00:22:38,520
+حكينا عن العلاقة بين الـ Cauchy Sequences والـ
+
+302
+00:22:38,520 --> 00:22:42,880
+Convergent Sequences قلنا أيش؟ قلنا Any Convergent
+
+303
+00:22:42,880 --> 00:22:46,140
+Sequences is Cauchy وكان برهانه سهل تلاقي البرهان
+
+304
+00:22:46,140 --> 00:22:51,600
+المشابه الآن العكس قلنا برضه بتحقق في R يعني اللي
+
+305
+00:22:51,600 --> 00:22:55,900
+هي الـ Cauchy convergent بس كانت اتغلبنا شوية في
+
+306
+00:22:55,900 --> 00:23:02,160
+البرهان خلينا نقول أصعب شوية بسيطة لكن كان برضه مش
+
+307
+00:23:02,160 --> 00:23:05,840
+صعب يعني وكأنه ليش أنا بقول لك وكأنه الآن على
+
+308
+00:23:05,840 --> 00:23:09,940
+تعريفي احنا بنقول إن ال space complete إذا كانت
+
+309
+00:23:09,940 --> 00:23:13,900
+every Cauchy sequence converges طب في R كانت هيك R
+
+310
+00:23:13,900 --> 00:23:17,660
+complete ومش هيك وكمان في الـ C complete والـ C
+
+311
+00:23:17,660 --> 00:23:20,380
+أشماله complete under the metric اللي احنا بنتحكي
+
+312
+00:23:20,380 --> 00:23:22,960
+عنه الـ usual metric اللي هو absolute value X minus
+
+313
+00:23:22,960 --> 00:23:28,020
+Y إذا صار في عندي مثلّين اللي هو الـ R والـ C على
+
+314
+00:23:28,020 --> 00:23:32,260
+complete metric spaces وهنشوف الباقي قدام إن شاء
+
+315
+00:23:32,260 --> 00:23:32,400
+الله
+
+316
+00:23:35,980 --> 00:23:38,560
+النقطة الأولى اللي قلتها هي الـ The real line and
+
+317
+00:23:38,560 --> 00:23:41,100
+the complex plane are complete metric spaces
+
+318
+00:23:52,240 --> 00:24:01,220
+ليش؟ لإن واحنا بنعرف اللي عندي لأي a في الـR بقدر
+
+319
+00:24:01,220 --> 00:24:07,080
+ألاقي sequence xn in R such that xn converges to
+
+320
+00:24:07,080 --> 00:24:10,420
+a يعني، حتى بقدر ألاقي sequence of rational
+
+321
+00:24:10,420 --> 00:24:13,540
+numbers، ده حالي بس وبقدر ألاقي sequence of
+
+322
+00:24:13,540 --> 00:24:15,880
+irrational numbers، ده حالي، خلاص الكتابة لكل
+
+323
+00:24:15,880 --> 00:24:21,140
+واحدة فيهم إذا أنا في الواقع عندي لو شيلت من الـ R
+
+324
+00:24:21,140 --> 00:24:26,440
+بضطر complete لإن لجيت هي ال sequence اللي هي xn
+
+325
+00:24:26,440 --> 00:24:33,460
+بتروح لـ a هتكون false في الواقع فبتصير xn كوشي in
+
+326
+00:24:33,460 --> 00:24:41,810
+R ناقص مين ناقص الـ a but its limit وما بدها تروح
+
+327
+00:24:41,810 --> 00:24:47,290
+للـ A مش موجودة في الـ R minus الـ A إذا هذا is
+
+328
+00:24:47,290 --> 00:24:52,130
+not a complete metric space والـ Q كله under مين؟
+
+329
+00:24:52,130 --> 00:24:55,270
+under the usual metric اللي هو absolute value للـ
+
+330
+00:24:55,270 --> 00:25:03,730
+X minus Y الـ Q كمان مش complete لأنه ليش؟ لأنه لو
+
+331
+00:25:03,730 --> 00:25:07,710
+أجيت بقدر
+
+332
+00:25:07,710 --> 00:25:11,470
+ألاقي الـ sequence اللي هو of rational numbers
+
+333
+00:25:11,470 --> 00:25:16,990
+converges لجذر الاثنين جذر الاثنين مش موجود في الـ
+
+334
+00:25:16,990 --> 00:25:21,090
+Q إذا ما زال مش موجود في الـ Q، إذا صار عندك الـ
+
+335
+00:25:21,090 --> 00:25:24,590
+Cauchy sequence اللي هاد اللي converges لجذر
+
+336
+00:25:24,590 --> 00:25:30,350
+الاثنين في الـ R لكن اللي أماله مش موجودة إذا إذا
+
+337
+00:25:30,350 --> 00:25:34,770
+إحنا لما نحكي عن الـ Cauchy sequence هي في الواقع
+
+338
+00:25:34,770 --> 00:25:39,770
+سلوك سلوك هو تقريبا بتقدر تقولي هو نفس سلوك الـ
+
+339
+00:25:39,770 --> 00:25:45,550
+convergence لكن بختلف في الآخر إن الـ convergence
+
+340
+00:25:45,550 --> 00:25:51,540
+بيروح لـ limit الـ limit هذه إذا في الـ space بصير إيه
+
+341
+00:25:51,540 --> 00:25:55,980
+أشماله الـ sequence converges إذا مش في الـ space
+
+342
+00:25:55,980 --> 00:26:01,420
+بظل كوشي لكن مش .. وهنا بحكم .. نحكم على الـ space
+
+343
+00:26:01,420 --> 00:26:05,380
+إنه complete أو لأ من خلال هذه الخاصية إذا الـ ..
+
+344
+00:26:05,380 --> 00:26:09,920
+الـ كوشي sequences هي في الواقع بتريحني أحيانا إنه
+
+345
+00:26:09,920 --> 00:26:13,860
+أنا أصلا مش عارف الـ limit لكن أنا بعرف سلوك اللي هي
+
+346
+00:26:13,860 --> 00:26:17,980
+الـ sequence اللي لأ هي سلوك هي يا عم هذه سلوك
+
+347
+00:26:17,980 --> 00:26:21,340
+رايحة رايحة لإشي بتتكوم حوالين إشي ماشي الحال
+
+348
+00:26:21,340 --> 00:26:26,580
+فالآن روحها حوالين نقطة معينة يمكن أني ما أعرفوش
+
+349
+00:26:26,580 --> 00:26:30,830
+أنا لكن ده عارف إن هما جعدات متكوّن من جانب بعض،
+
+350
+00:26:30,830 --> 00:26:35,490
+إذا سلوكهم إنه جعدات وكأنه كلهم بيروحوا حوالين منطقة
+
+351
+00:26:35,490 --> 00:26:38,730
+معينة و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+352
+00:26:38,730 --> 00:26:39,090
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+353
+00:26:39,090 --> 00:26:39,810
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+354
+00:26:39,810 --> 00:26:39,830
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+355
+00:26:39,830 --> 00:26:40,030
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+356
+00:26:40,030 --> 00:26:43,870
+و .. و .. و .. و
+
+357
+00:26:43,870 --> 00:26:55,480
+.. و .. فالآن الـ Cauchy مهم عشان اللي هو يعني
+
+358
+00:26:55,480 --> 00:27:01,440
+أحيانا ما كنتش أعرف إيش الـ limit فبتعامل مع اللي هو
+
+359
+00:27:01,440 --> 00:27:05,560
+العناصر بدل ما أتعامل مع الـ limit و لكن في حال
+
+360
+00:27:05,560 --> 00:27:07,700
+وجود الـ limit في الـ space وكده بيصير الـ space
+
+361
+00:27:07,700 --> 00:27:13,180
+أشماله is complete طيب theorem every convergent
+
+362
+00:27:13,180 --> 00:27:15,500
+sequence in a metric space is a Cauchy sequence
+
+363
+00:27:15,500 --> 00:27:21,960
+والبرهان مشابهتها بعد تبع التحليل اللي بيقولوا إنه
+
+364
+00:27:21,960 --> 00:27:27,390
+لو فرضنا XN أي خلق تنسيق X بالذات بتنهجوشي مدام xn
+
+365
+00:27:27,390 --> 00:27:30,390
+بتروح للـ x إذا لكل y أكبر من 0 there exists k such
+
+366
+00:27:30,390 --> 00:27:34,190
+that اللي هو x المسافة بين xn و x أصغر من y على 2
+
+367
+00:27:34,190 --> 00:27:37,270
+for all n أكبر من k أصغر من أي إبسلون في الدنيا من
+
+368
+00:27:37,270 --> 00:27:41,990
+جملة y على 2 هو دي للحسبة ومشروعة لإن هو أصلا
+
+369
+00:27:41,990 --> 00:27:45,190
+المسافة بين n وn تبقى لدرجة غيرها زي ما بده الآن
+
+370
+00:27:45,190 --> 00:27:51,270
+خدوا لكل m و m أكبر من k خدوا المسافة بين xn وxn
+
+371
+00:27:51,820 --> 00:27:56,080
+هتكون أصغر ونفسها والمسافة بين Xn و X زي المسافة
+
+372
+00:27:56,080 --> 00:28:01,700
+بين X و Xm وهذه من اللي فوق هنا أصغر ونفسها ونوع
+
+373
+00:28:01,700 --> 00:28:03,920
+اثنين زي اثنين ونفسها نوع اثنين ونفسها نوع اثنين و
+
+374
+00:28:03,920 --> 00:28:05,720
+نفسها نوع اثنين ونفسها نوع اثنين ونفسها نوع اثنين و
+
+375
+00:28:05,720 --> 00:28:07,900
+نفسها نوع اثنين ونفسها نوع اثنين ونفسها نوع اثنين و
+
+376
+00:28:07,900 --> 00:28:07,940
+نفسها نوع اثنين ونفسها نوع اثنين ونفسها نوع اثنين و
+
+377
+00:28:07,940 --> 00:28:10,440
+نفسها نوع اثنين ونفسها نوع اثنين ونفسها نوع اثنين و
+
+378
+00:28:10,440 --> 00:28:18,900
+نفسها نوع اثنين ونفسها نوع اثنين ونفس الآن ها
+
+379
+00:28:18,900 --> 00:28:26,320
+theorem بيقول لـ let M بيقى metric space X وD then
+
+380
+00:28:26,320 --> 00:28:31,460
+الـ M بدي يبدأ يحول الحديث احنا لما .. في المحاضرة
+
+381
+00:28:31,460 --> 00:28:34,760
+اللي فاتت كنا نحكي لما كنا نحكي عن الـ convergence
+
+382
+00:28:34,760 --> 00:28:41,890
+كنا نحول الحكي برضه لـ sequence specific في الـR أو
+
+383
+00:28:41,890 --> 00:28:46,130
+في الـC فكنا نشرود ناخد الـSequence اللي في الـP
+
+384
+00:28:46,130 --> 00:28:49,370
+كلها نقول بتروح للـX ونربطها بالـConvergence لأن
+
+385
+00:28:49,370 --> 00:28:52,850
+لأ الآن بدي أطوّركم بالـConvergence لأنه أعرف شو
+
+386
+00:28:52,850 --> 00:28:55,030
+معناه الـConvergence قبل ما كنتش عارف معناه
+
+387
+00:28:55,030 --> 00:28:58,740
+الـConvergence في الـMetric Space كنت أحول الدنيا
+
+388
+00:28:58,740 --> 00:29:01,000
+أروح وأديها لي الـ convergence اللي في R تبع
+
+389
+00:29:01,000 --> 00:29:03,740
+الزمان لكن مش دايمًا هذا بيظبط أو مش دايمًا أخليهم
+
+390
+00:29:03,740 --> 00:29:10,260
+أقول بسعّثني الآن بدي أحول كل الآن الحديث من الـ
+
+391
+00:29:10,260 --> 00:29:15,420
+unconvergence إلى sequences يعني المفهوم القاسي في
+
+392
+00:29:15,420 --> 00:29:20,240
+الـ closure من الـ closure اللي هو بواسطة الـ balls
+
+393
+00:29:20,240 --> 00:29:26,470
+إلى حكي بواسطة الـ sequences وده أسهل نبدأ نقول let
+
+394
+00:29:26,470 --> 00:29:32,310
+M be a anonymous if and only
+
+395
+00:29:32,310 --> 00:29:35,230
+if there exists a sequence xn in M such that xn
+
+396
+00:29:35,230 --> 00:29:39,990
+بتروح لمين؟ للـ X إذن الآن بنقول إن الـ X في الـ M
+
+397
+00:29:39,990 --> 00:29:44,650
+closure معناته إنه بقدر ألاقي sequence في الـ M
+
+398
+00:29:44,650 --> 00:29:50,160
+وعامله كلها الـ sequence بتروح لمين؟ للـ X أه إذا الـ
+
+399
+00:29:50,160 --> 00:29:55,200
+M هذه متكرب سا .. ال .. الـ XM متكرب سا حوالين الـ X
+
+400
+00:29:55,200 --> 00:29:59,940
+و XM ناقف الـ M إذا أكيد هي limit point جوا هذا
+
+401
+00:29:59,940 --> 00:30:05,110
+رفلي الكلام تشوف الكلام هذا بالتفصيل الآن الآن بدنا
+
+402
+00:30:05,110 --> 00:30:07,650
+نعرف اللي هو الـ M closed برضه بمانعش نقعد نقول
+
+403
+00:30:07,650 --> 00:30:10,550
+والله الـ compliment لها اه بإن نقعد نفحص إن اه
+
+404
+00:30:10,550 --> 00:30:13,270
+بإن معناته إنه خدوا أي نقطة وبتلاقوا اه اه نبرهن
+
+405
+00:30:13,270 --> 00:30:15,350
+جواتها يكون كله في جوات اللي هي الـ M compliment
+
+406
+00:30:15,350 --> 00:30:20,370
+لأ أسهلنا أسهلنا نحكي عن Sequences M is closed if
+
+407
+00:30:20,370 --> 00:30:23,170
+and only if the situation X and element in M و X
+
+408
+00:30:23,170 --> 00:30:28,050
+and بتروح للـ X and why is that X element in M يعني
+
+409
+00:30:28,050 --> 00:30:32,800
+بقول ليه M Closed إذا تحقق الشرط التاني إنه لو أخدت
+
+410
+00:30:32,800 --> 00:30:37,060
+أي Sequence XN في الـ M وكانت هذه Sequence
+
+411
+00:30:37,060 --> 00:30:42,000
+Converged لازم تقعد وين؟ في داخل الـ M ماشي الحال
+
+412
+00:30:42,000 --> 00:30:45,180
+إذا تمتعت بهذا الخاصية على طول M is Closed يعني
+
+413
+00:30:45,180 --> 00:30:48,760
+عشان نحكوا إن عمل M Closed اه ولا لأ باجي باخد أي
+
+414
+00:30:48,760 --> 00:30:55,360
+Sequence XN في الـ M وتكون XN بتروح للـ X هذا كله
+
+415
+00:30:55,360 --> 00:31:00,140
+على بعض يعطينا إن X في الـ M هذا معناته إنه صارت
+
+416
+00:31:00,140 --> 00:31:05,340
+الـ M is closed ولو كانت M is closed برضه لو جي
+
+417
+00:31:05,340 --> 00:31:08,320
+تأخدت أي sequence XN في الـ M وكانت XN بتروح للـ X
+
+418
+00:31:08,320 --> 00:31:12,480
+لازم تعطي الـ X mean في داخلها واضح؟ هذا الـ test
+
+419
+00:31:12,480 --> 00:31:19,120
+للـ convergence للـ M is closed ولا لأ طيب نيجي إلى
+
+420
+00:31:19,120 --> 00:31:24,740
+اللي هو الأولى let X element mean أن M closure في 
+
+421
+00:31:24,740 --> 00:31:28,970
+عندي حالتين إذا كانت X في الـ M، ادّيني سهلة، مين 
+
+422
+00:31:28,970 --> 00:31:32,430
+باخدها الـ sequence؟ X، X، X، X، X، X، X، X، X، X،
+
+423
+00:31:32,430 --> 00:31:34,550
+X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X،
+
+424
+00:31:34,550 --> 00:31:37,850
+X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X،
+
+425
+00:31:37,850 --> 00:31:37,990
+X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X،
+
+426
+00:31:37,990 --> 00:31:39,050
+X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X،
+
+427
+00:31:39,050 --> 00:31:39,870
+X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X،
+
+428
+00:31:39,870 --> 00:31:43,710
+X،
+
+429
+00:31:43,710 --> 00:31:47,350
+X، X مش في الـ M إذا نوعها بده تكون في الـ
+
+430
+00:31:47,350 --> 00:31:53,090
+accumulation points if X is not element of M it is 
+
+431
+00:31:53,090 --> 00:31:56,210
+accumulation point of M ايش معناه accumulation 
+
+432
+00:31:56,210 --> 00:32:02,710
+point يعني لكل نيبرود في الدنيا لكل نصف قطر بتاخد 
+
+433
+00:32:02,710 --> 00:32:07,120
+أنصاف الأقطار اسمه 1 على N لأي نسخة و تربسة أننا 
+
+434
+00:32:07,120 --> 00:32:09,680
+ناخد أنصاف الأكتر اسمين واحدة لأن ده سواء أخد نسخة و 
+
+435
+00:32:09,680 --> 00:32:14,280
+ترسم واحد و نص و تلت و ربع و خمس و ستس و في كل 
+
+436
+00:32:14,280 --> 00:32:19,600
+حاجة حلاجة اللي هو element فيه موجود فآنتقاطعه لا 
+
+437
+00:32:19,600 --> 00:32:24,360
+يساوي فاي ما أنا ايا الان hence for each n element 
+
+438
+00:32:24,360 --> 00:32:29,420
+in n بيكس و نصف قطر واحد الان تقاطع مع الان اشماله
+
+439
+00:32:29,420 --> 00:32:33,540
+لا يساوي فاي ماشي الحاجة واحد يقول ليه ما هو شيء
+
+440
+00:32:33,540 --> 00:32:36,660
+لل X انت طب هي اصلا ال X مش في ال M مش في ال M 
+
+441
+00:32:36,660 --> 00:32:41,040
+اصلا طبيعي مش هي اللي هتطلع التقاطع فاهمين اه طيب
+
+442
+00:32:41,040 --> 00:32:45,020
+so there exist x n element in b x واحد و الان
+
+443
+00:32:45,020 --> 00:32:51,920
+تقاطع مين ال M اذا Px1 لجت فيها x1 Px نص لجت فيها
+
+444
+00:32:51,920 --> 00:32:57,520
+x2 Px تلت لجت فيها x3 Px ربع لجت فيها x4 و هكذا
+
+445
+00:32:57,520 --> 00:33:01,900
+لأن هذا الكلام صحيح لمين لكل n بيجيلها xn المقابلة
+
+446
+00:33:01,900 --> 00:33:05,580
+اللي موجودة في التقاطع إذا صارت المسافة بين xn و x
+
+447
+00:33:05,580 --> 00:33:10,160
+أصغر من مين من 1 ل n في كل حالة لأن as n goes to
+
+448
+00:33:10,160 --> 00:33:14,040
+infinity و 1 hundred تروحللصفر وهذه بيصير مدام
+
+449
+00:33:14,040 --> 00:33:15,360
+هترا هترا هترا هترا هترا هترا هترا هترا هترا هترا
+
+450
+00:33:15,360 --> 00:33:15,480
+هترا هترا هترا هترا هترا هترا هترا هترا هترا هترا
+
+451
+00:33:15,480 --> 00:33:16,660
+هترا هترا هترا هترا هترا هترا هترا هترا هترا هترا
+
+452
+00:33:16,660 --> 00:33:17,220
+هترا هترا هترا هترا هترا هترا هترا هترا هترا هترا
+
+453
+00:33:17,220 --> 00:33:23,980
+هترا هترا هترا هترا هترا هترا هترا هترا هترا هترا
+
+454
+00:33:23,980 --> 00:33:25,400
+هترا هترا هترا هترا هترا هترا هترا هترا هترا هترا
+
+455
+00:33:25,400 --> 00:33:29,980
+هترا هترا هترا هترا هترا هترا هترا هترا هترا هترا
+
+456
+00:33:31,090 --> 00:33:34,450
+واضح هذا الان الاتجاه الأول لما ال X في ال M 
+
+457
+00:33:34,450 --> 00:33:38,990
+closure بيعطيني ل gate sequence في ال M حيث ان XN 
+
+458
+00:33:38,990 --> 00:33:44,930
+بتروح ل X نيجي الآن conversely suppose that ان 
+
+459
+00:33:44,930 --> 00:33:50,670
+الخاصية هذه تتحقق بدنا نثبت ان لو اتحققت هذه هتكون 
+
+460
+00:33:50,670 --> 00:33:59,760
+ال X موجودة في ال M closure طيب يا جماعة الان بنقول 
+
+461
+00:33:59,760 --> 00:34:06,220
+conversely suppose that xn وين موجودة في ال M و ال
+
+462
+00:34:06,220 --> 00:34:10,460
+xn converge لمين؟ لل x بيثبتلكم ال x وين موجودة في
+
+463
+00:34:10,460 --> 00:34:15,120
+ال M closure فبنخلصنا لأن if x element in M إذا x 
+
+464
+00:34:15,120 --> 00:34:20,140
+element in M closure خلصنا ماشي الحال أنا غلط
+
+465
+00:34:20,140 --> 00:34:23,480
+أثبتها في ال M closure لو كانت x مش اللي أه في ال
+
+466
+00:34:23,480 --> 00:34:25,600
+M بيثبتلكم إن ال X هتكون إيه شمال a little bit
+
+467
+00:34:25,600 --> 00:34:30,490
+word ماشيلو أثرت أنها limit point معناه أنها
+
+468
+00:34:30,490 --> 00:34:35,210
+موجودة في الـ M closure بكون خلصت الآن مدام X مش 
+
+469
+00:34:35,210 --> 00:34:40,170
+في الـ M إذا لكل Y و أنا عند XN بتروح لمين؟ XN
+
+470
+00:34:40,170 --> 00:34:44,370
+بتروح لل X إذا لكل Y أكبر من صفر بقدر ألاقي K بحيث
+
+471
+00:34:44,370 --> 00:34:47,850
+أن المسافة بين هذه و هذه أشمالها أزر من الـ Y لكل 
+
+472
+00:34:47,850 --> 00:34:53,410
+M أكبر من K إذا الآن من هذه بكون حصلت اللي بديها
+
+473
+00:34:53,410 --> 00:34:56,570
+ايش اللي حصلت اللي بديها بقولكم hence for every y 
+
+474
+00:34:56,570 --> 00:35:01,030
+أكبر من 0 بقدر ألاقي k بحيث أن ال ball اللي فيها x 
+
+475
+00:35:01,030 --> 00:35:06,230
+و y نصف قطرها y المسافة بين ال xn اللي هي ال xn
+
+476
+00:35:06,230 --> 00:35:10,790
+نات هايها بين ال xn و ال x ما انها أصغر من y كل ال
+
+477
+00:35:10,790 --> 00:35:17,170
+n أكبر من k يعني هذه فيها مين فيها xk زائد واحد و
+
+478
+00:35:17,170 --> 00:35:21,840
+xk زائد اتنينو XK زيادة تلاتة و XK زيادة أربعة كل
+
+479
+00:35:21,840 --> 00:35:25,260
+هين موجودة هنا لو شيلت منهم X تقاطع لهم أكيد A 
+
+480
+00:35:25,260 --> 00:35:28,960
+شمالهم لا يساوي فيه لأنهم كل ال XK و XK زيادة واحد
+
+481
+00:35:28,960 --> 00:35:31,880
+و XK زيادة اتنين كل هين موجودة في الأصل في الام
+
+482
+00:35:31,880 --> 00:35:34,080
+مازالت موجودة هنا موجودة في الأم ماذا ما تقاطعوا 
+
+483
+00:35:34,080 --> 00:35:38,040
+احد اشماله لا يساوي فيه إذا ال X وين موجودة في
+
+484
+00:35:38,040 --> 00:35:45,240
+الام مكلوجر إذا بكون خلصنا الجزء الأول نتيجي الآن
+
+485
+00:35:45,240 --> 00:35:46,500
+من B 
+
+486
+00:35:48,780 --> 00:35:55,360
+الان بيه من اللي فوق عندي M is closed if and only 
+
+487
+00:35:55,360 --> 00:36:00,320
+if ال M مش ميزه تساوي ال M closure مظبوط M is
+
+488
+00:36:00,320 --> 00:36:04,200
+closed اذا كانت اذا و فقط اذا M بيساوي M closure و
+
+489
+00:36:04,200 --> 00:36:08,440
+M بتساوي M closure و هذه سهل اتباعتها لو تبتوها من 
+
+490
+00:36:08,440 --> 00:36:14,010
+الاصل كمان سهل اتباعتها الآن M بيتساوى M closure if 
+
+491
+00:36:14,010 --> 00:36:19,190
+and only if the situation Xn بتروح لل X that means
+
+492
+00:36:19,190 --> 00:36:24,730
+X element in M هذا منذ قبل بشوية أنه لما تكون Xn
+
+493
+00:36:24,730 --> 00:36:28,590
+بتروح لل X و Xn في ال M تعطين X element in M هذا
+
+494
+00:36:28,590 --> 00:36:33,510
+if and only if إيه شمالها؟ اللي هو ال X موجودة في
+
+495
+00:36:33,510 --> 00:36:37,210
+ال M closure إذن الآن عندي M is closed if and only 
+
+496
+00:36:37,210 --> 00:36:45,720
+if اللي هو مين اللي قبل بشوية مش اللي قبل بشوية
+
+497
+00:36:45,720 --> 00:36:46,660
+احنا اثبتناها
+
+498
+00:36:49,310 --> 00:36:52,090
+اللي هو X المتقن عام الـ closure if and only if 
+
+499
+00:36:52,090 --> 00:36:56,450
+الـ sequence X المتروح للـ X أه طيب الآن if and 
+
+500
+00:36:56,450 --> 00:36:58,250
+only if أم is closed if and only if أم سواء الـ 
+
+501
+00:36:58,250 --> 00:37:01,630
+closure معناته ال .. ال .. ال .. كل اللي في الأم
+
+502
+00:37:01,630 --> 00:37:04,950
+إيه شمع الوجودات في الأم ال closure معناته اللي هو 
+
+503
+00:37:04,950 --> 00:37:09,510
+اللي هو هذا ال .. هذا الكلام بيعطينا أن هذا يتحقق
+
+504
+00:37:09,510 --> 00:37:13,150
+وزمان هذا يتحقق إذا هذا يؤدي لهذا ويكون عندنا
+
+505
+00:37:13,150 --> 00:37:16,650
+خلصنا اللي هي بيه أي سؤال طيب اللي بعدها 
+
+506
+00:37:21,190 --> 00:37:30,350
+theorem مش مطولى ان شاء الله theorem a subspace
+
+507
+00:37:30,350 --> 00:37:33,770
+M of a complete metric space X is itself complete
+
+508
+00:37:33,770 --> 00:37:39,030
+if and only if the set M is closed طبعا احنا فيه 
+
+509
+00:37:39,030 --> 00:37:44,030
+تفاصيل قدام ان 
+
+510
+00:37:44,030 --> 00:37:46,830
+لو كانت ال space
+
+511
+00:37:49,250 --> 00:37:53,950
+م closed مش شرط يكون complete لو كان ال space
+
+512
+00:37:53,950 --> 00:38:01,510
+closed مش شرط يكون complete لكن 
+
+513
+00:38:01,510 --> 00:38:11,670
+لو كان احنا بنحكي عن subspace M of a complete 
+
+514
+00:38:11,670 --> 00:38:18,890
+metric space X is itself complete if and only if M
+
+515
+00:38:18,890 --> 00:38:24,310
+أشماله is closed in X يعني الآن بالظبط الحالة كيف 
+
+516
+00:38:24,310 --> 00:38:33,430
+أنه أنا عايش عايش في إيش في complete metric space 
+
+517
+00:38:33,430 --> 00:38:39,570
+بصير عندي ال subspace M عشان أحكم عليه complete
+
+518
+00:38:39,570 --> 00:38:44,180
+ولا لأ بس بال closed إذا كان مقفل فهو مقفل وإذا كان 
+
+519
+00:38:44,180 --> 00:38:54,020
+مقفل فهو مقفل إذا كان مقفل فهو 
+
+520
+00:38:54,020 --> 00:38:54,420
+مقفل فهو مقفل إذا كان مقفل فهو مقفل إذا كان مقفل
+
+521
+00:38:54,420 --> 00:38:56,400
+فهو مقفل إذا كان مقفل فهو مقفل إذا كان مقفل فهو
+
+522
+00:38:56,400 --> 00:38:57,940
+مقفل إذا كان مقفل فهو مقفل إذا كان مقفل فهو مقفل
+
+523
+00:38:57,940 --> 00:39:00,200
+إذا كان مقفل فهو مقفل إذا كان مقفل فهو مقفل إذا
+
+524
+00:39:00,200 --> 00:39:04,500
+كان مقفل فهو مقفل إذا كان مقفل فهو مقفل إذا كان
+
+525
+00:39:04,500 --> 00:39:08,640
+مقفل فهو مقفل إذا كان مقفل فهو مقفل إذا كان مقف
+
+526
+00:39:10,310 --> 00:39:15,010
+نجلة اللي هو أو فيها مثلها طبعا أو حتى جابولها في
+
+527
+00:39:15,010 --> 00:39:19,290
+الخلال اللي هي الأسئلة اللي عندكم ماشي نجاوبها كل
+
+528
+00:39:19,290 --> 00:39:24,710
+شي suppose that M is إيه الشمالها complete and X
+
+529
+00:39:24,710 --> 00:39:33,260
+element in M closure ماشي then by theorem 1 4 7A,
+
+530
+00:39:33,260 --> 00:39:37,880
+there is a sequence xn in M such that xn بتروح للX
+
+531
+00:39:37,880 --> 00:39:40,940
+خلاص أنا بناعرف الترجم سيلنا لما X تكون في الـ M
+
+532
+00:39:40,940 --> 00:39:45,680
+closure معناته في sequence xn in M و الـ xn بتروح
+
+533
+00:39:45,680 --> 00:39:49,400
+لمين خلاص هذا بيصير سلوكة أننا بناسيه الترجم فيه
+
+534
+00:39:49,400 --> 00:39:54,700
+بسهل علينا الأمور كتير إذا الاجانب
+
+535
+00:39:54,700 --> 00:39:58,490
+sequence xn بتروح لمين لل X ما دام Xn convergence
+
+536
+00:39:58,490 --> 00:40:02,310
+لسة عامة قبل شوية قلنا hence Xn إيش ما لها is كوشي
+
+537
+00:40:02,310 --> 00:40:07,890
+لكن M is complete لكن M is complete و Xn كوشي في
+
+538
+00:40:07,890 --> 00:40:11,930
+ال M إذا أكيد أكيد limit هو M هيكون في ال M لأنها 
+
+539
+00:40:11,930 --> 00:40:16,570
+complete إذا X موجودة في ال M إذا بدأت الآن عندي X 
+
+540
+00:40:16,570 --> 00:40:19,870
+في ال M closure و لجأت هوي موجودة في ال M معناة
+
+541
+00:40:19,870 --> 00:40:23,830
+ال M إيش و ده تساوي M closure لأن M دايما subset 
+
+542
+00:40:23,830 --> 00:40:28,500
+من M closure أثبتلكم أن M closure subset من M ماشي،
+
+543
+00:40:28,500 --> 00:40:30,480
+إذا صحيح M بيسوي M كله وجهة محددة معينة و M
+
+544
+00:40:30,480 --> 00:40:37,220
+أشمالها is a closed set، conversely بدي أفترض M
+
+545
+00:40:37,220 --> 00:40:43,780
+بيه a closed set و أفترض إن Xn بيه any Cauchy 
+
+546
+00:40:43,780 --> 00:40:49,780
+sequence in M بدي أثبت لكم M is complete يعني الـ
+
+547
+00:40:49,780 --> 00:40:51,420
+Cauchy sequence اللي بدي أثبت هنا أشمالها
+
+548
+00:40:51,420 --> 00:40:58,950
+converges طيب مدام عندي xn كوشي in .. in .. in ..
+
+549
+00:40:58,950 --> 00:41:04,950
+in M وعندي اللي هي ال .. ال .. ال .. ال space كله
+
+550
+00:41:04,950 --> 00:41:09,910
+complete xn مظبوط هنا كوشي فيها دي لإن هي موجودة
+
+551
+00:41:09,910 --> 00:41:13,910
+في ال space كله المكبير إذا xn صارت كوشي sequence 
+
+552
+00:41:13,910 --> 00:41:18,130
+و M في ال complete space X إذا لازم يكون في عندي x
+
+553
+00:41:18,130 --> 00:41:24,560
+في ال X such that xn بتروح لميليين لكن انا بقول ان
+
+554
+00:41:24,560 --> 00:41:31,420
+ال subspace M is closed اذا
+
+555
+00:41:31,420 --> 00:41:35,620
+اي sequence فيها بتروح ل X لازم X وير تكون في ال M 
+
+556
+00:41:35,620 --> 00:41:40,660
+اذا X وير موجودة في ال M اذا صار is complete كمان
+
+557
+00:41:40,660 --> 00:41:48,200
+مرة شوفكم زي اللي بلعته الآن عند M ايش مارها is
+
+558
+00:41:48,200 --> 00:42:01,020
+closed بتثبتلكم ان هناك
+
+559
+00:42:01,020 --> 00:42:10,300
+هلونة ون في الام كوشي نمأزكيب Xn بزوء من موجودة في 
+
+560
+00:42:10,300 --> 00:42:14,360
+الـM معناته موجودة في الـX إذا صارت Xn كوش في مين؟ 
+
+561
+00:42:14,360 --> 00:42:18,880
+في الـX والـX Complete إذا لازم يكون في عنصر اللي
+
+562
+00:42:18,880 --> 00:42:23,360
+هو X بحيث أن Xn بتروح لمين؟ الـX موجود هُنا؟ في
+
+563
+00:42:23,360 --> 00:42:28,870
+الـX لكن أنا بقول إن M نفسه Closed وبيقول لك الـ
+
+564
+00:42:28,870 --> 00:42:32,750
+Closed إن أي شيء Sequence عندي بتروح للـ X لازم 
+
+565
+00:42:32,750 --> 00:42:36,590
+تجي الـ X تبقيتها عندي عشان أظل Closed فإذن صارت
+
+566
+00:42:36,590 --> 00:42:40,350
+الـ X هنا موجودة في الـ M إذن صارت اللي هي بدينا 
+
+567
+00:42:40,350 --> 00:42:44,110
+بـ Cauchy Sequence هنا وانتهينا بالـ Cauchy
+
+568
+00:42:44,110 --> 00:42:49,470
+Sequence Conversion فيها إذن M is Complete واضح؟
+
+569
+00:42:49,470 --> 00:43:02,130
+المفروض واضح نجي لا firm 149 I'm
+
+570
+00:43:02,130 --> 00:43:09,210
+having T من X لعند Y of a metric space X and Y into a
+
+571
+00:43:09,210 --> 00:43:13,570
+metric space Y. T is continuous at X0 if and only
+
+572
+00:43:13,570 --> 00:43:18,850
+if Xn بتروح للـ X0 implies that Xn بتروح لمين؟ للـ TX0
+
+573
+00:43:18,850 --> 00:43:22,130
+النظرية الصحيحة اللي بنعرفها دي عنا زمان في ال
+
+574
+00:43:22,130 --> 00:43:26,290
+continuity بنحول الحديث في الـ continuity من limit
+
+575
+00:43:26,290 --> 00:43:30,770
+F of X as X بتروح لـ X0 بيساوي F of X0 إلى لغة ال
+
+576
+00:43:30,770 --> 00:43:35,460
+sequences يعني بنقول الآن ميزان... الميزان تبع الـ
+
+577
+00:43:35,460 --> 00:43:41,480
+continuity عند نقطة X0 بدي يكون كالتالي بنقول 
+
+578
+00:43:41,480 --> 00:43:56,720
+أنه T is continuous T من X لعند Y continuous
+
+579
+00:43:56,720 --> 00:44:02,910
+at X0 إذا و فقط إذا شوفوا ميزان الـ continuity
+
+580
+00:44:02,910 --> 00:44:06,850
+الآن أنه... الـ sequences بتجيبوا أنه لو جينا أخدنا 
+
+581
+00:44:06,850 --> 00:44:13,570
+أي Xn بتروح للـ x لازم هذا يعطيني الـ T xn بتروح للـ
+
+582
+00:44:13,570 --> 00:44:18,510
+T x0 إذا هذا تحقق automatically الـ T هتكون
+
+583
+00:44:18,510 --> 00:44:22,500
+continuous عند نقطة عند x0 ولو الـ T
+
+584
+00:44:22,500 --> 00:44:27,600
+continuous عند X0 لازم يتحقق التالي إنه لما أخد XN
+
+585
+00:44:27,600 --> 00:44:32,380
+بتروح للـ X على طول تقول لي الـ TXN بتروح لمين لـ
+
+586
+00:44:32,380 --> 00:44:37,920
+TX0 وهذا اللي هو هوية الـ continuity للـ T زي ما
+
+587
+00:44:37,920 --> 00:44:41,800
+هويتها التعريف التابع لزمان اللي هو limit F of X
+
+588
+00:44:41,800 --> 00:44:45,320
+لما X بتروح لـ X0 بيساوي F of X0 هذه هويتها أو limit
+
+589
+00:44:45,320 --> 00:44:49,630
+T of X لما X بتروح لـ X0 بيساوي X0 هذه هويتها هذا حتى
+
+590
+00:44:49,630 --> 00:44:52,470
+in general حتى في الـ metric spaces الـ convergence
+
+591
+00:44:52,470 --> 00:44:55,710
+هذا مش convergence عادي الـ convergence إيش في ال
+
+592
+00:44:55,710 --> 00:44:59,790
+metric D لو هذا D وهذا D prime الـ convergence في
+
+593
+00:44:59,790 --> 00:45:06,570
+الـ metric في الـ D prime واضح نجي اللي هو إن نبرهن
+
+594
+00:45:06,570 --> 00:45:11,950
+النظرية نبرهن النظرية والبرهان كمان لطيف ومش
+
+595
+00:45:11,950 --> 00:45:15,910
+صعب نشوف
+
+596
+00:45:15,910 --> 00:45:19,890
+إيش بتقول النظرية في برهانها suppose that T is
+
+597
+00:45:19,890 --> 00:45:26,370
+continuous at X0 مادام continuous عند X0 حسب الـ
+
+598
+00:45:26,370 --> 00:45:31,150
+continuity اللي هو تعريف الـ Continuity إذا لكل Epsilon
+
+599
+00:45:31,150 --> 00:45:34,290
+أكبر من 0 there exists Delta أكبر من 0 such that
+
+600
+00:45:34,290 --> 00:45:39,530
+DX و X0 أصغر من Delta بيؤدي لـ D TX و TX0 أصغر
+
+601
+00:45:39,530 --> 00:45:43,390
+من Epsilon تعريف الـ Continuity تعريف الـ 
+
+602
+00:45:43,390 --> 00:45:48,930
+Continuity إنه بيقول الـ function T continuous at
+
+603
+00:45:48,930 --> 00:45:55,700
+X0 مش عارف لتبع زمان إنه limit فـ أو T of X0
+
+604
+00:45:55,700 --> 00:46:01,840
+إذا X بتروح لـ X0 بيساوي T of X صح؟
+
+605
+00:46:03,350 --> 00:46:06,890
+الآن هذه ترجمته أنه لكل epsilon لما تقترب المسافة
+
+606
+00:46:06,890 --> 00:46:09,870
+... لما... المسافة هذه تقترب... النقطة هذه تقترب من
+
+607
+00:46:09,870 --> 00:46:13,650
+هذه عبر مسافتها هذه بتقترب من هذه عبر مسافتها يعني
+
+608
+00:46:13,650 --> 00:46:16,070
+بمعنى آخر هذه... اللي بدأنا نعبرها عن هذه بـ Delta
+
+609
+00:46:16,070 --> 00:46:18,610
+وهذه بـ Epsilon ثم بقول عبّر ده for every Epsilon
+
+610
+00:46:18,610 --> 00:46:21,530
+أكبر من 0 there exists Delta أكبر من 0 such
+
+611
+00:46:21,530 --> 00:46:25,350
+that if اللي هو... اللي هو هذه ناقص هذه ميقولوش
+
+612
+00:46:25,350 --> 00:46:30,510
+عنها هيك بقول if dx و x0 أصغر من Delta then
+
+613
+00:46:31,830 --> 00:46:38,530
+هيكون عندي D  تبعها اللي هي metric space  TX و TX
+
+614
+00:46:38,530 --> 00:46:44,420
+0 أصغر من Epsilon هذا اللي هو الـ continuity أو
+
+615
+00:46:44,420 --> 00:46:46,340
+اللي هو هذا التعبير بالـ بول زي اللي حكيناها في
+
+616
+00:46:46,340 --> 00:46:50,000
+الأول أنه... أنه... اللي هو... أنه... لما تكون 
+
+617
+00:46:50,000 --> 00:46:54,420
+اللي هو الـ ball اللي هنا اللي... اللي... اللي...
+
+618
+00:46:54,420 --> 00:46:55,720
+اللي... اللي... اللي... اللي... اللي... اللي...
+
+619
+00:46:55,720 --> 00:46:57,020
+اللي... اللي... اللي... اللي... اللي... اللي...
+
+620
+00:46:57,020 --> 00:46:57,060
+اللي... اللي... اللي... اللي... اللي... اللي...
+
+621
+00:46:57,060 --> 00:46:57,080
+اللي... اللي... اللي... اللي... اللي... اللي...
+
+622
+00:46:57,080 --> 00:47:02,280
+اللي... اللي... اللي... اللي... اللي... اللي...
+
+623
+00:47:02,280 --> 00:47:05,520
+اللي
+
+624
+00:47:05,520 --> 00:47:11,380
+... لكل X هنا بناجيها الـ TX تبعتها فاهمين ما بحكيه
+
+625
+00:47:11,380 --> 00:47:17,780
+هون؟ ماشي طيب وصلى على النبي عليه الصلاة والسلام
+
+626
+00:47:17,780 --> 00:47:21,860
+such that T is continuous at X0 then for every Epsilon
+
+627
+00:47:21,860 --> 00:47:24,760
+أكبر من 0 there exists Delta أكبر من 0 such that
+
+628
+00:47:24,760 --> 00:47:28,220
+لما المسافة تضيق بين X و X0 أصغر من Delta بتعطيني
+
+629
+00:47:28,220 --> 00:47:32,080
+المسافة المقابلة D تبعها بين TX و DX أصغر من مين؟ من
+
+630
+00:47:32,080 --> 00:47:39,520
+Epsilon ماشي؟ الآن بدي أثبت لكم لما Xn بتروح لـ X0 يعطيني
+
+631
+00:47:39,520 --> 00:47:45,520
+TXn بتروح لمين TX0 سهل نفترض الآن Xn بتروح لمين للـ
+
+632
+00:47:45,520 --> 00:47:50,000
+X0 إذا مدام Xn بتروح للـ X0 إذا بقدر نلاقي K
+
+633
+00:47:50,000 --> 00:47:56,300
+عنصر  بـ Delta هذه إيش معناتها Xn بتروح لـ X0 لأي Epsilon
+
+634
+00:47:56,300 --> 00:47:59,020
+أكبر من 0 في الدنيا بتاخدها لمين الآن؟ لإيش...
+
+635
+00:47:59,020 --> 00:48:03,340
+لحاجة تخدمني؟ إيش اسمها Delta؟ ماشي؟ شو معناة Xn
+
+636
+00:48:03,340 --> 00:48:07,260
+بتروح لـ X0 لكل Epsilon أكبر من 0 there exists K عنصر
+
+637
+00:48:07,260 --> 00:48:10,820
+in N such that اللي هو الـ distance بين Xn و X0
+
+638
+00:48:10,820 --> 00:48:15,380
+أصغر من Epsilon لكل N أكبر من K اللي أنا 
+
+639
+00:48:15,380 --> 00:48:19,540
+مانديش أخد لكل Epsilon و أخد لـ Delta هذه اللي لجيتهاللـ
+
+640
+00:48:19,540 --> 00:48:23,040
+Delta اللي لجيتها بدي أشتغل بدي أقول for Delta
+
+641
+00:48:23,040 --> 00:48:27,960
+اللي لجيتها there exist K such that المسافة بين Xn
+
+642
+00:48:27,960 --> 00:48:33,600
+و X0 أصغر من الـ Delta لكل N أكبر من مين من K إذا
+
+643
+00:48:33,600 --> 00:48:41,320
+مباشرة احنا قلنا اللي بتحقق هذا بيعطينا هذا لأن
+
+644
+00:48:41,320 --> 00:48:44,740
+هذا تحقق الـ XN بعيد عن X0 بمسافة أقل من Delta
+
+645
+00:48:44,740 --> 00:48:50,880
+إذا أكيد صورة من الـ Delta تبعها بين TXN و TX0 
+
+646
+00:48:50,880 --> 00:48:57,260
+هتكون أصغر من Epsilon إذا عندي المسافة هذه 
+
+647
+00:48:57,260 --> 00:49:00,260
+تبعها بين TXN و TX0 أصغر من Epsilon فهو N أكبر من
+
+648
+00:49:00,260 --> 00:49:04,300
+K إيش معناة هذا أنه أنا بدأت بأي Epsilon في
+
+649
+00:49:04,300 --> 00:49:09,560
+الدنيا arbitrary اللي بدأت فيها أي Epsilon لجيت K
+
+650
+00:49:09,560 --> 00:49:13,780
+الآن بحيث أن المسافة بين TXN و TX0 أصغر من Epsilon
+
+651
+00:49:13,780 --> 00:49:18,180
+لكل N أكبر من مين من K وهذا معناته أن TXN بتروح لـ
+
+652
+00:49:18,180 --> 00:49:18,660
+TX0
+
+653
+00:49:27,640 --> 00:49:32,620
+Conversely نفرض أن الشرط تحقق و بدنا نثبت الـ
+
+654
+00:49:32,620 --> 00:49:43,720
+continuity طيب
+
+655
+00:49:43,720 --> 00:49:50,560
+Conversely Suppose that xₙ converges to xₙ implies
+
+656
+00:49:50,560 --> 00:49:53,280
+that T xₙ converges to T xₙ بتروح لمين؟ لـ Txₙ بتدفع
+
+657
+00:49:53,280 --> 00:49:56,600
+الـ continuity لان طيب، to prove that T is
+
+658
+00:49:56,600 --> 00:50:00,700
+continuous نفترض الـ Xₙ نستخدم الـ Contradiction
+
+659
+00:50:00,700 --> 00:50:05,520
+نفترض العكس ونصل لإيش؟ لتناقض أه، بدنا نفترض أن T
+
+660
+00:50:05,520 --> 00:50:10,040
+مش continuous عند الـ Xₙ Suppose that T is not
+
+661
+00:50:10,040 --> 00:50:11,380
+continuous at X0
+
+662
+00:50:38,310 --> 00:50:42,470
+إذن يعني بمعنى آخر بقى كأني بدي أقول for every
+
+663
+00:50:42,470 --> 00:50:50,190
+واحد على N يعني for every N بقدر ألاقي XN بحيث أنه
+
+664
+00:50:50,190 --> 00:50:55,910
+المسافة بين XN و X0 تكون أصغر من Delta حسب هذا Such
+
+665
+00:50:55,910 --> 00:50:59,890
+that d dxn و dx0 إيش مالها أكبر أو يساوي Epsilon
+
+666
+00:50:59,890 --> 00:51:04,310
+هذا إيش معناته هذا معناته هذه مدام أصغر من أي Delta
+
+667
+00:51:04,310 --> 00:51:08,530
+في الدنيا معناته الـ dxn بتروح لمين للـ x0 أو الـ
+
+668
+00:51:08,530 --> 00:51:12,890
+xn بتروح للـ x0 لكن هذه بتعني إيش but dxn does
+
+669
+00:51:12,890 --> 00:51:18,210
+not converge to metric to dx0 وهذا يناقض المعطى thus
+
+670
+00:51:18,210 --> 00:51:24,080
+or this contradicts the assumption therefore T is
+
+671
+00:51:24,080 --> 00:51:29,080
+continuous at x0 وهو المطلوب بيكون هيك احنا
+
+672
+00:51:29,080 --> 00:51:34,540
+خلصنا المحاضرة وعنا homework اللي هو اللي بدكم 
+
+673
+00:51:34,540 --> 00:51:38,500
+تسلموه اللي هو star ستة وثمانية والـ homework
+
+674
+00:51:38,500 --> 00:51:42,880
+الباقي هذا بتحلو أنتم وبارك الله فيكم الله
+
+675
+00:51:42,880 --> 00:51:43,540
+يعطيكم العافية 
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/g1UMuLpn1XM_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/g1UMuLpn1XM_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8b6c5a02d98b7406aa997d49f67e6549a8c8d7c2
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/g1UMuLpn1XM_postprocess.srt
@@ -0,0 +1,2700 @@
+1
+00:00:05,130 --> 00:00:07,790
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,790 --> 00:00:10,810
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,810 --> 00:00:14,850
+آله وصحبه أجمعين هذه هي المحاضرة الخامسة مساق
+
+4
+00:00:14,850 --> 00:00:19,890
+تحليل اقتراني أو تحليل دالي لطلاب وطالبات الجامعة
+
+5
+00:00:19,890 --> 00:00:27,820
+الإسلامية طلبة ال master أو master رياضياتوصلنا او
+
+6
+00:00:27,820 --> 00:00:32,020
+نهينا section واحد تلاتة حكينا عن اللي هو ال open
+
+7
+00:00:32,020 --> 00:00:35,240
+sets و ال neighborhoods و ال closed sets و حكينا
+
+8
+00:00:35,240 --> 00:00:40,780
+عن ايضا اللي هو ال dense sets و عرفنا اللي هو ال
+
+9
+00:00:40,780 --> 00:00:43,880
+spaces اللي ال infinity اللي قال ال infinity مثلا
+
+10
+00:00:43,880 --> 00:00:47,420
+مش separable بينما قال بي لكل بي بأنه أكبر سوى
+
+11
+00:00:47,420 --> 00:00:50,410
+واحد أصغر من ال infinityR-Separable Spaces والـ
+
+12
+00:00:50,410 --> 00:00:54,170
+Spaces التابعاتنا اللي عايشين فيها في الـ Calculus
+
+13
+00:00:54,170 --> 00:00:58,050
+وباقي موادنا اللي هو الـR والـC عبارة عن Separable
+
+14
+00:00:58,050 --> 00:01:03,030
+Spaces الآن بدنا نحكي عن مفهيم أخرى تبولوجية ولكن
+
+15
+00:01:03,030 --> 00:01:06,410
+خلينا نقول هذه لا يمكن نسيغنع عنها أيضا في اللي هو
+
+16
+00:01:06,410 --> 00:01:10,160
+التحليل اللي هي convergenceمعنى الـ convergence
+
+17
+00:01:10,160 --> 00:01:14,580
+اللي احنا بنعرفه اصلا بس بنعممه على metric space
+
+18
+00:01:14,580 --> 00:01:17,120
+in general ايش معنى الـ Cauchy sequences اللي
+
+19
+00:01:17,120 --> 00:01:19,260
+انتوا عارفينها في ال .. في ال .. اللي خدناها في
+
+20
+00:01:19,260 --> 00:01:23,340
+الـ real ولكن برضه بنعملمها على اي metric space و
+
+21
+00:01:23,340 --> 00:01:26,820
+ال completeness بروبرتها دي يعني شغلة جديدةعلينا
+
+22
+00:01:26,820 --> 00:01:32,780
+اللي هي ال space اللي يختص بخاصية الاكتمال ان يكون
+
+23
+00:01:32,780 --> 00:01:36,060
+ال space مكتمل وهذا ال spaces المكتملة هي spaces
+
+24
+00:01:36,060 --> 00:01:39,760
+خلينا نقول كتير كتير محترمة و بتريحنا و هنشوف ايش
+
+25
+00:01:39,760 --> 00:01:43,580
+اللي هو معناه الاكتمال و هيكون رحلتنا معاه شوية
+
+26
+00:01:43,580 --> 00:01:46,900
+طويلة لأنه هيلزمنا في ال section اللي بعده و اللي
+
+27
+00:01:46,900 --> 00:01:52,330
+بعدهبنشوف معنات الـ Sequence انها Convergent بنقول
+
+28
+00:01:52,330 --> 00:01:56,190
+a sequence xn in a metric space x وd إذا جاعد أنا
+
+29
+00:01:56,190 --> 00:02:00,390
+وان في metric space is said to be convergent ونقول
+
+30
+00:02:00,390 --> 00:02:03,710
+هذا الـ sequence convergent إذا بنلاقي x element
+
+31
+00:02:03,710 --> 00:02:06,810
+in x نفس المفهوم اللي احنا بنحكي فيه زمان في الـ
+
+32
+00:02:06,810 --> 00:02:12,470
+real such thatالان بنقولش limit xn بتروح لل x لأ
+
+33
+00:02:12,470 --> 00:02:16,370
+الان صار عندي اللي هو في metric ال metric اللي
+
+34
+00:02:16,370 --> 00:02:20,390
+بتحكي عنه اللي هو دي فبنقول عنه limit d xn وx ايش
+
+35
+00:02:20,390 --> 00:02:25,650
+بيساوي بيساوي سفر as n goes to infinity لاحظوا انا
+
+36
+00:02:25,650 --> 00:02:32,890
+بقول الان ان xn sequence في ال x بقول xn converts
+
+37
+00:02:32,890 --> 00:02:36,740
+لل xconvergence ده ال X بس وين هذا في ال metric
+
+38
+00:02:36,740 --> 00:02:40,840
+space اللي هو X وD يعني الدنيا تبعت ال convergence
+
+39
+00:02:40,840 --> 00:02:44,540
+هذا اللي هي ال X وD بدي أعرف هذا ال convergence
+
+40
+00:02:44,540 --> 00:02:49,160
+بإيش أنا أصلا بعرفه من الأصل فحولت الحديث كله من
+
+41
+00:02:49,160 --> 00:02:53,580
+عناصر في داخل ال X ال metric space اللي عندى إلى
+
+42
+00:02:53,580 --> 00:03:00,870
+limitDXN و X as N goes to infinity بساوي اللي هو
+
+43
+00:03:00,870 --> 00:03:05,530
+sum اللي هو number اللي هو ال zero بالظبط ال
+
+44
+00:03:05,530 --> 00:03:10,590
+number اللي بنحكي عنه مين ال zeroفي الواقع أنا هذا
+
+45
+00:03:10,590 --> 00:03:13,810
+الحديث أنا بعرفه لإن ال distance بين X و N أو X
+
+46
+00:03:13,810 --> 00:03:17,330
+أبريل ألاف أو أرقام إذا هذه أرقام و كأنه sequence
+
+47
+00:03:17,330 --> 00:03:20,790
+من أرقام بتديها تروح لمين للزيرو فعرفت ال
+
+48
+00:03:20,790 --> 00:03:24,210
+convergence ال XN في اللي بروح لل X في ال metric
+
+49
+00:03:24,210 --> 00:03:31,370
+space X بدلالة مين بدلالة اللي هو ال sequence of
+
+50
+00:03:31,370 --> 00:03:36,190
+numbers اللي عندي خلفية عنها من خلال الريال الأصلي
+
+51
+00:03:36,640 --> 00:03:41,520
+هذا معناه الـ convergence in this case X is called
+
+52
+00:03:41,520 --> 00:03:45,520
+the limit of Xn يعني X اللي هي X هي limit لل Xn or
+
+53
+00:03:45,520 --> 00:03:49,380
+Xn converge to X and we write limit Xn بسوا X or
+
+54
+00:03:49,380 --> 00:03:53,100
+Xn goes to infinity أو simply زي ما كتبت Xn بتروح
+
+55
+00:03:53,100 --> 00:03:58,750
+لل Xواضح هذا معناته اللي هو ال convergence الان if
+
+56
+00:03:58,750 --> 00:04:03,130
+xn is not convergent زي ما احنا متعودين then بنقول
+
+57
+00:04:03,130 --> 00:04:07,410
+عنها ايش ما لها is a divergent sequence نيجي
+
+58
+00:04:07,410 --> 00:04:11,350
+للملاحظات اللي بتخلينا نقول بتعمق المفهوم عندنا و
+
+59
+00:04:11,350 --> 00:04:17,380
+بتفهمنا المفهوم بشكل أكبرحينها لو طلعت لهذا انا
+
+60
+00:04:17,380 --> 00:04:21,300
+صرت اتعامل و كأنه هذا number اذا بعرف تعريفه مؤصل
+
+61
+00:04:21,300 --> 00:04:24,260
+انا ال epsilon definition او ال epsilon definition
+
+62
+00:04:24,260 --> 00:04:27,620
+تبع اللي هو تبع اللي هو ال calculus و تبع التحليل
+
+63
+00:04:27,620 --> 00:04:30,560
+بعرفه اللي هو forever epsilon أكبر من 0there
+
+64
+00:04:30,560 --> 00:04:34,140
+exists k element in n such that for every n أكبر
+
+65
+00:04:34,140 --> 00:04:40,160
+يساوي k ال distance بين ال xn و ال x أصغر من y for
+
+66
+00:04:40,160 --> 00:04:44,660
+every n أي شمالها أكبر أو يساوي k هذا ما طبعا احنا
+
+67
+00:04:44,660 --> 00:04:48,920
+ممكن نترجمه بشكل آخر انه اللي هو لكل y أكبر من 0
+
+68
+00:04:48,920 --> 00:04:53,180
+there exists k element in n such that اللي هو عندي
+
+69
+00:04:53,180 --> 00:05:01,520
+ال ballاللي مركزها X و نصف قطرها Y بتحتوي على كل
+
+70
+00:05:01,520 --> 00:05:07,820
+الـ X أنات المن N أكبر أو سوى واحد يعني XN element
+
+71
+00:05:07,820 --> 00:05:11,820
+in الـ ball هذه for every N أكبر أو سوى 100 يمكن
+
+72
+00:05:11,820 --> 00:05:16,520
+أن يحول الحديث من الـ metric هذا إلى الـ ball
+
+73
+00:05:16,520 --> 00:05:22,300
+المقابلة لها إذا بيصير عندي المراحضة الأولىLimit
+
+74
+00:05:22,300 --> 00:05:26,720
+xn بساوة x if and only if for every y أكبر من 0
+
+75
+00:05:26,720 --> 00:05:30,400
+there exists k بساوة k of y in element n طبعا ال k
+
+76
+00:05:30,400 --> 00:05:32,680
+بساوة k of y على أساس أن ال k اللي هتطلع عندى
+
+77
+00:05:32,680 --> 00:05:34,600
+بتاعتها تمد على مين؟ على ال epsilon ماعرفش علاقة
+
+78
+00:05:34,600 --> 00:05:40,960
+بال x such that xn element in pole لل x و y for
+
+79
+00:05:40,960 --> 00:05:45,580
+all n أكبر أو يساوي k هذا تعبير آخر عن اللي هو
+
+80
+00:05:45,580 --> 00:05:46,760
+معناه ال limit
+
+81
+00:05:49,870 --> 00:05:53,350
+المرحضة التانية The limit of a convergent sequence
+
+82
+00:05:53,350 --> 00:05:56,890
+must be a point of the space XN 4141
+
+83
+00:06:04,250 --> 00:06:07,430
+معناته إن الـ X اللي بتروحيلها الـ Xn لازم تكون في
+
+84
+00:06:07,430 --> 00:06:10,890
+مين؟ في الـ space اللي عندى يعني أنا .. هالجد
+
+85
+00:06:10,890 --> 00:06:14,410
+بتفهموه إيش اللي بقصده؟ إنه أنا لما أقول Xn
+
+86
+00:06:14,410 --> 00:06:21,210
+converges in X معناته limit الـ Xn بتتقارب نوح
+
+87
+00:06:21,210 --> 00:06:27,170
+نقطة اسمها X و الـ X هي الموجودةفي الـ x لكن لو
+
+88
+00:06:27,170 --> 00:06:31,990
+كانت ال limit xn جاي عبالها رايحة لإشي معين لكن
+
+89
+00:06:31,990 --> 00:06:35,490
+هذا مش موجود في ال set اللي هي ال x بنقولش عن ال
+
+90
+00:06:35,490 --> 00:06:39,770
+sequence إنها converges in this space لأ، بتكونش
+
+91
+00:06:39,770 --> 00:06:42,710
+converges إذا اللي بيقولهان في الملاحظة 2 الـ the
+
+92
+00:06:42,710 --> 00:06:46,110
+limit of a convergent sequence must be of the
+
+93
+00:06:46,110 --> 00:06:52,130
+space x اللي مذكور في أربعة واحد1 4 1 otherwise
+
+94
+00:06:52,130 --> 00:06:55,690
+بنقول الـ sequence إيش ما لها is divergent وماخدوا
+
+95
+00:06:55,690 --> 00:07:02,670
+لكم مثال بقولكم لو إحنا أخدنا ال X هي عبارة عن 0 1
+
+96
+00:07:02,670 --> 00:07:07,550
+و بس و أخدنا ال metric يعني جزء من R أخدته بس
+
+97
+00:07:07,550 --> 00:07:10,470
+المنطقة ده و ال metric هو ال metric تبع ال R اللي
+
+98
+00:07:10,470 --> 00:07:13,910
+هو إيش هو ال metric تبع ال R ال distance بين X و Y
+
+99
+00:07:13,910 --> 00:07:17,910
+بسوء ال absolute value X minus Y لكل X و Y اللي
+
+100
+00:07:17,910 --> 00:07:22,760
+موجودة في ال X اللي فوقبقولك الآن بدي أعطيك مثال
+
+101
+00:07:22,760 --> 00:07:25,700
+على الـ sequence دي هي عبالها تروح لشغلة لكن مش
+
+102
+00:07:25,700 --> 00:07:30,880
+موجودها يعني أخد اللي هو الـ xn أيش بتساوي 1 على n
+
+103
+00:07:30,880 --> 00:07:34,720
+أو n زايد واحدة منكم بجهها n أكبر أو أكبر من مين
+
+104
+00:07:34,720 --> 00:07:40,200
+من واحد وإذا بدنا نكون خلّيني نقول ألطف حطها هيكا
+
+105
+00:07:40,200 --> 00:07:44,570
+و ال n element in n وخلاصفاهمين عليها أن أكبر وسيء
+
+106
+00:07:44,570 --> 00:07:49,450
+واحد أي واحدة منها لاحظوا هذه ال Xn سهل لنا نثبتها
+
+107
+00:07:49,450 --> 00:07:54,510
+أن واحد على أن زائد واحد لو بدها تروح، هتروح لمين؟
+
+108
+00:07:54,510 --> 00:07:59,390
+للصفر لكن الصفر مش موجود في مين؟ عشان هيك بنقول
+
+109
+00:07:59,390 --> 00:08:05,510
+هذه اللي هو ال sequence does not converge الين؟ ال
+
+110
+00:08:05,510 --> 00:08:09,310
+X اللي هو Zero والواحد وهي it is clear that واحد
+
+111
+00:08:09,310 --> 00:08:12,310
+على أن is divergent because واحد على أنwants to
+
+112
+00:08:12,310 --> 00:08:16,790
+converge to zero which is not in zero أو واحد أي
+
+113
+00:08:16,790 --> 00:08:23,510
+سؤال واضح على الصورة الأمور طيب نيجي الآن اللي هو
+
+114
+00:08:23,510 --> 00:08:29,430
+بدنا نعرف اللي هو بدأ أروح باتجاه مدام بدي أحكي عن
+
+115
+00:08:29,430 --> 00:08:34,310
+convergence بعد بمشي زي ما كنا نمشي في R بحكي عن
+
+116
+00:08:34,310 --> 00:08:37,710
+convergence شكلي بدي أحكي عن bounded عشان أحكي عن
+
+117
+00:08:37,710 --> 00:08:42,220
+bounded بدي أشوف حاجة اسمها الـ diameterلمن؟ لل
+
+118
+00:08:42,220 --> 00:08:46,060
+set تشوف ايش اللي بنقوله وبدلالتها بدي اعرف ال
+
+119
+00:08:46,060 --> 00:08:56,920
+boundedness لو جيت قولت أخدت subset M a non-empty
+
+120
+00:08:56,920 --> 00:09:00,920
+subset M of a metric space X is said to be bounded
+
+121
+00:09:03,150 --> 00:09:08,430
+rounded if the diameter of M ايش ال diameter of M
+
+122
+00:09:08,430 --> 00:09:12,030
+ال diameter of M هو عبارة عن ال supremum لكل
+
+123
+00:09:12,030 --> 00:09:17,690
+الأبعاد اللي بيني الموجودة في ال M هذا بتسميه
+
+124
+00:09:17,690 --> 00:09:22,410
+اشماله ال diameter لكل ال M الان is finite لو كان
+
+125
+00:09:22,410 --> 00:09:27,880
+ال diameter is finite معناته انه انالأ هذا هيكون
+
+126
+00:09:27,880 --> 00:09:32,860
+عدد مظبوط عدد سموه مثلا اللي بتكون إيه سموه K مثلا
+
+127
+00:09:32,860 --> 00:09:40,460
+هذا العدد عدد الآن بيصير معناته الـ M is finite
+
+128
+00:09:40,460 --> 00:09:48,300
+أنه لكل X وY أو اللي هو there exist KElement in R
+
+129
+00:09:48,300 --> 00:09:53,340
+أو أكبر من سفر Such that المسافة بين X و Y أصغر من
+
+130
+00:09:53,340 --> 00:09:59,800
+K لكل X و Y موجودة في الـ M لأن الـ Supremum نفسه
+
+131
+00:09:59,800 --> 00:10:06,600
+محدود اسمه Kإذا كل المسافات اللي بين العناوز اللي
+
+132
+00:10:06,600 --> 00:10:10,460
+موجودة في هداك أصغر أو أساوي K أصغر أو أساوي K هذا
+
+133
+00:10:10,460 --> 00:10:15,080
+مشابه للأصل ال bounded العادي احنا لما نقول أن ال
+
+134
+00:10:15,080 --> 00:10:18,840
+6 M is bounded إذا بنلاقي K بحيث أن ال absolute
+
+135
+00:10:18,840 --> 00:10:23,340
+value لل X أصغر أو أساوي K لكل X وين موجودة في ال
+
+136
+00:10:23,340 --> 00:10:23,500
+M
+
+137
+00:10:27,700 --> 00:10:33,640
+ومنه أصلا بقدر أقول البسافة بين x و y اللي هي برضه
+
+138
+00:10:33,640 --> 00:10:36,400
+هتكون bargain زي اللي فوق لإنها هتكون أصغر بحكي عن
+
+139
+00:10:36,400 --> 00:10:40,740
+علامة تبع ال R أصغر بساوة x زاد absolute value ل y
+
+140
+00:10:40,740 --> 00:10:43,320
+و هذا أصغر من k و أصغر من k لإن هذا أصغر بساوة
+
+141
+00:10:43,320 --> 00:10:49,250
+102k يعني في النهاية اللي هو هذاأو هذا نفس الأشياء
+
+142
+00:10:49,250 --> 00:10:52,030
+بس هذا على الـ metric in general وهذا على mean على
+
+143
+00:10:52,030 --> 00:10:55,850
+absolute value تبع الزمان إذا تعريفي الجديد يتوافق
+
+144
+00:10:55,850 --> 00:11:00,950
+مع القديم والقديم بيصير حالة خاصة منه إذا الأن
+
+145
+00:11:00,950 --> 00:11:04,470
+ملخص حديثي إن الـ sequence Xm in X is called
+
+146
+00:11:04,470 --> 00:11:07,930
+bounded sequence if the corresponding point set
+
+147
+00:11:07,930 --> 00:11:11,870
+اللي هي X واحدة كل ال Xات اللي فيها is a bounded
+
+148
+00:11:11,870 --> 00:11:19,130
+subset of mean of Xأي سؤال؟ طيب نيجي لللمّة الأولى
+
+149
+00:11:19,130 --> 00:11:24,490
+اللمّة الأولى متوقعينها اللي هي زي اللي .. مش
+
+150
+00:11:24,490 --> 00:11:29,110
+هنحكي .. مش هنحكي و كأنه نصوص جديدة لأ النصوص هي
+
+151
+00:11:29,110 --> 00:11:31,430
+تبعات اللي كنا ناخدها في القارة عن الـ sequences
+
+152
+00:11:31,430 --> 00:11:35,130
+إيش
+
+153
+00:11:35,130 --> 00:11:40,540
+بتقول؟بتقول لو احنا عندنا let X و D بيه متر كسباس
+
+154
+00:11:40,540 --> 00:11:45,240
+then a convergent sequence in X is bounded هاي هنا
+
+155
+00:11:45,240 --> 00:11:47,200
+كنا نقول زمان انا convergence sequence is bounded
+
+156
+00:11:47,200 --> 00:11:50,960
+برضه فأي متر كسباس صح وال limit بقى اللي هي وحيدة
+
+157
+00:11:50,960 --> 00:11:55,980
+برضه نفس الكلام الأولاني برضه بظبط هناوالثانية
+
+158
+00:11:55,980 --> 00:11:59,300
+بقولك لو كانت ال XN بتروح لل X و ال YN بتروح لل Y
+
+159
+00:11:59,300 --> 00:12:04,600
+أكيد المسافة بين XN و YN برضه هتروح لمين للمسافة
+
+160
+00:12:04,600 --> 00:12:11,100
+بين X و Y ماشي الحال بدنا نثبتها اللي هو التنتين
+
+161
+00:12:11,100 --> 00:12:15,020
+اللي أمامناالإثبات برضه هتلاقوه مشابه للإثباتات
+
+162
+00:12:15,020 --> 00:12:18,240
+اللي كنا نثبتها في حالة اللي هي الـ Real Numbers
+
+163
+00:12:18,240 --> 00:12:22,220
+بس تشيلواها دي و تحطواها العصيتين اللي زمان كنا
+
+164
+00:12:22,220 --> 00:12:25,880
+ناخدهم العصيتين Absolute Value الآن احنا أياشي
+
+165
+00:12:25,880 --> 00:12:29,940
+بنحكي عن Animetric دي هتلاقوا الأمور كتير مشابهة
+
+166
+00:12:29,940 --> 00:12:35,160
+تشوف نطلع النبي عليه الصلاة والسلام نفترض ان X
+
+167
+00:12:35,160 --> 00:12:39,600
+Unconverts يعني X Un تروح لمين لSome X Element in
+
+168
+00:12:39,600 --> 00:12:45,620
+X Capitalالان برضه لو رجعته برهان اللي هو التحليل
+
+169
+00:12:45,620 --> 00:12:48,360
+هتلاقو نفس الأشياء إذا لكل أبسلون أكبر من سفر
+
+170
+00:12:48,360 --> 00:12:51,740
+there exist كده كده اللي بتاخد أبسلون تخدمني أخدت
+
+171
+00:12:51,740 --> 00:12:55,140
+أبسلون أربط أيه؟ يعني أخدت أبسلون محددة سميتها
+
+172
+00:12:55,140 --> 00:12:58,260
+واحد بنفع أخد اتنين، بنفع أخد تلاتة، بنفع أخد
+
+173
+00:12:58,260 --> 00:13:02,120
+أربع، بنفع أخد ربع، بنفع أخد درجتين، بس ألطف لنفس
+
+174
+00:13:02,120 --> 00:13:06,990
+الواحد، الواحد منيح مازال بتاخد، إذاthen for y
+
+175
+00:13:06,990 --> 00:13:09,790
+بيساوي واحد there is k limiting and such that
+
+176
+00:13:09,790 --> 00:13:13,450
+المسافة بين x أن وx أشمالها أصغر من واحد لكل أن
+
+177
+00:13:13,450 --> 00:13:17,330
+أشمالها أكبر من k هذا التعريف المباشر للـ limit
+
+178
+00:13:17,330 --> 00:13:24,750
+اللي جابناه بشوية حكينا عنه الآن بيقوللي بده الآن
+
+179
+00:13:24,750 --> 00:13:28,590
+أثبت انها bounded يعني بده أثبت المسافة بين أي
+
+180
+00:13:28,590 --> 00:13:36,560
+مقطين أصغر من number لجته الآن لاحظواإن المسافة
+
+181
+00:13:36,560 --> 00:13:42,960
+بين X و N و X أصغر من واحد لكل الانات اللي أكبر من
+
+182
+00:13:42,960 --> 00:13:46,580
+K ل XN زيادة واحد و XN زيادة اتنين و XN زيادة
+
+183
+00:13:46,580 --> 00:13:49,820
+تلاتة و XN زيادة أربعة كلهم ضمنتهم اللي أصغر من
+
+184
+00:13:49,820 --> 00:13:54,260
+واحد ده اللي قبل اللي قبل بتقول خلّي A تساوي ال
+
+185
+00:13:54,260 --> 00:13:58,180
+maximum بين المسافة X واحد و X و X اتنين و X لعند
+
+186
+00:13:58,180 --> 00:14:04,320
+X K minus واحد و مين و X إذن الآن خلصت من هذه و
+
+187
+00:14:04,320 --> 00:14:10,780
+هذههيها هخلص اللي بديها انا اضمنت لكم ان المسافة
+
+188
+00:14:10,780 --> 00:14:18,660
+DXN و X أصلا واحد لكل N أكبر أو يساوي K و دي أخدت
+
+189
+00:14:18,660 --> 00:14:23,120
+الـ A بالساوي ال maximum للمسافات X واحد مع ال X
+
+190
+00:14:23,120 --> 00:14:29,440
+اللي ضالن لعند ما أصل ل D X K minus واحد و X سميت
+
+191
+00:14:29,440 --> 00:14:32,400
+أكبر و روح فيه maximum لأن عددهم عشرة عشرين مية
+
+192
+00:14:32,400 --> 00:14:37,160
+finite إذا فينا ال maximum ماعشه اسمه M A إذا أكيد
+
+193
+00:14:37,160 --> 00:14:46,130
+أكيد أكيد صار عندي D X Mوأي x موجودة اللي هو عندى
+
+194
+00:14:46,130 --> 00:14:50,430
+في ال sequence اللي هي xm و ال x تبعتي هي اللي بقى
+
+195
+00:14:50,430 --> 00:14:57,890
+بحكي عنها أصغر من الواحد زائد a ليش؟ لإن الآن ال a
+
+196
+00:14:57,890 --> 00:15:02,930
+هي ال maximum لمسافاتي ده موجودة أو سفر صح ولا لأ؟
+
+197
+00:15:02,930 --> 00:15:08,190
+الآن ال .. ال .. ال x واحد لعند ال xk minus واحد
+
+198
+00:15:08,190 --> 00:15:12,290
+أكيد أصغر من ال a لحالهاإذا أكيد أصغر من مين؟ من
+
+199
+00:15:12,290 --> 00:15:15,330
+الواحد زائد إيه البجيات كلها أصغر من واحد لحاله
+
+200
+00:15:15,330 --> 00:15:18,250
+إذا أكيد أصغر من مين؟ واحد زائدة إذا هو ضرب على
+
+201
+00:15:18,250 --> 00:15:22,510
+صفرين وحجار وقال لك إذا دي Xn و X أصغر من واحد
+
+202
+00:15:22,510 --> 00:15:28,750
+زائد إيه hence for all n and m المسافة بين Xn وXm
+
+203
+00:15:28,750 --> 00:15:31,410
+أصغر أو ساوية تلقى inequality عشان أخلص على اللي
+
+204
+00:15:31,410 --> 00:15:35,240
+بدوياه وإيش بتثبت؟بدّون يثبت إنها bounded، إيش ال
+
+205
+00:15:35,240 --> 00:15:39,380
+bounded؟ إنه المسافات بين أي نقطتين كلهين يكون
+
+206
+00:15:39,380 --> 00:15:44,580
+أصغر من إشي، ماشي؟ لأن خدوا أي نقطتين XN و XM في
+
+207
+00:15:44,580 --> 00:15:47,400
+مين، أنا بقى برايح لمين، هاي ال sequence اللي عند
+
+208
+00:15:47,400 --> 00:15:52,220
+ال XMونقول عنها bounded إذا كان عناصرها X1 و X2
+
+209
+00:15:52,220 --> 00:15:56,680
+إلى ما لنهاية المسافات بين أي كنتين يكونون أصغر من
+
+210
+00:15:56,680 --> 00:16:00,480
+some number خدت الآن un-arbitrary و un-arbitrary
+
+211
+00:16:00,480 --> 00:16:04,360
+يعني دي X un-arbitrary و X un-arbitrary و حسبت
+
+212
+00:16:04,360 --> 00:16:07,580
+المسافة بينهم بال triangling quality أصغر أو سوى
+
+213
+00:16:07,580 --> 00:16:13,000
+دي X un و مين و X أنا هيأت حالي في اللي قبل زائد X
+
+214
+00:16:13,000 --> 00:16:17,440
+un و مين و X الأولى أصغر من واحد زائد ايه أثبتها
+
+215
+00:16:18,160 --> 00:16:21,580
+والتانية أصغر من واحد زاد إيه إذا التنتين أصغر من
+
+216
+00:16:21,580 --> 00:16:25,980
+اتنين زاد مين اتنين إيه إذا المسافة بين أي وقتين
+
+217
+00:16:25,980 --> 00:16:30,440
+الآن في داخل ال sequence اللي هي أصغر من اتنين زاد
+
+218
+00:16:30,440 --> 00:16:34,520
+اتنين إيه وهذا معناته أنه صارت عند ال sequence xn
+
+219
+00:16:34,520 --> 00:16:40,300
+is a bounded sequence طيب صلوا على النبي عليه
+
+220
+00:16:40,300 --> 00:16:42,420
+الصلاة والسلام الآن
+
+221
+00:16:45,850 --> 00:16:49,470
+والـ Limit X مالها واحدة بما أنك تضمن أنك تنتهي من
+
+222
+00:16:49,470 --> 00:16:54,070
+وصول الـ X مالها واحدة بنقول أسيوم ذات Xn بتروح لل
+
+223
+00:16:54,070 --> 00:16:57,590
+X و Xn بتروح لمين لزي ال two limits و في الآخر
+
+224
+00:16:57,590 --> 00:17:02,330
+هنطلع X بالساوة زي ال then المسافة بين X و Z أكيد
+
+225
+00:17:02,330 --> 00:17:07,070
+مالها أكبر أو ساوة سفربالنسبة لكم ان هذه 0 أصغر
+
+226
+00:17:07,070 --> 00:17:13,170
+سوى DX وXN زي DXN ومين وZ لكن هذه مش احنا بنقول XN
+
+227
+00:17:13,170 --> 00:17:17,210
+بتروح ل X إذا ال limit هي 0 حسب التعريف ومش بنقول
+
+228
+00:17:17,210 --> 00:17:20,730
+XN بتروح ل Z إذا ال limit هي 0 إذا هذول ال limit
+
+229
+00:17:20,730 --> 00:17:25,070
+هين سفر وهذه سفر إذا اللي في النص قطعنش هتكون سفر
+
+230
+00:17:25,070 --> 00:17:28,650
+ومعناته ال X أشبتها سوى Z so the limit is unique
+
+231
+00:17:28,650 --> 00:17:36,830
+ماشي الحل نيجي الآنلأ اللي هي بي الان ال بي بتقولك
+
+232
+00:17:36,830 --> 00:17:40,030
+إذا كانت x أن و y أن هذي converge ده ال x و هذي
+
+233
+00:17:40,030 --> 00:17:42,910
+converge ده ال y إذا المسافة بين ال converge ده
+
+234
+00:17:42,910 --> 00:17:48,490
+اللي هو المسافة بين اللي متين طيب برضه البرهان
+
+235
+00:17:48,490 --> 00:17:54,750
+هتجيب بمشي معنى زي الحلاوة و بكل سهولة إيش بقولنا
+
+236
+00:17:54,750 --> 00:18:01,770
+البرهان بقول التاليبقول نفرض أن Xn بتروح ل X و Yn
+
+237
+00:18:01,770 --> 00:18:05,170
+بتروح ل Y إيش معناة Xn بتروح ل X؟ يعني المسافة بين
+
+238
+00:18:05,170 --> 00:18:10,710
+Xn و Yn هذه المسافة بين Xn و X بيروح للصفر
+
+239
+00:18:10,710 --> 00:18:14,070
+والمسافة بين هذي و هذي بتروح لمين للصفر خلّيها نفل
+
+240
+00:18:14,070 --> 00:18:18,770
+جمال بعد شوية نستخدمهاالان تشوفوا الان xn و yn
+
+241
+00:18:18,770 --> 00:18:22,990
+المسافة بينهما أصغر أو سوى xn و x و x و mean و y و
+
+242
+00:18:22,990 --> 00:18:27,010
+y و yn استخدمت ال triangle inequality مرتين طبعا
+
+243
+00:18:27,010 --> 00:18:31,990
+في الي سبب انه عشان أثبتلكم ان xn و yn ناقص x و y
+
+244
+00:18:31,990 --> 00:18:35,550
+المسافة بينها absolute value أصغر أو سوى هذه
+
+245
+00:18:35,550 --> 00:18:38,330
+المسافة هذه هتروح لصفر و هذه كصفر معناته خلصت
+
+246
+00:18:38,330 --> 00:18:39,190
+دعونا نشوف كده
+
+247
+00:18:42,080 --> 00:18:45,180
+الان بال triangle inequality طلعت عندي هذه hence
+
+248
+00:18:45,180 --> 00:18:51,060
+جي بيها ديها بيصير عند المسافة هيها هيها هيها هيها
+
+249
+00:18:51,060 --> 00:18:53,740
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+250
+00:18:53,740 --> 00:18:53,760
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+251
+00:18:53,760 --> 00:18:53,960
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+252
+00:18:53,960 --> 00:18:56,440
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+253
+00:18:56,440 --> 00:18:58,920
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+254
+00:18:58,920 --> 00:18:58,960
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+255
+00:18:58,960 --> 00:19:00,400
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+256
+00:19:00,400 --> 00:19:00,480
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+257
+00:19:00,480 --> 00:19:07,970
+هيها هيها هيها هيبقدر اللي هو أخد المسافة أثبت أن
+
+258
+00:19:07,970 --> 00:19:13,590
+المسافة بين x و y ناقص xn و yn أصغر من المسافة بين
+
+259
+00:19:13,590 --> 00:19:20,150
+x و xn أو ناقص المسافة عشان أثبت لكم أنا اللي بدي
+
+260
+00:19:20,150 --> 00:19:24,290
+أثبته اللي هو absolute value ال absolute value
+
+261
+00:19:24,290 --> 00:19:32,170
+distance بين xnو Yn نقص المسافة بين X و Y أصغر أو
+
+262
+00:19:32,170 --> 00:19:35,550
+يساوي هذي طبعا أكبر و يساوي سفر غرضي أثبتها أصغر
+
+263
+00:19:35,550 --> 00:19:43,490
+أو ساوي المسافة بين Xn و X زائد المسافة بين Yn و
+
+264
+00:19:43,490 --> 00:19:49,690
+100 و Y آسف بدون أفسنان أنت فاهم معايا؟ هذي هتروح
+
+265
+00:19:49,690 --> 00:19:52,150
+للسفر و هذي هتروح للسفر إذا هذي هيروح للسفر يكون
+
+266
+00:19:52,150 --> 00:19:57,480
+خلصتاللي أول واحدة عملتها اللي هي المسافة بين XN و
+
+267
+00:19:57,480 --> 00:20:01,880
+YN ناقص هذا أصغر أو ساوي هذه يعني بدي أثبتلكم أن
+
+268
+00:20:01,880 --> 00:20:06,940
+هذه أصغر أو ساوي هذه و بعدين اللي هو مفكوك هيش هذه
+
+269
+00:20:06,940 --> 00:20:10,440
+اللي هو على الجهة الثانية بالسالب بظبط يعني بدي
+
+270
+00:20:10,440 --> 00:20:16,520
+أعكسها بنعكسها بنفس الطريقة بتنعمل سهلة يعني بس ال
+
+271
+00:20:16,520 --> 00:20:19,720
+triangle inequality بنستخدمها بالشكل الثاني اللي
+
+272
+00:20:19,720 --> 00:20:25,590
+هو similarly DXY ناقص DXN YNاللي هي أصغر أو يساوي
+
+273
+00:20:25,590 --> 00:20:34,510
+دي إكس و إكس أن زائد دي وي أو وي أن إذا بيصير
+
+274
+00:20:34,510 --> 00:20:37,530
+بتدربيها في ناقص عكستها أنا عشان أدرب في ناقص لما
+
+275
+00:20:37,530 --> 00:20:41,070
+أدرب في ناقص بيصير ناقص هذا أصغر أو يساوي إكس أن و
+
+276
+00:20:41,070 --> 00:20:45,090
+وي أن و إكس و .. و مين و وي أنتوا فاهمين إيش
+
+277
+00:20:45,090 --> 00:20:48,450
+بيعمل؟ أنا بدي أجيب هذه بدي مبدأ هذه بدي أبدأ بإكس
+
+278
+00:20:48,450 --> 00:20:55,580
+و وي فاهمين؟أعملها الان بدل ان ابدأ بهذه ببدأ بال
+
+279
+00:20:55,580 --> 00:20:58,020
+X وY بحصل على نفسي الاشي هذه بانجله على الجهة
+
+280
+00:20:58,020 --> 00:21:01,000
+التانية بضربه في ناقص بالSeer المعقوسة هذه بالظبط
+
+281
+00:21:01,000 --> 00:21:04,480
+الSeer عندي اللي هو عبارة عن ناقص هذه أصغر وشاوي
+
+282
+00:21:04,480 --> 00:21:07,900
+هذه وفي الأصل أصغر وشاوي اللي هي الأصلية هذه إذا
+
+283
+00:21:07,900 --> 00:21:11,220
+صار ال absolute value أكبر وشاوي سفر وأصغر وشاوي
+
+284
+00:21:11,220 --> 00:21:15,960
+هذه الان هذه راحت للسفر وهذه راحت للسفر إذا هذه
+
+285
+00:21:15,960 --> 00:21:20,000
+راحت للسفر إذا DX عن وY عن بتروح ل DX وY ماشي
+
+286
+00:21:26,520 --> 00:21:30,900
+أذا نعرف الـ Cauchy Sequence أكيد اتوقعتوها بس
+
+287
+00:21:30,900 --> 00:21:33,680
+شيلوا absolute ده اللي حطوه بدلها الـD
+
+288
+00:21:37,650 --> 00:21:40,810
+بنقول إن Xn كوشي سيكوينس إذا اتحقق اللي التالي for
+
+289
+00:21:40,810 --> 00:21:43,530
+every y أكبر من سفر there exists k element in n
+
+290
+00:21:43,530 --> 00:21:48,010
+such that for every n و m أكبر أو يساوي k عندي
+
+291
+00:21:48,010 --> 00:21:53,290
+بيكون ال absolute value لل Xn نقص ال Xn أصغر من
+
+292
+00:21:53,290 --> 00:21:58,610
+مين؟ من أبسلون، مظبوط ولا لا؟ هذا اللي كنا نحكيه
+
+293
+00:21:58,610 --> 00:22:05,240
+زمان في الريال، بس خيانة، حطوا Dو بس دي xn و كده
+
+294
+00:22:05,240 --> 00:22:10,940
+بس هي كل الجثة اذا عشان ما نغلبكم مش بنقول a
+
+295
+00:22:10,940 --> 00:22:14,160
+sequence xn in a metric space xz is said to be
+
+296
+00:22:14,160 --> 00:22:17,260
+Cauchy if for every y أكبر من 0 there exists k
+
+297
+00:22:17,260 --> 00:22:21,080
+such that is مسافة بين xn و xm أصغر من y لكل n و m
+
+298
+00:22:21,080 --> 00:22:25,000
+أكبر من k the space x is called complete ال space
+
+299
+00:22:25,000 --> 00:22:29,380
+بنقول عنه complete space إذا كان every Cauchy
+
+300
+00:22:29,380 --> 00:22:35,980
+sequence convertsإذا بتذكروا في تحليل واحد لما
+
+301
+00:22:35,980 --> 00:22:38,520
+حكينا عن العلاقة بين الـ Cauchy Sequences والـ
+
+302
+00:22:38,520 --> 00:22:42,880
+Convergent Sequences قلنا أيش؟ قلنا Any Convergent
+
+303
+00:22:42,880 --> 00:22:46,140
+Sequences Cauchy وكان برهانة سهلهتلاقي البرهان
+
+304
+00:22:46,140 --> 00:22:51,600
+المشابه الآن العكس قلنا برضه بتحقق في R يعني اللي
+
+305
+00:22:51,600 --> 00:22:55,900
+هي الـ Cauchy convergent بس كانت اتغلبنا شوية في
+
+306
+00:22:55,900 --> 00:23:02,160
+البرهان خلينا نقول أصعب سنة بسيطة لكن كان برضه مش
+
+307
+00:23:02,160 --> 00:23:05,840
+صعب يعني وكأنه ليش أنا بقوليك وكأنه الآن على
+
+308
+00:23:05,840 --> 00:23:09,940
+تعريفي احنا بنقول ان ال space complete اذا كانت
+
+309
+00:23:09,940 --> 00:23:13,900
+every Cauchy sequence converge طب في R كانت هيك R
+
+310
+00:23:13,900 --> 00:23:17,660
+completeومش هيك وكمان في الـ C complete و الـ C
+
+311
+00:23:17,660 --> 00:23:20,380
+أشماله complete under the metric اللي احنا بتحكي
+
+312
+00:23:20,380 --> 00:23:22,960
+عنه ال usual metric اللي هو absolute value X minus
+
+313
+00:23:22,960 --> 00:23:28,020
+Y إذا صار في عندي مثلين اللي هو ال R و ال C على
+
+314
+00:23:28,020 --> 00:23:32,260
+complete metric spaces و هنشوف الباقي قدام ان شاء
+
+315
+00:23:32,260 --> 00:23:32,400
+الله
+
+316
+00:23:35,980 --> 00:23:38,560
+النقطة الأولى اللي قلتها هي الـ The real line and
+
+317
+00:23:38,560 --> 00:23:41,100
+the complex plane are complete metric spaces
+
+318
+00:23:52,240 --> 00:24:01,220
+ليش؟ لإن واحنا بنعرف اللي عندي لأي a في الـR بقدر
+
+319
+00:24:01,220 --> 00:24:07,080
+ألاقي sequence xn in R such that xn converts to
+
+320
+00:24:07,080 --> 00:24:10,420
+mean لليه، حتى بقدر ألاقي sequence of rational
+
+321
+00:24:10,420 --> 00:24:13,540
+numbers، ده حالي بس و بقدر ألاقي sequence of
+
+322
+00:24:13,540 --> 00:24:15,880
+irrational numbers، ده حالي، خلاص الكتابة لكل
+
+323
+00:24:15,880 --> 00:24:21,140
+واحدة فيهمإذا أنا في الواقع عندى لو شيلت من الارض
+
+324
+00:24:21,140 --> 00:24:26,440
+بضطر complete لإن لجيت هى ال sequence اللى هى xn
+
+325
+00:24:26,440 --> 00:24:33,460
+بتروح لليه هتكون false في الواقع فبتصير xn كوشي in
+
+326
+00:24:33,460 --> 00:24:41,810
+R ناقص مين ناقص ال a but its limitوما بدها تروح
+
+327
+00:24:41,810 --> 00:24:47,290
+للـ A مش موجودة في الـ R minus الـ A إذا هذا is
+
+328
+00:24:47,290 --> 00:24:52,130
+not a complete metric space و الـ Q كله under مين؟
+
+329
+00:24:52,130 --> 00:24:55,270
+under the usual metric اللي هو absolute value للـ
+
+330
+00:24:55,270 --> 00:25:03,730
+X minus Y الـ Q كمان مش complete لأنه ليش؟ لأنه لو
+
+331
+00:25:03,730 --> 00:25:07,710
+أجيت بقدر
+
+332
+00:25:07,710 --> 00:25:11,470
+ألاقي الـ sequenceاللي هو of rational numbers
+
+333
+00:25:11,470 --> 00:25:16,990
+converges لجدر التنين الجدر التنين مش موجود في الـ
+
+334
+00:25:16,990 --> 00:25:21,090
+Q إذا ما زال مش موجود في الـ Q، إذا صار عندك الـ
+
+335
+00:25:21,090 --> 00:25:24,590
+Cauchy sequence اللي هاد اللي converges لجدر
+
+336
+00:25:24,590 --> 00:25:30,350
+التنين في الـ R لكن اللي أمالها مش موجودة إذا إذا
+
+337
+00:25:30,350 --> 00:25:34,770
+إحنا لما نحكي عن الـ Cauchy sequenceهي في الواقع
+
+338
+00:25:34,770 --> 00:25:39,770
+سلوك سلوك هو تقريبا بتقدر تقولي هو نفس سلوك ال
+
+339
+00:25:39,770 --> 00:25:45,550
+convergence لكن بختلف في الآخر ان ال convergence
+
+340
+00:25:45,550 --> 00:25:51,540
+بيروح ل limit ال limit هذه إذا في ال spaceبصير إيه
+
+341
+00:25:51,540 --> 00:25:55,980
+أشمالها الـ sequence converges إذا مش في ال space
+
+342
+00:25:55,980 --> 00:26:01,420
+بظل كوشي لكن مش .. و هنا بحكم .. نحكم على ال space
+
+343
+00:26:01,420 --> 00:26:05,380
+انه complete أو لأ من خلال هذه الخاصية إذا ال ..
+
+344
+00:26:05,380 --> 00:26:09,920
+ال كوشي sequences هي في الواقع بتريحني أحيانا إنه
+
+345
+00:26:09,920 --> 00:26:13,860
+أنا أصلا مش عارف ال limitلكن أنا بعرف سلوك اللي هي
+
+346
+00:26:13,860 --> 00:26:17,980
+الـ sequence اللي لأ هي سلوك هي يا عم هذه سلوك
+
+347
+00:26:17,980 --> 00:26:21,340
+رايحة رايحة لإشي بتتكوم حوالين إشي ماشي الحال
+
+348
+00:26:21,340 --> 00:26:26,580
+فالان روحها حوالين نقطة معينة يمكن أني مايعرفوش
+
+349
+00:26:26,580 --> 00:26:30,830
+أنالكن ده عارف إن هما جعدات متكوّن من جانب بعض،
+
+350
+00:26:30,830 --> 00:26:35,490
+إذا سلوكهم إنه جعدات وكأنه كلهم بروح حوالهم منطقة
+
+351
+00:26:35,490 --> 00:26:38,730
+معينة و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+352
+00:26:38,730 --> 00:26:39,090
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+353
+00:26:39,090 --> 00:26:39,810
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+354
+00:26:39,810 --> 00:26:39,830
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+355
+00:26:39,830 --> 00:26:40,030
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+356
+00:26:40,030 --> 00:26:43,870
+و .. و .. و .. و
+
+357
+00:26:43,870 --> 00:26:55,480
+.. و ..فالان الـ Cauchy مهم عشان اللي هو يعني
+
+358
+00:26:55,480 --> 00:27:01,440
+أحيانا ماكنتش أعرف إيش ال limit فبتعامل مع اللي هو
+
+359
+00:27:01,440 --> 00:27:05,560
+العناصر بدل ما أتعامل مع ال limit و لكن في حال
+
+360
+00:27:05,560 --> 00:27:07,700
+وجود ال limit في ال space و كده بيصير ال space
+
+361
+00:27:07,700 --> 00:27:13,180
+أشماله is complete طيب theorem every convergent
+
+362
+00:27:13,180 --> 00:27:15,500
+sequence in a metric space is a Cauchy sequence
+
+363
+00:27:15,500 --> 00:27:21,960
+والبرنامج مشابهتها بعد تبع التحليلاللي بيقولوا أنه
+
+364
+00:27:21,960 --> 00:27:27,390
+لو فرضنا XN أي خلق تنسيق Xبالذات بتنهجوشي مدام xn
+
+365
+00:27:27,390 --> 00:27:30,390
+بتروح لل x إذا لكل y أكبر من 0 there exists k such
+
+366
+00:27:30,390 --> 00:27:34,190
+that اللي هو x المسافة بين xn و x أصغر من y على 2
+
+367
+00:27:34,190 --> 00:27:37,270
+for all n أكبر من k أصغر من أي أبسل في الدنيا من
+
+368
+00:27:37,270 --> 00:27:41,990
+جملة y على 2 هو دي للحسبة ومشروعة لإن هو أصلا
+
+369
+00:27:41,990 --> 00:27:45,190
+المسافة بين n وn تبقى لدرجة غيرها زي ما بده الآن
+
+370
+00:27:45,190 --> 00:27:51,270
+خدوا لكل m وm أكبر من k خدوا المسافة بين xn وxn
+
+371
+00:27:51,820 --> 00:27:56,080
+هتكون أصغر و نفسه و المسافة بين Xn و X زي المسافة
+
+372
+00:27:56,080 --> 00:28:01,700
+بين X و Xm وهذه من اللي فوق هنا أصغر و نفسه و نوع
+
+373
+00:28:01,700 --> 00:28:03,920
+اتنين زي اتنين و نفسه نوع اتنين و نفسه نوع اتنين و
+
+374
+00:28:03,920 --> 00:28:05,720
+نفسه نوع اتنين و نفسه نوع اتنين و نفسه نوع اتنين و
+
+375
+00:28:05,720 --> 00:28:07,900
+نفسه نوع اتنين و نفسه نوع اتنين و نفسه نوع اتنين و
+
+376
+00:28:07,900 --> 00:28:07,940
+نفسه نوع اتنين و نفسه نوع اتنين و نفسه نوع اتنين و
+
+377
+00:28:07,940 --> 00:28:10,440
+نفسه نوع اتنين و نفسه نوع اتنين و نفسه نوع اتنين و
+
+378
+00:28:10,440 --> 00:28:18,900
+نفسه نوع اتنين و نفسه نوع اتنين و نفسالان ها
+
+379
+00:28:18,900 --> 00:28:26,320
+theorem بيقول لـ let M بيقى metric space X وD then
+
+380
+00:28:26,320 --> 00:28:31,460
+الـ M بدي يبدأ يحول الحديث احنا لما .. في المحاضرة
+
+381
+00:28:31,460 --> 00:28:34,760
+اللي فاتت كنا نحكي لما كنا نحكي عن ال convergence
+
+382
+00:28:34,760 --> 00:28:41,890
+كنا نحول الحكي برضه ل sequence specificفي الـR أو
+
+383
+00:28:41,890 --> 00:28:46,130
+في الـC فكنا نشرود ناخد الـSequence اللي في الـP
+
+384
+00:28:46,130 --> 00:28:49,370
+كلها أنجول بتروح للـX ونربطها بالـConvergence لأن
+
+385
+00:28:49,370 --> 00:28:52,850
+لأ الآن بدر بطوركم بالـConvergence لأنه أعرف شو
+
+386
+00:28:52,850 --> 00:28:55,030
+معناه الـConvergence قبل ماكنتش عارف معناه
+
+387
+00:28:55,030 --> 00:28:58,740
+الـConvergence في الـMetric Spaceكنت أحول الدنيا
+
+388
+00:28:58,740 --> 00:29:01,000
+أروح و أديها لي ال convergence اللي في R تبع
+
+389
+00:29:01,000 --> 00:29:03,740
+الزمان لكن مش دايما هذا بظبط أو مش دايما أخلهم
+
+390
+00:29:03,740 --> 00:29:10,260
+أقول بسعثني الآن بدي أحول كل الآن الحديث من ال
+
+391
+00:29:10,260 --> 00:29:15,420
+unconvergence إلى sequences يعني المفهوم القاسي في
+
+392
+00:29:15,420 --> 00:29:20,240
+ال closure من ال closure اللي هو بواسطة ال balls
+
+393
+00:29:20,240 --> 00:29:26,470
+إلى حكي بواسطة ال sequences وده أسهلنابدأ قول let
+
+394
+00:29:26,470 --> 00:29:32,310
+M be anonymous if and only
+
+395
+00:29:32,310 --> 00:29:35,230
+if there exists a sequence xn in M such that xn
+
+396
+00:29:35,230 --> 00:29:39,990
+بتروح لمين لل X إذن الآن بنقول إن ال X في ال M
+
+397
+00:29:39,990 --> 00:29:44,650
+closure معناته أنه بقدر ألاقي sequence في ال M
+
+398
+00:29:44,650 --> 00:29:50,160
+وعامالها كلها ال sequence بتروح لمين لل Xأه إذا ال
+
+399
+00:29:50,160 --> 00:29:55,200
+M هذه متكرب سا .. ال .. ال XM متكرب سا حوالين ال X
+
+400
+00:29:55,200 --> 00:29:59,940
+و XM ناقف ال M إذا أكيد هي limit point جوا هذا
+
+401
+00:29:59,940 --> 00:30:05,110
+رفلي الكلام تشوف الكلام هذا بالتفصيل الأنالآن بدنا
+
+402
+00:30:05,110 --> 00:30:07,650
+نعرف اللي هو الـ M closed برضه بمانعش نقعد نقول
+
+403
+00:30:07,650 --> 00:30:10,550
+والله الـ compliment لها اه بانه نقعد نفحص انه اه
+
+404
+00:30:10,550 --> 00:30:13,270
+بان معناته انه خدوا اي نقطة و بتلاقوا اه اه نبرهو
+
+405
+00:30:13,270 --> 00:30:15,350
+جواتها يكون كله في جوات اللي هي الـ M compliment
+
+406
+00:30:15,350 --> 00:30:20,370
+لأ أسهلنا أسهلنا نحكي عن Sequences M is closed if
+
+407
+00:30:20,370 --> 00:30:23,170
+and only if the situation X and element in M و X
+
+408
+00:30:23,170 --> 00:30:28,050
+and بتروح لل X and why is that X element in M يعني
+
+409
+00:30:28,050 --> 00:30:32,800
+بقول ليهM Closed إذا تحقق الشرط التاني إنه لو أخدت
+
+410
+00:30:32,800 --> 00:30:37,060
+أي Sequence XN في الـ M وكانت هذه Sequence
+
+411
+00:30:37,060 --> 00:30:42,000
+Converged لازم تقعد وين؟ في داخل الـ M ماشي الحال
+
+412
+00:30:42,000 --> 00:30:45,180
+إذا تمتعت بهذا الخاصية على طول M is Closed يعني
+
+413
+00:30:45,180 --> 00:30:48,760
+عشان نحكوا إن عمل M Closed أه ولا لأ باجي باخد أي
+
+414
+00:30:48,760 --> 00:30:55,360
+Sequence XN في الـ M و تكون XN بتروح لل X هذا كله
+
+415
+00:30:55,360 --> 00:31:00,140
+على بعض يعطينا إن X في الـ Mهذا معناته إنه صارت
+
+416
+00:31:00,140 --> 00:31:05,340
+الـ M is closed ولو كانت M is closed برضه لو جي
+
+417
+00:31:05,340 --> 00:31:08,320
+تأخدت أي sequence XN في الـ M وكانت XN بتروح لل X
+
+418
+00:31:08,320 --> 00:31:12,480
+لازم تعطي الـ X mean في داخلها واضح؟ هذا ال test
+
+419
+00:31:12,480 --> 00:31:19,120
+لل convergence للـ M is closed ولا لأ طيب نيجي إلى
+
+420
+00:31:19,120 --> 00:31:24,740
+اللي هو الأولى let X element mean أن M closure في
+
+421
+00:31:24,740 --> 00:31:28,970
+عندي حالتينإذا كانت X في الـ M، ادّيني سهلة، مين
+
+422
+00:31:28,970 --> 00:31:32,430
+باخدها الـ sequence؟ X، X، X، X، X، X، X، X، X، X،
+
+423
+00:31:32,430 --> 00:31:34,550
+X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X،
+
+424
+00:31:34,550 --> 00:31:37,850
+X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X،
+
+425
+00:31:37,850 --> 00:31:37,990
+X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X،
+
+426
+00:31:37,990 --> 00:31:39,050
+X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X،
+
+427
+00:31:39,050 --> 00:31:39,870
+X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X،
+
+428
+00:31:39,870 --> 00:31:43,710
+X،
+
+429
+00:31:43,710 --> 00:31:47,350
+X، Xمش في الـ M إذا نوعها بده تكون في الـ
+
+430
+00:31:47,350 --> 00:31:53,090
+accumulation points if X is not element of M it is
+
+431
+00:31:53,090 --> 00:31:56,210
+accumulation point of M ايش معناه accumulation
+
+432
+00:31:56,210 --> 00:32:02,710
+point يعني لكل نيبرود في الدنيا لكل نصف قطر بتاخد
+
+433
+00:32:02,710 --> 00:32:07,120
+أنصاف الأقطار اسمه 1 على Nلأي نسخة و تربسة أننا
+
+434
+00:32:07,120 --> 00:32:09,680
+ناخد أنصاف الأكترسمين واحدة لأن ده سواء أخد نسخة و
+
+435
+00:32:09,680 --> 00:32:14,280
+ترسم واحد و نص و تلت و ربع و خمس و ستس و في كل
+
+436
+00:32:14,280 --> 00:32:19,600
+حاجة حلاجة اللي هو element فيه موجود فآنتقاطعه لا
+
+437
+00:32:19,600 --> 00:32:24,360
+يساوي فاي ما أنا ايا الان hence for each n element
+
+438
+00:32:24,360 --> 00:32:29,420
+in n بيكس و نصف قطر واحد الان تقاطع مع الان اشماله
+
+439
+00:32:29,420 --> 00:32:33,540
+لا يساوي فاي ماشي الحاجة واحد يقول ليه ما هو شيء
+
+440
+00:32:33,540 --> 00:32:36,660
+لل X انت طب هي اصلا ال X مش في ال M مش في ال M
+
+441
+00:32:36,660 --> 00:32:41,040
+اصلا طبيعي مش هي اللي هتطلع التقاطع فاهمين اه طيب
+
+442
+00:32:41,040 --> 00:32:45,020
+so there exist x n element in b x واحد و الان
+
+443
+00:32:45,020 --> 00:32:51,920
+تقاطع مين ال M اذاPx1 لجت فيها x1 Px نص لجت فيها
+
+444
+00:32:51,920 --> 00:32:57,520
+x2 Px تلت لجت فيها x3 Px ربع لجت فيها x4 و هكذا
+
+445
+00:32:57,520 --> 00:33:01,900
+لأن هذا الكلام صحيح لمين لكل n بيجيلها xn المقابلة
+
+446
+00:33:01,900 --> 00:33:05,580
+اللي موجودة في التقاطع إذا صارت المسافة بين xn و x
+
+447
+00:33:05,580 --> 00:33:10,160
+أصغر من مين من 1 ل n في كل حالة لأن as n goes to
+
+448
+00:33:10,160 --> 00:33:14,040
+infinity و 1 hundred تروحللصفر وهذه بيصير مدام
+
+449
+00:33:14,040 --> 00:33:15,360
+هترا هترا هترا هترا هترا هترا هترا هترا هترا هترا
+
+450
+00:33:15,360 --> 00:33:15,480
+هترا هترا هترا هترا هترا هترا هترا هترا هترا هترا
+
+451
+00:33:15,480 --> 00:33:16,660
+هترا هترا هترا هترا هترا هترا هترا هترا هترا هترا
+
+452
+00:33:16,660 --> 00:33:17,220
+هترا هترا هترا هترا هترا هترا هترا هترا هترا هترا
+
+453
+00:33:17,220 --> 00:33:23,980
+هترا هترا هترا هترا هترا هترا هترا هترا هترا هترا
+
+454
+00:33:23,980 --> 00:33:25,400
+هترا هترا هترا هترا هترا هترا هترا هترا هترا هترا
+
+455
+00:33:25,400 --> 00:33:29,980
+هترا هترا هترا هترا هترا هترا هترا هترا هترا هترا
+
+456
+00:33:31,090 --> 00:33:34,450
+واضح هذا الان الاتجاه الأول لما ال X في ال M
+
+457
+00:33:34,450 --> 00:33:38,990
+closure بيعطيني ل gate sequence في ال M حيث ان XN
+
+458
+00:33:38,990 --> 00:33:44,930
+بتروح ل X نيجي الآن conversely suppose that ان
+
+459
+00:33:44,930 --> 00:33:50,670
+الخاصية هذه تتحقق بدنا نثبت ان لو اتحققت هذه هتكون
+
+460
+00:33:50,670 --> 00:33:59,760
+ال X موجودة في ال M closure طيب يا جماعةالان بنقول
+
+461
+00:33:59,760 --> 00:34:06,220
+conversely suppose that xn وين موجودة في ال M و ال
+
+462
+00:34:06,220 --> 00:34:10,460
+xn converge لمين؟ لل x بيثبتلكم ال x وين موجودة في
+
+463
+00:34:10,460 --> 00:34:15,120
+ال M closure فبنخلصنا لأن if x element in M إذا x
+
+464
+00:34:15,120 --> 00:34:20,140
+element in M closure خلصنا ماشي الحال أنا غلط
+
+465
+00:34:20,140 --> 00:34:23,480
+أثبتها في ال M closure لو كانت x مش اللي أه في ال
+
+466
+00:34:23,480 --> 00:34:25,600
+M بيثبتلكم إن ال X هتكون إيه شمال a little bit
+
+467
+00:34:25,600 --> 00:34:30,490
+word ماشيلو أثرت أنها limit point معناه أنها
+
+468
+00:34:30,490 --> 00:34:35,210
+موجودة في الـ M closure بكون خلصت الآن مدام X مش
+
+469
+00:34:35,210 --> 00:34:40,170
+في الـ M إذا لكل Y و أنا عند XN بتروح لمين؟ XN
+
+470
+00:34:40,170 --> 00:34:44,370
+بتروح لل X إذا لكل Y أكبر من صفر بقدر ألاقي K بحيث
+
+471
+00:34:44,370 --> 00:34:47,850
+أن المسافة بين هذه و هذه أشمالها أزر من الـ Y لكل
+
+472
+00:34:47,850 --> 00:34:53,410
+M أكبر من K إذا الآن من هذهبكون حصلت اللي بديها
+
+473
+00:34:53,410 --> 00:34:56,570
+ايش اللي حصلت اللي بديها بقولكم hence for every y
+
+474
+00:34:56,570 --> 00:35:01,030
+أكبر من 0 بقدر ألاقي k بحيث أن ال ball اللي فيها x
+
+475
+00:35:01,030 --> 00:35:06,230
+و y نصف قطرها y المسافة بين ال xn اللي هي ال xn
+
+476
+00:35:06,230 --> 00:35:10,790
+نات هايها بين ال xn و ال x ما انها أصغر من y كل ال
+
+477
+00:35:10,790 --> 00:35:17,170
+n أكبر من k يعني هذه فيها مين فيها xk زائد واحد و
+
+478
+00:35:17,170 --> 00:35:21,840
+xk زائد اتنينو XK زيادة تلاتة و XK زيادة أربعة كل
+
+479
+00:35:21,840 --> 00:35:25,260
+هين موجودة هنا لو شيلت منهم X تقاطع لهم أكيد A
+
+480
+00:35:25,260 --> 00:35:28,960
+شمالهم لا يساوي فيه لأنهم كل ال XK و XK زيادة واحد
+
+481
+00:35:28,960 --> 00:35:31,880
+و XK زيادة اتنين كل هين موجودة في الأصل في الام
+
+482
+00:35:31,880 --> 00:35:34,080
+مازالت موجودة هنا موجودة في الأم ماذا ما تقاطعوا
+
+483
+00:35:34,080 --> 00:35:38,040
+احد اشماله لا يساوي فيه إذا ال X وين موجودة في
+
+484
+00:35:38,040 --> 00:35:45,240
+الام مكلوجر إذا بكون خلصنا الجزء الأول نتيجي الآن
+
+485
+00:35:45,240 --> 00:35:46,500
+من B
+
+486
+00:35:48,780 --> 00:35:55,360
+الان بيه من اللي فوق عندي M is closed if and only
+
+487
+00:35:55,360 --> 00:36:00,320
+if ال M مش ميزه تساوي ال M closure مظبوط M is
+
+488
+00:36:00,320 --> 00:36:04,200
+closed اذا كانت اذا و فقط اذا M بيساوي M closure و
+
+489
+00:36:04,200 --> 00:36:08,440
+M بتساوي M closure و هذه سهل اتباعتها لو تبتوها من
+
+490
+00:36:08,440 --> 00:36:14,010
+الاصل كمان سهل اتباعتهاالآن M بيتساوى M closure if
+
+491
+00:36:14,010 --> 00:36:19,190
+and only if the situation Xn بتروح لل X that means
+
+492
+00:36:19,190 --> 00:36:24,730
+X element in M هذا منذ قبل بشوية أنه لما تكون Xn
+
+493
+00:36:24,730 --> 00:36:28,590
+بتروح لل X و Xn في ال M تعطين X element in M هذا
+
+494
+00:36:28,590 --> 00:36:33,510
+if and only if إيه شمالها؟ اللي هو ال X موجودة في
+
+495
+00:36:33,510 --> 00:36:37,210
+ال M closure إذن الآن عندي M is closed if and only
+
+496
+00:36:37,210 --> 00:36:45,720
+ifاللي هو مين اللي قبل بشوية مش اللي قبل بشوية
+
+497
+00:36:45,720 --> 00:36:46,660
+احنا اثبتناها
+
+498
+00:36:49,310 --> 00:36:52,090
+اللي هو X المتقن عام الـ closure if and only if
+
+499
+00:36:52,090 --> 00:36:56,450
+الـ sequence X المتروح للـ X أه طيب الآن if and
+
+500
+00:36:56,450 --> 00:36:58,250
+only if أم is closed if and only if أم سواء الـ
+
+501
+00:36:58,250 --> 00:37:01,630
+closure معناته ال .. ال .. ال .. كل اللي في الأم
+
+502
+00:37:01,630 --> 00:37:04,950
+إيه شمع الوجودات في الأم ال closure معناته اللي هو
+
+503
+00:37:04,950 --> 00:37:09,510
+اللي هو هذا ال .. هذا الكلام بيعطينا أن هذا يتحقق
+
+504
+00:37:09,510 --> 00:37:13,150
+وزمان هذا يتحقق إذا هذا يؤدي لهذا ويكون عندنا
+
+505
+00:37:13,150 --> 00:37:16,650
+خلصنا اللي هي بيه أي سؤال طيب اللي بعدها
+
+506
+00:37:21,190 --> 00:37:30,350
+theorem مش مطولى ان شاء الله theorem a subspace
+
+507
+00:37:30,350 --> 00:37:33,770
+M of a complete metric space X is itself complete
+
+508
+00:37:33,770 --> 00:37:39,030
+if and only if the set M is closed طبعا احنا فيه
+
+509
+00:37:39,030 --> 00:37:44,030
+تفاصيل قدام ان
+
+510
+00:37:44,030 --> 00:37:46,830
+لو كانت ال space
+
+511
+00:37:49,250 --> 00:37:53,950
+م closed مش شرط يكون complete لو كان ال space
+
+512
+00:37:53,950 --> 00:38:01,510
+closed مش شرط يكون complete لكن
+
+513
+00:38:01,510 --> 00:38:11,670
+لو كان احنا بنحكي عن subspace M of a complete
+
+514
+00:38:11,670 --> 00:38:18,890
+metric space Xis itself complete if and only if M
+
+515
+00:38:18,890 --> 00:38:24,310
+أشماله is closed in X يعني الآن بالظبط الحالة كيف
+
+516
+00:38:24,310 --> 00:38:33,430
+أنه أنا عايش عايش في إيش في complete metric space
+
+517
+00:38:33,430 --> 00:38:39,570
+بصير عندي ال subspace M عشان أحكم عليه complete
+
+518
+00:38:39,570 --> 00:38:44,180
+ولا لأ بس بال closedإذا كان مقفل فهو مقفل وإذا كان
+
+519
+00:38:44,180 --> 00:38:54,020
+مقفل فهو مقفل إذا كان مقفل فهو
+
+520
+00:38:54,020 --> 00:38:54,420
+مقفل فهو مقفل إذا كان مقفل فهو مقفل إذا كان مقفل
+
+521
+00:38:54,420 --> 00:38:56,400
+فهو مقفل إذا كان مقفل فهو مقفل إذا كان مقفل فهو
+
+522
+00:38:56,400 --> 00:38:57,940
+مقفل إذا كان مقفل فهو مقفل إذا كان مقفل فهو مقفل
+
+523
+00:38:57,940 --> 00:39:00,200
+إذا كان مقفل فهو مقفل إذا كان مقفل فهو مقفل إذا
+
+524
+00:39:00,200 --> 00:39:04,500
+كان مقفل فهو مقفل إذا كان مقفل فهو مقفل إذا كان
+
+525
+00:39:04,500 --> 00:39:08,640
+مقفل فهو مقفل إذا كان مقفل فهو مقفل إذا كان مقف
+
+526
+00:39:10,310 --> 00:39:15,010
+نجلة اللي هو أو فيها مثلها طبعا أو حتى جابولها في
+
+527
+00:39:15,010 --> 00:39:19,290
+الخلال اللي هي الأسئلة اللي عندكم ماشي نجاوبها كل
+
+528
+00:39:19,290 --> 00:39:24,710
+شي suppose that M is إيه الشمالها complete and X
+
+529
+00:39:24,710 --> 00:39:33,260
+element in M closure ماشي then by theorem 1 4 7A,
+
+530
+00:39:33,260 --> 00:39:37,880
+there is a sequence xn in M such that xn بتروح للX
+
+531
+00:39:37,880 --> 00:39:40,940
+خلاص أنا بناعرف الترجم سيلنا لما X تكون في الـ M
+
+532
+00:39:40,940 --> 00:39:45,680
+closure معناته في sequence xn in M و الـ xn بتروح
+
+533
+00:39:45,680 --> 00:39:49,400
+لمين خلاص هذا بيصير سلوكة أننا بناسيه الترجم فيه
+
+534
+00:39:49,400 --> 00:39:54,700
+بسهل علينا الأمور كتير إذا الاجانب
+
+535
+00:39:54,700 --> 00:39:58,490
+sequence xn بتروح لمين لل Xما دام Xn convergence
+
+536
+00:39:58,490 --> 00:40:02,310
+لسة عامة قبل شوية قلنا hence Xn إيش ما لها is كوشي
+
+537
+00:40:02,310 --> 00:40:07,890
+لكن M is complete لكن M is complete و Xn كوشي في
+
+538
+00:40:07,890 --> 00:40:11,930
+ال M إذا أكيد أكيد limit هو M هيكون في ال M لأنها
+
+539
+00:40:11,930 --> 00:40:16,570
+complete إذا X موجودة في ال M إذا بدأت الآن عندي X
+
+540
+00:40:16,570 --> 00:40:19,870
+في ال M closure و لجأت هوي موجودة في ال M ماعناته
+
+541
+00:40:19,870 --> 00:40:23,830
+ال M إيش و ده تساوي M closure لأن M دايما subset
+
+542
+00:40:23,830 --> 00:40:28,500
+من M closure أثبتلكم أن M closure subset من Mماشي،
+
+543
+00:40:28,500 --> 00:40:30,480
+إذا صحيح M بيسوي M كله وجهة محددة معينة و M
+
+544
+00:40:30,480 --> 00:40:37,220
+أشمالها is a closed set، conversely بدي أفترض M
+
+545
+00:40:37,220 --> 00:40:43,780
+بيه a closed set و أفترض إن Xn بيه any Cauchy
+
+546
+00:40:43,780 --> 00:40:49,780
+sequence in M بدي أثبت لكم M is complete يعني الـ
+
+547
+00:40:49,780 --> 00:40:51,420
+Cauchy sequence اللي بدي أثبت هنا أشمالها
+
+548
+00:40:51,420 --> 00:40:58,950
+converges طيبمدام عندي xn كوشي in .. in .. in ..
+
+549
+00:40:58,950 --> 00:41:04,950
+in M وعندي اللي هي ال .. ال .. ال .. ال space كله
+
+550
+00:41:04,950 --> 00:41:09,910
+complete xn مظبوط هنا كوشي فيها دي لإن هي موجودة
+
+551
+00:41:09,910 --> 00:41:13,910
+في ال space كله المكبير إذا xn صارت كوشي sequence
+
+552
+00:41:13,910 --> 00:41:18,130
+و M في ال complete space X إذا لازم يكون في عندي x
+
+553
+00:41:18,130 --> 00:41:24,560
+في ال X such that xn بتروح لميليينلكن انا بقول ان
+
+554
+00:41:24,560 --> 00:41:31,420
+ال subspace M is closed اذا
+
+555
+00:41:31,420 --> 00:41:35,620
+اي sequence فيها بتروح ل X لازم X وير تكون في ال M
+
+556
+00:41:35,620 --> 00:41:40,660
+اذا X وير موجودة في ال M اذا صار is complete كمان
+
+557
+00:41:40,660 --> 00:41:48,200
+مرة شوفكم زي اللي بلعته الآن عند M ايش مارها is
+
+558
+00:41:48,200 --> 00:42:01,020
+closedبتثبتلكم ان هناك
+
+559
+00:42:01,020 --> 00:42:10,300
+هلونة ون في الام كوشي نمأزكيب Xn بزوء من موجودة في
+
+560
+00:42:10,300 --> 00:42:14,360
+الـM معناته موجودة في الـX إذا صارت Xn كوش في مين؟
+
+561
+00:42:14,360 --> 00:42:18,880
+في الـX والـX Complete إذا لازم يكون في علدي اللي
+
+562
+00:42:18,880 --> 00:42:23,360
+هو X بحيث ان Xn بتروح لمين؟ الـX موجود هدى؟ في
+
+563
+00:42:23,360 --> 00:42:28,870
+الـXلكن أنا بقول إن M نفسه Closed وبيقول لك الـ
+
+564
+00:42:28,870 --> 00:42:32,750
+Closed إن أي شيء Sequence عندي بتروح لل X لازم
+
+565
+00:42:32,750 --> 00:42:36,590
+تيجي الـ X تبقيتها عندي عشان أظل Closed فإذن صارت
+
+566
+00:42:36,590 --> 00:42:40,350
+الـ X هنا موجودة في الـ M إذن صارت اللي هي بدينا
+
+567
+00:42:40,350 --> 00:42:44,110
+بـ Cauchy Sequence هنا وانتهينا بالـ Cauchy
+
+568
+00:42:44,110 --> 00:42:49,470
+Sequence Conversion فيها إذن M is Complete واضح؟
+
+569
+00:42:49,470 --> 00:43:02,130
+المفروض واضحنيجي لا firm 149 I'm
+
+570
+00:43:02,130 --> 00:43:09,210
+having T من X لعند Yof a metric space XOD into a
+
+571
+00:43:09,210 --> 00:43:13,570
+metric space YOD is continuous at X0 if and only
+
+572
+00:43:13,570 --> 00:43:18,850
+if Xn بتروح لل X0 implies دي Xn بتروح لمين؟ لل TX0
+
+573
+00:43:18,850 --> 00:43:22,130
+نظرية الصحيحة اللي بنعرفها دي عنا زمان في ال
+
+574
+00:43:22,130 --> 00:43:26,290
+continuity بنحول الحديث في ال continuity من limit
+
+575
+00:43:26,290 --> 00:43:30,770
+F of X as X بتروح ل X0 بيساوي F of X0 إلى لغة ال
+
+576
+00:43:30,770 --> 00:43:35,460
+sequencesيعني بنقول الآن ميزان .. الميزان تبع الـ
+
+577
+00:43:35,460 --> 00:43:41,480
+continuity عند نقطة X note بدي يكون كالتالي بنقول
+
+578
+00:43:41,480 --> 00:43:56,720
+أنه أنه T is continuous T من X لعند Y continuous
+
+579
+00:43:56,720 --> 00:44:02,910
+at X noteإذا و فقط إذا شوفوا مزار ال continuity
+
+580
+00:44:02,910 --> 00:44:06,850
+الآن أنه .. ال sequences بتجيبوا أنه لو جينا أخدنا
+
+581
+00:44:06,850 --> 00:44:13,570
+أي xn بتروح لل x لازم هذا يعطيني ال T xn بتروح لل
+
+582
+00:44:13,570 --> 00:44:18,510
+T x naught إذا هذا تحقق automatic ال T هتكون
+
+583
+00:44:18,510 --> 00:44:22,500
+continuous عند main عند x naughtولو الـ T
+
+584
+00:44:22,500 --> 00:44:27,600
+continuous عند X0 لازم يتحقق التالي إنه لما أخد XN
+
+585
+00:44:27,600 --> 00:44:32,380
+بتروح لل X على طول تقول لي الـ TXN بتروح لمين لـ
+
+586
+00:44:32,380 --> 00:44:37,920
+TX0 وهذا اللي هو هوية الـ continuity للـ T زي ما
+
+587
+00:44:37,920 --> 00:44:41,800
+هويتها التعريف التابع الزمان اللي هو limit F of X
+
+588
+00:44:41,800 --> 00:44:45,320
+لما X بتروح ل X0 بسوء F of X0 هذه هويتها أو limit
+
+589
+00:44:45,320 --> 00:44:49,630
+T of X لما X بتروح ل X0 بسوء X0 هذه هويتهاهذا حتى
+
+590
+00:44:49,630 --> 00:44:52,470
+in general حتى في ال metric spaces ال convergence
+
+591
+00:44:52,470 --> 00:44:55,710
+هذا مش convergence عادي ال convergence ايش في ال
+
+592
+00:44:55,710 --> 00:44:59,790
+metric D لو هذا D و هذا D prime ال convergence في
+
+593
+00:44:59,790 --> 00:45:06,570
+ال mean في ال D prime واضح نيجي اللي هو انبرهن
+
+594
+00:45:06,570 --> 00:45:11,950
+النظرية انبرهن النظرية و البرهان كمان لطيف و مش
+
+595
+00:45:11,950 --> 00:45:15,910
+صعب نشوف
+
+596
+00:45:15,910 --> 00:45:19,890
+ايش بتقول النظريةفي برهانها suppose that T is
+
+597
+00:45:19,890 --> 00:45:26,370
+continuous at X0 مادام continuous عند X0حسب الـ
+
+598
+00:45:26,370 --> 00:45:31,150
+Continuity اللي هو تعريف الـ Continuity إذا لكل Y
+
+599
+00:45:31,150 --> 00:45:34,290
+أكبر من 0 there exists Delta أكبر من 0 such that
+
+600
+00:45:34,290 --> 00:45:39,530
+DX و X0 أصغر من Delta بيؤدي ل D TX0 TX و TX0 أصغر
+
+601
+00:45:39,530 --> 00:45:43,390
+من 100 من إبسلون تعريف الـ Continuity تعريف الـ
+
+602
+00:45:43,390 --> 00:45:48,930
+Continuity إنه بيقول الـ function T continuous at
+
+603
+00:45:48,930 --> 00:45:55,700
+X0 مش عارف لتبع الزمان إنه limitف او T of X note
+
+604
+00:45:55,700 --> 00:46:01,840
+اذا X بتروح ل X note بسوة T of X صح؟
+
+605
+00:46:03,350 --> 00:46:06,890
+الان هذه ترجمته انه لكل epsilon لما تقترب المسافة
+
+606
+00:46:06,890 --> 00:46:09,870
+.. لما .. المسافة هذه تقترب .. النقطة ده تقترب من
+
+607
+00:46:09,870 --> 00:46:13,650
+هذه عبر مسافتها هذه بتقترب من هذه عبر مسافتها يعني
+
+608
+00:46:13,650 --> 00:46:16,070
+بمعنى اخر هذه .. اللي بدأنا نعبرها عن هذه ب delta
+
+609
+00:46:16,070 --> 00:46:18,610
+وهذه ب epsilon ثم بقول عبّر ده for every epsilon
+
+610
+00:46:18,610 --> 00:46:21,530
+أكبر من سفر there exists delta أكبر من سفر such
+
+611
+00:46:21,530 --> 00:46:25,350
+that if اللي هو .. اللي هو هذه ناقص هذه ميقولوش
+
+612
+00:46:25,350 --> 00:46:30,510
+عنها هيك بقول if dx و x not أصغر من delta then
+
+613
+00:46:31,830 --> 00:46:38,530
+هيكون عندى D تلده اللى هى المتر اتبعها TX و TX
+
+614
+00:46:38,530 --> 00:46:44,420
+Noteأصغر من إبسلون هذا اللي هو الcontinuity أو
+
+615
+00:46:44,420 --> 00:46:46,340
+اللي هو هذا التعبير بالبول زي اللي حكيناها في
+
+616
+00:46:46,340 --> 00:46:50,000
+الأول انه .. انه .. اللي هو .. انه .. لما تكون
+
+617
+00:46:50,000 --> 00:46:54,420
+اللي هو ال bowl اللي هنا اللي .. اللي .. اللي ..
+
+618
+00:46:54,420 --> 00:46:55,720
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+619
+00:46:55,720 --> 00:46:57,020
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+620
+00:46:57,020 --> 00:46:57,060
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+621
+00:46:57,060 --> 00:46:57,080
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+622
+00:46:57,080 --> 00:47:02,280
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+623
+00:47:02,280 --> 00:47:05,520
+اللي
+
+624
+00:47:05,520 --> 00:47:11,380
+.. اللكل X هنا بناجيها الـ TX تبعتها فاهمين ماحكيه
+
+625
+00:47:11,380 --> 00:47:17,780
+هون؟ ماشي طيب وصلّى على النبي عليه الصلاة والسلام
+
+626
+00:47:17,780 --> 00:47:21,860
+such that T is continuous at X0 then for every Y
+
+627
+00:47:21,860 --> 00:47:24,760
+أكبر من 0 there exists Delta أكبر من 0 such that
+
+628
+00:47:24,760 --> 00:47:28,220
+لما المسافة تضيق بين X وX0 أصغر من Delta بتعطين
+
+629
+00:47:28,220 --> 00:47:32,080
+المسافة المقابلة D تلد بين TX وDX أصغر من مين؟ من
+
+630
+00:47:32,080 --> 00:47:39,520
+Y ماشي؟الان بدي أثبتلكم لما Xn بتروح ل X0 يعطيني
+
+631
+00:47:39,520 --> 00:47:45,520
+TXn بتروح لمين TX0 سهل نفترض الآن Xn بتروح لمين لل
+
+632
+00:47:45,520 --> 00:47:50,000
+X0 إذا مدام Xn بتروح لل X0 إذا بقدر نلاقي K
+
+633
+00:47:50,000 --> 00:47:56,300
+element انلدلتة هذه إيش معنات Xn بتروح ل X0 لأي Y
+
+634
+00:47:56,300 --> 00:47:59,020
+أكبر من 0 في الدنيا بتاخدها لمين الآن؟ لإيش ..
+
+635
+00:47:59,020 --> 00:48:03,340
+لحاجة تخدمني؟ إيش اسمها Delta؟ ماشي؟ شو معناة Xn
+
+636
+00:48:03,340 --> 00:48:07,260
+بتروح ل X0 لكل Y أكبر من 0 there exists K element
+
+637
+00:48:07,260 --> 00:48:10,820
+in N such that اللي هو ال distance بين Xn و X0
+
+638
+00:48:10,820 --> 00:48:15,380
+أكثر من Y أكثر من Y لكل N أكبر سوى 100K اللي أنا
+
+639
+00:48:15,380 --> 00:48:19,540
+مانديش أخد لكل Y و أخد لDelta هذه اللي لجيتهاللـ
+
+640
+00:48:19,540 --> 00:48:23,040
+delta اللي لجيتها بدي أشتغل بدي أقول for delta
+
+641
+00:48:23,040 --> 00:48:27,960
+اللي لجيتها there exist K such that المسافة بين Xn
+
+642
+00:48:27,960 --> 00:48:33,600
+وX0 أصغر من الـ Delta لكل N أكبر من مين من Kإذا
+
+643
+00:48:33,600 --> 00:48:41,320
+مباشرة احنا قلنا اللي بتحقق هذا بيعطينا هذا لأن
+
+644
+00:48:41,320 --> 00:48:44,740
+هذا تحقق ال XN بعيد عن X Note بمسافة جال من Delta
+
+645
+00:48:44,740 --> 00:48:50,880
+إذا أكيد صورة من ال Delta تلدة بين TXN و TX Note
+
+646
+00:48:50,880 --> 00:48:57,260
+هتكون أصغر من 100من Epsilon إذا عندي المسافة دي
+
+647
+00:48:57,260 --> 00:49:00,260
+تلده بين TXN و TX0 أصغر من Epsilon فهو N أكبر سوء
+
+648
+00:49:00,260 --> 00:49:04,300
+K إيش معناته هذا أنه أنا بدأت بأي Epsilon في
+
+649
+00:49:04,300 --> 00:49:09,560
+الدنيا arbitrary اللي بدأت فيها أي Epsilon لجيت K
+
+650
+00:49:09,560 --> 00:49:13,780
+الآن بحيث أن المسافة بين TXN و TX0 أصغر من Epsilon
+
+651
+00:49:13,780 --> 00:49:18,180
+لكل N أكبر منين من K وهذا معناته أن TXN بتروح ل
+
+652
+00:49:18,180 --> 00:49:18,660
+TX0
+
+653
+00:49:27,640 --> 00:49:32,620
+Conversely نفرض أن الشرط تحقق و بدنا نثبت ال
+
+654
+00:49:32,620 --> 00:49:43,720
+continuity طيب
+
+655
+00:49:43,720 --> 00:49:50,560
+ConverselySuppose that xₙ converges to xₙ implies
+
+656
+00:49:50,560 --> 00:49:53,280
+that xₙ converges to xₙ بتروح لمين؟ لـ Txₙ بتدفع
+
+657
+00:49:53,280 --> 00:49:56,600
+الـ Continuity لان طيب، to prove that T is
+
+658
+00:49:56,600 --> 00:50:00,700
+continuous نفترض الـ Xₙ نستخدم الـ Contradiction
+
+659
+00:50:00,700 --> 00:50:05,520
+نفترض العكس و نصل لإيش؟ لتناقض أه، بدنا نفترض أن T
+
+660
+00:50:05,520 --> 00:50:10,040
+مش continuous عند ال XₙSuppose that T is not
+
+661
+00:50:10,040 --> 00:50:11,380
+continuous at X0
+
+662
+00:50:38,310 --> 00:50:42,470
+إذن يعني بمعنى آخر بقى كأني بدي أقول for every
+
+663
+00:50:42,470 --> 00:50:50,190
+واحد على N يعني for every N بقدر ألاقي XN بحيث أنه
+
+664
+00:50:50,190 --> 00:50:55,910
+المسافة بين XN و X0 تكون أصغر من Delta حسب هذاSuch
+
+665
+00:50:55,910 --> 00:50:59,890
+that d dxn و dx0 ايش مالها أكبر أو يساوي إبسلون
+
+666
+00:50:59,890 --> 00:51:04,310
+هذا إيش معناته هذا معناته هذي مدام أصغر من أي دلتا
+
+667
+00:51:04,310 --> 00:51:08,530
+في الدنيا معناته ال dxn بتروح لمين لل x note أو ال
+
+668
+00:51:08,530 --> 00:51:12,890
+xn بتروح لل x note لكن هذي بتعني إيش but dxn does
+
+669
+00:51:12,890 --> 00:51:18,210
+not converge to mean to dx0 وهذا يناقض المعطى thus
+
+670
+00:51:18,210 --> 00:51:24,080
+أو this contradicts the assumptiontherefore t is
+
+671
+00:51:24,080 --> 00:51:29,080
+continuous at x naught وهو المطلوب بيكون هيك احنا
+
+672
+00:51:29,080 --> 00:51:34,540
+خلصنا المحاضرة وعنا homework اللي هو اللي بدكم
+
+673
+00:51:34,540 --> 00:51:38,500
+تسلموه اللي هو star ستة و تمانية و ال homework
+
+674
+00:51:38,500 --> 00:51:42,880
+الباقي هذا بتحلو انتوا و بارك الله فيكم الله
+
+675
+00:51:42,880 --> 00:51:43,540
+يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/g1UMuLpn1XM_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/g1UMuLpn1XM_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..968aec5f7a0ec0ca0cf1a0d052e4807c505c0263
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/g1UMuLpn1XM_raw.srt
@@ -0,0 +1,2728 @@
+1
+00:00:05,130 --> 00:00:07,790
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,790 --> 00:00:10,810
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,810 --> 00:00:14,850
+آله وصحبه أجمعين هذه هي المحاضرة الخامسة مساق
+
+4
+00:00:14,850 --> 00:00:19,890
+تحليل اقتراني أو تحليل دالي لطلاب وطالبات الجامعة
+
+5
+00:00:19,890 --> 00:00:27,820
+الإسلامية طلبة ال master أو master رياضياتوصلنا او
+
+6
+00:00:27,820 --> 00:00:32,020
+نهينا section واحد تلاتة حكينا عن اللي هو ال open
+
+7
+00:00:32,020 --> 00:00:35,240
+sets و ال neighborhoods و ال closed sets و حكينا
+
+8
+00:00:35,240 --> 00:00:40,780
+عن ايضا اللي هو ال dense sets و عرفنا اللي هو ال
+
+9
+00:00:40,780 --> 00:00:43,880
+spaces اللي ال infinity اللي قال ال infinity مثلا
+
+10
+00:00:43,880 --> 00:00:47,420
+مش separable بينما قال بي لكل بي بأنه أكبر سوى
+
+11
+00:00:47,420 --> 00:00:50,410
+واحد أصغر من ال infinityR-Separable Spaces والـ
+
+12
+00:00:50,410 --> 00:00:54,170
+Spaces التابعاتنا اللي عايشين فيها في الـ Calculus
+
+13
+00:00:54,170 --> 00:00:58,050
+وباقي موادنا اللي هو الـR والـC عبارة عن Separable
+
+14
+00:00:58,050 --> 00:01:03,030
+Spaces الآن بدنا نحكي عن مفهيم أخرى تبولوجية ولكن
+
+15
+00:01:03,030 --> 00:01:06,410
+خلينا نقول هذه لا يمكن نسيغنع عنها أيضا في اللي هو
+
+16
+00:01:06,410 --> 00:01:10,160
+التحليل اللي هي convergenceمعنى الـ convergence
+
+17
+00:01:10,160 --> 00:01:14,580
+اللي احنا بنعرفه اصلا بس بنعممه على metric space
+
+18
+00:01:14,580 --> 00:01:17,120
+in general ايش معنى الـ Cauchy sequences اللي
+
+19
+00:01:17,120 --> 00:01:19,260
+انتوا عارفينها في ال .. في ال .. اللي خدناها في
+
+20
+00:01:19,260 --> 00:01:23,340
+الـ real ولكن برضه بنعملمها على اي metric space و
+
+21
+00:01:23,340 --> 00:01:26,820
+ال completeness بروبرتها دي يعني شغلة جديدةعلينا
+
+22
+00:01:26,820 --> 00:01:32,780
+اللي هي ال space اللي يختص بخاصية الاكتمال ان يكون
+
+23
+00:01:32,780 --> 00:01:36,060
+ال space مكتمل وهذا ال spaces المكتملة هي spaces
+
+24
+00:01:36,060 --> 00:01:39,760
+خلينا نقول كتير كتير محترمة و بتريحنا و هنشوف ايش
+
+25
+00:01:39,760 --> 00:01:43,580
+اللي هو معناه الاكتمال و هيكون رحلتنا معاه شوية
+
+26
+00:01:43,580 --> 00:01:46,900
+طويلة لأنه هيلزمنا في ال section اللي بعده و اللي
+
+27
+00:01:46,900 --> 00:01:52,330
+بعدهبنشوف معنات الـ Sequence انها Convergent بنقول
+
+28
+00:01:52,330 --> 00:01:56,190
+a sequence xn in a metric space x وd إذا جاعد أنا
+
+29
+00:01:56,190 --> 00:02:00,390
+وان في metric space is said to be convergent ونقول
+
+30
+00:02:00,390 --> 00:02:03,710
+هذا الـ sequence convergent إذا بنلاقي x element
+
+31
+00:02:03,710 --> 00:02:06,810
+in x نفس المفهوم اللي احنا بنحكي فيه زمان في الـ
+
+32
+00:02:06,810 --> 00:02:12,470
+real such thatالان بنقولش limit xn بتروح لل x لأ
+
+33
+00:02:12,470 --> 00:02:16,370
+الان صار عندي اللي هو في metric ال metric اللي
+
+34
+00:02:16,370 --> 00:02:20,390
+بتحكي عنه اللي هو دي فبنقول عنه limit d xn وx ايش
+
+35
+00:02:20,390 --> 00:02:25,650
+بيساوي بيساوي سفر as n goes to infinity لاحظوا انا
+
+36
+00:02:25,650 --> 00:02:32,890
+بقول الان ان xn sequence في ال x بقول xn converts
+
+37
+00:02:32,890 --> 00:02:36,740
+لل xconvergence ده ال X بس وين هذا في ال metric
+
+38
+00:02:36,740 --> 00:02:40,840
+space اللي هو X وD يعني الدنيا تبعت ال convergence
+
+39
+00:02:40,840 --> 00:02:44,540
+هذا اللي هي ال X وD بدي أعرف هذا ال convergence
+
+40
+00:02:44,540 --> 00:02:49,160
+بإيش أنا أصلا بعرفه من الأصل فحولت الحديث كله من
+
+41
+00:02:49,160 --> 00:02:53,580
+عناصر في داخل ال X ال metric space اللي عندى إلى
+
+42
+00:02:53,580 --> 00:03:00,870
+limitDXN و X as N goes to infinity بساوي اللي هو
+
+43
+00:03:00,870 --> 00:03:05,530
+sum اللي هو number اللي هو ال zero بالظبط ال
+
+44
+00:03:05,530 --> 00:03:10,590
+number اللي بنحكي عنه مين ال zeroفي الواقع أنا هذا
+
+45
+00:03:10,590 --> 00:03:13,810
+الحديث أنا بعرفه لإن ال distance بين X و N أو X
+
+46
+00:03:13,810 --> 00:03:17,330
+أبريل ألاف أو أرقام إذا هذه أرقام و كأنه sequence
+
+47
+00:03:17,330 --> 00:03:20,790
+من أرقام بتديها تروح لمين للزيرو فعرفت ال
+
+48
+00:03:20,790 --> 00:03:24,210
+convergence ال XN في اللي بروح لل X في ال metric
+
+49
+00:03:24,210 --> 00:03:31,370
+space X بدلالة مين بدلالة اللي هو ال sequence of
+
+50
+00:03:31,370 --> 00:03:36,190
+numbers اللي عندي خلفية عنها من خلال الريال الأصلي
+
+51
+00:03:36,640 --> 00:03:41,520
+هذا معناه الـ convergence in this case X is called
+
+52
+00:03:41,520 --> 00:03:45,520
+the limit of Xn يعني X اللي هي X هي limit لل Xn or
+
+53
+00:03:45,520 --> 00:03:49,380
+Xn converge to X and we write limit Xn بسوا X or
+
+54
+00:03:49,380 --> 00:03:53,100
+Xn goes to infinity أو simply زي ما كتبت Xn بتروح
+
+55
+00:03:53,100 --> 00:03:58,750
+لل Xواضح هذا معناته اللي هو ال convergence الان if
+
+56
+00:03:58,750 --> 00:04:03,130
+xn is not convergent زي ما احنا متعودين then بنقول
+
+57
+00:04:03,130 --> 00:04:07,410
+عنها ايش ما لها is a divergent sequence نيجي
+
+58
+00:04:07,410 --> 00:04:11,350
+للملاحظات اللي بتخلينا نقول بتعمق المفهوم عندنا و
+
+59
+00:04:11,350 --> 00:04:17,380
+بتفهمنا المفهوم بشكل أكبرحينها لو طلعت لهذا انا
+
+60
+00:04:17,380 --> 00:04:21,300
+صرت اتعامل و كأنه هذا number اذا بعرف تعريفه مؤصل
+
+61
+00:04:21,300 --> 00:04:24,260
+انا ال epsilon definition او ال epsilon definition
+
+62
+00:04:24,260 --> 00:04:27,620
+تبع اللي هو تبع اللي هو ال calculus و تبع التحليل
+
+63
+00:04:27,620 --> 00:04:30,560
+بعرفه اللي هو forever epsilon أكبر من 0there
+
+64
+00:04:30,560 --> 00:04:34,140
+exists k element in n such that for every n أكبر
+
+65
+00:04:34,140 --> 00:04:40,160
+يساوي k ال distance بين ال xn و ال x أصغر من y for
+
+66
+00:04:40,160 --> 00:04:44,660
+every n أي شمالها أكبر أو يساوي k هذا ما طبعا احنا
+
+67
+00:04:44,660 --> 00:04:48,920
+ممكن نترجمه بشكل آخر انه اللي هو لكل y أكبر من 0
+
+68
+00:04:48,920 --> 00:04:53,180
+there exists k element in n such that اللي هو عندي
+
+69
+00:04:53,180 --> 00:05:01,520
+ال ballاللي مركزها X و نصف قطرها Y بتحتوي على كل
+
+70
+00:05:01,520 --> 00:05:07,820
+الـ X أنات المن N أكبر أو سوى واحد يعني XN element
+
+71
+00:05:07,820 --> 00:05:11,820
+in الـ ball هذه for every N أكبر أو سوى 100 يمكن
+
+72
+00:05:11,820 --> 00:05:16,520
+أن يحول الحديث من الـ metric هذا إلى الـ ball
+
+73
+00:05:16,520 --> 00:05:22,300
+المقابلة لها إذا بيصير عندي المراحضة الأولىLimit
+
+74
+00:05:22,300 --> 00:05:26,720
+xn بساوة x if and only if for every y أكبر من 0
+
+75
+00:05:26,720 --> 00:05:30,400
+there exists k بساوة k of y in element n طبعا ال k
+
+76
+00:05:30,400 --> 00:05:32,680
+بساوة k of y على أساس أن ال k اللي هتطلع عندى
+
+77
+00:05:32,680 --> 00:05:34,600
+بتاعتها تمد على مين؟ على ال epsilon ماعرفش علاقة
+
+78
+00:05:34,600 --> 00:05:40,960
+بال x such that xn element in pole لل x و y for
+
+79
+00:05:40,960 --> 00:05:45,580
+all n أكبر أو يساوي k هذا تعبير آخر عن اللي هو
+
+80
+00:05:45,580 --> 00:05:46,760
+معناه ال limit
+
+81
+00:05:49,870 --> 00:05:53,350
+المرحضة التانية The limit of a convergent sequence
+
+82
+00:05:53,350 --> 00:05:56,890
+must be a point of the space XN 4141
+
+83
+00:06:04,250 --> 00:06:07,430
+معناته إن الـ X اللي بتروحيلها الـ Xn لازم تكون في
+
+84
+00:06:07,430 --> 00:06:10,890
+مين؟ في الـ space اللي عندى يعني أنا .. هالجد
+
+85
+00:06:10,890 --> 00:06:14,410
+بتفهموه إيش اللي بقصده؟ إنه أنا لما أقول Xn
+
+86
+00:06:14,410 --> 00:06:21,210
+converges in X معناته limit الـ Xn بتتقارب نوح
+
+87
+00:06:21,210 --> 00:06:27,170
+نقطة اسمها X و الـ X هي الموجودةفي الـ x لكن لو
+
+88
+00:06:27,170 --> 00:06:31,990
+كانت ال limit xn جاي عبالها رايحة لإشي معين لكن
+
+89
+00:06:31,990 --> 00:06:35,490
+هذا مش موجود في ال set اللي هي ال x بنقولش عن ال
+
+90
+00:06:35,490 --> 00:06:39,770
+sequence إنها converges in this space لأ، بتكونش
+
+91
+00:06:39,770 --> 00:06:42,710
+converges إذا اللي بيقولهان في الملاحظة 2 الـ the
+
+92
+00:06:42,710 --> 00:06:46,110
+limit of a convergent sequence must be of the
+
+93
+00:06:46,110 --> 00:06:52,130
+space x اللي مذكور في أربعة واحد1 4 1 otherwise
+
+94
+00:06:52,130 --> 00:06:55,690
+بنقول الـ sequence إيش ما لها is divergent وماخدوا
+
+95
+00:06:55,690 --> 00:07:02,670
+لكم مثال بقولكم لو إحنا أخدنا ال X هي عبارة عن 0 1
+
+96
+00:07:02,670 --> 00:07:07,550
+و بس و أخدنا ال metric يعني جزء من R أخدته بس
+
+97
+00:07:07,550 --> 00:07:10,470
+المنطقة ده و ال metric هو ال metric تبع ال R اللي
+
+98
+00:07:10,470 --> 00:07:13,910
+هو إيش هو ال metric تبع ال R ال distance بين X و Y
+
+99
+00:07:13,910 --> 00:07:17,910
+بسوء ال absolute value X minus Y لكل X و Y اللي
+
+100
+00:07:17,910 --> 00:07:22,760
+موجودة في ال X اللي فوقبقولك الآن بدي أعطيك مثال
+
+101
+00:07:22,760 --> 00:07:25,700
+على الـ sequence دي هي عبالها تروح لشغلة لكن مش
+
+102
+00:07:25,700 --> 00:07:30,880
+موجودها يعني أخد اللي هو الـ xn أيش بتساوي 1 على n
+
+103
+00:07:30,880 --> 00:07:34,720
+أو n زايد واحدة منكم بجهها n أكبر أو أكبر من مين
+
+104
+00:07:34,720 --> 00:07:40,200
+من واحد وإذا بدنا نكون خلّيني نقول ألطف حطها هيكا
+
+105
+00:07:40,200 --> 00:07:44,570
+و ال n element in n وخلاصفاهمين عليها أن أكبر وسيء
+
+106
+00:07:44,570 --> 00:07:49,450
+واحد أي واحدة منها لاحظوا هذه ال Xn سهل لنا نثبتها
+
+107
+00:07:49,450 --> 00:07:54,510
+أن واحد على أن زائد واحد لو بدها تروح، هتروح لمين؟
+
+108
+00:07:54,510 --> 00:07:59,390
+للصفر لكن الصفر مش موجود في مين؟ عشان هيك بنقول
+
+109
+00:07:59,390 --> 00:08:05,510
+هذه اللي هو ال sequence does not converge الين؟ ال
+
+110
+00:08:05,510 --> 00:08:09,310
+X اللي هو Zero والواحد وهي it is clear that واحد
+
+111
+00:08:09,310 --> 00:08:12,310
+على أن is divergent because واحد على أنwants to
+
+112
+00:08:12,310 --> 00:08:16,790
+converge to zero which is not in zero أو واحد أي
+
+113
+00:08:16,790 --> 00:08:23,510
+سؤال واضح على الصورة الأمور طيب نيجي الآن اللي هو
+
+114
+00:08:23,510 --> 00:08:29,430
+بدنا نعرف اللي هو بدأ أروح باتجاه مدام بدي أحكي عن
+
+115
+00:08:29,430 --> 00:08:34,310
+convergence بعد بمشي زي ما كنا نمشي في R بحكي عن
+
+116
+00:08:34,310 --> 00:08:37,710
+convergence شكلي بدي أحكي عن bounded عشان أحكي عن
+
+117
+00:08:37,710 --> 00:08:42,220
+bounded بدي أشوف حاجة اسمها الـ diameterلمن؟ لل
+
+118
+00:08:42,220 --> 00:08:46,060
+set تشوف ايش اللي بنقوله وبدلالتها بدي اعرف ال
+
+119
+00:08:46,060 --> 00:08:56,920
+boundedness لو جيت قولت أخدت subset M a non-empty
+
+120
+00:08:56,920 --> 00:09:00,920
+subset M of a metric space X is said to be bounded
+
+121
+00:09:03,150 --> 00:09:08,430
+rounded if the diameter of M ايش ال diameter of M
+
+122
+00:09:08,430 --> 00:09:12,030
+ال diameter of M هو عبارة عن ال supremum لكل
+
+123
+00:09:12,030 --> 00:09:17,690
+الأبعاد اللي بيني الموجودة في ال M هذا بتسميه
+
+124
+00:09:17,690 --> 00:09:22,410
+اشماله ال diameter لكل ال M الان is finite لو كان
+
+125
+00:09:22,410 --> 00:09:27,880
+ال diameter is finite معناته انه انالأ هذا هيكون
+
+126
+00:09:27,880 --> 00:09:32,860
+عدد مظبوط عدد سموه مثلا اللي بتكون إيه سموه K مثلا
+
+127
+00:09:32,860 --> 00:09:40,460
+هذا العدد عدد الآن بيصير معناته الـ M is finite
+
+128
+00:09:40,460 --> 00:09:48,300
+أنه لكل X وY أو اللي هو there exist KElement in R
+
+129
+00:09:48,300 --> 00:09:53,340
+أو أكبر من سفر Such that المسافة بين X و Y أصغر من
+
+130
+00:09:53,340 --> 00:09:59,800
+K لكل X و Y موجودة في الـ M لأن الـ Supremum نفسه
+
+131
+00:09:59,800 --> 00:10:06,600
+محدود اسمه Kإذا كل المسافات اللي بين العناوز اللي
+
+132
+00:10:06,600 --> 00:10:10,460
+موجودة في هداك أصغر أو أساوي K أصغر أو أساوي K هذا
+
+133
+00:10:10,460 --> 00:10:15,080
+مشابه للأصل ال bounded العادي احنا لما نقول أن ال
+
+134
+00:10:15,080 --> 00:10:18,840
+6 M is bounded إذا بنلاقي K بحيث أن ال absolute
+
+135
+00:10:18,840 --> 00:10:23,340
+value لل X أصغر أو أساوي K لكل X وين موجودة في ال
+
+136
+00:10:23,340 --> 00:10:23,500
+M
+
+137
+00:10:27,700 --> 00:10:33,640
+ومنه أصلا بقدر أقول البسافة بين x و y اللي هي برضه
+
+138
+00:10:33,640 --> 00:10:36,400
+هتكون bargain زي اللي فوق لإنها هتكون أصغر بحكي عن
+
+139
+00:10:36,400 --> 00:10:40,740
+علامة تبع ال R أصغر بساوة x زاد absolute value ل y
+
+140
+00:10:40,740 --> 00:10:43,320
+و هذا أصغر من k و أصغر من k لإن هذا أصغر بساوة
+
+141
+00:10:43,320 --> 00:10:49,250
+102k يعني في النهاية اللي هو هذاأو هذا نفس الأشياء
+
+142
+00:10:49,250 --> 00:10:52,030
+بس هذا على الـ metric in general وهذا على mean على
+
+143
+00:10:52,030 --> 00:10:55,850
+absolute value تبع الزمان إذا تعريفي الجديد يتوافق
+
+144
+00:10:55,850 --> 00:11:00,950
+مع القديم والقديم بيصير حالة خاصة منه إذا الأن
+
+145
+00:11:00,950 --> 00:11:04,470
+ملخص حديثي إن الـ sequence Xm in X is called
+
+146
+00:11:04,470 --> 00:11:07,930
+bounded sequence if the corresponding point set
+
+147
+00:11:07,930 --> 00:11:11,870
+اللي هي X واحدة كل ال Xات اللي فيها is a bounded
+
+148
+00:11:11,870 --> 00:11:19,130
+subset of mean of Xأي سؤال؟ طيب نيجي لللمّة الأولى
+
+149
+00:11:19,130 --> 00:11:24,490
+اللمّة الأولى متوقعينها اللي هي زي اللي .. مش
+
+150
+00:11:24,490 --> 00:11:29,110
+هنحكي .. مش هنحكي و كأنه نصوص جديدة لأ النصوص هي
+
+151
+00:11:29,110 --> 00:11:31,430
+تبعات اللي كنا ناخدها في القارة عن الـ sequences
+
+152
+00:11:31,430 --> 00:11:35,130
+إيش
+
+153
+00:11:35,130 --> 00:11:40,540
+بتقول؟بتقول لو احنا عندنا let X و D بيه متر كسباس
+
+154
+00:11:40,540 --> 00:11:45,240
+then a convergent sequence in X is bounded هاي هنا
+
+155
+00:11:45,240 --> 00:11:47,200
+كنا نقول زمان انا convergence sequence is bounded
+
+156
+00:11:47,200 --> 00:11:50,960
+برضه فأي متر كسباس صح وال limit بقى اللي هي وحيدة
+
+157
+00:11:50,960 --> 00:11:55,980
+برضه نفس الكلام الأولاني برضه بظبط هناوالثانية
+
+158
+00:11:55,980 --> 00:11:59,300
+بقولك لو كانت ال XN بتروح لل X و ال YN بتروح لل Y
+
+159
+00:11:59,300 --> 00:12:04,600
+أكيد المسافة بين XN و YN برضه هتروح لمين للمسافة
+
+160
+00:12:04,600 --> 00:12:11,100
+بين X و Y ماشي الحال بدنا نثبتها اللي هو التنتين
+
+161
+00:12:11,100 --> 00:12:15,020
+اللي أمامناالإثبات برضه هتلاقوه مشابه للإثباتات
+
+162
+00:12:15,020 --> 00:12:18,240
+اللي كنا نثبتها في حالة اللي هي الـ Real Numbers
+
+163
+00:12:18,240 --> 00:12:22,220
+بس تشيلواها دي و تحطواها العصيتين اللي زمان كنا
+
+164
+00:12:22,220 --> 00:12:25,880
+ناخدهم العصيتين Absolute Value الآن احنا أياشي
+
+165
+00:12:25,880 --> 00:12:29,940
+بنحكي عن Animetric دي هتلاقوا الأمور كتير مشابهة
+
+166
+00:12:29,940 --> 00:12:35,160
+تشوف نطلع النبي عليه الصلاة والسلام نفترض ان X
+
+167
+00:12:35,160 --> 00:12:39,600
+Unconverts يعني X Un تروح لمين لSome X Element in
+
+168
+00:12:39,600 --> 00:12:45,620
+X Capitalالان برضه لو رجعته برهان اللي هو التحليل
+
+169
+00:12:45,620 --> 00:12:48,360
+هتلاقو نفس الأشياء إذا لكل أبسلون أكبر من سفر
+
+170
+00:12:48,360 --> 00:12:51,740
+there exist كده كده اللي بتاخد أبسلون تخدمني أخدت
+
+171
+00:12:51,740 --> 00:12:55,140
+أبسلون أربط أيه؟ يعني أخدت أبسلون محددة سميتها
+
+172
+00:12:55,140 --> 00:12:58,260
+واحد بنفع أخد اتنين، بنفع أخد تلاتة، بنفع أخد
+
+173
+00:12:58,260 --> 00:13:02,120
+أربع، بنفع أخد ربع، بنفع أخد درجتين، بس ألطف لنفس
+
+174
+00:13:02,120 --> 00:13:06,990
+الواحد، الواحد منيح مازال بتاخد، إذاthen for y
+
+175
+00:13:06,990 --> 00:13:09,790
+بيساوي واحد there is k limiting and such that
+
+176
+00:13:09,790 --> 00:13:13,450
+المسافة بين x أن وx أشمالها أصغر من واحد لكل أن
+
+177
+00:13:13,450 --> 00:13:17,330
+أشمالها أكبر من k هذا التعريف المباشر للـ limit
+
+178
+00:13:17,330 --> 00:13:24,750
+اللي جابناه بشوية حكينا عنه الآن بيقوللي بده الآن
+
+179
+00:13:24,750 --> 00:13:28,590
+أثبت انها bounded يعني بده أثبت المسافة بين أي
+
+180
+00:13:28,590 --> 00:13:36,560
+مقطين أصغر من number لجته الآن لاحظواإن المسافة
+
+181
+00:13:36,560 --> 00:13:42,960
+بين X و N و X أصغر من واحد لكل الانات اللي أكبر من
+
+182
+00:13:42,960 --> 00:13:46,580
+K ل XN زيادة واحد و XN زيادة اتنين و XN زيادة
+
+183
+00:13:46,580 --> 00:13:49,820
+تلاتة و XN زيادة أربعة كلهم ضمنتهم اللي أصغر من
+
+184
+00:13:49,820 --> 00:13:54,260
+واحد ده اللي قبل اللي قبل بتقول خلّي A تساوي ال
+
+185
+00:13:54,260 --> 00:13:58,180
+maximum بين المسافة X واحد و X و X اتنين و X لعند
+
+186
+00:13:58,180 --> 00:14:04,320
+X K minus واحد و مين و X إذن الآن خلصت من هذه و
+
+187
+00:14:04,320 --> 00:14:10,780
+هذههيها هخلص اللي بديها انا اضمنت لكم ان المسافة
+
+188
+00:14:10,780 --> 00:14:18,660
+DXN و X أصلا واحد لكل N أكبر أو يساوي K و دي أخدت
+
+189
+00:14:18,660 --> 00:14:23,120
+الـ A بالساوي ال maximum للمسافات X واحد مع ال X
+
+190
+00:14:23,120 --> 00:14:29,440
+اللي ضالن لعند ما أصل ل D X K minus واحد و X سميت
+
+191
+00:14:29,440 --> 00:14:32,400
+أكبر و روح فيه maximum لأن عددهم عشرة عشرين مية
+
+192
+00:14:32,400 --> 00:14:37,160
+finite إذا فينا ال maximum ماعشه اسمه M A إذا أكيد
+
+193
+00:14:37,160 --> 00:14:46,130
+أكيد أكيد صار عندي D X Mوأي x موجودة اللي هو عندى
+
+194
+00:14:46,130 --> 00:14:50,430
+في ال sequence اللي هي xm و ال x تبعتي هي اللي بقى
+
+195
+00:14:50,430 --> 00:14:57,890
+بحكي عنها أصغر من الواحد زائد a ليش؟ لإن الآن ال a
+
+196
+00:14:57,890 --> 00:15:02,930
+هي ال maximum لمسافاتي ده موجودة أو سفر صح ولا لأ؟
+
+197
+00:15:02,930 --> 00:15:08,190
+الآن ال .. ال .. ال x واحد لعند ال xk minus واحد
+
+198
+00:15:08,190 --> 00:15:12,290
+أكيد أصغر من ال a لحالهاإذا أكيد أصغر من مين؟ من
+
+199
+00:15:12,290 --> 00:15:15,330
+الواحد زائد إيه البجيات كلها أصغر من واحد لحاله
+
+200
+00:15:15,330 --> 00:15:18,250
+إذا أكيد أصغر من مين؟ واحد زائدة إذا هو ضرب على
+
+201
+00:15:18,250 --> 00:15:22,510
+صفرين وحجار وقال لك إذا دي Xn و X أصغر من واحد
+
+202
+00:15:22,510 --> 00:15:28,750
+زائد إيه hence for all n and m المسافة بين Xn وXm
+
+203
+00:15:28,750 --> 00:15:31,410
+أصغر أو ساوية تلقى inequality عشان أخلص على اللي
+
+204
+00:15:31,410 --> 00:15:35,240
+بدوياه وإيش بتثبت؟بدّون يثبت إنها bounded، إيش ال
+
+205
+00:15:35,240 --> 00:15:39,380
+bounded؟ إنه المسافات بين أي نقطتين كلهين يكون
+
+206
+00:15:39,380 --> 00:15:44,580
+أصغر من إشي، ماشي؟ لأن خدوا أي نقطتين XN و XM في
+
+207
+00:15:44,580 --> 00:15:47,400
+مين، أنا بقى برايح لمين، هاي ال sequence اللي عند
+
+208
+00:15:47,400 --> 00:15:52,220
+ال XMونقول عنها bounded إذا كان عناصرها X1 و X2
+
+209
+00:15:52,220 --> 00:15:56,680
+إلى ما لنهاية المسافات بين أي كنتين يكونون أصغر من
+
+210
+00:15:56,680 --> 00:16:00,480
+some number خدت الآن un-arbitrary و un-arbitrary
+
+211
+00:16:00,480 --> 00:16:04,360
+يعني دي X un-arbitrary و X un-arbitrary و حسبت
+
+212
+00:16:04,360 --> 00:16:07,580
+المسافة بينهم بال triangling quality أصغر أو سوى
+
+213
+00:16:07,580 --> 00:16:13,000
+دي X un و مين و X أنا هيأت حالي في اللي قبل زائد X
+
+214
+00:16:13,000 --> 00:16:17,440
+un و مين و X الأولى أصغر من واحد زائد ايه أثبتها
+
+215
+00:16:18,160 --> 00:16:21,580
+والتانية أصغر من واحد زاد إيه إذا التنتين أصغر من
+
+216
+00:16:21,580 --> 00:16:25,980
+اتنين زاد مين اتنين إيه إذا المسافة بين أي وقتين
+
+217
+00:16:25,980 --> 00:16:30,440
+الآن في داخل ال sequence اللي هي أصغر من اتنين زاد
+
+218
+00:16:30,440 --> 00:16:34,520
+اتنين إيه وهذا معناته أنه صارت عند ال sequence xn
+
+219
+00:16:34,520 --> 00:16:40,300
+is a bounded sequence طيب صلوا على النبي عليه
+
+220
+00:16:40,300 --> 00:16:42,420
+الصلاة والسلام الآن
+
+221
+00:16:45,850 --> 00:16:49,470
+والـ Limit X مالها واحدة بما أنك تضمن أنك تنتهي من
+
+222
+00:16:49,470 --> 00:16:54,070
+وصول الـ X مالها واحدة بنقول أسيوم ذات Xn بتروح لل
+
+223
+00:16:54,070 --> 00:16:57,590
+X و Xn بتروح لمين لزي ال two limits و في الآخر
+
+224
+00:16:57,590 --> 00:17:02,330
+هنطلع X بالساوة زي ال then المسافة بين X و Z أكيد
+
+225
+00:17:02,330 --> 00:17:07,070
+مالها أكبر أو ساوة سفربالنسبة لكم ان هذه 0 أصغر
+
+226
+00:17:07,070 --> 00:17:13,170
+سوى DX وXN زي DXN ومين وZ لكن هذه مش احنا بنقول XN
+
+227
+00:17:13,170 --> 00:17:17,210
+بتروح ل X إذا ال limit هي 0 حسب التعريف ومش بنقول
+
+228
+00:17:17,210 --> 00:17:20,730
+XN بتروح ل Z إذا ال limit هي 0 إذا هذول ال limit
+
+229
+00:17:20,730 --> 00:17:25,070
+هين سفر وهذه سفر إذا اللي في النص قطعنش هتكون سفر
+
+230
+00:17:25,070 --> 00:17:28,650
+ومعناته ال X أشبتها سوى Z so the limit is unique
+
+231
+00:17:28,650 --> 00:17:36,830
+ماشي الحل نيجي الآنلأ اللي هي بي الان ال بي بتقولك
+
+232
+00:17:36,830 --> 00:17:40,030
+إذا كانت x أن و y أن هذي converge ده ال x و هذي
+
+233
+00:17:40,030 --> 00:17:42,910
+converge ده ال y إذا المسافة بين ال converge ده
+
+234
+00:17:42,910 --> 00:17:48,490
+اللي هو المسافة بين اللي متين طيب برضه البرهان
+
+235
+00:17:48,490 --> 00:17:54,750
+هتجيب بمشي معنى زي الحلاوة و بكل سهولة إيش بقولنا
+
+236
+00:17:54,750 --> 00:18:01,770
+البرهان بقول التاليبقول نفرض أن Xn بتروح ل X و Yn
+
+237
+00:18:01,770 --> 00:18:05,170
+بتروح ل Y إيش معناة Xn بتروح ل X؟ يعني المسافة بين
+
+238
+00:18:05,170 --> 00:18:10,710
+Xn و Yn هذه المسافة بين Xn و X بيروح للصفر
+
+239
+00:18:10,710 --> 00:18:14,070
+والمسافة بين هذي و هذي بتروح لمين للصفر خلّيها نفل
+
+240
+00:18:14,070 --> 00:18:18,770
+جمال بعد شوية نستخدمهاالان تشوفوا الان xn و yn
+
+241
+00:18:18,770 --> 00:18:22,990
+المسافة بينهما أصغر أو سوى xn و x و x و mean و y و
+
+242
+00:18:22,990 --> 00:18:27,010
+y و yn استخدمت ال triangle inequality مرتين طبعا
+
+243
+00:18:27,010 --> 00:18:31,990
+في الي سبب انه عشان أثبتلكم ان xn و yn ناقص x و y
+
+244
+00:18:31,990 --> 00:18:35,550
+المسافة بينها absolute value أصغر أو سوى هذه
+
+245
+00:18:35,550 --> 00:18:38,330
+المسافة هذه هتروح لصفر و هذه كصفر معناته خلصت
+
+246
+00:18:38,330 --> 00:18:39,190
+دعونا نشوف كده
+
+247
+00:18:42,080 --> 00:18:45,180
+الان بال triangle inequality طلعت عندي هذه hence
+
+248
+00:18:45,180 --> 00:18:51,060
+جي بيها ديها بيصير عند المسافة هيها هيها هيها هيها
+
+249
+00:18:51,060 --> 00:18:53,740
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+250
+00:18:53,740 --> 00:18:53,760
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+251
+00:18:53,760 --> 00:18:53,960
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+252
+00:18:53,960 --> 00:18:56,440
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+253
+00:18:56,440 --> 00:18:58,920
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+254
+00:18:58,920 --> 00:18:58,960
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+255
+00:18:58,960 --> 00:19:00,400
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+256
+00:19:00,400 --> 00:19:00,400
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+257
+00:19:00,400 --> 00:19:00,480
+هيها هيها هيها هيها هيها هيها هيها هيها هيها هيها
+
+258
+00:19:00,480 --> 00:19:07,970
+هيها هيها هيها هيبقدر اللي هو أخد المسافة أثبت أن
+
+259
+00:19:07,970 --> 00:19:13,590
+المسافة بين x و y ناقص xn و yn أصغر من المسافة بين
+
+260
+00:19:13,590 --> 00:19:20,150
+x و xn أو ناقص المسافة عشان أثبت لكم أنا اللي بدي
+
+261
+00:19:20,150 --> 00:19:24,290
+أثبته اللي هو absolute value ال absolute value
+
+262
+00:19:24,290 --> 00:19:32,170
+distance بين xnو Yn نقص المسافة بين X و Y أصغر أو
+
+263
+00:19:32,170 --> 00:19:35,550
+يساوي هذي طبعا أكبر و يساوي سفر غرضي أثبتها أصغر
+
+264
+00:19:35,550 --> 00:19:43,490
+أو ساوي المسافة بين Xn و X زائد المسافة بين Yn و
+
+265
+00:19:43,490 --> 00:19:49,690
+100 و Y آسف بدون أفسنان أنت فاهم معايا؟ هذي هتروح
+
+266
+00:19:49,690 --> 00:19:52,150
+للسفر و هذي هتروح للسفر إذا هذي هيروح للسفر يكون
+
+267
+00:19:52,150 --> 00:19:57,480
+خلصتاللي أول واحدة عملتها اللي هي المسافة بين XN و
+
+268
+00:19:57,480 --> 00:20:01,880
+YN ناقص هذا أصغر أو ساوي هذه يعني بدي أثبتلكم أن
+
+269
+00:20:01,880 --> 00:20:06,940
+هذه أصغر أو ساوي هذه و بعدين اللي هو مفكوك هيش هذه
+
+270
+00:20:06,940 --> 00:20:10,440
+اللي هو على الجهة الثانية بالسالب بظبط يعني بدي
+
+271
+00:20:10,440 --> 00:20:16,520
+أعكسها بنعكسها بنفس الطريقة بتنعمل سهلة يعني بس ال
+
+272
+00:20:16,520 --> 00:20:19,720
+triangle inequality بنستخدمها بالشكل الثاني اللي
+
+273
+00:20:19,720 --> 00:20:25,590
+هو similarly DXY ناقص DXN YNاللي هي أصغر أو يساوي
+
+274
+00:20:25,590 --> 00:20:34,510
+دي إكس و إكس أن زائد دي وي أو وي أن إذا بيصير
+
+275
+00:20:34,510 --> 00:20:37,530
+بتدربيها في ناقص عكستها أنا عشان أدرب في ناقص لما
+
+276
+00:20:37,530 --> 00:20:41,070
+أدرب في ناقص بيصير ناقص هذا أصغر أو يساوي إكس أن و
+
+277
+00:20:41,070 --> 00:20:45,090
+وي أن و إكس و .. و مين و وي أنتوا فاهمين إيش
+
+278
+00:20:45,090 --> 00:20:48,450
+بيعمل؟ أنا بدي أجيب هذه بدي مبدأ هذه بدي أبدأ بإكس
+
+279
+00:20:48,450 --> 00:20:55,580
+و وي فاهمين؟أعملها الان بدل ان ابدأ بهذه ببدأ بال
+
+280
+00:20:55,580 --> 00:20:58,020
+X وY بحصل على نفسي الاشي هذه بانجله على الجهة
+
+281
+00:20:58,020 --> 00:21:01,000
+التانية بضربه في ناقص بالSeer المعقوسة هذه بالظبط
+
+282
+00:21:01,000 --> 00:21:04,480
+الSeer عندي اللي هو عبارة عن ناقص هذه أصغر وشاوي
+
+283
+00:21:04,480 --> 00:21:07,900
+هذه وفي الأصل أصغر وشاوي اللي هي الأصلية هذه إذا
+
+284
+00:21:07,900 --> 00:21:11,220
+صار ال absolute value أكبر وشاوي سفر وأصغر وشاوي
+
+285
+00:21:11,220 --> 00:21:15,960
+هذه الان هذه راحت للسفر وهذه راحت للسفر إذا هذه
+
+286
+00:21:15,960 --> 00:21:20,000
+راحت للسفر إذا DX عن وY عن بتروح ل DX وY ماشي
+
+287
+00:21:26,520 --> 00:21:30,900
+أذا نعرف الـ Cauchy Sequence أكيد اتوقعتوها بس
+
+288
+00:21:30,900 --> 00:21:33,680
+شيلوا absolute ده اللي حطوه بدلها الـD
+
+289
+00:21:37,650 --> 00:21:40,810
+بنقول إن Xn كوشي سيكوينس إذا اتحقق اللي التالي for
+
+290
+00:21:40,810 --> 00:21:43,530
+every y أكبر من سفر there exists k element in n
+
+291
+00:21:43,530 --> 00:21:48,010
+such that for every n و m أكبر أو يساوي k عندي
+
+292
+00:21:48,010 --> 00:21:53,290
+بيكون ال absolute value لل Xn نقص ال Xn أصغر من
+
+293
+00:21:53,290 --> 00:21:58,610
+مين؟ من أبسلون، مظبوط ولا لا؟ هذا اللي كنا نحكيه
+
+294
+00:21:58,610 --> 00:22:05,240
+زمان في الريال، بس خيانة، حطوا Dو بس دي xn و كده
+
+295
+00:22:05,240 --> 00:22:10,940
+بس هي كل الجثة اذا عشان ما نغلبكم مش بنقول a
+
+296
+00:22:10,940 --> 00:22:14,160
+sequence xn in a metric space xz is said to be
+
+297
+00:22:14,160 --> 00:22:17,260
+Cauchy if for every y أكبر من 0 there exists k
+
+298
+00:22:17,260 --> 00:22:21,080
+such that is مسافة بين xn و xm أصغر من y لكل n و m
+
+299
+00:22:21,080 --> 00:22:25,000
+أكبر من k the space x is called complete ال space
+
+300
+00:22:25,000 --> 00:22:29,380
+بنقول عنه complete space إذا كان every Cauchy
+
+301
+00:22:29,380 --> 00:22:35,980
+sequence convertsإذا بتذكروا في تحليل واحد لما
+
+302
+00:22:35,980 --> 00:22:38,520
+حكينا عن العلاقة بين الـ Cauchy Sequences والـ
+
+303
+00:22:38,520 --> 00:22:42,880
+Convergent Sequences قلنا أيش؟ قلنا Any Convergent
+
+304
+00:22:42,880 --> 00:22:46,140
+Sequences Cauchy وكان برهانة سهلهتلاقي البرهان
+
+305
+00:22:46,140 --> 00:22:51,600
+المشابه الآن العكس قلنا برضه بتحقق في R يعني اللي
+
+306
+00:22:51,600 --> 00:22:55,900
+هي الـ Cauchy convergent بس كانت اتغلبنا شوية في
+
+307
+00:22:55,900 --> 00:23:02,160
+البرهان خلينا نقول أصعب سنة بسيطة لكن كان برضه مش
+
+308
+00:23:02,160 --> 00:23:05,840
+صعب يعني وكأنه ليش أنا بقوليك وكأنه الآن على
+
+309
+00:23:05,840 --> 00:23:09,940
+تعريفي احنا بنقول ان ال space complete اذا كانت
+
+310
+00:23:09,940 --> 00:23:13,900
+every Cauchy sequence converge طب في R كانت هيك R
+
+311
+00:23:13,900 --> 00:23:17,660
+completeومش هيك وكمان في الـ C complete و الـ C
+
+312
+00:23:17,660 --> 00:23:20,380
+أشماله complete under the metric اللي احنا بتحكي
+
+313
+00:23:20,380 --> 00:23:22,960
+عنه ال usual metric اللي هو absolute value X minus
+
+314
+00:23:22,960 --> 00:23:28,020
+Y إذا صار في عندي مثلين اللي هو ال R و ال C على
+
+315
+00:23:28,020 --> 00:23:32,260
+complete metric spaces و هنشوف الباقي قدام ان شاء
+
+316
+00:23:32,260 --> 00:23:32,400
+الله
+
+317
+00:23:35,980 --> 00:23:38,560
+النقطة الأولى اللي قلتها هي الـ The real line and
+
+318
+00:23:38,560 --> 00:23:41,100
+the complex plane are complete metric spaces
+
+319
+00:23:52,240 --> 00:24:01,220
+ليش؟ لإن واحنا بنعرف اللي عندي لأي a في الـR بقدر
+
+320
+00:24:01,220 --> 00:24:07,080
+ألاقي sequence xn in R such that xn converts to
+
+321
+00:24:07,080 --> 00:24:10,420
+mean لليه، حتى بقدر ألاقي sequence of rational
+
+322
+00:24:10,420 --> 00:24:13,540
+numbers، ده حالي بس و بقدر ألاقي sequence of
+
+323
+00:24:13,540 --> 00:24:15,880
+irrational numbers، ده حالي، خلاص الكتابة لكل
+
+324
+00:24:15,880 --> 00:24:21,140
+واحدة فيهمإذا أنا في الواقع عندى لو شيلت من الارض
+
+325
+00:24:21,140 --> 00:24:26,440
+بضطر complete لإن لجيت هى ال sequence اللى هى xn
+
+326
+00:24:26,440 --> 00:24:33,460
+بتروح لليه هتكون false في الواقع فبتصير xn كوشي in
+
+327
+00:24:33,460 --> 00:24:41,810
+R ناقص مين ناقص ال a but its limitوما بدها تروح
+
+328
+00:24:41,810 --> 00:24:47,290
+للـ A مش موجودة في الـ R minus الـ A إذا هذا is
+
+329
+00:24:47,290 --> 00:24:52,130
+not a complete metric space و الـ Q كله under مين؟
+
+330
+00:24:52,130 --> 00:24:55,270
+under the usual metric اللي هو absolute value للـ
+
+331
+00:24:55,270 --> 00:25:03,730
+X minus Y الـ Q كمان مش complete لأنه ليش؟ لأنه لو
+
+332
+00:25:03,730 --> 00:25:07,710
+أجيت بقدر
+
+333
+00:25:07,710 --> 00:25:11,470
+ألاقي الـ sequenceاللي هو of rational numbers
+
+334
+00:25:11,470 --> 00:25:16,990
+converges لجدر التنين الجدر التنين مش موجود في الـ
+
+335
+00:25:16,990 --> 00:25:21,090
+Q إذا ما زال مش موجود في الـ Q، إذا صار عندك الـ
+
+336
+00:25:21,090 --> 00:25:24,590
+Cauchy sequence اللي هاد اللي converges لجدر
+
+337
+00:25:24,590 --> 00:25:30,350
+التنين في الـ R لكن اللي أمالها مش موجودة إذا إذا
+
+338
+00:25:30,350 --> 00:25:34,770
+إحنا لما نحكي عن الـ Cauchy sequenceهي في الواقع
+
+339
+00:25:34,770 --> 00:25:39,770
+سلوك سلوك هو تقريبا بتقدر تقولي هو نفس سلوك ال
+
+340
+00:25:39,770 --> 00:25:45,550
+convergence لكن بختلف في الآخر ان ال convergence
+
+341
+00:25:45,550 --> 00:25:51,540
+بيروح ل limit ال limit هذه إذا في ال spaceبصير إيه
+
+342
+00:25:51,540 --> 00:25:55,980
+أشمالها الـ sequence converges إذا مش في ال space
+
+343
+00:25:55,980 --> 00:26:01,420
+بظل كوشي لكن مش .. و هنا بحكم .. نحكم على ال space
+
+344
+00:26:01,420 --> 00:26:05,380
+انه complete أو لأ من خلال هذه الخاصية إذا ال ..
+
+345
+00:26:05,380 --> 00:26:09,920
+ال كوشي sequences هي في الواقع بتريحني أحيانا إنه
+
+346
+00:26:09,920 --> 00:26:13,860
+أنا أصلا مش عارف ال limitلكن أنا بعرف سلوك اللي هي
+
+347
+00:26:13,860 --> 00:26:17,980
+الـ sequence اللي لأ هي سلوك هي يا عم هذه سلوك
+
+348
+00:26:17,980 --> 00:26:21,340
+رايحة رايحة لإشي بتتكوم حوالين إشي ماشي الحال
+
+349
+00:26:21,340 --> 00:26:26,580
+فالان روحها حوالين نقطة معينة يمكن أني مايعرفوش
+
+350
+00:26:26,580 --> 00:26:30,830
+أنالكن ده عارف إن هما جعدات متكوّن من جانب بعض،
+
+351
+00:26:30,830 --> 00:26:35,490
+إذا سلوكهم إنه جعدات وكأنه كلهم بروح حوالهم منطقة
+
+352
+00:26:35,490 --> 00:26:38,730
+معينة و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+353
+00:26:38,730 --> 00:26:39,090
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+354
+00:26:39,090 --> 00:26:39,810
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+355
+00:26:39,810 --> 00:26:39,810
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+356
+00:26:39,810 --> 00:26:39,830
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+357
+00:26:39,830 --> 00:26:40,030
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+358
+00:26:40,030 --> 00:26:40,030
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+359
+00:26:40,030 --> 00:26:40,030
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+360
+00:26:40,030 --> 00:26:43,870
+و .. و .. و .. و
+
+361
+00:26:43,870 --> 00:26:55,480
+.. و ..فالان الـ Cauchy مهم عشان اللي هو يعني
+
+362
+00:26:55,480 --> 00:27:01,440
+أحيانا ماكنتش أعرف إيش ال limit فبتعامل مع اللي هو
+
+363
+00:27:01,440 --> 00:27:05,560
+العناصر بدل ما أتعامل مع ال limit و لكن في حال
+
+364
+00:27:05,560 --> 00:27:07,700
+وجود ال limit في ال space و كده بيصير ال space
+
+365
+00:27:07,700 --> 00:27:13,180
+أشماله is complete طيب theorem every convergent
+
+366
+00:27:13,180 --> 00:27:15,500
+sequence in a metric space is a Cauchy sequence
+
+367
+00:27:15,500 --> 00:27:21,960
+والبرنامج مشابهتها بعد تبع التحليلاللي بيقولوا أنه
+
+368
+00:27:21,960 --> 00:27:27,390
+لو فرضنا XN أي خلق تنسيق Xبالذات بتنهجوشي مدام xn
+
+369
+00:27:27,390 --> 00:27:30,390
+بتروح لل x إذا لكل y أكبر من 0 there exists k such
+
+370
+00:27:30,390 --> 00:27:34,190
+that اللي هو x المسافة بين xn و x أصغر من y على 2
+
+371
+00:27:34,190 --> 00:27:37,270
+for all n أكبر من k أصغر من أي أبسل في الدنيا من
+
+372
+00:27:37,270 --> 00:27:41,990
+جملة y على 2 هو دي للحسبة ومشروعة لإن هو أصلا
+
+373
+00:27:41,990 --> 00:27:45,190
+المسافة بين n وn تبقى لدرجة غيرها زي ما بده الآن
+
+374
+00:27:45,190 --> 00:27:51,270
+خدوا لكل m وm أكبر من k خدوا المسافة بين xn وxn
+
+375
+00:27:51,820 --> 00:27:56,080
+هتكون أصغر و نفسه و المسافة بين Xn و X زي المسافة
+
+376
+00:27:56,080 --> 00:28:01,700
+بين X و Xm وهذه من اللي فوق هنا أصغر و نفسه و نوع
+
+377
+00:28:01,700 --> 00:28:03,920
+اتنين زي اتنين و نفسه نوع اتنين و نفسه نوع اتنين و
+
+378
+00:28:03,920 --> 00:28:05,720
+نفسه نوع اتنين و نفسه نوع اتنين و نفسه نوع اتنين و
+
+379
+00:28:05,720 --> 00:28:07,900
+نفسه نوع اتنين و نفسه نوع اتنين و نفسه نوع اتنين و
+
+380
+00:28:07,900 --> 00:28:07,940
+نفسه نوع اتنين و نفسه نوع اتنين و نفسه نوع اتنين و
+
+381
+00:28:07,940 --> 00:28:10,440
+نفسه نوع اتنين و نفسه نوع اتنين و نفسه نوع اتنين و
+
+382
+00:28:10,440 --> 00:28:18,900
+نفسه نوع اتنين و نفسه نوع اتنين و نفسالان ها
+
+383
+00:28:18,900 --> 00:28:26,320
+theorem بيقول لـ let M بيقى metric space X وD then
+
+384
+00:28:26,320 --> 00:28:31,460
+الـ M بدي يبدأ يحول الحديث احنا لما .. في المحاضرة
+
+385
+00:28:31,460 --> 00:28:34,760
+اللي فاتت كنا نحكي لما كنا نحكي عن ال convergence
+
+386
+00:28:34,760 --> 00:28:41,890
+كنا نحول الحكي برضه ل sequence specificفي الـR أو
+
+387
+00:28:41,890 --> 00:28:46,130
+في الـC فكنا نشرود ناخد الـSequence اللي في الـP
+
+388
+00:28:46,130 --> 00:28:49,370
+كلها أنجول بتروح للـX ونربطها بالـConvergence لأن
+
+389
+00:28:49,370 --> 00:28:52,850
+لأ الآن بدر بطوركم بالـConvergence لأنه أعرف شو
+
+390
+00:28:52,850 --> 00:28:55,030
+معناه الـConvergence قبل ماكنتش عارف معناه
+
+391
+00:28:55,030 --> 00:28:58,740
+الـConvergence في الـMetric Spaceكنت أحول الدنيا
+
+392
+00:28:58,740 --> 00:29:01,000
+أروح و أديها لي ال convergence اللي في R تبع
+
+393
+00:29:01,000 --> 00:29:03,740
+الزمان لكن مش دايما هذا بظبط أو مش دايما أخلهم
+
+394
+00:29:03,740 --> 00:29:10,260
+أقول بسعثني الآن بدي أحول كل الآن الحديث من ال
+
+395
+00:29:10,260 --> 00:29:15,420
+unconvergence إلى sequences يعني المفهوم القاسي في
+
+396
+00:29:15,420 --> 00:29:20,240
+ال closure من ال closure اللي هو بواسطة ال balls
+
+397
+00:29:20,240 --> 00:29:26,470
+إلى حكي بواسطة ال sequences وده أسهلنابدأ قول let
+
+398
+00:29:26,470 --> 00:29:32,310
+M be anonymous if and only
+
+399
+00:29:32,310 --> 00:29:35,230
+if there exists a sequence xn in M such that xn
+
+400
+00:29:35,230 --> 00:29:39,990
+بتروح لمين لل X إذن الآن بنقول إن ال X في ال M
+
+401
+00:29:39,990 --> 00:29:44,650
+closure معناته أنه بقدر ألاقي sequence في ال M
+
+402
+00:29:44,650 --> 00:29:50,160
+وعامالها كلها ال sequence بتروح لمين لل Xأه إذا ال
+
+403
+00:29:50,160 --> 00:29:55,200
+M هذه متكرب سا .. ال .. ال XM متكرب سا حوالين ال X
+
+404
+00:29:55,200 --> 00:29:59,940
+و XM ناقف ال M إذا أكيد هي limit point جوا هذا
+
+405
+00:29:59,940 --> 00:30:05,110
+رفلي الكلام تشوف الكلام هذا بالتفصيل الأنالآن بدنا
+
+406
+00:30:05,110 --> 00:30:07,650
+نعرف اللي هو الـ M closed برضه بمانعش نقعد نقول
+
+407
+00:30:07,650 --> 00:30:10,550
+والله الـ compliment لها اه بانه نقعد نفحص انه اه
+
+408
+00:30:10,550 --> 00:30:13,270
+بان معناته انه خدوا اي نقطة و بتلاقوا اه اه نبرهو
+
+409
+00:30:13,270 --> 00:30:15,350
+جواتها يكون كله في جوات اللي هي الـ M compliment
+
+410
+00:30:15,350 --> 00:30:20,370
+لأ أسهلنا أسهلنا نحكي عن Sequences M is closed if
+
+411
+00:30:20,370 --> 00:30:23,170
+and only if the situation X and element in M و X
+
+412
+00:30:23,170 --> 00:30:28,050
+and بتروح لل X and why is that X element in M يعني
+
+413
+00:30:28,050 --> 00:30:32,800
+بقول ليهM Closed إذا تحقق الشرط التاني إنه لو أخدت
+
+414
+00:30:32,800 --> 00:30:37,060
+أي Sequence XN في الـ M وكانت هذه Sequence
+
+415
+00:30:37,060 --> 00:30:42,000
+Converged لازم تقعد وين؟ في داخل الـ M ماشي الحال
+
+416
+00:30:42,000 --> 00:30:45,180
+إذا تمتعت بهذا الخاصية على طول M is Closed يعني
+
+417
+00:30:45,180 --> 00:30:48,760
+عشان نحكوا إن عمل M Closed أه ولا لأ باجي باخد أي
+
+418
+00:30:48,760 --> 00:30:55,360
+Sequence XN في الـ M و تكون XN بتروح لل X هذا كله
+
+419
+00:30:55,360 --> 00:31:00,140
+على بعض يعطينا إن X في الـ Mهذا معناته إنه صارت
+
+420
+00:31:00,140 --> 00:31:05,340
+الـ M is closed ولو كانت M is closed برضه لو جي
+
+421
+00:31:05,340 --> 00:31:08,320
+تأخدت أي sequence XN في الـ M وكانت XN بتروح لل X
+
+422
+00:31:08,320 --> 00:31:12,480
+لازم تعطي الـ X mean في داخلها واضح؟ هذا ال test
+
+423
+00:31:12,480 --> 00:31:19,120
+لل convergence للـ M is closed ولا لأ طيب نيجي إلى
+
+424
+00:31:19,120 --> 00:31:24,740
+اللي هو الأولى let X element mean أن M closure في
+
+425
+00:31:24,740 --> 00:31:28,970
+عندي حالتينإذا كانت X في الـ M، ادّيني سهلة، مين
+
+426
+00:31:28,970 --> 00:31:32,430
+باخدها الـ sequence؟ X، X، X، X، X، X، X، X، X، X،
+
+427
+00:31:32,430 --> 00:31:34,550
+X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X،
+
+428
+00:31:34,550 --> 00:31:37,850
+X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X،
+
+429
+00:31:37,850 --> 00:31:37,990
+X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X،
+
+430
+00:31:37,990 --> 00:31:39,050
+X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X،
+
+431
+00:31:39,050 --> 00:31:39,870
+X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X، X،
+
+432
+00:31:39,870 --> 00:31:43,710
+X،
+
+433
+00:31:43,710 --> 00:31:47,350
+X، Xمش في الـ M إذا نوعها بده تكون في الـ
+
+434
+00:31:47,350 --> 00:31:53,090
+accumulation points if X is not element of M it is
+
+435
+00:31:53,090 --> 00:31:56,210
+accumulation point of M ايش معناه accumulation
+
+436
+00:31:56,210 --> 00:32:02,710
+point يعني لكل نيبرود في الدنيا لكل نصف قطر بتاخد
+
+437
+00:32:02,710 --> 00:32:07,120
+أنصاف الأقطار اسمه 1 على Nلأي نسخة و تربسة أننا
+
+438
+00:32:07,120 --> 00:32:09,680
+ناخد أنصاف الأكترسمين واحدة لأن ده سواء أخد نسخة و
+
+439
+00:32:09,680 --> 00:32:14,280
+ترسم واحد و نص و تلت و ربع و خمس و ستس و في كل
+
+440
+00:32:14,280 --> 00:32:19,600
+حاجة حلاجة اللي هو element فيه موجود فآنتقاطعه لا
+
+441
+00:32:19,600 --> 00:32:24,360
+يساوي فاي ما أنا ايا الان hence for each n element
+
+442
+00:32:24,360 --> 00:32:29,420
+in n بيكس و نصف قطر واحد الان تقاطع مع الان اشماله
+
+443
+00:32:29,420 --> 00:32:33,540
+لا يساوي فاي ماشي الحاجة واحد يقول ليه ما هو شيء
+
+444
+00:32:33,540 --> 00:32:36,660
+لل X انت طب هي اصلا ال X مش في ال M مش في ال M
+
+445
+00:32:36,660 --> 00:32:41,040
+اصلا طبيعي مش هي اللي هتطلع التقاطع فاهمين اه طيب
+
+446
+00:32:41,040 --> 00:32:45,020
+so there exist x n element in b x واحد و الان
+
+447
+00:32:45,020 --> 00:32:51,920
+تقاطع مين ال M اذاPx1 لجت فيها x1 Px نص لجت فيها
+
+448
+00:32:51,920 --> 00:32:57,520
+x2 Px تلت لجت فيها x3 Px ربع لجت فيها x4 و هكذا
+
+449
+00:32:57,520 --> 00:33:01,900
+لأن هذا الكلام صحيح لمين لكل n بيجيلها xn المقابلة
+
+450
+00:33:01,900 --> 00:33:05,580
+اللي موجودة في التقاطع إذا صارت المسافة بين xn و x
+
+451
+00:33:05,580 --> 00:33:10,160
+أصغر من مين من 1 ل n في كل حالة لأن as n goes to
+
+452
+00:33:10,160 --> 00:33:14,040
+infinity و 1 hundred تروحللصفر وهذه بيصير مدام
+
+453
+00:33:14,040 --> 00:33:15,360
+هترا هترا هترا هترا هترا هترا هترا هترا هترا هترا
+
+454
+00:33:15,360 --> 00:33:15,480
+هترا هترا هترا هترا هترا هترا هترا هترا هترا هترا
+
+455
+00:33:15,480 --> 00:33:16,660
+هترا هترا هترا هترا هترا هترا هترا هترا هترا هترا
+
+456
+00:33:16,660 --> 00:33:17,220
+هترا هترا هترا هترا هترا هترا هترا هترا هترا هترا
+
+457
+00:33:17,220 --> 00:33:23,980
+هترا هترا هترا هترا هترا هترا هترا هترا هترا هترا
+
+458
+00:33:23,980 --> 00:33:25,400
+هترا هترا هترا هترا هترا هترا هترا هترا هترا هترا
+
+459
+00:33:25,400 --> 00:33:29,980
+هترا هترا هترا هترا هترا هترا هترا هترا هترا هترا
+
+460
+00:33:31,090 --> 00:33:34,450
+واضح هذا الان الاتجاه الأول لما ال X في ال M
+
+461
+00:33:34,450 --> 00:33:38,990
+closure بيعطيني ل gate sequence في ال M حيث ان XN
+
+462
+00:33:38,990 --> 00:33:44,930
+بتروح ل X نيجي الآن conversely suppose that ان
+
+463
+00:33:44,930 --> 00:33:50,670
+الخاصية هذه تتحقق بدنا نثبت ان لو اتحققت هذه هتكون
+
+464
+00:33:50,670 --> 00:33:59,760
+ال X موجودة في ال M closure طيب يا جماعةالان بنقول
+
+465
+00:33:59,760 --> 00:34:06,220
+conversely suppose that xn وين موجودة في ال M و ال
+
+466
+00:34:06,220 --> 00:34:10,460
+xn converge لمين؟ لل x بيثبتلكم ال x وين موجودة في
+
+467
+00:34:10,460 --> 00:34:15,120
+ال M closure فبنخلصنا لأن if x element in M إذا x
+
+468
+00:34:15,120 --> 00:34:20,140
+element in M closure خلصنا ماشي الحال أنا غلط
+
+469
+00:34:20,140 --> 00:34:23,480
+أثبتها في ال M closure لو كانت x مش اللي أه في ال
+
+470
+00:34:23,480 --> 00:34:25,600
+M بيثبتلكم إن ال X هتكون إيه شمال a little bit
+
+471
+00:34:25,600 --> 00:34:30,490
+word ماشيلو أثرت أنها limit point معناه أنها
+
+472
+00:34:30,490 --> 00:34:35,210
+موجودة في الـ M closure بكون خلصت الآن مدام X مش
+
+473
+00:34:35,210 --> 00:34:40,170
+في الـ M إذا لكل Y و أنا عند XN بتروح لمين؟ XN
+
+474
+00:34:40,170 --> 00:34:44,370
+بتروح لل X إذا لكل Y أكبر من صفر بقدر ألاقي K بحيث
+
+475
+00:34:44,370 --> 00:34:47,850
+أن المسافة بين هذه و هذه أشمالها أزر من الـ Y لكل
+
+476
+00:34:47,850 --> 00:34:53,410
+M أكبر من K إذا الآن من هذهبكون حصلت اللي بديها
+
+477
+00:34:53,410 --> 00:34:56,570
+ايش اللي حصلت اللي بديها بقولكم hence for every y
+
+478
+00:34:56,570 --> 00:35:01,030
+أكبر من 0 بقدر ألاقي k بحيث أن ال ball اللي فيها x
+
+479
+00:35:01,030 --> 00:35:06,230
+و y نصف قطرها y المسافة بين ال xn اللي هي ال xn
+
+480
+00:35:06,230 --> 00:35:10,790
+نات هايها بين ال xn و ال x ما انها أصغر من y كل ال
+
+481
+00:35:10,790 --> 00:35:17,170
+n أكبر من k يعني هذه فيها مين فيها xk زائد واحد و
+
+482
+00:35:17,170 --> 00:35:21,840
+xk زائد اتنينو XK زيادة تلاتة و XK زيادة أربعة كل
+
+483
+00:35:21,840 --> 00:35:25,260
+هين موجودة هنا لو شيلت منهم X تقاطع لهم أكيد A
+
+484
+00:35:25,260 --> 00:35:28,960
+شمالهم لا يساوي فيه لأنهم كل ال XK و XK زيادة واحد
+
+485
+00:35:28,960 --> 00:35:31,880
+و XK زيادة اتنين كل هين موجودة في الأصل في الام
+
+486
+00:35:31,880 --> 00:35:34,080
+مازالت موجودة هنا موجودة في الأم ماذا ما تقاطعوا
+
+487
+00:35:34,080 --> 00:35:38,040
+احد اشماله لا يساوي فيه إذا ال X وين موجودة في
+
+488
+00:35:38,040 --> 00:35:45,240
+الام مكلوجر إذا بكون خلصنا الجزء الأول نتيجي الآن
+
+489
+00:35:45,240 --> 00:35:46,500
+من B
+
+490
+00:35:48,780 --> 00:35:55,360
+الان بيه من اللي فوق عندي M is closed if and only
+
+491
+00:35:55,360 --> 00:36:00,320
+if ال M مش ميزه تساوي ال M closure مظبوط M is
+
+492
+00:36:00,320 --> 00:36:04,200
+closed اذا كانت اذا و فقط اذا M بيساوي M closure و
+
+493
+00:36:04,200 --> 00:36:08,440
+M بتساوي M closure و هذه سهل اتباعتها لو تبتوها من
+
+494
+00:36:08,440 --> 00:36:14,010
+الاصل كمان سهل اتباعتهاالآن M بيتساوى M closure if
+
+495
+00:36:14,010 --> 00:36:19,190
+and only if the situation Xn بتروح لل X that means
+
+496
+00:36:19,190 --> 00:36:24,730
+X element in M هذا منذ قبل بشوية أنه لما تكون Xn
+
+497
+00:36:24,730 --> 00:36:28,590
+بتروح لل X و Xn في ال M تعطين X element in M هذا
+
+498
+00:36:28,590 --> 00:36:33,510
+if and only if إيه شمالها؟ اللي هو ال X موجودة في
+
+499
+00:36:33,510 --> 00:36:37,210
+ال M closure إذن الآن عندي M is closed if and only
+
+500
+00:36:37,210 --> 00:36:45,720
+ifاللي هو مين اللي قبل بشوية مش اللي قبل بشوية
+
+501
+00:36:45,720 --> 00:36:46,660
+احنا اثبتناها
+
+502
+00:36:49,310 --> 00:36:52,090
+اللي هو X المتقن عام الـ closure if and only if
+
+503
+00:36:52,090 --> 00:36:56,450
+الـ sequence X المتروح للـ X أه طيب الآن if and
+
+504
+00:36:56,450 --> 00:36:58,250
+only if أم is closed if and only if أم سواء الـ
+
+505
+00:36:58,250 --> 00:37:01,630
+closure معناته ال .. ال .. ال .. كل اللي في الأم
+
+506
+00:37:01,630 --> 00:37:04,950
+إيه شمع الوجودات في الأم ال closure معناته اللي هو
+
+507
+00:37:04,950 --> 00:37:09,510
+اللي هو هذا ال .. هذا الكلام بيعطينا أن هذا يتحقق
+
+508
+00:37:09,510 --> 00:37:13,150
+وزمان هذا يتحقق إذا هذا يؤدي لهذا ويكون عندنا
+
+509
+00:37:13,150 --> 00:37:16,650
+خلصنا اللي هي بيه أي سؤال طيب اللي بعدها
+
+510
+00:37:21,190 --> 00:37:30,350
+theorem مش مطولى ان شاء الله theorem a subspace
+
+511
+00:37:30,350 --> 00:37:33,770
+M of a complete metric space X is itself complete
+
+512
+00:37:33,770 --> 00:37:39,030
+if and only if the set M is closed طبعا احنا فيه
+
+513
+00:37:39,030 --> 00:37:44,030
+تفاصيل قدام ان
+
+514
+00:37:44,030 --> 00:37:46,830
+لو كانت ال space
+
+515
+00:37:49,250 --> 00:37:53,950
+م closed مش شرط يكون complete لو كان ال space
+
+516
+00:37:53,950 --> 00:38:01,510
+closed مش شرط يكون complete لكن
+
+517
+00:38:01,510 --> 00:38:11,670
+لو كان احنا بنحكي عن subspace M of a complete
+
+518
+00:38:11,670 --> 00:38:18,890
+metric space Xis itself complete if and only if M
+
+519
+00:38:18,890 --> 00:38:24,310
+أشماله is closed in X يعني الآن بالظبط الحالة كيف
+
+520
+00:38:24,310 --> 00:38:33,430
+أنه أنا عايش عايش في إيش في complete metric space
+
+521
+00:38:33,430 --> 00:38:39,570
+بصير عندي ال subspace M عشان أحكم عليه complete
+
+522
+00:38:39,570 --> 00:38:44,180
+ولا لأ بس بال closedإذا كان مقفل فهو مقفل وإذا كان
+
+523
+00:38:44,180 --> 00:38:54,020
+مقفل فهو مقفل إذا كان مقفل فهو
+
+524
+00:38:54,020 --> 00:38:54,420
+مقفل فهو مقفل إذا كان مقفل فهو مقفل إذا كان مقفل
+
+525
+00:38:54,420 --> 00:38:56,400
+فهو مقفل إذا كان مقفل فهو مقفل إذا كان مقفل فهو
+
+526
+00:38:56,400 --> 00:38:57,940
+مقفل إذا كان مقفل فهو مقفل إذا كان مقفل فهو مقفل
+
+527
+00:38:57,940 --> 00:39:00,200
+إذا كان مقفل فهو مقفل إذا كان مقفل فهو مقفل إذا
+
+528
+00:39:00,200 --> 00:39:04,500
+كان مقفل فهو مقفل إذا كان مقفل فهو مقفل إذا كان
+
+529
+00:39:04,500 --> 00:39:08,640
+مقفل فهو مقفل إذا كان مقفل فهو مقفل إذا كان مقف
+
+530
+00:39:10,310 --> 00:39:15,010
+نجلة اللي هو أو فيها مثلها طبعا أو حتى جابولها في
+
+531
+00:39:15,010 --> 00:39:19,290
+الخلال اللي هي الأسئلة اللي عندكم ماشي نجاوبها كل
+
+532
+00:39:19,290 --> 00:39:24,710
+شي suppose that M is إيه الشمالها complete and X
+
+533
+00:39:24,710 --> 00:39:33,260
+element in M closure ماشي then by theorem 1 4 7A,
+
+534
+00:39:33,260 --> 00:39:37,880
+there is a sequence xn in M such that xn بتروح للX
+
+535
+00:39:37,880 --> 00:39:40,940
+خلاص أنا بناعرف الترجم سيلنا لما X تكون في الـ M
+
+536
+00:39:40,940 --> 00:39:45,680
+closure معناته في sequence xn in M و الـ xn بتروح
+
+537
+00:39:45,680 --> 00:39:49,400
+لمين خلاص هذا بيصير سلوكة أننا بناسيه الترجم فيه
+
+538
+00:39:49,400 --> 00:39:54,700
+بسهل علينا الأمور كتير إذا الاجانب
+
+539
+00:39:54,700 --> 00:39:58,490
+sequence xn بتروح لمين لل Xما دام Xn convergence
+
+540
+00:39:58,490 --> 00:40:02,310
+لسة عامة قبل شوية قلنا hence Xn إيش ما لها is كوشي
+
+541
+00:40:02,310 --> 00:40:07,890
+لكن M is complete لكن M is complete و Xn كوشي في
+
+542
+00:40:07,890 --> 00:40:11,930
+ال M إذا أكيد أكيد limit هو M هيكون في ال M لأنها
+
+543
+00:40:11,930 --> 00:40:16,570
+complete إذا X موجودة في ال M إذا بدأت الآن عندي X
+
+544
+00:40:16,570 --> 00:40:19,870
+في ال M closure و لجأت هوي موجودة في ال M ماعناته
+
+545
+00:40:19,870 --> 00:40:23,830
+ال M إيش و ده تساوي M closure لأن M دايما subset
+
+546
+00:40:23,830 --> 00:40:28,500
+من M closure أثبتلكم أن M closure subset من Mماشي،
+
+547
+00:40:28,500 --> 00:40:30,480
+إذا صحيح M بيسوي M كله وجهة محددة معينة و M
+
+548
+00:40:30,480 --> 00:40:37,220
+أشمالها is a closed set، conversely بدي أفترض M
+
+549
+00:40:37,220 --> 00:40:43,780
+بيه a closed set و أفترض إن Xn بيه any Cauchy
+
+550
+00:40:43,780 --> 00:40:49,780
+sequence in M بدي أثبت لكم M is complete يعني الـ
+
+551
+00:40:49,780 --> 00:40:51,420
+Cauchy sequence اللي بدي أثبت هنا أشمالها
+
+552
+00:40:51,420 --> 00:40:58,950
+converges طيبمدام عندي xn كوشي in .. in .. in ..
+
+553
+00:40:58,950 --> 00:41:04,950
+in M وعندي اللي هي ال .. ال .. ال .. ال space كله
+
+554
+00:41:04,950 --> 00:41:09,910
+complete xn مظبوط هنا كوشي فيها دي لإن هي موجودة
+
+555
+00:41:09,910 --> 00:41:13,910
+في ال space كله المكبير إذا xn صارت كوشي sequence
+
+556
+00:41:13,910 --> 00:41:18,130
+و M في ال complete space X إذا لازم يكون في عندي x
+
+557
+00:41:18,130 --> 00:41:24,560
+في ال X such that xn بتروح لميليينلكن انا بقول ان
+
+558
+00:41:24,560 --> 00:41:31,420
+ال subspace M is closed اذا
+
+559
+00:41:31,420 --> 00:41:35,620
+اي sequence فيها بتروح ل X لازم X وير تكون في ال M
+
+560
+00:41:35,620 --> 00:41:40,660
+اذا X وير موجودة في ال M اذا صار is complete كمان
+
+561
+00:41:40,660 --> 00:41:48,200
+مرة شوفكم زي اللي بلعته الآن عند M ايش مارها is
+
+562
+00:41:48,200 --> 00:42:01,020
+closedبتثبتلكم ان هناك
+
+563
+00:42:01,020 --> 00:42:10,300
+هلونة ون في الام كوشي نمأزكيب Xn بزوء من موجودة في
+
+564
+00:42:10,300 --> 00:42:14,360
+الـM معناته موجودة في الـX إذا صارت Xn كوش في مين؟
+
+565
+00:42:14,360 --> 00:42:18,880
+في الـX والـX Complete إذا لازم يكون في علدي اللي
+
+566
+00:42:18,880 --> 00:42:23,360
+هو X بحيث ان Xn بتروح لمين؟ الـX موجود هدى؟ في
+
+567
+00:42:23,360 --> 00:42:28,870
+الـXلكن أنا بقول إن M نفسه Closed وبيقول لك الـ
+
+568
+00:42:28,870 --> 00:42:32,750
+Closed إن أي شيء Sequence عندي بتروح لل X لازم
+
+569
+00:42:32,750 --> 00:42:36,590
+تيجي الـ X تبقيتها عندي عشان أظل Closed فإذن صارت
+
+570
+00:42:36,590 --> 00:42:40,350
+الـ X هنا موجودة في الـ M إذن صارت اللي هي بدينا
+
+571
+00:42:40,350 --> 00:42:44,110
+بـ Cauchy Sequence هنا وانتهينا بالـ Cauchy
+
+572
+00:42:44,110 --> 00:42:49,470
+Sequence Conversion فيها إذن M is Complete واضح؟
+
+573
+00:42:49,470 --> 00:43:02,130
+المفروض واضحنيجي لا firm 149 I'm
+
+574
+00:43:02,130 --> 00:43:09,210
+having T من X لعند Yof a metric space XOD into a
+
+575
+00:43:09,210 --> 00:43:13,570
+metric space YOD is continuous at X0 if and only
+
+576
+00:43:13,570 --> 00:43:18,850
+if Xn بتروح لل X0 implies دي Xn بتروح لمين؟ لل TX0
+
+577
+00:43:18,850 --> 00:43:22,130
+نظرية الصحيحة اللي بنعرفها دي عنا زمان في ال
+
+578
+00:43:22,130 --> 00:43:26,290
+continuity بنحول الحديث في ال continuity من limit
+
+579
+00:43:26,290 --> 00:43:30,770
+F of X as X بتروح ل X0 بيساوي F of X0 إلى لغة ال
+
+580
+00:43:30,770 --> 00:43:35,460
+sequencesيعني بنقول الآن ميزان .. الميزان تبع الـ
+
+581
+00:43:35,460 --> 00:43:41,480
+continuity عند نقطة X note بدي يكون كالتالي بنقول
+
+582
+00:43:41,480 --> 00:43:56,720
+أنه أنه T is continuous T من X لعند Y continuous
+
+583
+00:43:56,720 --> 00:44:02,910
+at X noteإذا و فقط إذا شوفوا مزار ال continuity
+
+584
+00:44:02,910 --> 00:44:06,850
+الآن أنه .. ال sequences بتجيبوا أنه لو جينا أخدنا
+
+585
+00:44:06,850 --> 00:44:13,570
+أي xn بتروح لل x لازم هذا يعطيني ال T xn بتروح لل
+
+586
+00:44:13,570 --> 00:44:18,510
+T x naught إذا هذا تحقق automatic ال T هتكون
+
+587
+00:44:18,510 --> 00:44:22,500
+continuous عند main عند x naughtولو الـ T
+
+588
+00:44:22,500 --> 00:44:27,600
+continuous عند X0 لازم يتحقق التالي إنه لما أخد XN
+
+589
+00:44:27,600 --> 00:44:32,380
+بتروح لل X على طول تقول لي الـ TXN بتروح لمين لـ
+
+590
+00:44:32,380 --> 00:44:37,920
+TX0 وهذا اللي هو هوية الـ continuity للـ T زي ما
+
+591
+00:44:37,920 --> 00:44:41,800
+هويتها التعريف التابع الزمان اللي هو limit F of X
+
+592
+00:44:41,800 --> 00:44:45,320
+لما X بتروح ل X0 بسوء F of X0 هذه هويتها أو limit
+
+593
+00:44:45,320 --> 00:44:49,630
+T of X لما X بتروح ل X0 بسوء X0 هذه هويتهاهذا حتى
+
+594
+00:44:49,630 --> 00:44:52,470
+in general حتى في ال metric spaces ال convergence
+
+595
+00:44:52,470 --> 00:44:55,710
+هذا مش convergence عادي ال convergence ايش في ال
+
+596
+00:44:55,710 --> 00:44:59,790
+metric D لو هذا D و هذا D prime ال convergence في
+
+597
+00:44:59,790 --> 00:45:06,570
+ال mean في ال D prime واضح نيجي اللي هو انبرهن
+
+598
+00:45:06,570 --> 00:45:11,950
+النظرية انبرهن النظرية و البرهان كمان لطيف و مش
+
+599
+00:45:11,950 --> 00:45:15,910
+صعب نشوف
+
+600
+00:45:15,910 --> 00:45:19,890
+ايش بتقول النظريةفي برهانها suppose that T is
+
+601
+00:45:19,890 --> 00:45:26,370
+continuous at X0 مادام continuous عند X0حسب الـ
+
+602
+00:45:26,370 --> 00:45:31,150
+Continuity اللي هو تعريف الـ Continuity إذا لكل Y
+
+603
+00:45:31,150 --> 00:45:34,290
+أكبر من 0 there exists Delta أكبر من 0 such that
+
+604
+00:45:34,290 --> 00:45:39,530
+DX و X0 أصغر من Delta بيؤدي ل D TX0 TX و TX0 أصغر
+
+605
+00:45:39,530 --> 00:45:43,390
+من 100 من إبسلون تعريف الـ Continuity تعريف الـ
+
+606
+00:45:43,390 --> 00:45:48,930
+Continuity إنه بيقول الـ function T continuous at
+
+607
+00:45:48,930 --> 00:45:55,700
+X0 مش عارف لتبع الزمان إنه limitف او T of X note
+
+608
+00:45:55,700 --> 00:46:01,840
+اذا X بتروح ل X note بسوة T of X صح؟
+
+609
+00:46:03,350 --> 00:46:06,890
+الان هذه ترجمته انه لكل epsilon لما تقترب المسافة
+
+610
+00:46:06,890 --> 00:46:09,870
+.. لما .. المسافة هذه تقترب .. النقطة ده تقترب من
+
+611
+00:46:09,870 --> 00:46:13,650
+هذه عبر مسافتها هذه بتقترب من هذه عبر مسافتها يعني
+
+612
+00:46:13,650 --> 00:46:16,070
+بمعنى اخر هذه .. اللي بدأنا نعبرها عن هذه ب delta
+
+613
+00:46:16,070 --> 00:46:18,610
+وهذه ب epsilon ثم بقول عبّر ده for every epsilon
+
+614
+00:46:18,610 --> 00:46:21,530
+أكبر من سفر there exists delta أكبر من سفر such
+
+615
+00:46:21,530 --> 00:46:25,350
+that if اللي هو .. اللي هو هذه ناقص هذه ميقولوش
+
+616
+00:46:25,350 --> 00:46:30,510
+عنها هيك بقول if dx و x not أصغر من delta then
+
+617
+00:46:31,830 --> 00:46:38,530
+هيكون عندى D تلده اللى هى المتر اتبعها TX و TX
+
+618
+00:46:38,530 --> 00:46:44,420
+Noteأصغر من إبسلون هذا اللي هو الcontinuity أو
+
+619
+00:46:44,420 --> 00:46:46,340
+اللي هو هذا التعبير بالبول زي اللي حكيناها في
+
+620
+00:46:46,340 --> 00:46:50,000
+الأول انه .. انه .. اللي هو .. انه .. لما تكون
+
+621
+00:46:50,000 --> 00:46:54,420
+اللي هو ال bowl اللي هنا اللي .. اللي .. اللي ..
+
+622
+00:46:54,420 --> 00:46:55,720
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+623
+00:46:55,720 --> 00:46:57,020
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+624
+00:46:57,020 --> 00:46:57,020
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+625
+00:46:57,020 --> 00:46:57,020
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+626
+00:46:57,020 --> 00:46:57,020
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+627
+00:46:57,020 --> 00:46:57,060
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+628
+00:46:57,060 --> 00:46:57,080
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+629
+00:46:57,080 --> 00:47:02,280
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+630
+00:47:02,280 --> 00:47:05,520
+اللي
+
+631
+00:47:05,520 --> 00:47:11,380
+.. اللكل X هنا بناجيها الـ TX تبعتها فاهمين ماحكيه
+
+632
+00:47:11,380 --> 00:47:17,780
+هون؟ ماشي طيب وصلّى على النبي عليه الصلاة والسلام
+
+633
+00:47:17,780 --> 00:47:21,860
+such that T is continuous at X0 then for every Y
+
+634
+00:47:21,860 --> 00:47:24,760
+أكبر من 0 there exists Delta أكبر من 0 such that
+
+635
+00:47:24,760 --> 00:47:28,220
+لما المسافة تضيق بين X وX0 أصغر من Delta بتعطين
+
+636
+00:47:28,220 --> 00:47:32,080
+المسافة المقابلة D تلد بين TX وDX أصغر من مين؟ من
+
+637
+00:47:32,080 --> 00:47:39,520
+Y ماشي؟الان بدي أثبتلكم لما Xn بتروح ل X0 يعطيني
+
+638
+00:47:39,520 --> 00:47:45,520
+TXn بتروح لمين TX0 سهل نفترض الآن Xn بتروح لمين لل
+
+639
+00:47:45,520 --> 00:47:50,000
+X0 إذا مدام Xn بتروح لل X0 إذا بقدر نلاقي K
+
+640
+00:47:50,000 --> 00:47:56,300
+element انلدلتة هذه إيش معنات Xn بتروح ل X0 لأي Y
+
+641
+00:47:56,300 --> 00:47:59,020
+أكبر من 0 في الدنيا بتاخدها لمين الآن؟ لإيش ..
+
+642
+00:47:59,020 --> 00:48:03,340
+لحاجة تخدمني؟ إيش اسمها Delta؟ ماشي؟ شو معناة Xn
+
+643
+00:48:03,340 --> 00:48:07,260
+بتروح ل X0 لكل Y أكبر من 0 there exists K element
+
+644
+00:48:07,260 --> 00:48:10,820
+in N such that اللي هو ال distance بين Xn و X0
+
+645
+00:48:10,820 --> 00:48:15,380
+أكثر من Y أكثر من Y لكل N أكبر سوى 100K اللي أنا
+
+646
+00:48:15,380 --> 00:48:19,540
+مانديش أخد لكل Y و أخد لDelta هذه اللي لجيتهاللـ
+
+647
+00:48:19,540 --> 00:48:23,040
+delta اللي لجيتها بدي أشتغل بدي أقول for delta
+
+648
+00:48:23,040 --> 00:48:27,960
+اللي لجيتها there exist K such that المسافة بين Xn
+
+649
+00:48:27,960 --> 00:48:33,600
+وX0 أصغر من الـ Delta لكل N أكبر من مين من Kإذا
+
+650
+00:48:33,600 --> 00:48:41,320
+مباشرة احنا قلنا اللي بتحقق هذا بيعطينا هذا لأن
+
+651
+00:48:41,320 --> 00:48:44,740
+هذا تحقق ال XN بعيد عن X Note بمسافة جال من Delta
+
+652
+00:48:44,740 --> 00:48:50,880
+إذا أكيد صورة من ال Delta تلدة بين TXN و TX Note
+
+653
+00:48:50,880 --> 00:48:57,260
+هتكون أصغر من 100من Epsilon إذا عندي المسافة دي
+
+654
+00:48:57,260 --> 00:49:00,260
+تلده بين TXN و TX0 أصغر من Epsilon فهو N أكبر سوء
+
+655
+00:49:00,260 --> 00:49:04,300
+K إيش معناته هذا أنه أنا بدأت بأي Epsilon في
+
+656
+00:49:04,300 --> 00:49:09,560
+الدنيا arbitrary اللي بدأت فيها أي Epsilon لجيت K
+
+657
+00:49:09,560 --> 00:49:13,780
+الآن بحيث أن المسافة بين TXN و TX0 أصغر من Epsilon
+
+658
+00:49:13,780 --> 00:49:18,180
+لكل N أكبر منين من K وهذا معناته أن TXN بتروح ل
+
+659
+00:49:18,180 --> 00:49:18,660
+TX0
+
+660
+00:49:27,640 --> 00:49:32,620
+Conversely نفرض أن الشرط تحقق و بدنا نثبت ال
+
+661
+00:49:32,620 --> 00:49:43,720
+continuity طيب
+
+662
+00:49:43,720 --> 00:49:50,560
+ConverselySuppose that xₙ converges to xₙ implies
+
+663
+00:49:50,560 --> 00:49:53,280
+that xₙ converges to xₙ بتروح لمين؟ لـ Txₙ بتدفع
+
+664
+00:49:53,280 --> 00:49:56,600
+الـ Continuity لان طيب، to prove that T is
+
+665
+00:49:56,600 --> 00:50:00,700
+continuous نفترض الـ Xₙ نستخدم الـ Contradiction
+
+666
+00:50:00,700 --> 00:50:05,520
+نفترض العكس و نصل لإيش؟ لتناقض أه، بدنا نفترض أن T
+
+667
+00:50:05,520 --> 00:50:10,040
+مش continuous عند ال XₙSuppose that T is not
+
+668
+00:50:10,040 --> 00:50:11,380
+continuous at X0
+
+669
+00:50:38,310 --> 00:50:42,470
+إذن يعني بمعنى آخر بقى كأني بدي أقول for every
+
+670
+00:50:42,470 --> 00:50:50,190
+واحد على N يعني for every N بقدر ألاقي XN بحيث أنه
+
+671
+00:50:50,190 --> 00:50:55,910
+المسافة بين XN و X0 تكون أصغر من Delta حسب هذاSuch
+
+672
+00:50:55,910 --> 00:50:59,890
+that d dxn و dx0 ايش مالها أكبر أو يساوي إبسلون
+
+673
+00:50:59,890 --> 00:51:04,310
+هذا إيش معناته هذا معناته هذي مدام أصغر من أي دلتا
+
+674
+00:51:04,310 --> 00:51:08,530
+في الدنيا معناته ال dxn بتروح لمين لل x note أو ال
+
+675
+00:51:08,530 --> 00:51:12,890
+xn بتروح لل x note لكن هذي بتعني إيش but dxn does
+
+676
+00:51:12,890 --> 00:51:18,210
+not converge to mean to dx0 وهذا يناقض المعطى thus
+
+677
+00:51:18,210 --> 00:51:24,080
+أو this contradicts the assumptiontherefore t is
+
+678
+00:51:24,080 --> 00:51:29,080
+continuous at x naught وهو المطلوب بيكون هيك احنا
+
+679
+00:51:29,080 --> 00:51:34,540
+خلصنا المحاضرة وعنا homework اللي هو اللي بدكم
+
+680
+00:51:34,540 --> 00:51:38,500
+تسلموه اللي هو star ستة و تمانية و ال homework
+
+681
+00:51:38,500 --> 00:51:42,880
+الباقي هذا بتحلو انتوا و بارك الله فيكم الله
+
+682
+00:51:42,880 --> 00:51:43,540
+يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/gwzFsK74bdc_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/gwzFsK74bdc_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..265051917101e54c1167f8dfd1498e26f08c1314
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/gwzFsK74bdc_postprocess.srt
@@ -0,0 +1,2764 @@
+1
+00:00:05,080 --> 00:00:08,520
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,520 --> 00:00:11,720
+والصلاة والسلام على سيد المسلم سيدنا محمد وعلى آله
+
+3
+00:00:11,720 --> 00:00:16,040
+وصحبه أجمعين اليوم إن شاء الله المحاضرة الثالثة في
+
+4
+00:00:16,040 --> 00:00:21,120
+مساق تحليل اقتراني لطلاب وطالبات الجامعة الإسلامية
+
+5
+00:00:21,120 --> 00:00:22,280
+مساق الماجستير
+
+6
+00:00:24,670 --> 00:00:29,530
+وصلنا لعند اللي هو ال section الثالث اللي هو 1.3
+
+7
+00:00:29,530 --> 00:00:33,470
+وفي هذا ال section طبعا الحديث هيكون حول اللي هو
+
+8
+00:00:33,470 --> 00:00:36,690
+العنوان open sets و closed sets و neighborhoods
+
+9
+00:00:36,690 --> 00:00:40,730
+وفي الواقع يعني هذا اللي هو يعني هيتم الحديث عن
+
+10
+00:00:40,730 --> 00:00:44,390
+مفاهيم topologية أو topological concepts أو
+
+11
+00:00:44,390 --> 00:00:48,270
+topological properties in the metric اللي هو SBS
+
+12
+00:00:48,610 --> 00:00:52,930
+هنشوف الموضوع الموضوع ان شاء الله سهل وان شاء الله
+
+13
+00:00:52,930 --> 00:00:57,390
+مش صعب الان نيجي للتعريف الأول ال definition أول
+
+14
+00:00:57,390 --> 00:01:02,750
+بده اعرف اللي هو لو جيت أخدت X وD متر كسباس و X
+
+15
+00:01:02,750 --> 00:01:06,950
+not اي X في ال .. في ال space وR positive real
+
+16
+00:01:06,950 --> 00:01:12,300
+numberDefine the sets الان بدي اعرف اللي هو B X0
+
+17
+00:01:12,300 --> 00:01:16,680
+وR اللي هي عبارة عن احرف حاجة اسمها open ball بنصف
+
+18
+00:01:16,680 --> 00:01:22,060
+قطر R واللي هو مركز X0 طبعا هتلاقوا اللي هو
+
+19
+00:01:22,060 --> 00:01:26,560
+التعريف اللي بحكي فيه تيمنا باللي احنا كنا نعرفه
+
+20
+00:01:26,560 --> 00:01:29,580
+ال open ball او ال closed ball او الاسفير اللي في
+
+21
+00:01:29,580 --> 00:01:34,290
+ال R تربيعالان انا لكن بحكي عن X وD in general هي
+
+22
+00:01:34,290 --> 00:01:38,670
+X وهي D X انا 6 وD مترك عليها فصار مترك space
+
+23
+00:01:38,670 --> 00:01:43,370
+واخدت X note موجودة في مين؟ في الـ X الان بدمثلكم
+
+24
+00:01:43,370 --> 00:01:48,650
+إياها بالرسم تامنا بالـ R تربية لكن هو كيف شكله
+
+25
+00:01:48,650 --> 00:01:51,910
+اللي هو ال ball في ال X وD ماعرفش كيف شكله لأن X
+
+26
+00:01:51,910 --> 00:01:54,670
+وD مش شرط ان يكون R او R تربية او رتقعيب او
+
+27
+00:01:54,670 --> 00:02:00,210
+الاخرين فالان عندي اللي هو بقول X note مركزوعندي
+
+28
+00:02:00,210 --> 00:02:04,630
+اللي هو النقاط اللي بتبعد ببعد R كل هذه النقاط هي
+
+29
+00:02:04,630 --> 00:02:09,710
+اللي بتسميها ال ball of X note وR إذا ال ball of X
+
+30
+00:02:09,710 --> 00:02:13,450
+note وR هي عبارة عن كل النقاط اللي من ال space X
+
+31
+00:02:13,450 --> 00:02:18,970
+التي تبعد وفق ال metric دي عندي بمسافة أقل من 100
+
+32
+00:02:18,970 --> 00:02:23,990
+من R هذا بتسميها أيهاش عبارة عن open ballاللي قال
+
+33
+00:02:23,990 --> 00:02:28,750
+closed ball similarly بس بدي ادخل فيها مين اللي هو
+
+34
+00:02:28,750 --> 00:02:34,010
+المحيط ان صح التعبير بدي ادخل اللي هي اقول B تلدة
+
+35
+00:02:34,010 --> 00:02:38,130
+of X0 وR هي عبارة عن كل الاكسات اللي في الـD اللي
+
+36
+00:02:38,130 --> 00:02:44,550
+بعضها عن X0 بمسافة تساوي او اقل اذا هذه بالاضافة
+
+37
+00:02:44,550 --> 00:02:49,830
+أيش للي بعضها متساوي عن X0 هذه بدي اسميها closed
+
+38
+00:02:49,830 --> 00:02:56,350
+ballالان التعريف الثالث اللي هو عبارة عن احنا
+
+39
+00:02:56,350 --> 00:02:59,130
+عرفنا الان اللي هو الـ open ball اللي جوا ال
+
+40
+00:02:59,130 --> 00:03:02,650
+closed ball اللي هنا اللي على اللي هي المساواة
+
+41
+00:03:02,650 --> 00:03:06,450
+بالاضافة للي جوا سميتها اللي هي closed ball الان
+
+42
+00:03:06,450 --> 00:03:12,670
+هذا لحاله هذا لحاله اللي هي المقاطالـ X في الـ X
+
+43
+00:03:12,670 --> 00:03:16,650
+اللي بتبعد عن X Note بمقدار بالظبط R هذا بدي
+
+44
+00:03:16,650 --> 00:03:19,230
+أسميها S of X Note وR و بدي أقول هي إيه إيه إيه
+
+45
+00:03:19,230 --> 00:03:20,690
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+46
+00:03:20,690 --> 00:03:22,150
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+47
+00:03:22,150 --> 00:03:22,790
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+48
+00:03:22,790 --> 00:03:23,810
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+49
+00:03:23,810 --> 00:03:31,710
+إيه إيه إيه إيه إيه إيه إيه إيه
+
+50
+00:03:31,710 --> 00:03:39,840
+إيه إطيب صلوا على النبي عليه الصلاة والسلام من
+
+51
+00:03:39,840 --> 00:03:43,940
+التعريف اللي جوه فوق و أثناء الحديث أكيد كلكم شاف
+
+52
+00:03:43,940 --> 00:03:48,120
+و قال و الله ما هو أصلا لو انت قلت B تلده و شنت
+
+53
+00:03:48,120 --> 00:03:52,200
+منها ال B هيطلع مين ال S يعني لو أخدت ال close
+
+54
+00:03:52,200 --> 00:03:56,080
+bone و شنت فيها البون اللي جوه حتى المين الجشرة
+
+55
+00:03:56,080 --> 00:03:59,800
+اللي برا اللي بمعنى أخر هي الاسفير عشان هيك اللي
+
+56
+00:03:59,800 --> 00:04:06,210
+في الملاحظة أسفل هنا from the definitionone can
+
+57
+00:04:06,210 --> 00:04:10,810
+easily see that S of X not of R بساوي الـ B تلدى
+
+58
+00:04:10,810 --> 00:04:16,490
+ناقص الـ B ماشي الحالة من الآن و طالع على أساس أنه
+
+59
+00:04:16,490 --> 00:04:20,650
+نتفج مع بعض بدي أبطل أظل أقول X و D metric space
+
+60
+00:04:20,650 --> 00:04:24,790
+خلاص لما أقول X بحاجة بقصد أن X عليها metric اسم
+
+61
+00:04:24,790 --> 00:04:27,790
+مين اسم دي على أساس أنه احنا بنضل عشان نغلب حالنا
+
+62
+00:04:27,790 --> 00:04:33,040
+و هيك توافقنا على أن X نقصد فيها X و Dطيب نيجي
+
+63
+00:04:33,040 --> 00:04:40,040
+الآن للتعريف واحد تلاتة اتنين التعريف بيقوللي اللي
+
+64
+00:04:40,040 --> 00:04:46,990
+انا بده يعرفلي اللي هو حاجة اسمها open setلما ندخل
+
+65
+00:04:46,990 --> 00:04:50,650
+لشكل ندخلين مدخل أنه بتعرف ال open set أنا عرفت
+
+66
+00:04:50,650 --> 00:04:53,950
+الأن ال open ball وعرفت ال closed ball وعرفت ال
+
+67
+00:04:53,950 --> 00:04:58,750
+sphere بتستعين بال open ball أن يعرف ال open set
+
+68
+00:04:58,750 --> 00:05:04,210
+وحتلاجيني في النهاية وصلت إلى إشي متوافق مع اللي
+
+69
+00:05:04,210 --> 00:05:07,190
+احنا بنعرفه في الأصل اللي هو مفهوم ال open set
+
+70
+00:05:07,190 --> 00:05:10,550
+سواء في التحليل أو حتى في ال topology in general
+
+71
+00:05:11,120 --> 00:05:16,160
+نأتي الآن نشوف أيش معنات اللي هو الـ 6 تكون Open
+
+72
+00:05:16,160 --> 00:05:24,620
+بنقول أن M هي M جزء من متر كسبية اسمه Xبقول أن الـ
+
+73
+00:05:24,620 --> 00:05:33,400
+M هذا أنها open set M is open إذا تحقق الشرط
+
+74
+00:05:33,400 --> 00:05:38,880
+التالي أنه لو أتيت أخدت أي X في الـ M أو X Note في
+
+75
+00:05:38,880 --> 00:05:44,060
+الـ M أخدت أي X Note في الـ M لازم ألاقي there
+
+76
+00:05:44,060 --> 00:05:48,900
+exists goalنصف مركزها الـ X note هذه اللي بدأت
+
+77
+00:05:48,900 --> 00:05:54,700
+فيها ونصف خطرها R تكون كلها جوات مين؟ جوات الـ M
+
+78
+00:05:54,700 --> 00:05:57,900
+لو لجيت الخاصية هذه على طول بقول ان الـ M إيه
+
+79
+00:05:57,900 --> 00:06:02,660
+شمالها؟ is an open set يعني a subset M of a metric
+
+80
+00:06:02,660 --> 00:06:08,410
+space X set to be openif it contains a ball about
+
+81
+00:06:08,410 --> 00:06:11,750
+each of its points يعني كل مقطة من نقاطها بلاقي
+
+82
+00:06:11,750 --> 00:06:16,450
+ball كلها جواتها a subset K بنسميه K it has closed
+
+83
+00:06:16,450 --> 00:06:21,230
+set إذا كانت مكملتها open هذه تعريف اللي بديها
+
+84
+00:06:21,230 --> 00:06:26,030
+لحظة هذه ممكن أنت تتخيلها كالتالي أنه لو أخدنا set
+
+85
+00:06:26,030 --> 00:06:31,200
+X ام اي setبقول عنها أنها open set إذا جيت أخدت
+
+86
+00:06:31,200 --> 00:06:34,260
+أنا طبعا احنا برسم برسم مكاني برسم في لعبة تربية
+
+87
+00:06:34,260 --> 00:06:37,260
+بس هو احنا بنحكي عن أي space لكن أنا بقرر بالكم
+
+88
+00:06:37,260 --> 00:06:41,460
+الصورة بالرسم ماشي لو بنقول عنها دي open set إذا
+
+89
+00:06:41,460 --> 00:06:45,560
+جيت أخدت أي نقطة X أي نقطة X وين وجودة؟ في ال M
+
+90
+00:06:45,560 --> 00:06:50,620
+بدي ألاقي open ball حواليها بنصف قطر R تكون كلها
+
+91
+00:06:50,620 --> 00:06:53,860
+ال open wall جوات مين؟ جوات ال M في هذا الحالة
+
+92
+00:06:53,860 --> 00:07:00,160
+بنقول M is an open set واضح ياطيب .. صلوا على
+
+93
+00:07:00,160 --> 00:07:05,130
+النبي عليه الصلاة والسلامعندي في تعريف واحدة تلاتة
+
+94
+00:07:05,130 --> 00:07:09,830
+قبلها خلّيني نشوف أيش الملاحظة اللي بيقولها it is
+
+95
+00:07:09,830 --> 00:07:14,470
+easy بيقول من السهل to see from the definition
+
+96
+00:07:14,470 --> 00:07:19,070
+above that the open balls is an open set and the
+
+97
+00:07:19,070 --> 00:07:21,990
+closed ball is a closed set انتبهوا علينا خلّيني
+
+98
+00:07:21,990 --> 00:07:25,910
+نشوف هذه بيقولوا انه من السهل انك تثبت انه اي open
+
+99
+00:07:25,910 --> 00:07:32,380
+ball open setبنشوف كلامه صحيح صحيح لكن بتنشوف اللي
+
+100
+00:07:32,380 --> 00:07:38,320
+هو كيف نثبت كلامه لو جينا أخدنا N اللي هو أخدنا ال
+
+101
+00:07:38,320 --> 00:07:44,100
+ball X note و Epsilon بدنا نشوف هذه كيف هي open
+
+102
+00:07:44,100 --> 00:07:47,760
+set ماشي الحال عشان نثبت إنها open
+
+103
+00:07:51,130 --> 00:07:55,610
+خلّينا نص خطرها R ليش نسميه Y ر نص خطرها R هي جي
+
+104
+00:07:55,610 --> 00:08:01,730
+تاخدت open pool هي نص اللي هو مركزها X node و نص
+
+105
+00:08:01,730 --> 00:08:07,870
+خطرها R ماشي الحال بدي أثبت أن هذه عبارة عن مين عن
+
+106
+00:08:07,870 --> 00:08:12,030
+open set عشان أثبت open إيش بدي أخد بدي أخد أي
+
+107
+00:08:12,030 --> 00:08:18,260
+نقطة في داخلها أي نقطة X في داخلهاوأناجي open ball
+
+108
+00:08:18,260 --> 00:08:23,380
+حواليها تكون كلها جواة مين جواة الست يعني أو هذا
+
+109
+00:08:23,380 --> 00:08:26,800
+الست لأ سميتها بي اكس نوت يعني جواة مين بي اكس نوت
+
+110
+00:08:26,800 --> 00:08:34,440
+وR راحظوا يعني بيدا لاجيلي بي واحد ball اللي هو
+
+111
+00:08:34,440 --> 00:08:40,620
+مركزها X ونصف قطرها H اللي أجمل يكون معله جواة ال
+
+112
+00:08:40,620 --> 00:08:43,820
+B of X نوت ومين وR
+
+113
+00:08:46,130 --> 00:08:50,790
+خُد الآن X أربترانية كلكم بالعين بيقولّي تدور على
+
+114
+00:08:50,790 --> 00:08:53,950
+نصف القطر اللي بيخلّي البُقْل حوالين هذا كله جوا
+
+115
+00:08:53,950 --> 00:08:58,690
+من البُقْل الكبيرة هذه الان واحد هيقولّي ابعد عن
+
+116
+00:08:58,690 --> 00:09:03,070
+هنا عن المسافة هذه بالمقدار هذا نصف القطر هذه
+
+117
+00:09:03,070 --> 00:09:07,290
+بتضمن انك تلاقيها جوا يعني خُد نصف القطر هذه طب
+
+118
+00:09:07,290 --> 00:09:13,970
+هذه ايش بتساوي هذه بتساوي المسافة كلها هذه ال E R
+
+119
+00:09:15,390 --> 00:09:20,190
+هذه كلها منها نقار شيل منها مين المسافة بين
+
+120
+00:09:20,190 --> 00:09:27,370
+النقطين ناقص dx وx note هذا لو أخدته نصف فطر بضمنك
+
+121
+00:09:27,370 --> 00:09:29,670
+ال goal هذه الكور كلها جوا تنين ال goal الكبيرة
+
+122
+00:09:29,670 --> 00:09:36,110
+يعني الآن و كأنه بقولك جوابي لخد أي x note خد اللي
+
+123
+00:09:36,110 --> 00:09:42,270
+هو أي x في داخل اللي هو ال 6 هذه وخد اللي هوالـ
+
+124
+00:09:42,270 --> 00:09:49,510
+ball اللي نقصها X و نصف خطورها عبارة عن R ناقص DX
+
+125
+00:09:49,510 --> 00:09:55,610
+و X Note بضمنك في هذه الحالة نصف الخطور هذا ان
+
+126
+00:09:55,610 --> 00:10:00,620
+يخليني هذه الـ ball جواد هذه الـ ballماشي الحال طب
+
+127
+00:10:00,620 --> 00:10:03,420
+واحد يقول لي طب هو اصلا ممكن تكون هذه X مش جريبة
+
+128
+00:10:03,420 --> 00:10:06,500
+هان ممكن تكون X هنا و اقول له حتى لو كانت جريبة او
+
+129
+00:10:06,500 --> 00:10:10,360
+ما كانت باخدها نفس الاشي هي بتطلع هيك و بتضلها
+
+130
+00:10:10,360 --> 00:10:15,420
+وين؟ جواك ال ball و جبريا هذا الكلام صحيح طب ايش
+
+131
+00:10:15,420 --> 00:10:18,980
+.. كيف اعرف انه صحيح؟ خد بدفعة هذه جزية من مين؟ من
+
+132
+00:10:18,980 --> 00:10:26,860
+هذه خد الآن netزد element in B X و R نقص D of X و
+
+133
+00:10:26,860 --> 00:10:29,620
+X Note بتثبتلك عشان انت بتاخد ال substance من هنا
+
+134
+00:10:29,620 --> 00:10:33,500
+بتاخد أي element هنا ولا بيها و لاش الحال طب الآن
+
+135
+00:10:33,500 --> 00:10:37,140
+زد في هذه ايش معناه زد في هذه معناته زد كيف بتكون
+
+136
+00:10:37,140 --> 00:10:40,820
+في ال ball انها تكون المسافة بين ال z و ال x اللي
+
+137
+00:10:40,820 --> 00:10:45,400
+عندى أصغر من مين من نصف القطر نصف القطر في هذه
+
+138
+00:10:45,400 --> 00:10:52,820
+الحالة R نقص D of X و X Noteطب ما هو يا جماعة عندي
+
+139
+00:10:52,820 --> 00:11:03,240
+الان صار عندي دي لو جيه اخدت دي z و x0 دي z و x0
+
+140
+00:11:03,240 --> 00:11:08,600
+ايش مالها دي انا ايش بدثبت بدثبت انه z هان عشان
+
+141
+00:11:08,600 --> 00:11:11,700
+اثبت انه z هان لازم اثبت المسافة بين z و x0 اصغر
+
+142
+00:11:11,700 --> 00:11:16,610
+من مين؟ من Rصح ولا لأ؟ عشان أثبت أن الـ z في هذه
+
+143
+00:11:16,610 --> 00:11:21,030
+بتثبت أن المسافة بين z و بين x0 أصغر منها فنشوف خد
+
+144
+00:11:21,030 --> 00:11:26,150
+المسافة بين z و main و x0 شوفوا نفكر مع بعض هذه
+
+145
+00:11:26,150 --> 00:11:34,070
+اللي هي بتكون أصغر أو ساوي d z و x زائد dx و x0 صح
+
+146
+00:11:34,070 --> 00:11:38,430
+ولا لأ؟ بتريانجلين كواليتي بتريانجلين كواليتي لأن
+
+147
+00:11:38,430 --> 00:11:46,240
+اتطلع إلى d z و x و dx و x0هذه أصغر من R، عارفين
+
+148
+00:11:46,240 --> 00:11:50,900
+ليه؟ من هنا، من هنا، من هنا، جيب هذه على الجهة
+
+149
+00:11:50,900 --> 00:11:55,640
+هنا، بيصير D زد و X زائد D X و X Note أصغر من مين؟
+
+150
+00:11:55,640 --> 00:11:59,460
+من R، فالآن هذه أصغر من هذه، و هذه نفسها من اللي
+
+151
+00:11:59,460 --> 00:12:02,940
+فوق أصغر من R، إذا صارت D زد و X Note أشملها أصغر
+
+152
+00:12:02,940 --> 00:12:08,140
+من R، إذا Automatic هتكون الـ Z و موجودة في الـ
+
+153
+00:12:08,140 --> 00:12:15,800
+ball الليمركزها X0 ونصف قطرها R معناته بدأنا في Z
+
+154
+00:12:15,800 --> 00:12:20,100
+هنا وانتهينا في Z هنا صارت هذه مجموعة جزئية من هذه
+
+155
+00:12:20,100 --> 00:12:24,840
+يعني بمعنى أنه أخدت أي نقطة X عشوائية في داخل ال
+
+156
+00:12:24,840 --> 00:12:29,320
+ball هذا لجتلها ball بنصف قطر اللي حكيته كله جواها
+
+157
+00:12:29,320 --> 00:12:37,460
+هذه وهذا التسبب في النجول هذه is an open setاللي
+
+158
+00:12:37,460 --> 00:12:42,120
+حكيته صحيح البرهان بطاقة اللي هو الإجابة اللي
+
+159
+00:12:42,120 --> 00:12:49,760
+حكيتها طيب يا جماعة لأن مكملتها بيقول ليه مكملتها
+
+160
+00:12:49,760 --> 00:12:55,000
+مكملت ال closed ball is open ده نشوف كيف بدنا نثبت
+
+161
+00:12:55,000 --> 00:12:59,260
+الآن مكملت مياه ال closed ball is open ده نشوف كيف
+
+162
+00:12:59,260 --> 00:13:04,540
+نثبت مكملت ال closed ball is open هي عندي ال ball
+
+163
+00:13:04,540 --> 00:13:13,770
+تلدةof X note OR هذي بنثبتها إنها نالها إنها
+
+164
+00:13:13,770 --> 00:13:20,410
+مكملتها open طيب خلينا نطلع بس على الرسم هيك
+
+165
+00:13:20,410 --> 00:13:24,570
+التقريبي X note و هذا مين و هذا R أو الاستئناسي
+
+166
+00:13:24,570 --> 00:13:27,030
+الرسم الاستئناسي اللي نتسانس فيه ما هو مش شرط أن
+
+167
+00:13:27,030 --> 00:13:29,890
+نكون شكل الرسم هيك لأننا بس ما نعرفوش احنا كيف
+
+168
+00:13:29,890 --> 00:13:35,120
+شكلهطيب X note وهي نصف القطر R هذه اللي هي .. هذه
+
+169
+00:13:35,120 --> 00:13:39,440
+مع الجشرة الخارجية هي اللي بتمثل B تل ده وكملت
+
+170
+00:13:39,440 --> 00:13:44,480
+همين؟ اللي برا صح ولا لأ؟ لأن عشان أثبت اللي برا
+
+171
+00:13:44,480 --> 00:13:50,540
+أنه open بتاخد أي نقطة برا واسميها X وألاقي ball
+
+172
+00:13:50,540 --> 00:13:56,190
+كامل وين برا يعني في المنطقة هذهإذا أثبتت هذا
+
+173
+00:13:56,190 --> 00:14:02,310
+الكلام يعني الأن بدي أخد IX في مكملة هذه إيش
+
+174
+00:14:02,310 --> 00:14:09,550
+مكملتها هي X ناقص الـ BX0 وR تلدة و بدي ألاقي اللي
+
+175
+00:14:09,550 --> 00:14:17,210
+هو ball بدي ألاقي بقول أنا there exists ball اللي
+
+176
+00:14:17,210 --> 00:14:24,150
+هي ballالنصف اللي هي مركزها X هذه ونصف الخطورة
+
+177
+00:14:24,150 --> 00:14:28,790
+بتاعي أشوفه يكون كلها جزء من مين؟ من اللي برا هذا
+
+178
+00:14:28,790 --> 00:14:34,850
+اللي هو جزء من X minus B tilde of X0 OR إذا عملت
+
+179
+00:14:34,850 --> 00:14:38,670
+هيك بكون أثبتت إنه فعلا الست اللي برا هذا إيش ما
+
+180
+00:14:38,670 --> 00:14:44,060
+لها is open سهل شوف لها نصف الخطورةهذا نصف القطر
+
+181
+00:14:44,060 --> 00:14:48,500
+نهما كانت بعيدة بقدر أخد هو نصف القطر لأن هذا اللي
+
+182
+00:14:48,500 --> 00:14:50,880
+بيظل لما لنهاية مافيش خوف منها خوف من وين المنطقة
+
+183
+00:14:50,880 --> 00:14:55,440
+هذه فأخدت البعد من هالهال هو نصف القطر طب كدهش
+
+184
+00:14:55,440 --> 00:15:04,860
+البعد من هالهال هو عبارة عن R A مظبوط هذا هي R طب
+
+185
+00:15:04,860 --> 00:15:10,080
+و هذه المنطقة كيف بدي أحسبها بقول المسافة بين هذه
+
+186
+00:15:10,080 --> 00:15:18,090
+و هذهشيل منها هذه تطلع هذه يعني بمعنى آخر اللي
+
+187
+00:15:18,090 --> 00:15:22,750
+جابل بس بالنار بس هذه الان بتاخد المسافة العكسها
+
+188
+00:15:22,750 --> 00:15:26,550
+يعني عكس اللي جابل في الإشارة هي عبارة عن هذه
+
+189
+00:15:26,550 --> 00:15:31,890
+المنطقة دي إيش بتساوي المسافة بين X و X note شيل
+
+190
+00:15:31,890 --> 00:15:35,770
+منها منهم ال R اللي جابل كانت إيش العكس R معقصها
+
+191
+00:15:37,190 --> 00:15:41,750
+واضحة فالان هذه ال ball اللي هي بالنصف قطر هذا
+
+192
+00:15:41,750 --> 00:15:45,610
+بضمنكم انها تكون كلها جاعدة في ال set اللي احنا
+
+193
+00:15:45,610 --> 00:15:49,570
+بيقول عنها X نقص بيه X not وR not وثباتها دي
+
+194
+00:15:49,570 --> 00:15:52,630
+subset سهل بنفس الاسئوبة اللي جابها قبل شوية خد Z
+
+195
+00:15:52,630 --> 00:15:57,630
+هان هتلاقي Z وDX أصغر من هذه وبستعين بال triangle
+
+196
+00:15:57,630 --> 00:16:01,690
+inequality بأصل انه اللي هو موجودة وين في المنطقة
+
+197
+00:16:01,690 --> 00:16:07,550
+الثانية طيب يا جماعة إذا اللي أثبتناه هناإن ال
+
+198
+00:16:07,550 --> 00:16:10,470
+open هي أول open sets اتعرفنا عليها أن ال open
+
+199
+00:16:10,470 --> 00:16:16,370
+balls are open sets و ال complement لل closed
+
+200
+00:16:16,370 --> 00:16:22,830
+balls برضه open sets الآن نيجي للتعريف اللي بعده
+
+201
+00:16:22,830 --> 00:16:33,350
+بدنا نعرف حاجة اسمها الجوار بنصف قطر إبسلونباختصار
+
+202
+00:16:33,350 --> 00:16:39,150
+بدي أعرفلكم الجوار للمقطة X0 بنفس خطر Y هي عبارة
+
+203
+00:16:39,150 --> 00:16:43,550
+عن الـ open ball اللي نفس خطرها اللي هو الـ Y
+
+204
+00:16:43,550 --> 00:16:54,640
+مركزها X0 إذا الأن بقول أن Bx0 وy هو عبارة عن
+
+205
+00:16:54,640 --> 00:17:01,680
+neighborhood of x0 with radius y أو بدي أسميه الـ
+
+206
+00:17:01,680 --> 00:17:06,980
+y neighborhood of main of x0 إذا لو قلنا x metric
+
+207
+00:17:06,980 --> 00:17:14,700
+space an open ball بx0 وy of radius y إيش بنسميه
+
+208
+00:17:14,700 --> 00:17:20,740
+is called an y neighborhood of x0 element in xإذا
+
+209
+00:17:20,740 --> 00:17:25,620
+الـ neighborhood أو الجوار للـ X0 بنصف قطر Y ما هو
+
+210
+00:17:25,620 --> 00:17:33,020
+إلا عبارة عن الـ open ball اللي أمامي طيب بنقول إن
+
+211
+00:17:33,020 --> 00:17:41,300
+أن .. أن of X0 هو عبارة عن جوار بس بنقول جوار و
+
+212
+00:17:41,300 --> 00:17:49,110
+بنسكت جوار للـ X0 بنعني في إن هذا الست أنبغض النظر
+
+213
+00:17:49,110 --> 00:17:52,190
+كيف شكلها هيك ولا هيك ولا هيك ولا هيك ماعرفش احنا
+
+214
+00:17:52,190 --> 00:17:57,950
+كيف شكلها بنقول أن هذا جوار لل X0 إذا قدرت ألاقي
+
+215
+00:17:57,950 --> 00:18:05,770
+اللي هو داخله جوار بنصف قطر Y يعني قدرت ألاقي اللي
+
+216
+00:18:05,770 --> 00:18:13,840
+هو P of X0 وY كله جوات مين؟ جوات Nإذاً N is a
+
+217
+00:18:13,840 --> 00:18:19,340
+neighbourhood أو جوار لـ X0 if we can find an
+
+218
+00:18:19,340 --> 00:18:25,320
+epsilon neighbourhood inside mean N فاضح؟ إذاً هذا
+
+219
+00:18:25,320 --> 00:18:33,120
+بيحكي بصراحة a neighbourhood of X0 which is
+
+220
+00:18:33,120 --> 00:18:41,320
+denoted by N of X0 isa subset of X which contains
+
+221
+00:18:41,320 --> 00:18:49,020
+ايش ماله الـY numberhood of mean of X0 طيب نيجي
+
+222
+00:18:49,020 --> 00:19:03,280
+لاللي هو definition 134 definition 134 فبدنا
+
+223
+00:19:03,280 --> 00:19:13,670
+نعرف يا جماعة شو معناتX0 نقطة داخلية يعني الآن لو
+
+224
+00:19:13,670 --> 00:19:24,970
+أجيت أخدتلكم اللي هو 6M أي 6M أي 6M هذي M6 ماشي
+
+225
+00:19:24,970 --> 00:19:30,860
+هذي جزئية من metric spaceبقول النقطة X note هذه
+
+226
+00:19:30,860 --> 00:19:36,180
+إنها نقطة داخلية في الـ M يعني X note عبارة عن
+
+227
+00:19:36,180 --> 00:19:41,180
+interior point يعني element in M أو نرمز لها X
+
+228
+00:19:41,180 --> 00:19:45,700
+note element in interior of M أي من هذا الرمز أو
+
+229
+00:19:45,700 --> 00:19:50,160
+هذا الرمز بنقصد فيه ما له ال interior pointأو the
+
+230
+00:19:50,160 --> 00:19:54,480
+set of interior balls نقول X0 هي عبارة عن element
+
+231
+00:19:54,480 --> 00:19:57,620
+in M interior يعني عبارة عن نقطة داخلية للـ M
+
+232
+00:19:57,620 --> 00:20:03,540
+انتبهوا إذا لجيت جوار بوثقة الـ Epsilon كله
+
+233
+00:20:03,540 --> 00:20:09,720
+الموجود في داخل الـ M ماشي الحال يعني لجيت ball of
+
+234
+00:20:09,720 --> 00:20:15,150
+X0 و Epsilon subset من Mلأن لحظة لو النقطة هنا على
+
+235
+00:20:15,150 --> 00:20:19,530
+ال .. على ال .. على الحدود بتكون مش داخلية لأن هو
+
+236
+00:20:19,530 --> 00:20:22,330
+هياخد من برا و من وهمد و زي ما كنا فيقول في ال
+
+237
+00:20:22,330 --> 00:20:25,490
+calculus وهذا خلّيني أقول استئناس اللي يبقى إذا لو
+
+238
+00:20:25,490 --> 00:20:30,150
+بدأت أحكي هذا الكلام بالرموز بقول X not element in
+
+239
+00:20:30,150 --> 00:20:39,130
+M interior إيش تعني أنه there existاللي هو B of X0
+
+240
+00:20:39,130 --> 00:20:44,870
+وY كل جزء من مين منها إذا اللي بجزده إنه X0
+
+241
+00:20:44,870 --> 00:20:49,230
+interior point إذا كان لجهة بول بنص في خطورة Y أو
+
+242
+00:20:49,230 --> 00:20:53,810
+neighborhood بنص في خطورة Y كل جزء من مين منها
+
+243
+00:20:53,810 --> 00:20:57,790
+معايا؟
+
+244
+00:20:57,790 --> 00:21:03,290
+زي
+
+245
+00:21:03,290 --> 00:21:07,500
+ما اتفجناthe set of all interior points of M
+
+246
+00:21:07,500 --> 00:21:12,260
+بنرمزلها بالرمز interior of M or M interior هذه
+
+247
+00:21:12,260 --> 00:21:16,680
+مجموعة كل النقاط الداخلية للـ Mطيب نيجي الآن بقول
+
+248
+00:21:16,680 --> 00:21:20,200
+لي it is easy to see that interior of M is an open
+
+249
+00:21:20,200 --> 00:21:25,540
+set يعني بتقدر احنا بنقول انه الآن اعلان وفق
+
+250
+00:21:25,540 --> 00:21:30,180
+الكلام هذا ان ال interior point the set of all
+
+251
+00:21:30,180 --> 00:21:36,680
+interior point interior point of M هذه is an open
+
+252
+00:21:36,680 --> 00:21:43,870
+set عارف؟ is an open set يعني بدك تاخد أي XX في
+
+253
+00:21:43,870 --> 00:21:50,750
+الـ interior للـ M X في الـ interior للـ M و تصل
+
+254
+00:21:50,750 --> 00:21:58,910
+.. و تصل .. و تصل من خلالها أنه there exist B of X
+
+255
+00:21:58,910 --> 00:22:05,070
+أو X note B of X note و some radius R كله جزء من
+
+256
+00:22:05,070 --> 00:22:13,580
+مين من الـ interior لمين للـ M هش الحالهذا بتعملوا
+
+257
+00:22:13,580 --> 00:22:17,100
+لحالكم انه اللي هو تاخدوا x note في ال interior من
+
+258
+00:22:17,100 --> 00:22:21,220
+ال M و تصلوا انه بتلاقي ال ball بالنفس الخطور كذا
+
+259
+00:22:21,220 --> 00:22:23,880
+صبصة في ال interior من ال M طبعا انتوا بتعرفوا ان
+
+260
+00:22:23,880 --> 00:22:28,820
+مدام ات X interior اذا بلاقي ball جزئية من مين؟ من
+
+261
+00:22:28,820 --> 00:22:33,370
+ال Mأه كيف الآن تلاقي ال ball جزئية من الان و في
+
+262
+00:22:33,370 --> 00:22:37,790
+الآخر تلاقي ball منها جزئية من مين من ال interior
+
+263
+00:22:37,790 --> 00:22:42,870
+للان هذا بيضل معاكم طيب نيجي الآن لل theorem اللي
+
+264
+00:22:42,870 --> 00:22:49,110
+أمامنا ال theorem اللي هواللي أمامي أنا حكيتها
+
+265
+00:22:49,110 --> 00:22:54,090
+الآن عن ال .. ركزوا معايا عن ال open sets الآن
+
+266
+00:22:54,090 --> 00:22:56,710
+هدولة ال collection of open sets يعني هائلة ال
+
+267
+00:22:56,710 --> 00:23:00,770
+open sets بتحطها مع بعض وبتثبتلكم الآن هي بتحقق
+
+268
+00:23:00,770 --> 00:23:05,710
+تلت شروط التلت شروط هذه اللي بتحققها هي في الواقع
+
+269
+00:23:05,710 --> 00:23:09,690
+الشروط اللي بتخلي ال collection هي topology يعني
+
+270
+00:23:09,690 --> 00:23:13,410
+وكأني الآن بدأت من ال B trickأعرفت منه الـ open
+
+271
+00:23:13,410 --> 00:23:17,270
+sets الـ open sets عملين لـ collection of sets هذه
+
+272
+00:23:17,270 --> 00:23:20,610
+ال collection of sets هي عملكة topology يعني هذا
+
+273
+00:23:20,610 --> 00:23:24,090
+ال topology بنسميه the topology induced by ال
+
+274
+00:23:24,090 --> 00:23:28,290
+metric يعني ال topology المولد من مين من ال metric
+
+275
+00:23:28,290 --> 00:23:33,110
+إذا .. إذا واضح أنه any metric space هيكون أزأة
+
+276
+00:23:33,110 --> 00:23:37,340
+topological spaceلكن إذا كان topological space ليس
+
+277
+00:23:37,340 --> 00:23:40,880
+شرط أن يكون metric space وهذا الكلام طبعا اللي هو
+
+278
+00:23:40,880 --> 00:23:44,240
+تاخده بالتفصيل في مادة ال topology خلّيني احنا
+
+279
+00:23:44,240 --> 00:23:49,680
+نشوف النظرية اللي عندى اللي بتوصلني للي بحكيه في
+
+280
+00:23:49,680 --> 00:23:52,540
+رموح تلاتة خمسة بيقول لي let x be a metric space
+
+281
+00:23:53,070 --> 00:24:00,410
+and let G script be the collection of all open
+
+282
+00:24:00,410 --> 00:24:05,390
+subsets of N of X هي عائلة من اللي هي الـ open
+
+283
+00:24:05,390 --> 00:24:09,430
+sets اللي هي زي ما عرفناها then the following
+
+284
+00:24:09,430 --> 00:24:13,310
+properties اشمالها hold الشروط التلاتة التالية
+
+285
+00:24:13,310 --> 00:24:17,310
+محققة من الشروط التالية الشرط الأول أنه في element
+
+286
+00:24:17,310 --> 00:24:22,090
+in G scriptو X element in G script يعني فاي
+
+287
+00:24:22,090 --> 00:24:26,310
+المجموعة الخالية open set والمجموعة ال universal
+
+288
+00:24:26,310 --> 00:24:31,190
+set is an open set اتنين the union of any members
+
+289
+00:24:31,190 --> 00:24:35,130
+of open sets ايش مالها is again open يعني لو أخدت
+
+290
+00:24:35,130 --> 00:24:37,990
+ال union من ال open sets countable و non countable
+
+291
+00:24:37,990 --> 00:24:44,140
+مش مشكلة هيكون عبارة عن open setالشرط الثالث أو
+
+292
+00:24:44,140 --> 00:24:48,420
+الخاصية الثالث ان the finite intersection of open
+
+293
+00:24:48,420 --> 00:24:51,420
+sets is open sets يعني لو كان في عند ا واحد ا
+
+294
+00:24:51,420 --> 00:24:55,680
+اتنين عند ا and open sets هيكون اللي هو union
+
+295
+00:24:55,680 --> 00:25:00,820
+اتقطحن is an open set اما ال infinite اللي هو
+
+296
+00:25:00,820 --> 00:25:05,080
+intersection ليس شرطا ولا مثل على هذه موجودة طيب
+
+297
+00:25:05,750 --> 00:25:08,730
+الان نجي نبرهم الأولى وبعدين التانية وبعدين
+
+298
+00:25:08,730 --> 00:25:13,590
+التالتة خلنا نبرهم نوضح لكم يا البرهان هان فأول
+
+299
+00:25:13,590 --> 00:25:18,070
+اشي بالنسبة ل X انها open set سهل خالص هذه عشان
+
+300
+00:25:18,070 --> 00:25:22,790
+اثبت انها open بقول let XElement of X عشان لا اثبت
+
+301
+00:25:22,790 --> 00:25:26,090
+انها open بتاخد اي X في الـ X ولاقي ball كلها
+
+302
+00:25:26,090 --> 00:25:28,970
+جواها ال X طب هي ال X هي العالم تبعي كل العالم تبع
+
+303
+00:25:28,970 --> 00:25:32,650
+النقاط اللي تبعوني اذا اي ball هنا في هذه الحالة
+
+304
+00:25:32,650 --> 00:25:38,910
+انه لو اخترت الان اي ball B of X وR هتلاقيها جزء
+
+305
+00:25:38,910 --> 00:25:43,570
+من مين؟ من X لانه العالم تبعي اذا الان اكيد X is
+
+306
+00:25:43,570 --> 00:25:52,580
+an open set واضح نيجي الآن نثبتنثبت أن فاي is an
+
+307
+00:25:52,580 --> 00:25:57,020
+open set فاي is an open set أيش معناه open؟ نقول X
+
+308
+00:25:57,020 --> 00:26:04,940
+element في يؤدي إلى there exist ball of X وR جزئية
+
+309
+00:26:04,940 --> 00:26:09,430
+من مين من فاي هذا معناه أنها تكون openإن كل X في
+
+310
+00:26:09,430 --> 00:26:14,170
+الـ Phi لازم يعطينا إنه فيه ball تكون اللي هو وين
+
+311
+00:26:14,170 --> 00:26:16,790
+وجودة في الـ Phi طب ما هي هذه اللي هي الجملة
+
+312
+00:26:16,790 --> 00:26:21,210
+شرطية؟ هذه false واحنا بنعرف الجملة كلها على معاك
+
+313
+00:26:21,210 --> 00:26:26,070
+بتكون true دائما اللي هي false implies تحت عنوان
+
+314
+00:26:26,070 --> 00:26:29,110
+false implies anything is trueيعني لو كانت اللي هي
+
+315
+00:26:29,110 --> 00:26:32,530
+هذا الـ False إيش ما يكون هنا كل الجملة بتكون إيش
+
+316
+00:26:32,530 --> 00:26:36,570
+مالها true إذا فعلا يتحقق الشرط أن فاي is an open
+
+317
+00:26:36,570 --> 00:26:40,230
+set واحد بده ينظر لها نظرة تانية أو بده يقول لأ طب
+
+318
+00:26:40,230 --> 00:26:43,310
+أنا يخليني بس أقبل هنا بطريقة تانية بقول يا سيدي
+
+319
+00:26:43,310 --> 00:26:51,180
+suppose that suppose thatفاية ليست مفتوحة مازالت
+
+320
+00:26:51,180 --> 00:27:00,840
+ليست مفتوحة إذن أكيد في X في الفاية لكي يكون هناك
+
+321
+00:27:00,840 --> 00:27:03,480
+X في الفاية لكي يكون هناك X في الفاية لكي يكون
+
+322
+00:27:03,480 --> 00:27:05,040
+هناك X في الفاية لكي يكون هناك X في الفاية لكي
+
+323
+00:27:05,040 --> 00:27:05,860
+يكون هناك X في الفاية لكي يكون هناك X في الفاية
+
+324
+00:27:05,860 --> 00:27:09,480
+لكي يكون هناك X في الفاية لكي يكون هناك X في
+
+325
+00:27:09,480 --> 00:27:13,060
+الفاية لكي يكون هناك X في الفاية لكي يكون هناك X
+
+326
+00:27:13,060 --> 00:27:13,660
+X في الفاية لكي يكون هناك X في الفاية لكي يكون
+
+327
+00:27:13,660 --> 00:27:16,000
+هناك X في الفاية لكي يكون هناك X في الفاية لكي
+
+328
+00:27:16,000 --> 00:27:22,580
+يكون هناك X فيواضح ؟ إذا أكيد Phi مستحيل اللي هو
+
+329
+00:27:22,580 --> 00:27:27,580
+نفي
+
+330
+00:27:27,580 --> 00:27:33,200
+Phi إنها open إنه نفترض إنها مش open هذا وصلني ل
+
+331
+00:27:33,200 --> 00:27:36,780
+contradiction لكن أنا بفضل اعتمد على هذه عشان ما
+
+332
+00:27:36,780 --> 00:27:45,080
+تجودش في مشكلة إنه اللي هي مش open ممكن تكونالـ
+
+333
+00:27:45,080 --> 00:27:48,400
+contradiction أنها تكون .. يعني اللي احنا بنعرف
+
+334
+00:27:48,400 --> 00:27:52,040
+أنه لـ closed set ممكن ناجي ال set اللي هي open و
+
+335
+00:27:52,040 --> 00:27:56,140
+لا هي closed بس برضه لإن مافي حقه اللي حاكيناه
+
+336
+00:27:56,140 --> 00:27:59,880
+مافي صحيح و ممكن الاعتماد عليه في الوصول ل
+
+337
+00:27:59,880 --> 00:28:04,260
+contradiction و من ثم نقول فقهي is an open set طيب
+
+338
+00:28:04,260 --> 00:28:10,880
+ايش اللي بدقوله بعد هيك ان ال union is open طيب هو
+
+339
+00:28:10,880 --> 00:28:17,820
+شوفواخلّيني أخد الـ U عبارة عن .. بتمثّل .. هو
+
+340
+00:28:17,820 --> 00:28:22,780
+عبارة عن الـ union للـ O .. O element in B and in
+
+341
+00:28:22,780 --> 00:28:28,860
+J .. Any أو الـ element in Delta subset من الجهة
+
+342
+00:28:28,860 --> 00:28:34,550
+عساس أنك تاخد أي اللي هو .. اللي هو unionيعني تاخد
+
+343
+00:28:34,550 --> 00:28:37,310
+أي نيون من أي انكانة دي من من من ل open sets
+
+344
+00:28:37,310 --> 00:28:41,910
+سمينين اليوم لان اثبت ان هذا open set سهل اثبات
+
+345
+00:28:41,910 --> 00:28:49,190
+كيف؟ بدك تقول let X element in U ايش غرضك؟ اتلاقي
+
+346
+00:28:49,190 --> 00:28:55,710
+open ball حوالين ال X كل جواه اتنين اليوم مدان X
+
+347
+00:28:55,710 --> 00:29:02,990
+في اليوم اذا اكيدthere exist O element in J such
+
+348
+00:29:02,990 --> 00:29:07,330
+that X element in O صح ولا لأ؟ مدام X في ال union
+
+349
+00:29:07,330 --> 00:29:13,090
+إذا X واحدة منهم ماشي؟ مدام X في ال union لمن؟ لأ،
+
+350
+00:29:13,090 --> 00:29:17,290
+O من ست ساة مدام ال X في ال union إذا X واحدة من
+
+351
+00:29:17,290 --> 00:29:22,350
+هدول إيش سميتها O؟ و ال O من وين جاية؟ من ال J لأن
+
+352
+00:29:22,350 --> 00:29:25,270
+اللي بتيجي منها اللي بتيجي من وين اللي جنبها اللي
+
+353
+00:29:25,270 --> 00:29:28,610
+subset منهاإذا صار عندى there exists o element in
+
+354
+00:29:28,610 --> 00:29:33,330
+jesus that x element in o but o is open مدام open
+
+355
+00:29:33,330 --> 00:29:41,310
+إذا بناجي بي of x وإبسلون جزئية من مين من ال o لإن
+
+356
+00:29:41,310 --> 00:29:46,030
+o is open طيب ال b هذى x وإبسلون جزئية من ال o و
+
+357
+00:29:46,030 --> 00:29:49,150
+ال o أصلا جزئية من ال u لإن واحدة منهم هذول من
+
+358
+00:29:49,150 --> 00:29:52,490
+هذول إذا أكيد subset من مين من u إذا أخدت x في ال
+
+359
+00:29:52,490 --> 00:29:59,780
+u لجهة open ballكلها جواة الـ U وهذا يعني أن U is
+
+360
+00:29:59,780 --> 00:30:05,880
+open وهي البرهان واضح بضوح الشمس بدكم تمر عليه
+
+361
+00:30:05,880 --> 00:30:10,540
+البرهان المكتوب مافيش مشكلة اللي هو let U be the
+
+362
+00:30:10,540 --> 00:30:15,300
+union of L arbitrary elements of open sets of X in
+
+363
+00:30:15,300 --> 00:30:20,060
+J and let X be any element in U زي ما قلت then X
+
+364
+00:30:20,060 --> 00:30:24,660
+لكن لازم تكون belongs to someأتوا at least one of
+
+365
+00:30:24,660 --> 00:30:33,160
+these open sets اللي سميتها O غاض اتوا at least
+
+366
+00:30:33,160 --> 00:30:35,100
+one of these open sets اللي سميتها O غاض اتوا at
+
+367
+00:30:35,100 --> 00:30:36,660
+least one of these open sets اللي سميتها O غاض
+
+368
+00:30:36,660 --> 00:30:38,600
+اتوا at least one of these open sets اللي سميتها O
+
+369
+00:30:38,600 --> 00:30:39,440
+غاض اتوا at least one of these open sets اللي
+
+370
+00:30:39,440 --> 00:30:43,620
+سميتها O غاض اتوا at least one of these open sets
+
+371
+00:30:43,620 --> 00:30:43,640
+اللي سميتها O غاض اتوا at least one of these open
+
+372
+00:30:43,640 --> 00:30:43,720
+open sets اللي سميتها O غاض اتوا at least one of
+
+373
+00:30:43,720 --> 00:30:48,380
+these open sets اللي سميتها O غاض اتوا at least
+
+374
+00:30:48,380 --> 00:30:49,780
+one of these open sets اللي سميتها O غاض اتوا at
+
+375
+00:30:49,780 --> 00:30:52,560
+least one of these open sets اللي سميتها O غاض
+
+376
+00:30:52,560 --> 00:30:53,020
+اتوا at least one of these open sets اللي سميت
+
+377
+00:30:57,140 --> 00:31:00,440
+شوفوا خلّيني أخد نفس الرموز اللي كاتبها اللي أخدها
+
+378
+00:31:00,440 --> 00:31:06,160
+بالنسبة لنا و أخد رموز مختلفة حبت أقول عشان أثبت
+
+379
+00:31:06,160 --> 00:31:17,780
+أقول لت لت M1 و M2 لعند MN بي open sets any finite
+
+380
+00:31:17,780 --> 00:31:22,770
+number of open sets من ال J script هذهالان بدي
+
+381
+00:31:22,770 --> 00:31:27,930
+اشوف تقاطحن اثبت انه تقاطحن اللي هو open بقولك let
+
+382
+00:31:27,930 --> 00:31:34,270
+X element ان التقاطع لـM I I من واحد لعند مين عدنا
+
+383
+00:31:34,270 --> 00:31:38,230
+بدي اخد X في التقاطع و اثبتلك ان فيه ball حوالين
+
+384
+00:31:38,230 --> 00:31:42,650
+ال X وجودة في التقاطع و بكون خلصنا طيب let X
+
+385
+00:31:42,650 --> 00:31:49,130
+element في التقاطع اذا عندي X في الـM I لكل I
+
+386
+00:31:49,130 --> 00:31:54,610
+فحولهافيهم كلها فإن كل واحدة فيهم is an open set
+
+387
+00:31:54,610 --> 00:31:59,590
+إذا كل واحدة بلقيلها open بالجواتها إذا for every
+
+388
+00:31:59,590 --> 00:32:08,790
+I there exist B of X وRI كلها جوات منين؟ الـMI صح
+
+389
+00:32:08,790 --> 00:32:14,030
+ولا لأ؟ طيب، هالجهة الصار عندي الآن اللي إن مركز
+
+390
+00:32:14,030 --> 00:32:22,650
+واحد Xوالنصف قطار ما له R1 وR2 وR3 وR4 وR5 بدي أخد
+
+391
+00:32:22,650 --> 00:32:27,310
+اللي هو نصف .. بدي أخد إيش يكون جواتهم كلهم إذا
+
+392
+00:32:27,310 --> 00:32:30,830
+أخي أكيد هاخد نصف القطر إيش أصغر واحد فيهم عشان
+
+393
+00:32:30,830 --> 00:32:34,250
+أضمن بولو تكون إيش ما لها جوات الكل إذا بدي أقول
+
+394
+00:32:34,250 --> 00:32:41,690
+let .. let R بتساوي ال minimum بين R1 وR2 لعند RN
+
+395
+00:32:41,690 --> 00:32:47,910
+صح ولا لأ؟مدام أخدت هي ال minimum إذا أكيد هتعطيني
+
+396
+00:32:47,910 --> 00:32:55,270
+الغرض تلبيلي غرضي إذا then there exist ball of X
+
+397
+00:32:55,270 --> 00:33:03,770
+وR واحدة منهم subsequent من ال ball of X وR I لكل
+
+398
+00:33:03,770 --> 00:33:07,730
+I لأن هي مركزين واحد وهي أصغر نصف وطول ده ما هتكون
+
+399
+00:33:07,730 --> 00:33:11,490
+فيهم كلهم مدام هتكون فيهم كلهم إذا موجودة فتقطع
+
+400
+00:33:11,490 --> 00:33:21,370
+حينإذا B of X و R subset من تقاطع ال boils X و R I
+
+401
+00:33:21,370 --> 00:33:29,330
+I من عند 1 لعند Nلكن احنا بنعرف ان هذا سبسفت من M
+
+402
+00:33:29,330 --> 00:33:35,150
+I لكل I اذا تقاطح هذول جزء من مين تقاطع ال M I اذا
+
+403
+00:33:35,150 --> 00:33:40,590
+تقاطع هذا نفس جزء تقاطع ال M I I من عند واحد لعند
+
+404
+00:33:40,590 --> 00:33:46,900
+ن اذا بدأت في ال X في التقاطعالـ X في التقاطع و
+
+405
+00:33:46,900 --> 00:33:51,120
+لاجئت أنه فيه ball حوالين الـ X بنص خطور R جزئية
+
+406
+00:33:51,120 --> 00:33:56,620
+من هذا التقاطع إذا therefore اللي هو التقاطع is an
+
+407
+00:33:56,620 --> 00:34:03,730
+open set إذا فعلا اللي هوعندي .. انا .. the
+
+408
+00:34:03,730 --> 00:34:05,490
+intersection of .. if I not intersection of an
+
+409
+00:34:05,490 --> 00:34:09,090
+open set is an open set وهيه بقولك let Y be an
+
+410
+00:34:09,090 --> 00:34:13,250
+element in the intersection of M1 and MN then each
+
+411
+00:34:13,250 --> 00:34:17,650
+M I contains a ball about Y and the smallest of
+
+412
+00:34:17,650 --> 00:34:21,870
+these balls هي اللي contained in the intersection
+
+413
+00:34:21,870 --> 00:34:26,050
+therefore the intersection is an open set وهذا
+
+414
+00:34:26,050 --> 00:34:35,090
+تفصيل اللي هي البرهان اللي موجودهنجي الآن تعريف
+
+415
+00:34:35,090 --> 00:34:38,110
+بدنا
+
+416
+00:34:38,110 --> 00:34:42,830
+الآن اللي حكيناه قبل شوية بدنا نحطه فى ثمرة بدنا
+
+417
+00:34:42,830 --> 00:34:47,730
+ناخد ثمرته الآن بدنا نعرفلك a topological space X
+
+418
+00:34:47,730 --> 00:34:52,970
+وG script بنسمي X وG script topological space
+
+419
+00:34:55,700 --> 00:35:01,040
+إذا كانت G script هو a collection of subsets of G
+
+420
+00:35:01,040 --> 00:35:08,880
+بتحقق منهم T1 وT2 وT3 يعني الآن بنسمي X وTau أو G
+
+421
+00:35:08,880 --> 00:35:13,810
+script هذه بنسميهم الـ topological spaceإذا كانت
+
+422
+00:35:13,810 --> 00:35:18,290
+الـ G script هذه اللي هي عائلة من المجموعات
+
+423
+00:35:18,290 --> 00:35:22,550
+الجزئية من X تحقق تلت شروط الشرط الأول X و Phi
+
+424
+00:35:22,550 --> 00:35:26,850
+فيها الشرط التاني اتحاد أي عناصر فيها فيها الشرط
+
+425
+00:35:26,850 --> 00:35:29,890
+التالت تقاطع أي finite تقاطع من اللي فيها فيها
+
+426
+00:35:29,890 --> 00:35:33,250
+ماشي الحال إذا اتحققت التلت شروط بنسميه
+
+427
+00:35:33,250 --> 00:35:39,100
+topological spaceإذا من هذا التعريف ومن النظرية
+
+428
+00:35:39,100 --> 00:35:42,400
+اللي قبل بشوية أثبتناها اللي هي التلات خواصها لها
+
+429
+00:35:42,400 --> 00:35:47,680
+ده لجينا إن ال metric space is a topological space
+
+430
+00:35:49,180 --> 00:35:55,220
+إذن واضح from theorem 1.3.5 اللي قبله شوية and
+
+431
+00:35:55,220 --> 00:35:58,920
+above definition هذا we can say that a metric
+
+432
+00:35:58,920 --> 00:36:02,600
+space is a topological space وقلنا العكس ليس شطر
+
+433
+00:36:02,600 --> 00:36:07,440
+وصحيح لكن لجيت مش مجننة اللي هو نيجي الآن التعريف
+
+434
+00:36:07,440 --> 00:36:15,580
+اللي بعده طيب التعريف الآن يا جماعة بتتعريفلكم
+
+435
+00:36:15,580 --> 00:36:17,960
+اللي هو ال continuous functions
+
+436
+00:36:20,830 --> 00:36:26,470
+بدأ أشوف أورديك كيف احنا يعني التعريف هو يعني
+
+437
+00:36:26,470 --> 00:36:31,870
+خلّيني نقول مستقى من تعريف ال continuity اللي احنا
+
+438
+00:36:31,870 --> 00:36:35,230
+بنعرفه في ال calculus ولكن اللي هو بما يناسب ال
+
+439
+00:36:35,230 --> 00:36:38,790
+metric space طبعا احنا يمكن اللي هو في ال topology
+
+440
+00:36:39,760 --> 00:36:42,520
+لما نحكي عن الـ topological spaces نحكيش أنه الـ
+
+441
+00:36:42,520 --> 00:36:46,400
+function من X لعند Y انها continuous و نقول بواسطة
+
+442
+00:36:46,400 --> 00:36:49,140
+ال limit أو بواسطة اللي هو ال metric أو كده لأ لأ
+
+443
+00:36:49,140 --> 00:36:52,820
+لأ لأ نعرفش ايش احنا ال metric هنا احنا ممكن نعرفه
+
+444
+00:36:52,820 --> 00:36:56,850
+هناك يا اما بواسطة اللي هو ال neighborhoodsأو
+
+445
+00:36:56,850 --> 00:37:00,770
+بواسطة أن نقول أن الـ inverse image of any .. of
+
+446
+00:37:00,770 --> 00:37:04,310
+any اللي هو open set is an open كنا نعرفه في
+
+447
+00:37:04,310 --> 00:37:07,130
+الطبال الجهيك و نبدأ فيه و نبدأ نصل لما نصل لموضوع
+
+448
+00:37:07,130 --> 00:37:10,710
+ال limit لما نصير نعرف ال limit عن طريق الجوار طيب
+
+449
+00:37:10,710 --> 00:37:15,550
+الآن احنا دخلت نهام مشابه للدخلة في ال calculusفي
+
+450
+00:37:15,550 --> 00:37:17,270
+الـ metric space لان ال metric space شغلها من
+
+451
+00:37:17,270 --> 00:37:20,890
+الشغلات الجميلة يعني اللي اللي خليني نقول اللي
+
+452
+00:37:20,890 --> 00:37:24,190
+فيها metric فيها مسافة فيه دالة مسافة فيها معناه
+
+453
+00:37:24,190 --> 00:37:28,270
+اقتراب اقتراب طبعا بالمفهوم اللي احنا بنحكي فيه او
+
+454
+00:37:28,270 --> 00:37:32,730
+خليني نقول ال .. ال .. ال .. الاقتراب بواسطة ال
+
+455
+00:37:32,730 --> 00:37:37,370
+metric لكن الاقترابك limit في الـ topological
+
+456
+00:37:37,370 --> 00:37:41,090
+space in general كنا بنحكي في معنى الاقتراب عن
+
+457
+00:37:41,090 --> 00:37:43,850
+طريق ال neighborhoods نذاكر neighborhood جد ما
+
+458
+00:37:43,850 --> 00:37:47,590
+بدنا أو نكبره جد ما بدنا عشان نودّي ال X لل X note
+
+459
+00:37:47,590 --> 00:37:50,790
+و الاخرين و ده موضوع أخر في ال topology بتاخده
+
+460
+00:37:50,790 --> 00:37:57,150
+خلّيني بس نحكي عن الموضوع نحنا الآن لو عندي T من X
+
+461
+00:37:57,150 --> 00:38:01,570
+لعند Y زمان زمان هتبع زمان يعني من R لR يعني اذا
+
+462
+00:38:01,570 --> 00:38:06,400
+بدكم ترتاحوا خليها من R لعند Rكنا نقول إن الـ
+
+463
+00:38:06,400 --> 00:38:09,960
+function هذه T continuous على الـ R إذا كانت
+
+464
+00:38:09,960 --> 00:38:13,200
+continuous على كل نقطة من النقاطها وكنا نقول إن T
+
+465
+00:38:13,200 --> 00:38:16,540
+continuous على الـ X knot يعني T continuous على
+
+466
+00:38:16,540 --> 00:38:21,600
+الـ X knot إذا كانت limit T of X لما X تروح للـ X
+
+467
+00:38:21,600 --> 00:38:27,390
+knot إيش بتساوي T of X knotإذا تحقق هذا الشرط كنا
+
+468
+00:38:27,390 --> 00:38:31,510
+نقول عن الدالة إشمالها continuous هذا كنا نعبر عنه
+
+469
+00:38:31,510 --> 00:38:34,630
+بتعبير آخر كنا نقول لو كنا نعبر عنه بالـ epsilon
+
+470
+00:38:34,630 --> 00:38:38,310
+delta definition نعبر عنه ونقول لكل epsilon أكبر
+
+471
+00:38:38,310 --> 00:38:41,050
+من صفر there exists delta أكبر من صفر such that
+
+472
+00:38:41,050 --> 00:38:44,070
+هذا تعبر عن اقتراح بهذه من هذه وهذه تعبر عن اقتراح
+
+473
+00:38:44,070 --> 00:38:46,630
+بهذه من هذه هي كنا نقول في ال calculus أو في
+
+474
+00:38:46,630 --> 00:38:50,890
+التحليل الحقيقيلكل y أكبر من 0 there exists دلت
+
+475
+00:38:50,890 --> 00:38:55,290
+أكبر من 0 فجدت لما x تقترب من x0 يعني ال x minus
+
+476
+00:38:55,290 --> 00:39:02,010
+x0 تكون أصغر من دلت يعطيني ال Tx ناقص ال Tx أشماله
+
+477
+00:39:02,010 --> 00:39:06,750
+أصغر من y هذا تعريفنا تبع زمان اللي هو في التحليل
+
+478
+00:39:06,750 --> 00:39:12,950
+أو في ال calculus لأن
+
+479
+00:39:12,950 --> 00:39:18,590
+تعريف في ال .. في ال metric نفس الشيء بدأ أقولإن
+
+480
+00:39:18,590 --> 00:39:23,470
+لو كانت X وD وY وD تلدة metric spaces يعني هذا
+
+481
+00:39:23,470 --> 00:39:28,050
+metric space وهذا metric space ثاني بقول إن T من X
+
+482
+00:39:28,050 --> 00:39:32,070
+لعند Y is set to be continuous عند X not لعند X if
+
+483
+00:39:32,070 --> 00:39:42,170
+and only if يعني T من X أو D لعند Y وD تلدة بقول
+
+484
+00:39:42,170 --> 00:39:48,710
+إن T continuous عند X not في Xإذا اتحقق قمالي لكل
+
+485
+00:39:48,710 --> 00:39:53,670
+Y أكبر من 0 there exist نفسه نفسه لفوق Delta أكبر
+
+486
+00:39:53,670 --> 00:39:58,650
+من 0 such that الآن هذا في الواقع metric بس تبع
+
+487
+00:39:58,650 --> 00:40:03,130
+metric تبع الار زمان الآن بشيل اللي هو ال absolute
+
+488
+00:40:03,130 --> 00:40:07,090
+value و بكتب ال metric in general لما X يعني و كأن
+
+489
+00:40:07,090 --> 00:40:11,510
+لما ال X تقترب من X note تعبر عنها أن المسافة بين
+
+490
+00:40:11,510 --> 00:40:18,310
+X و X note تكون أصغر من مينمن Delta يؤدي إلى
+
+491
+00:40:18,310 --> 00:40:23,210
+المسافة بين اللي هو TX و TX0 اللي هي تحت هذا
+
+492
+00:40:23,210 --> 00:40:33,390
+البتريك اللي هي دي .. دي Delta of TX و TX0 يكون
+
+493
+00:40:33,390 --> 00:40:40,490
+أشماله أصغر من أبسلون إذن هذا هو نفسه هذا التعريف
+
+494
+00:40:40,490 --> 00:40:45,520
+معمّم عليه هذا معمّم على هذايعني الـ metric اللي
+
+495
+00:40:45,520 --> 00:40:48,340
+هان صار metric in general و ال metric اللي هان
+
+496
+00:40:48,340 --> 00:40:52,620
+برضه صار metric آخر in general فهذا هو معناته اللي
+
+497
+00:40:52,620 --> 00:40:55,940
+هو إنها تكون الدالة متصلة وهنا كاتبينه هان إنه
+
+498
+00:40:55,940 --> 00:40:58,940
+متصل عند X node إذا كان لكل ي أكبر من صفر there
+
+499
+00:40:58,940 --> 00:41:03,040
+exist دلتة أكبر من صفر such that D تلد of TX و TX
+
+500
+00:41:03,040 --> 00:41:06,900
+node تكون أصغر من يبسون عندنا اللي هو for all X
+
+501
+00:41:06,900 --> 00:41:12,840
+satisfying أو whenever DX و X node أصغر من دلتةلأن
+
+502
+00:41:12,840 --> 00:41:16,360
+T is said to be continuous ونسكت إذا كانت هي
+
+503
+00:41:16,360 --> 00:41:21,660
+continuous عند كل نقاط الدمين هذا معناته اللي هو
+
+504
+00:41:21,660 --> 00:41:26,680
+ال continuity الآن بيجينا النظرية التالية اللي هي
+
+505
+00:41:26,680 --> 00:41:31,740
+النظرية اللي أنا قلت قبلها قبل شوية أنه احنا بنعرف
+
+506
+00:41:41,300 --> 00:41:46,280
+اللي أنا أدهل كده احنا هنطلعها نتيجة هنطلعها نظرية
+
+507
+00:41:46,280 --> 00:41:48,300
+من اللي قبل اللي أحكي عنها قبل شوية أشياء اللي
+
+508
+00:41:48,300 --> 00:41:54,960
+بتقولوا هذا theorem 138 بتقول let x و d and y و d
+
+509
+00:41:54,960 --> 00:42:00,030
+تلدى be metric spacesالان هذا الإعلان كان تالي a
+
+510
+00:42:00,030 --> 00:42:06,190
+metric T من X لعين Y is continuous if and only if
+
+511
+00:42:06,190 --> 00:42:10,450
+ال inverse image of any open subset of Y اي شماله
+
+512
+00:42:10,450 --> 00:42:16,190
+is an open subset of X هذا الإعلان كما يليه هستخدم
+
+513
+00:42:16,190 --> 00:42:23,550
+هذا طبعا في الإثبات النظرية
+
+514
+00:42:23,550 --> 00:42:34,530
+بتقول أن Tمن X و D لعند Y و D تلدة is continuous
+
+515
+00:42:34,530 --> 00:42:42,750
+if and only if أي open set في هنا ال inverse M دي
+
+516
+00:42:42,750 --> 00:42:48,490
+لها لازم يكون إيه شماله open set يعني كل S open in
+
+517
+00:42:48,490 --> 00:42:57,500
+Y هيعطيني أنهاللي هو T inverse of S open inين in X
+
+518
+00:42:57,500 --> 00:43:03,620
+فهي المظهرية، بدنا نثبتها بدنا نفترض أوليشي T is
+
+519
+00:43:03,620 --> 00:43:08,340
+open is continuous أسف، T is continuous و بعدين
+
+520
+00:43:08,340 --> 00:43:13,960
+نثبت هذهكيف بتثبت هذه؟ بتاخد أي S Open Set في الـY
+
+521
+00:43:13,960 --> 00:43:18,600
+واتبتلك إن الـT Inverse اللي هي أشمالها Open كيف
+
+522
+00:43:18,600 --> 00:43:21,520
+بتثبت الـCommunity T Inverse Open؟ ركزوا عشان نحط
+
+523
+00:43:21,520 --> 00:43:24,240
+الخطوط العامة للبرمجان بتثبتوا إن الـCommunity T
+
+524
+00:43:24,240 --> 00:43:29,660
+Inverse of S Us Open احنا خلّينا نسميها G عشان
+
+525
+00:43:29,660 --> 00:43:35,260
+أثبت هذه Open في X بدي أناجي لو أخدت أي X في الـG
+
+526
+00:43:35,260 --> 00:43:46,110
+أناجي there exists BX وصم اللي هو نصف فطر يكون كله
+
+527
+00:43:46,110 --> 00:43:51,430
+جزء من الـG إذا عملت هذه معناته صارت الـT inverse
+
+528
+00:43:51,430 --> 00:43:56,850
+في أسفل دي أشمالها is open طبعا هستعين بهذه من وين
+
+529
+00:43:56,850 --> 00:43:59,850
+من ال continuity المعطنية لأن عليها بدأ السند ماشي
+
+530
+00:43:59,850 --> 00:44:03,110
+الحال شوفوا ركزوا معايا الآن كيف بدأ أسأل هذا
+
+531
+00:44:03,110 --> 00:44:09,820
+الكلام كلام ان شاء الله سهل ومافي مشكلةركزوا في
+
+532
+00:44:09,820 --> 00:44:13,120
+اللي مكتوب هنا، الكتابة هنا منيح ومرتب إلى أن
+
+533
+00:44:13,120 --> 00:44:16,820
+بيقولّي suppose that T is continuous، هذا الاتجاه
+
+534
+00:44:16,820 --> 00:44:23,300
+الأول أو let S be any open set in B in Y، بتثبتلك
+
+535
+00:44:23,300 --> 00:44:29,180
+أن T inverse of S is open من مين مين in Xعشان أثبت
+
+536
+00:44:29,180 --> 00:44:34,540
+الـ T inverse للـ S element in X بدي أسهل على حالي
+
+537
+00:44:34,540 --> 00:44:37,540
+بس الرموز بدي أسمّه T inverse للـ S ده إيش بدي
+
+538
+00:44:37,540 --> 00:44:43,270
+أسميه G بدي أقول G تسميها T inverse للـ Sالان لو
+
+539
+00:44:43,270 --> 00:44:48,730
+كانت الـ G هذه في ف automatic الـ G هتكون open في
+
+540
+00:44:48,730 --> 00:44:53,790
+مين؟ في ال .. في ال X يعني مافيش إيش أثبته الان لو
+
+541
+00:44:53,790 --> 00:44:57,330
+طبعا عملت هذه لإن بعد شوية بدت طر أخد element في
+
+542
+00:44:57,330 --> 00:45:00,870
+الـ G عشان هي فرضت لحالها ان الـ G بتسوي في لحالها
+
+543
+00:45:00,870 --> 00:45:06,750
+الان بقولك let G لتسوي في وخد أي element X note في
+
+544
+00:45:06,750 --> 00:45:12,350
+مين في الـ G أخدت X note في الـ Gبدي أتسلسلك في
+
+545
+00:45:12,350 --> 00:45:16,310
+الخطوات وامشي وامشي لما أسألك أنه في بي X note و
+
+546
+00:45:16,310 --> 00:45:21,990
+some اللي هو نصف فطر كله some من مين؟ من الـG
+
+547
+00:45:21,990 --> 00:45:27,450
+واضح؟ إذا هذه الطريق اللي رايح لها أنا طيب خليني
+
+548
+00:45:27,450 --> 00:45:32,230
+نشوف كيف بدنا نحقق اللي هو اللي بدنا يعني أخدنا X
+
+549
+00:45:32,230 --> 00:45:38,070
+note أي element وين في الـG هاي عندى اللي هو الـX
+
+550
+00:45:39,810 --> 00:45:50,010
+وهي ال Y وهي اللي هو ال S وهي T inverse لل S واخدت
+
+551
+00:45:50,010 --> 00:45:56,930
+ايش اسمها G ماشي لما اخد X note هان X note في ال G
+
+552
+00:45:56,930 --> 00:46:01,630
+اللي هو T inverse لل S اذا اكيد فيها صورة سموها
+
+553
+00:46:01,630 --> 00:46:09,260
+ايش Y noteماشي اذا let x0 be element in G اذا اكيد
+
+554
+00:46:09,260 --> 00:46:13,020
+there is y لانه function لازم كل صورة there is y0
+
+555
+00:46:13,020 --> 00:46:20,010
+element in Such that y0 اكت ساوي T x0 طيبلكن S is
+
+556
+00:46:20,010 --> 00:46:24,990
+an open set S نفسها إيه شمالها open set مدام open
+
+557
+00:46:24,990 --> 00:46:29,630
+set إذا بقدر ألاقي اللي هو open point جوات مين؟
+
+558
+00:46:29,630 --> 00:46:34,450
+جوات الـ S الآن صارت Y note في الـ S تنسوش أنا X
+
+559
+00:46:34,450 --> 00:46:37,730
+note مين واخدها من رأس الدور ها يعني أخدت X note
+
+560
+00:46:37,730 --> 00:46:42,840
+مين موجودة في الـ Gو لقبية الـ G اللي هي موجودة
+
+561
+00:46:42,840 --> 00:46:47,000
+هان أكيد الـ TX Note فيها صورة وسمّيتها من هي Y
+
+562
+00:46:47,000 --> 00:46:52,500
+Note الـ Y Note منها دي موجودة في الـ S ماشي معايا
+
+563
+00:46:52,500 --> 00:46:56,500
+أه؟ إذن الآن Y Note في الـ S مدام Y Note في الـ S
+
+564
+00:46:56,500 --> 00:47:01,800
+انتبهوا عليها إذا إنه SO بن ستأخدت أس open بثبتين
+
+565
+00:47:01,800 --> 00:47:06,140
+بيسمها open y not element less و open أس إذن أكيد
+
+566
+00:47:06,140 --> 00:47:11,700
+there exist بي إكس no there exist بي و ي نوت و
+
+567
+00:47:11,700 --> 00:47:17,700
+إبسنون كلها duetين duet less صح أنت عارف ال open
+
+568
+00:47:17,700 --> 00:47:21,520
+طيب
+
+569
+00:47:21,520 --> 00:47:30,250
+طب ما أنا عارف ما أنا عارف أنهX نوت موجود أويان في
+
+570
+00:47:30,250 --> 00:47:33,490
+الـ domain هذا و احنا بنقول ان الـ tree continuous
+
+571
+00:47:33,490 --> 00:47:37,050
+هذا اذا continuous عند الـ X نوت ايه معناه
+
+572
+00:47:37,050 --> 00:47:40,610
+continuous عند الـ X نوت ان اي ابسلون في الدنيا من
+
+573
+00:47:40,610 --> 00:47:45,060
+بين هذه الابسلون for ابسلوناللي جيت أكبر من صفر
+
+574
+00:47:45,060 --> 00:47:49,380
+بقدر ألاقي delta أكبر من صفر such that ال distance
+
+575
+00:47:49,380 --> 00:47:53,780
+بين ال X وال X0 أصغر من دلتا بيعطيني ال distance
+
+576
+00:47:53,780 --> 00:48:00,240
+بين ال TX والTX0 أصغر من مين الأيسرون صح ولا لأ
+
+577
+00:48:00,240 --> 00:48:05,540
+أكيد أكيد هذا منين جبته من اللي هو تعريف ال
+
+578
+00:48:05,540 --> 00:48:11,580
+continuity لأنه بسبب ان Xاللي هو T إذا كنتوا معيصة
+
+579
+00:48:11,580 --> 00:48:15,160
+عندي X Note طبعا هذه X تي X Note إيش سميناها احنا؟
+
+580
+00:48:15,160 --> 00:48:19,200
+Y Note عشان تكون في الصورة صح ولا لأ؟ معايا أه؟
+
+581
+00:48:19,200 --> 00:48:24,220
+طيب لأن أنا أين رايح؟ أنا رايح هذا كله هستعين فيه
+
+582
+00:48:24,220 --> 00:48:29,780
+إن X Note في الـG وأصلكم من خلاله إن أت إلى أخدت
+
+583
+00:48:29,780 --> 00:48:34,860
+أي X لازم ألاقي ball كلها سبست من مين؟ من الـG
+
+584
+00:48:34,860 --> 00:48:41,650
+ماشي الحال إذا اللي عملناه لحد تلانإنه لجينا ..
+
+585
+00:48:41,650 --> 00:48:45,350
+مادام أخدنا وقلنا دي ده تسوى فاى إذا الـ X0 الـ
+
+586
+00:48:45,350 --> 00:48:49,310
+element MG أخدناها إذا لجينا Y0 element S بحيث Y0
+
+587
+00:48:49,310 --> 00:48:53,650
+بساوة T X0 لكن قلنا S Open Set إذا بنلاقي اللي هو
+
+588
+00:48:53,650 --> 00:48:56,810
+ball كل هوا اللي موجودة في الـ S بعدين استخدمنا ال
+
+589
+00:48:56,810 --> 00:49:01,030
+continuity عند ال X0 وقولنا إنه بنلاقي Delta بحيث
+
+590
+00:49:01,030 --> 00:49:05,230
+إن المسافة بين X و X0 أصغر من Delta بيعطي المسافة
+
+591
+00:49:05,230 --> 00:49:10,040
+بين X و .. TX و X0 إيش ماله؟أصغر من Epsilon الآن
+
+592
+00:49:10,040 --> 00:49:15,900
+بيدثبتلك إنه هذه نص القطر اللي بيقدّي الغرض اللي
+
+593
+00:49:15,900 --> 00:49:23,500
+هو عبارة عن Delta لـGeta لـGeta صارت من ده يا
+
+594
+00:49:23,500 --> 00:49:28,520
+Delta، مظبوط؟ إذن الآن بيدثبتلك إنه P X Note
+
+595
+00:49:28,520 --> 00:49:32,540
+وDelta subset من إيش؟ من D، هذا بيدثبتك، لو
+
+596
+00:49:32,540 --> 00:49:35,880
+أثبتتوا يكونوا خلاصين، إن أنا قلت
+
+597
+00:49:37,580 --> 00:49:45,400
+زد element in B X0 ومين أو دلتا ماشي هو ماخدها زد
+
+598
+00:49:45,400 --> 00:49:51,100
+ولا إيش؟ ماخدها X أظن مش مشكلة خلّيني أخدها احنا
+
+599
+00:49:51,100 --> 00:49:58,940
+هيك سميها X هو ايش
+
+600
+00:49:58,940 --> 00:50:04,000
+معنات X في ال B X0 ودلتا؟هذا بيعطيني أنه إذا
+
+601
+00:50:04,000 --> 00:50:08,760
+المسافة بين X و X0 لازم أصغر من أصغر من مين من
+
+602
+00:50:08,760 --> 00:50:14,040
+بلتا okay طيب ما هي المقاط اللي X و X0 أصغر من
+
+603
+00:50:14,040 --> 00:50:17,540
+بلتا حسب ال continuity اللي هنا لازم تعطيني
+
+604
+00:50:17,540 --> 00:50:22,300
+المسافة بين TX و Y0 أشمالها إذا هذا بيعطيني أن ال
+
+605
+00:50:22,300 --> 00:50:29,560
+distance بين TX و Y0 أصغر من مين من إبشرون واضحة
+
+606
+00:50:30,390 --> 00:50:37,090
+إيش معنات هذه؟ هذه معناتها إن الـ TX هذه الـ TX
+
+607
+00:50:37,090 --> 00:50:43,750
+موجودة في مين؟ الـ TX معناته موجودة في الـ ball أه
+
+608
+00:50:43,750 --> 00:50:51,130
+اللي مركزها Y نوت و نصف قطرةها مين؟ إبسلونهذا
+
+609
+00:50:51,130 --> 00:50:54,430
+عملناه .. عملناه إيش ماله قبل هيك أثبتنا أنه
+
+610
+00:50:54,430 --> 00:50:58,510
+subset من مين؟ من S فهذه صارت T X elementين هذه
+
+611
+00:50:58,510 --> 00:51:02,850
+اللي هي subset من S إذا صار عندي ال T X هذه
+
+612
+00:51:02,850 --> 00:51:08,650
+element في ال S إيش معناته؟ إن ال X element in T
+
+613
+00:51:08,650 --> 00:51:15,330
+inverse of S اللي هي مين هي؟ اللي هي ال G اللي
+
+614
+00:51:15,330 --> 00:51:17,690
+نسيته أه
+
+615
+00:51:19,300 --> 00:51:25,520
+عندي S أو G متساوي الـ T inverse لـ S إذا بدأت في
+
+616
+00:51:25,520 --> 00:51:28,940
+الـ X في الـ B X not و Delta ووصلتلكم اللي من الـ
+
+617
+00:51:28,940 --> 00:51:32,260
+X و اللي موجودة في الـ G يعني أثبتلكم البُقى
+
+618
+00:51:32,260 --> 00:51:38,500
+الهادي بزق من الـ G إذا من كله دي اتأخدت أي X not
+
+619
+00:51:38,500 --> 00:51:45,150
+في الـ Gو لجتلكم اللي هو open ball حوالينها جوا
+
+620
+00:51:45,150 --> 00:51:48,810
+الـG إيش معناته هذا الكلام؟ معناته إنه صارت الـG
+
+621
+00:51:48,810 --> 00:51:54,570
+is an open set إذن اللي بدأنا فيه إن S is any open
+
+622
+00:51:54,570 --> 00:51:58,730
+set في الـY لجينا الـT inverse للـS is an open set
+
+623
+00:51:58,730 --> 00:52:02,790
+في الـX وهو المطلوب، الاتجاه التاني الآن
+
+624
+00:52:02,790 --> 00:52:09,890
+conversely
+
+625
+00:52:14,860 --> 00:52:19,240
+Conversely Assume that the inverse image of every
+
+626
+00:52:19,240 --> 00:52:25,480
+open set in Y is an open set in X وبدأ أثبت لك أن
+
+627
+00:52:25,480 --> 00:52:32,140
+الـ T is continuous عند اللي هي H على اللي هي الـ
+
+628
+00:52:32,140 --> 00:52:37,480
+X كلها إذن الآن اللي مفترضه .. اللي أنا بدأ أثبت
+
+629
+00:52:37,480 --> 00:52:46,600
+عكس النظرية إيش عكس النظرية؟بدي افترض انه اللي هو
+
+630
+00:52:46,600 --> 00:52:49,800
+assume that the inverse image of every open set is
+
+631
+00:52:49,800 --> 00:52:54,160
+an open set in Y and X و بدي اثبتلك ان الـ T is
+
+632
+00:52:54,160 --> 00:53:01,140
+continuous عشان اثبت الـ T continuous من X and Y
+
+633
+00:53:01,140 --> 00:53:05,900
+بدي اخدلك اي X نقطة في الـ X و اثبتلك ان الـ T
+
+634
+00:53:05,900 --> 00:53:10,480
+continuous عندهاما هي معناته الـ Continuity عندها؟
+
+635
+00:53:10,480 --> 00:53:14,900
+إن لكل Y أكبر من 0، يجب أن أجد دلتا أكبر من 0 Such
+
+636
+00:53:14,900 --> 00:53:20,340
+that لما تكون الـDX وX0 أصغر من Y، يعطينا الـD بين
+
+637
+00:53:20,340 --> 00:53:26,540
+TX وTX0 أصغر من مين؟ أصغر من مين؟ من Y، صح ولا لأ؟
+
+638
+00:53:26,540 --> 00:53:29,060
+هل مش عارف معناته الـ Continuity؟ إذن، هذه اللي
+
+639
+00:53:29,060 --> 00:53:34,360
+بدأ أثبتهبدايتي الأن أخدت بين إيديا أن الـ inverse
+
+640
+00:53:34,360 --> 00:53:40,480
+image of any open set is open طيب، الآن عشان أثبت
+
+641
+00:53:40,480 --> 00:53:46,040
+هيك، قلتلك let X0 be any fixed point in X and let
+
+642
+00:53:46,040 --> 00:53:50,560
+Y إيه شمالها أكبر من صفر بيه arbitrary أخدت Y أكبر
+
+643
+00:53:50,560 --> 00:53:53,340
+من صفر arbitrary بالدرجة Delta اللي بيتحقق، هذا
+
+644
+00:53:53,340 --> 00:53:57,020
+بكون خلصت، ماشي؟ طيب، صلى الله عليه الصلاة والسلام
+
+645
+00:53:58,750 --> 00:54:05,070
+الآن الـ ball اللي هي T X Note و Epsilon is 1 أو 6
+
+646
+00:54:05,070 --> 00:54:10,040
+أكيد .. أكيدإذن الـ inverse image اللي حسب الخصية
+
+647
+00:54:10,040 --> 00:54:13,720
+اللي مقضيني هيها هتكون open set in main in X إذا
+
+648
+00:54:13,720 --> 00:54:17,160
+ال T inverse لها T inverse ده ال P of T X not Y
+
+649
+00:54:17,160 --> 00:54:21,920
+إيش معناها إذا open set in main in X إيش معنات هذه
+
+650
+00:54:21,920 --> 00:54:28,480
+تكون open set بقدر ألاقي اللي هو open ball اللي هو
+
+651
+00:54:28,480 --> 00:54:33,280
+كلها جوات هذهأكيد ما هي معناه open set إذا .. إذا
+
+652
+00:54:33,280 --> 00:54:36,420
+there is delta اللي هذا نصف القطر له اللي بتكون
+
+653
+00:54:36,420 --> 00:54:40,420
+جوا there is delta أكبر من صفر such that ال ball
+
+654
+00:54:40,420 --> 00:54:47,380
+of X not أو delta أصغر من ال T inverse لل B T X
+
+655
+00:54:47,380 --> 00:54:53,340
+not أو إبسلون كمان مرة أقولكم إياها دي يتبعوا الآن
+
+656
+00:54:53,340 --> 00:54:56,900
+احنا قلنا B T X not أو إبسلون إيش معناها open set
+
+657
+00:54:58,340 --> 00:55:01,660
+من الخاصية في I من الخاصية اللي ماعطينيها أن الـ T
+
+658
+00:55:01,660 --> 00:55:07,540
+inverse لها open صارت هذه open مدام هذه open وعندي
+
+659
+00:55:07,540 --> 00:55:13,220
+ال X note في داخلها ال X note في داخل هذه عارفين
+
+660
+00:55:13,220 --> 00:55:16,720
+ليش ال X note في داخل هذه لأن ال T X note موجودة
+
+661
+00:55:16,720 --> 00:55:19,380
+في هذه اللي جوا وماقدر ال T inverse ده اكيد ال X
+
+662
+00:55:19,380 --> 00:55:24,860
+note جوتها ماشي بما أن X note هانإذا بقدر ألاقي بو
+
+663
+00:55:24,860 --> 00:55:28,440
+.. وهذه open .. وهذه open .. إذا بي of x0 و sum
+
+664
+00:55:28,440 --> 00:55:32,980
+اللي هو .. اللي هو نصف قطر سميته delta كل جزء من
+
+665
+00:55:32,980 --> 00:55:39,580
+مين؟ جزء من الـ T inverse لل بي of T x0 و إبسل
+
+666
+00:55:39,580 --> 00:55:47,300
+واضح؟ بعد؟ إذا اللي حصلته الآن .. اللي حصلته كان
+
+667
+00:55:47,300 --> 00:55:51,640
+التالي إن لكل إبسل أكبر من 0 لجيت مين؟ الدلت هادي
+
+668
+00:55:52,490 --> 00:55:58,250
+بحيث إن هذا subset من هذا ماشي لأن أنا بدي أخد
+
+669
+00:55:58,250 --> 00:56:01,490
+أوصل للي بديها اللي بديها forever ي أكبر من سفر
+
+670
+00:56:01,490 --> 00:56:05,390
+لجد delta أكبر من سفر such that بدي أثبت لكم إن
+
+671
+00:56:05,390 --> 00:56:10,590
+لما تكون المسافة بين x و x0 أصغر من دلتا يعطيني
+
+672
+00:56:10,590 --> 00:56:15,070
+المسافة بين Tx و Tx أصغر من ي و بكون خلصت طيب
+
+673
+00:56:15,070 --> 00:56:18,890
+المسافة بين x و x0 أصغر من دلتا إيش معناته هذا
+
+674
+00:56:18,890 --> 00:56:25,030
+معناته إن ال Xهتكون في الـ pole للـ X0 وDelta صح
+
+675
+00:56:25,030 --> 00:56:29,470
+أو لا؟ هذا معناته هذا طيب، مدام الـ X في الـ pole
+
+676
+00:56:29,470 --> 00:56:33,630
+تبقى X0 وDelta وهذه subset من هذه إذا أكيد، أكيد
+
+677
+00:56:33,630 --> 00:56:41,970
+الـ X element in T inverse of B of T X0 وY، أكيد؟
+
+678
+00:56:41,970 --> 00:56:45,450
+بقى هذه، لأن هذه جزئية من هذه إيش معناة X في الـ T
+
+679
+00:56:45,450 --> 00:56:50,310
+inverse لهذه؟ معناته، هذا هيعطيني إن الـ TX نفسها
+
+680
+00:56:54,690 --> 00:56:57,550
+أكس في الـ T inverse أدكّي ده الـ TX و الموجودة في
+
+681
+00:56:57,550 --> 00:57:01,950
+هذا طيب إيش معناة الـ TX هنا هذا معناته أنه
+
+682
+00:57:01,950 --> 00:57:07,550
+المسافة بين الـ TX هذه و الـ TX naught أصغر من
+
+683
+00:57:07,550 --> 00:57:12,780
+مين؟ من إبسطإذا خدت لكل Y اللي جاءت Delta بحيث أن
+
+684
+00:57:12,780 --> 00:57:14,980
+المسافة هذه أزرق من Delta و أضفت أن المسافة هذه
+
+685
+00:57:14,980 --> 00:57:17,780
+أزرق من Y وهذا يعني أن ال function continuous عند
+
+686
+00:57:17,780 --> 00:57:20,760
+X0 و X0 بطأة was arbitrarily إذا ال T is
+
+687
+00:57:20,760 --> 00:57:24,380
+continuous على ال X في ضوء اللي هي الخاصية اللي
+
+688
+00:57:24,380 --> 00:57:28,040
+حكيناها معطينيها وبهيك ان شاء الله بنصل لعين ال
+
+689
+00:57:28,040 --> 00:57:30,820
+definition واحدة تلاتة ساعة المرة القادمة ان شاء
+
+690
+00:57:30,820 --> 00:57:33,400
+الله بنكمل وبرك الله فيكم والسلام عليكم ورحمة الله
+
+691
+00:57:33,400 --> 00:57:34,020
+وبركاته
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/mRYCDgWMxU8_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/mRYCDgWMxU8_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..44aff79449bc661c22f74c5811a5eea46523f602
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/mRYCDgWMxU8_postprocess.srt
@@ -0,0 +1,1452 @@
+1
+00:00:05,030 --> 00:00:07,610
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,610 --> 00:00:10,370
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,370 --> 00:00:14,910
+آله وصحبه أجمعينهذه المحاضرة رقم خمسة وعشرين مساق
+
+4
+00:00:14,910 --> 00:00:19,230
+تحليل اقتراني او تحليل دالي طولة بطالبات الجامعة
+
+5
+00:00:19,230 --> 00:00:25,110
+الإسلامية قسم الرياضيات ماجستير الرياضيات الان ان
+
+6
+00:00:25,110 --> 00:00:28,330
+شاء الله هناخد اخر section في شبطر تلاتة اللي هو
+
+7
+00:00:28,330 --> 00:00:32,550
+انواع ال operators اللي هنحكي عنها اللي هي self
+
+8
+00:00:32,550 --> 00:00:36,010
+-adjoint وunitary وnormal operators المحاضرة
+
+9
+00:00:36,010 --> 00:00:41,210
+الماضية عرفنا شو معنات a joint operatorالان هنحكي
+
+10
+00:00:41,210 --> 00:00:45,630
+عن شو معناه الـ self-adjoint operator شو معناه الـ
+
+11
+00:00:45,630 --> 00:00:49,450
+normal operator شو معناه الـ unitary operator و
+
+12
+00:00:49,450 --> 00:00:53,110
+بالمناسبة في طبعا احنا هذه الأسماء مرت علينا في
+
+13
+00:00:53,110 --> 00:00:59,090
+الجبر الخطي فكلها مقابل في الجبر الخطي اصلا ال
+
+14
+00:00:59,090 --> 00:01:01,890
+matrix في الآخر اللي هو احنا بنقدر نعمل نشتغل و
+
+15
+00:01:01,890 --> 00:01:06,360
+كأنهoperator على finite dimensional فاحنا طبعا
+
+16
+00:01:06,360 --> 00:01:10,080
+هنحكي عن ال operators بصورة عامة مش هنتطرق لتفاصيل
+
+17
+00:01:10,080 --> 00:01:13,860
+ال matrices نيجي نشوف اللي هو ال definition
+
+18
+00:01:13,860 --> 00:01:18,060
+التلاتة عشرة واحد a bounded linear operator T من H
+
+19
+00:01:18,060 --> 00:01:21,820
+لعند H انه Hilbert space H ال set to be اذا انا
+
+20
+00:01:21,820 --> 00:01:26,080
+تصنيفي في هذا الاتجاه لمين ال bounded linear
+
+21
+00:01:26,080 --> 00:01:30,020
+operator على مين على Hilbert space بنقول عنه كمان
+
+22
+00:01:30,020 --> 00:01:34,220
+من H لمين لHاللي احنا حاكينا عنه الـ Adjoint قبل
+
+23
+00:01:34,220 --> 00:01:39,840
+شوية من H1 أو الـ H2 لأن لأ بحكي عن اللي بتدعرفهم
+
+24
+00:01:39,840 --> 00:01:43,760
+الآن لحاليا من HLH اللي هو مين اولاشي self-adjoint
+
+25
+00:01:43,760 --> 00:01:47,600
+او hermitian اذا كان الـT ستار تبعه ايش بيساوي
+
+26
+00:01:47,600 --> 00:01:51,020
+بيساوي الـT اللي هو الـadjoint بيساوي نفس الـT
+
+27
+00:01:51,020 --> 00:01:55,740
+بنسميه ايش ماله hermitian او self-adjoint operator
+
+28
+00:01:55,740 --> 00:02:00,700
+بنسميه unitary اذا كان الـT bidictive
+
+29
+00:02:02,270 --> 00:02:09,150
+والـ T*) ايش بيساوي الـ T انفرس والـ
+
+30
+00:02:09,150 --> 00:02:16,330
+T نفسه unitary بيجيكشن او بيجيكتف ماب بيصير عندي
+
+31
+00:02:16,330 --> 00:02:19,930
+اللي هو شرطين انفرسياللي هو الـ T تكون bijective
+
+32
+00:02:19,930 --> 00:02:23,850
+شرط التاني T star بيساوي T inverse تلاتة ال normal
+
+33
+00:02:23,850 --> 00:02:27,410
+operator إذا كان ال T في ال T star إيش بيساوي
+
+34
+00:02:27,410 --> 00:02:30,430
+بيساوي T star في T طبعا في أنواع ال operators
+
+35
+00:02:30,430 --> 00:02:33,850
+عديدة يعني غير هذه اللي هي ال operators بس خلينا
+
+36
+00:02:33,850 --> 00:02:38,070
+نركز على هذه في هذا ال course المحدود طيب الآن أول
+
+37
+00:02:38,070 --> 00:02:42,780
+ملاحظة إذا كان ال T self-adjointهيكون عند الـ T X
+
+38
+00:02:42,780 --> 00:02:46,160
+وال Y بيساوي X و T Star Y ومزام الـ T Star Y
+
+39
+00:02:46,160 --> 00:02:50,220
+بيساوي T إذا بيصير الـ T X و Y بيساوي X و T Y يعني
+
+40
+00:02:50,220 --> 00:02:53,360
+بتنقل الـ T من هنا إلى هنا زي ما بدك في حالك مين
+
+41
+00:02:53,360 --> 00:02:59,310
+أن يكون T self-adjointلأن لو كان الـ T self
+
+42
+00:02:59,310 --> 00:03:04,850
+-adjoint أو unitary بتكون الـ T normal شوف كيف لو
+
+43
+00:03:04,850 --> 00:03:09,310
+كان self-adjoint بيصير الـ T في الـ T star هي
+
+44
+00:03:09,310 --> 00:03:12,810
+عبارة عن الـ T في T إذا كان self-adjoint اللي هي T
+
+45
+00:03:12,810 --> 00:03:15,710
+تربيع اللي هي نفس الـ T star في T اللي هي T في T
+
+46
+00:03:15,710 --> 00:03:19,110
+في T تربيع إذا لما يكون self-adjoint automatic
+
+47
+00:03:19,110 --> 00:03:25,880
+هيكون يشماله normalلو كان unitary بيكون الـ T*) هو
+
+48
+00:03:25,880 --> 00:03:30,060
+T inverse ماشي الحال و تنسوش الـ T bijective إذا
+
+49
+00:03:30,060 --> 00:03:32,340
+الـ T inverse bijective يعني الـ T في الـ T
+
+50
+00:03:32,340 --> 00:03:36,460
+inverse هيساوي ال identity و الآن الـ T inverse في
+
+51
+00:03:36,460 --> 00:03:39,520
+الـ T برضه هيساوي ال identity لأنه bijectiveإذاً
+
+52
+00:03:39,520 --> 00:03:41,940
+هيكون الـ T في الـ T*) بيساوي الـ T*) في الـ T
+
+53
+00:03:41,940 --> 00:03:46,280
+Automatic مادام إيش اسمه Unitary إذاً إذا كانت
+
+54
+00:03:46,280 --> 00:03:49,460
+Unitary أو self-adjoint Automatic هيكون Normal
+
+55
+00:03:49,460 --> 00:03:54,380
+الآن Normal Operators need not to be self-adjoint
+
+56
+00:03:54,380 --> 00:03:58,440
+ولا Unitary يعني ليس شرطاً ليكون self-adjoint ولا
+
+57
+00:03:58,440 --> 00:04:01,780
+يكون إيش ما له Unitary الآن بدنا مثال على Normal
+
+58
+00:04:01,780 --> 00:04:06,060
+Operator لا يكون self-adjoint ولا يكون Unitary خد
+
+59
+00:04:06,690 --> 00:04:09,830
+خد المثال التالي To see this consider the identity
+
+60
+00:04:09,830 --> 00:04:13,970
+operator I من H لعند مين لعند H ال identity العادى
+
+61
+00:04:13,970 --> 00:04:18,810
+اه الان ان هيلبرت اسمه H it is easy to see that ال
+
+62
+00:04:18,810 --> 00:04:23,650
+T خدوا ال T لان بساوة 2I في مين في I اذا المثال
+
+63
+00:04:23,650 --> 00:04:27,750
+اللي انا بدأ اقولكم انه عبارة عن اللي هو ال ال ال
+
+64
+00:04:27,750 --> 00:04:34,070
+normal لكن مش self-adjoint T بساوة 2I في مين في I
+
+65
+00:04:34,670 --> 00:04:39,910
+ماشي الحال الان لو جينا أخدنا ال T star له ال T
+
+66
+00:04:39,910 --> 00:04:44,370
+star اللي هو هيساوي اللي هو سالب اتنين I في مين
+
+67
+00:04:44,370 --> 00:04:48,850
+فال identity ماشي الحال هذا اللي هو إيش ال T star
+
+68
+00:04:48,850 --> 00:04:52,570
+له الكون جيت له طبعا و اثباته سهل هذا لو اللي هو
+
+69
+00:04:52,570 --> 00:05:00,220
+عندك ال T X و ال Y بساوي اللي هو Xأو الآن الـ T
+
+70
+00:05:00,220 --> 00:05:05,220
+star خُذ 2I الآن على الجهة الثانية لما يحصل كنت
+
+71
+00:05:05,220 --> 00:05:08,820
+جيب C سالب 2I، مظبوط؟ إذن طبيعي بيكون اللي هو T
+
+72
+00:05:08,820 --> 00:05:13,960
+star هو مين الـ T نفسه، بسوء تناقص 2I في I طيب،
+
+73
+00:05:13,960 --> 00:05:20,660
+الآن الـ T inverse هيسوي 1 على 2I في مين في I،
+
+74
+00:05:20,660 --> 00:05:25,040
+ماشي الحالة واضح إن الـ T بتسويش الـ T inverse
+
+75
+00:05:25,040 --> 00:05:31,960
+والـ T star بتسويش الـ Tمعايا واضح ان ال T في T
+
+76
+00:05:31,960 --> 00:05:38,380
+star T في T star بساوي اللي هو T star في T بساوي
+
+77
+00:05:38,380 --> 00:05:45,980
+أربعة I بظبط لإن اضربه هذي اتنين I في اتنين I
+
+78
+00:05:45,980 --> 00:05:49,520
+بيطلع اللي هو أربعة ال identity I تربية ما هي ال I
+
+79
+00:05:49,520 --> 00:05:52,200
+ما انتوا عارفين اذا اللي عندي الان
+
+80
+00:05:54,790 --> 00:05:57,610
+هذا مثال على الـ Normal operator need not to be
+
+81
+00:05:57,610 --> 00:06:01,670
+self-adjoint normally تبقى اطلع على فوقهنجي الان
+
+82
+00:06:01,670 --> 00:06:05,690
+نظريتنا الأولى theorem 13-3 let T من H مع اند H be
+
+83
+00:06:05,690 --> 00:06:09,010
+a bounded linear operator on a Hilbert space H
+
+84
+00:06:09,010 --> 00:06:14,310
+then if T self-adjoint then ال T X والX هيكون إيش
+
+85
+00:06:14,310 --> 00:06:18,650
+ماله real لكل X في ال X هذا كلام مهم إذا كانت ال T
+
+86
+00:06:18,650 --> 00:06:22,070
+عبارة عن self-adjoint هيكون automatic ال T X والX
+
+87
+00:06:22,070 --> 00:06:27,350
+إيش ماله دايماً real ماشي الان إذا كان H complex
+
+88
+00:06:28,260 --> 00:06:32,280
+إذا كان نفسه H is a complex هذا اللي فوق بغض النظر
+
+89
+00:06:32,280 --> 00:06:35,980
+إيش هي الـH هيكون الـTX والX إيش ما له real الآن
+
+90
+00:06:35,980 --> 00:06:40,380
+اللي كانت H complex وكان الـTX والX real automatic
+
+91
+00:06:40,380 --> 00:06:46,520
+هيكون عند الـT self-adjointلكن لو كان H مش Complex
+
+92
+00:06:46,520 --> 00:06:51,520
+وكانت الـ TX والـ X ريال ليس شرطاً انه تكون الهو T
+
+93
+00:06:51,520 --> 00:06:55,620
+سلف الدولة اصلا ممكن تكون TX والX مزام ريال هيكون
+
+94
+00:06:55,620 --> 00:07:01,970
+TX والX ريال طبيعي اه فهذا طبعا ليس شرطاإنه لو
+
+95
+00:07:01,970 --> 00:07:06,950
+بدنا نسلم بهذا if H is real و T X و X real إذن الـ
+
+96
+00:07:06,950 --> 00:07:09,830
+T الـ self-adjoint ما هو كل الـ T .. كل اللي في
+
+97
+00:07:09,830 --> 00:07:13,030
+الدنيا الـ T اللي على الـ real هيكون الـ T X و الـ
+
+98
+00:07:13,030 --> 00:07:15,450
+X real يعني هذا الشرط متحقق اوتوماتيكي يعني كل
+
+99
+00:07:15,450 --> 00:07:18,670
+اللي هيطلع الـ self-adjoint لأ طبعا واضح إذن ..
+
+100
+00:07:18,670 --> 00:07:22,450
+إذن .. إذن النظرية الجزء B هذا وين بيحدث في حالة
+
+101
+00:07:22,450 --> 00:07:30,160
+main H is complex نيجي لبنهم نيجي الآنالـ subpose
+
+102
+00:07:30,160 --> 00:07:33,420
+ده الـ T السلفة الـ joint تن لكل X في الـ H احسب
+
+103
+00:07:33,420 --> 00:07:36,620
+ما يليه عشان اثبت ان الـ T X وال X الريالد ده تبت
+
+104
+00:07:36,620 --> 00:07:39,180
+أن ال conjugate هيطلع نفسه ماشي ان انا اخد ال
+
+105
+00:07:39,180 --> 00:07:44,460
+conjugate ل T X وال X بسوء X و T X مظبوط X و T X
+
+106
+00:07:44,460 --> 00:07:50,170
+وT سلفة ال joint هيسوء T X و Xبس هيفضّوهم إذا صار
+
+107
+00:07:50,170 --> 00:07:56,110
+عندي اللي هو TX و X is real الآن ال B suppose that
+
+108
+00:07:56,110 --> 00:08:00,250
+H is complex هستخدم شكلي النظرية تبعت المرة اللي
+
+109
+00:08:00,250 --> 00:08:03,990
+فاتت اللي مال اللي فاتت للمحاضر اللي فاتت suppose
+
+110
+00:08:03,990 --> 00:08:09,430
+that H is complex and TX و X أشماله is real لكل X
+
+111
+00:08:09,430 --> 00:08:14,090
+element in H هذا الفرضية then شوف كيف يثبت لك إنه
+
+112
+00:08:14,090 --> 00:08:21,180
+اللي هو ال T بتساوي ال T starعندي TX و X بيساوي TX
+
+113
+00:08:21,180 --> 00:08:27,100
+و X conjugate صح ولا لأ لإنها real و يساوي الآن ال
+
+114
+00:08:27,100 --> 00:08:33,160
+TX و ال X من تعريف ال joint بيساوي X و T star X صح
+
+115
+00:08:33,160 --> 00:08:38,270
+ال conjugate اللي هو هيطلع T star X و 100 و Xالان
+
+116
+00:08:38,270 --> 00:08:45,770
+عند خدق الآن السفر بساوي T X و X ناقص T Star X و X
+
+117
+00:08:45,770 --> 00:08:49,110
+نجلناها ما هو على طول احنا جابلنا كلنا مادام هذا
+
+118
+00:08:49,110 --> 00:08:51,710
+بساوي و هذا دايما ايضا على طول بساوي T Star بس
+
+119
+00:08:51,710 --> 00:08:57,570
+خلينا الان نبسطها للاخر الان صار عند T X و X ناقص
+
+120
+00:08:57,570 --> 00:09:01,600
+T Star X و X بتساوي سفر و يساويجيبوا الـ inner
+
+121
+00:09:01,600 --> 00:09:07,280
+product مع بعض بيصير T نقص T star X O X بساوة سفر
+
+122
+00:09:07,280 --> 00:09:11,320
+وهذا الكلام صحيح لكل X في الدنيا إذن هذا اللي
+
+123
+00:09:11,320 --> 00:09:15,160
+كانوا بيسمونه Q احنا في المرة اللي فاتت فهيطلع Q
+
+124
+00:09:15,160 --> 00:09:18,820
+بتساوة سفر من اللمّة تلاتة تسعة تلاتة بيه إذا صار
+
+125
+00:09:18,820 --> 00:09:22,340
+عند Q اللي هو T minus T star بساوة سفر ومن ثم T
+
+126
+00:09:22,340 --> 00:09:25,200
+بساوة T star ومن ثم T is self-adjoint إذا انا
+
+127
+00:09:25,200 --> 00:09:30,180
+automatic اللي هو T is self-adjointطبعاً اللي
+
+128
+00:09:30,180 --> 00:09:33,920
+بتطلب التطبيق هذي لإنما ان يكون Hاش ما له Complex
+
+129
+00:09:33,920 --> 00:09:39,480
+اطلع لفوق الان the product of two bounded self
+
+130
+00:09:39,480 --> 00:09:43,900
+-adjoint linear operators S and T ان هيلبرت سبيس H
+
+131
+00:09:43,900 --> 00:09:47,140
+is self-adjoint if and only if S في T بيساوي TS
+
+132
+00:09:47,140 --> 00:09:55,460
+يعني بقوللي الآن لو كان عندي T و S self-adjoint كل
+
+133
+00:09:55,460 --> 00:10:01,480
+واحد ماشي الحالبقول لي إذا .. إذا اللي هو S في T
+
+134
+00:10:01,480 --> 00:10:11,800
+is self-adjoint if and only if ST أش بيساوي TS
+
+135
+00:10:11,800 --> 00:10:18,000
+ماشي الحال؟ طيب هذا الأمر بسيط وسهل a proof .. a
+
+136
+00:10:18,000 --> 00:10:24,720
+proof بنا نفض صباز that
+
+137
+00:10:25,640 --> 00:10:35,740
+S T الـ self-adjoint ماشي الحال؟ لأ دهن، دهن S T
+
+138
+00:10:35,740 --> 00:10:45,280
+بساوي S T اللي هو S Star في T Star صح ولا لأ؟ من
+
+139
+00:10:45,280 --> 00:10:51,230
+التعريف، لأن T و S يشمل أنه self-adjointمعايا اه
+
+140
+00:10:51,230 --> 00:10:59,390
+الان S T لكل Star بساوي انا بدأ اثبت هذه الان اه S
+
+141
+00:10:59,390 --> 00:11:04,890
+T بساوية T S معايا الان S Star في T Star ماهو الان
+
+142
+00:11:04,890 --> 00:11:12,950
+S T silver joint اذا هو عبارة عن S T Star T S لكل
+
+143
+00:11:12,950 --> 00:11:22,620
+Star ده خليني ابدأ بالعكس عشان T S وهناA T Star S
+
+144
+00:11:22,620 --> 00:11:30,240
+Star فبساوي S في T الكل Star بتظبط بحيط بتظبط صحيح
+
+145
+00:11:30,240 --> 00:11:33,620
+دايما صحيح هو يساوي S في T سلفة ال joint ايش
+
+146
+00:11:33,620 --> 00:11:39,560
+هيساوي عشان بس هذه عشان الأخيرة S في T Star سلفة S
+
+147
+00:11:39,560 --> 00:11:43,420
+T لأنه مفترض من سلفة ال joint S T اذا T S ايش
+
+148
+00:11:43,420 --> 00:11:50,210
+بتساوي S T conversely conversely suppose thatأس تي
+
+149
+00:11:50,210 --> 00:11:55,070
+بيساوي TS ماشي الحال الان بدي اتبعتلكم أس تي سيلفا
+
+150
+00:11:55,070 --> 00:12:00,810
+جون الان أس تي لكل ستار مش هيساوياللي هو حسب
+
+151
+00:12:00,810 --> 00:12:06,270
+القانون T Star S Star صح؟ و يساوي T Star هو الـ T
+
+152
+00:12:06,270 --> 00:12:09,950
+لأن الـ self-adjoint من رأس الدور و الـ S Star S
+
+153
+00:12:09,950 --> 00:12:13,230
+اللي هي الـ self-adjoint من رأس الدور و أنا الآن
+
+154
+00:12:13,230 --> 00:12:18,770
+مفترض S T إيش بيساوي P S إذا T فاس إيش هتساوي S في
+
+155
+00:12:18,770 --> 00:12:23,550
+T إذا صار S في T بيساوي S في T إيش لكل Star إذا S
+
+156
+00:12:23,550 --> 00:12:28,290
+T is self-adjoint هذه اللي هي theorem
+
+157
+00:12:31,340 --> 00:12:37,200
+اللي هو تلاتة عشر خمسة الان تخليني تخليني على
+
+158
+00:12:37,200 --> 00:12:42,400
+النظرية اللي قبلها theorem تلاتة عشر خمسة let TN
+
+159
+00:12:42,400 --> 00:12:45,520
+be a sequence of bounded linear self and joint
+
+160
+00:12:45,520 --> 00:12:49,820
+linear operators وTN من H لعند H انها ال
+
+161
+00:12:49,820 --> 00:12:56,190
+participate Hsuppose that TN بتروح لـ T S اللي هو
+
+162
+00:12:56,190 --> 00:13:01,910
+that is norm of TN بتروح لنخستي بتروح لصفر where
+
+163
+00:13:01,910 --> 00:13:05,470
+this norm is the norm on the space BHWH عارفينه
+
+164
+00:13:05,470 --> 00:13:08,590
+طبعا يعني then T is a bounded self-adjoint linear
+
+165
+00:13:08,590 --> 00:13:12,810
+operator يعني و كأنه بيقول اللي خلّي بيقول انه
+
+166
+00:13:12,810 --> 00:13:16,550
+اللي هو sequence of sequence of self-adjoint
+
+167
+00:13:16,550 --> 00:13:22,350
+operatorsلو converged لـ some T لازم الـ T تكون
+
+168
+00:13:22,350 --> 00:13:24,370
+إيه أشمالها؟ self-adjoint
+
+169
+00:13:27,030 --> 00:13:32,650
+معنى إيش بقول؟ لو كانت عندى اللى بقوله TN sequence
+
+170
+00:13:32,650 --> 00:13:37,170
+of self-adjoint linear operators و هدى conveges
+
+171
+00:13:37,170 --> 00:13:42,890
+لصم T لازم الـ T هدى إيش تطلع self-adjoint يعني
+
+172
+00:13:42,890 --> 00:13:47,550
+بمعنى أخر لازم أثبتلك إنه norm T نقص T star اللى
+
+173
+00:13:47,550 --> 00:13:51,930
+هو بساوي سفر ماشي معناته ال T بتساوي مين؟ T star
+
+174
+00:13:51,930 --> 00:14:00,750
+شوف عليها الآن ال TNالـ TN الـ TN اللي هو Silver
+
+175
+00:14:00,750 --> 00:14:07,030
+Joint مظبوط ولا لأ؟ إذا الـ TN converts للـ T و
+
+176
+00:14:07,030 --> 00:14:12,410
+TN*) converts للـ T ليش؟ لأن كل واحدة من هدول هي
+
+177
+00:14:12,410 --> 00:14:17,110
+هدول ماشي الحال إذا هذه بتعطيني هدولة بيعطيني نورم
+
+178
+00:14:17,110 --> 00:14:24,300
+الـ TN ناقص الـ T بروح للـ 0أه و هذا بيعطيني نورم
+
+179
+00:14:24,300 --> 00:14:29,460
+الـ T N Star ناقص الـ T برضه هيروح لين للـ Zero
+
+180
+00:14:29,460 --> 00:14:39,620
+احسبلي الآن نورم الـ T ناقص الـ T Star اللي
+
+181
+00:14:39,620 --> 00:14:48,420
+هو أصغر أو يساوي أصغر أو يساوي نورم الـ T ناقص
+
+182
+00:14:50,680 --> 00:15:06,660
+الـ TN زائد نورم الـ TN ناقص TN*) مظبوط زائد
+
+183
+00:15:06,660 --> 00:15:15,320
+نورم فعله بس على الكتاب بالله فعله الكتاب زائد
+
+184
+00:15:16,400 --> 00:15:26,940
+Norm نزل نزل نزل نزل نزل نزل نزل نزل نزل
+
+185
+00:15:26,940 --> 00:15:30,100
+نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل
+
+186
+00:15:30,100 --> 00:15:36,100
+نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل
+
+187
+00:15:36,100 --> 00:15:37,840
+نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل
+
+188
+00:15:37,840 --> 00:15:38,380
+نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل
+
+189
+00:15:38,380 --> 00:15:38,460
+نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل
+
+190
+00:15:38,460 --> 00:15:43,040
+نزل نزل نزل نزل
+
+191
+00:15:43,040 --> 00:15:53,880
+نزلالـ TN ناقص T أسطار أسطار ماشي الحال طيب الآن
+
+192
+00:15:53,880 --> 00:16:02,400
+هذه بتروح لمين للسفر وهذه ايش بتساوي سفر ماشي وهذه
+
+193
+00:16:02,400 --> 00:16:11,030
+بتساوي norm ال TN ناقص T الكل نالهماشي الحال هذه
+
+194
+00:16:11,030 --> 00:16:15,110
+اللي جوه بتروح لمين برضه للصفر اذا هذا الان كمان
+
+195
+00:16:15,110 --> 00:16:20,830
+هيروح لمين كله للزيرو اذا صار عندي norm of T نقص T
+
+196
+00:16:20,830 --> 00:16:23,310
+طبعا هذا دايما اكبر تساوي مين صفر يعني اخدنا نمية
+
+197
+00:16:23,310 --> 00:16:28,130
+اذا الان goes to infinity فبطلع T بتساوي T star
+
+198
+00:16:28,130 --> 00:16:34,040
+ومن ثم Tيشملها الـ self-adjoint طبعا كل وين هذا ال
+
+199
+00:16:34,040 --> 00:16:38,880
+convergence في ال B H وH اللي هي اللي هي the set
+
+200
+00:16:38,880 --> 00:16:43,220
+of all bounded linear operators من H لعند H اذا
+
+201
+00:16:43,220 --> 00:16:49,780
+احنا اللي اثبتنا انه ال TN لو كانت sequence of
+
+202
+00:16:49,780 --> 00:16:53,420
+bounded self-adjoint linear operatorsconverge the
+
+203
+00:16:53,420 --> 00:16:57,440
+sum T هيكون limitها برضه ايش ماله اللي هو self
+
+204
+00:16:57,440 --> 00:17:04,760
+-adjoint linear operator اطلع لفوق اطلع لفوق يالا
+
+205
+00:17:04,760 --> 00:17:10,080
+البعد خلاص خليني اشرح منها خلاص خلاص خليني اشرح
+
+206
+00:17:10,080 --> 00:17:14,160
+منها let the operator U من H لعند H و V من H لH be
+
+207
+00:17:14,160 --> 00:17:20,710
+unitary او H is a Hilbert space thenالخاص التالية
+
+208
+00:17:20,710 --> 00:17:25,910
+متحققة خاص كلها يعني محسبتها حتى سريعة U is
+
+209
+00:17:25,910 --> 00:17:30,010
+isometric اخد معاه ايش هو معناه انزومتري نورم ال U
+
+210
+00:17:30,010 --> 00:17:32,910
+X ايش بيساوي نورم ال X لكل X هو اللي موجودة في ال
+
+211
+00:17:32,910 --> 00:17:38,110
+H و نورم ال U ال unitary هذا طبعا احنا اخدنا اللي
+
+212
+00:17:38,110 --> 00:17:42,190
+هو ال U ايش ماله و ال V unitary operators هذه خاص
+
+213
+00:17:42,190 --> 00:17:47,420
+ال unitary operatorsبيصير Normal U بساوي واحد على
+
+214
+00:17:47,420 --> 00:17:52,640
+اعتبار ان الـH أشمالها مش الـ0 ال part space و ال
+
+215
+00:17:52,640 --> 00:17:58,040
+U inverse اللي هو طبعا مادام Unitary اللي هو الـU
+
+216
+00:17:58,040 --> 00:18:02,600
+inverse نفسه برضه أشماله is Unitaryوهذه سهلة برضه
+
+217
+00:18:02,600 --> 00:18:06,440
+و ال U في V إيش برضه هيطلع Unitary إذا كانت U
+
+218
+00:18:06,440 --> 00:18:10,380
+Unitary و V Unitary برضه حاصر ضربين Unitary و برضه
+
+219
+00:18:10,380 --> 00:18:14,520
+كلام كله سهل و ال U إيش مالها Normal أثبتناها
+
+220
+00:18:14,520 --> 00:18:17,720
+قولناها المرة الفاترة أو في أول محاضرة اطلع لفوق
+
+221
+00:18:17,720 --> 00:18:23,360
+اطلع الان a bounded linear operator T on a Hilbert
+
+222
+00:18:23,360 --> 00:18:26,920
+.. on a complex Hilbert space H is unitary if and
+
+223
+00:18:26,920 --> 00:18:30,790
+only if T إيش مالها is isometricلو كانت Unitary
+
+224
+00:18:30,790 --> 00:18:34,210
+بتعطينا زيومتريك بتكون أثبتناها في الأول بتظهر الـ
+
+225
+00:18:34,210 --> 00:18:38,450
+Main العكس خلّينا نشوف الأولى بدنا نثبت أنها الـ
+
+226
+00:18:38,450 --> 00:18:42,570
+Unitary is isometry خد النورم لـUX لكل تربيع إيش
+
+227
+00:18:42,570 --> 00:18:47,010
+بيساوي اللي هي نورمبردكت بين الـUX والـUXماشي
+
+228
+00:18:47,010 --> 00:18:50,610
+الانوي ساوي X من خلاص ال joint بيصير X و U Star في
+
+229
+00:18:50,610 --> 00:18:54,050
+U U Star في U ماهي ال U Star في ال Unitary بيساوي
+
+230
+00:18:54,050 --> 00:18:56,870
+U Inverse فال U Inverse في ال U و ال U is
+
+231
+00:18:56,870 --> 00:19:00,750
+bijective إذن هيصير ال identity إذن X و ال IX اللي
+
+232
+00:19:00,750 --> 00:19:03,950
+هو نورم ال X تربيه إذن ال U X بيساوي نورم ال X إذن
+
+233
+00:19:03,950 --> 00:19:06,510
+he preserved the norm أو preserve the distance أو
+
+234
+00:19:06,510 --> 00:19:11,860
+preserve the inner product ده العيزومتريالان الجزء
+
+235
+00:19:11,860 --> 00:19:16,860
+الثاني بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+236
+00:19:16,860 --> 00:19:17,520
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+237
+00:19:17,520 --> 00:19:17,540
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+238
+00:19:17,540 --> 00:19:17,800
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+239
+00:19:17,800 --> 00:19:20,900
+بي بي بي
+
+240
+00:19:20,900 --> 00:19:27,140
+بي بي بي بي
+
+241
+00:19:27,140 --> 00:19:27,520
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+242
+00:19:27,520 --> 00:19:30,640
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+243
+00:19:30,640 --> 00:19:36,320
+بي
+
+244
+00:19:36,320 --> 00:19:42,230
+بي ببسوء norm ال X هذا في ال unitary إذا الأن norm
+
+245
+00:19:42,230 --> 00:19:48,110
+اللي هو ال U X على norm ال X اللي هو بسوء واحد ال
+
+246
+00:19:48,110 --> 00:19:53,150
+supremum اللي هو norm ال U هي سوء واحد إذا طبيعي
+
+247
+00:19:53,150 --> 00:19:59,250
+norm ال unitary بسوء واحد طيبالان ال .. ال .. ال
+
+248
+00:19:59,250 --> 00:20:03,030
+.. ال U inverse ال U bijective لنثبت ان ال U
+
+249
+00:20:03,030 --> 00:20:07,830
+inverse unitary U unitary اذا bijective و ال U
+
+250
+00:20:07,830 --> 00:20:12,670
+inverse يساوي U star طيب الان U is bijective اذا
+
+251
+00:20:12,670 --> 00:20:17,530
+ال U inverse موجودة و برضه bijective ماشي؟ اذا
+
+252
+00:20:17,530 --> 00:20:20,310
+الان الشرط الاول بالنسبة لل U inverse هتكون
+
+253
+00:20:20,310 --> 00:20:25,000
+unitary تحقق ان هي bijectiveو لو أخدنا ال U
+
+254
+00:20:25,000 --> 00:20:28,560
+Inverse Star هي ساوي ال U Inverse ما هي Unitary
+
+255
+00:20:28,560 --> 00:20:34,060
+ماشي؟ إذا ال U Star Star صارت اليمين بيساوي ال U
+
+256
+00:20:34,060 --> 00:20:37,400
+اللي هي بتساوي U Inverse Inverse إذا صارت ال U
+
+257
+00:20:37,400 --> 00:20:41,860
+Inverse Star بيساوي U Inverse Inverse إذا صارت
+
+258
+00:20:41,860 --> 00:20:46,640
+اللي هي ال U Inverse نفسها is Unitaryفاضح؟ طيب
+
+259
+00:20:46,640 --> 00:20:52,140
+الان ال U V بتثبت انها Unitary ال U Unitary و ال V
+
+260
+00:20:52,140 --> 00:20:56,100
+Unitary اذا ال U بيجيكتف و ال V بيجيكتف اذا ال
+
+261
+00:20:56,100 --> 00:21:00,340
+composition اللي هنا ال U V بيجيكتف هو مش هيك كمان
+
+262
+00:21:00,340 --> 00:21:04,500
+و لو اخدت ال U V لكل Star هيساوي ال U V لكل
+
+263
+00:21:04,500 --> 00:21:08,760
+Inverse ليش؟لأن هذا الـ U V لكل Star من خلاص اللي
+
+264
+00:21:08,760 --> 00:21:12,140
+هي الـ Star اللي هي V Star U Star و الـ V Star
+
+265
+00:21:12,140 --> 00:21:15,320
+مدام V Unitary بيساوي الـ V Inverse و الـ U Star
+
+266
+00:21:15,320 --> 00:21:18,280
+برضه بيساوي U Inverse لأنها Unitary برضه اللي هي
+
+267
+00:21:18,280 --> 00:21:22,160
+هذه بتساوي إيش U في V لكل إيش Inverse إذا صار U V
+
+268
+00:21:22,160 --> 00:21:25,820
+لكل Star بيساوي U V لكل Inverse بمعنى آخر صارت الـ
+
+269
+00:21:25,820 --> 00:21:29,600
+U في V is Unitary طيب الان
+
+270
+00:21:31,660 --> 00:21:35,620
+U inverse بيساوي U star اللي هو و ال U في ال U
+
+271
+00:21:35,620 --> 00:21:38,680
+inverse بيساوي ال U inverse في ال U بيساوي مين
+
+272
+00:21:38,680 --> 00:21:45,220
+بيساوي ال ايش ال identity مباشرة طيب الان صار عندي
+
+273
+00:21:45,220 --> 00:21:48,460
+الان اللي هو هذا بالنسبة ليه انزل انزل انزل انزل
+
+274
+00:21:48,460 --> 00:21:52,480
+بالنسبة ليه انزل انزل انزل بالنسبة ليه بالنسبة ليه
+
+275
+00:21:52,480 --> 00:21:56,420
+الان U is ايش ماله normal اخببته انا اه اطلع لفوق
+
+276
+00:21:56,420 --> 00:21:57,880
+طيب
+
+277
+00:22:00,640 --> 00:22:03,960
+النجلة اللي هي الجزء الأول اللي قلنا automatic
+
+278
+00:22:03,960 --> 00:22:09,700
+صبوس that is isometric and surjective ماشي and
+
+279
+00:22:09,700 --> 00:22:14,520
+surjective isometry implies injectivityقلناها إذا
+
+280
+00:22:14,520 --> 00:22:18,160
+كانت isometric قبلها ذكرناها كثير إذا كانت اللي ..
+
+281
+00:22:18,160 --> 00:22:21,700
+اللي هي isometric على طول أشملها indicative عندي T
+
+282
+00:22:21,700 --> 00:22:25,260
+دثويت الكوم الان انتوا عارفين وين راح دثويت الكوم
+
+283
+00:22:25,260 --> 00:22:28,900
+اللي هي ال F and O ال F أنزل .. أنزل .. أنزل ..
+
+284
+00:22:28,900 --> 00:22:32,160
+أنزل .. أنزل .. أنزل .. أنزل .. أنزل .. أنزل ..
+
+285
+00:22:32,160 --> 00:22:34,420
+أنزل .. أنزل .. أنزل .. أنزل .. أنزل .. أنزل ..
+
+286
+00:22:34,420 --> 00:22:34,580
+أنزل .. أنزل .. أنزل .. أنزل .. أنزل .. أنزل ..
+
+287
+00:22:34,580 --> 00:22:37,460
+أنزل .. أنزل .. أنزل .. أنزلA bounded linear
+
+288
+00:22:37,460 --> 00:22:41,800
+operator T in a complex Hilbert space H is unitary
+
+289
+00:22:41,800 --> 00:22:45,120
+if and only if T is isometric and surjective
+
+290
+00:22:52,540 --> 00:22:56,400
+و Unitary بالجكتف إذا صارت اللي هو ال Unitary
+
+291
+00:22:56,400 --> 00:23:00,020
+اوتوماتيكي بتعطي ايزومتريكي بتعطي سيرجكتف الآن بدي
+
+292
+00:23:00,020 --> 00:23:04,760
+العكس إذا كانت ايزومتري و سيرجكتف يعطيني مين؟
+
+293
+00:23:04,760 --> 00:23:13,020
+Unitary واضح؟ اطلع لفظك نفترض الآن أن TT نفترض أنه
+
+294
+00:23:13,020 --> 00:23:18,000
+الآن T نفترض أنه الآن T is isometric and
+
+295
+00:23:18,000 --> 00:23:22,840
+surjective مدام isometric وقبل هيك قلنا احنا ال
+
+296
+00:23:22,840 --> 00:23:27,000
+isometric operator هيطلع one to one إذا صار عندي
+
+297
+00:23:27,000 --> 00:23:29,960
+one to one و surjective يعني bijective إذا دلت
+
+298
+00:23:29,960 --> 00:23:35,160
+خاصية أخيرة أنه نثبت أنه اللي هو ال T star بساوي T
+
+299
+00:23:35,160 --> 00:23:40,400
+inverse بكون خلصنا بكون أثبتنا أنه T is unitary
+
+300
+00:23:40,820 --> 00:23:44,500
+واضح؟ طيب، شوفوا الآن اللي ضال اللي بدأت بيقولكوا
+
+301
+00:23:44,500 --> 00:23:48,720
+انه T Star بيساوي T Inverse من الـ Isometry الآن،
+
+302
+00:23:48,720 --> 00:23:52,440
+تشوفوا الآن T Star في Txa و في X، إيش بيساوي؟
+
+303
+00:23:52,440 --> 00:23:57,360
+انجلة عادية هنا، بيصير Tx و Tx، واضح؟ما هي عنده
+
+304
+00:23:57,360 --> 00:24:04,500
+اللي هي TX و TX بيساوي X و X لإيزومتري ماشي طيب ال
+
+305
+00:24:04,500 --> 00:24:08,160
+X و X إذا صار I X و مينه X إذا صار هذا الكلام صحيح
+
+306
+00:24:08,160 --> 00:24:12,410
+لكل X في الدنيا إذا ال I إيش هتساوي T Star في Tأو
+
+307
+00:24:12,410 --> 00:24:17,610
+بالتفصيل بنجل هذه هنا و بيصير T star في T نقص I X
+
+308
+00:24:17,610 --> 00:24:20,770
+بيساوي X لكل X و من اللمّة اللي بنستخدمها دايما
+
+309
+00:24:20,770 --> 00:24:24,970
+هيكون اللي هو هذا بيساوي إيه؟ بيساوي سفر إذا صار
+
+310
+00:24:24,970 --> 00:24:30,850
+عندي T star في T اللي هو بيساوي ال identity، ماشي؟
+
+311
+00:24:30,850 --> 00:24:34,530
+الآن تعالوا أحسبوا T في T star
+
+312
+00:24:38,510 --> 00:24:46,570
+التانية هي similar لزيها و سهلة تفت
+
+313
+00:24:46,570 --> 00:24:55,180
+تستار تفت تستار تفت تستارالان بدي أجيب T Star في T
+
+314
+00:24:55,180 --> 00:24:59,500
+عشان أستخدمها من اللي فوق فبصير T في T Star مع بعض
+
+315
+00:24:59,500 --> 00:25:03,420
+و T في T Inverse هدولة ال identity فبصير T في ال
+
+316
+00:25:03,420 --> 00:25:06,680
+identity في T Inverse بصير T في T Inverse و يسوا
+
+317
+00:25:06,680 --> 00:25:09,220
+ال identity إذا طلعت برضه T في T Star بيسوا ال
+
+318
+00:25:09,220 --> 00:25:12,180
+identity إذا من الجهتين T Star في T بيسوا ال
+
+319
+00:25:12,180 --> 00:25:15,960
+identity و T في T Star بيسوا ال identity إذا صارت
+
+320
+00:25:15,960 --> 00:25:20,570
+هذه T Star هي ال inverseإذا صارت P star يبقى 17
+
+321
+00:25:20,570 --> 00:25:24,110
+versus So T is unitary The converse is clear قولنا
+
+322
+00:25:24,110 --> 00:25:37,590
+إيش معناة الـ Converse ارجعلي على التلخيص طيب
+
+323
+00:25:37,590 --> 00:25:41,110
+الآن
+
+324
+00:25:41,110 --> 00:25:43,710
+المثال أو ال remark الأخيرة
+
+325
+00:25:46,190 --> 00:25:53,570
+بتقول ايه؟ ايزيومتريك لحالها لتكفل انها تكون ايه
+
+326
+00:25:53,570 --> 00:25:57,250
+شمالها؟ Unitary لازم تحطلها زججة زججة يعني ان هي
+
+327
+00:25:57,250 --> 00:26:01,940
+surjectiveالأن الـ Geometric Operators need not be
+
+328
+00:26:01,940 --> 00:26:05,620
+unitary وخد مثال بدي أجيبك مثال أكيد مش subjective
+
+329
+00:26:05,620 --> 00:26:10,080
+بس هاي كل الجزء الان consider the bounded linear
+
+330
+00:26:10,080 --> 00:26:15,220
+operator T من L2 لعند L2 given by بس بيعملني shift
+
+331
+00:26:15,220 --> 00:26:19,720
+shift operator بيشتد اللي هو ال XI1 XI2 XI3
+
+332
+00:26:19,720 --> 00:26:23,980
+وبيعمله shift لقدام شوية و بيحط ال zero في ال
+
+333
+00:26:23,980 --> 00:26:28,050
+entry الأول و بعدين بيبقوا ماشي زي ما هوإذا الـ T
+
+334
+00:26:28,050 --> 00:26:30,970
+of XI واحد XI اتنين XI تلعب تلعب إلى ما لا نهاية
+
+335
+00:26:30,970 --> 00:26:35,130
+بيساوي Zero XI واحد وXI اتنين إلى ما لا نهاية لأن
+
+336
+00:26:35,130 --> 00:26:39,230
+it is easy to see that T is an isometric سهل خالص
+
+337
+00:26:39,230 --> 00:26:43,290
+خدوا ال TX، إيش هو ال TX؟ هو لحاله طالع ايزومتري
+
+338
+00:26:43,290 --> 00:26:49,550
+شوفوا
+
+339
+00:26:49,550 --> 00:26:51,890
+كيف بيطلع Automatic Isometry
+
+340
+00:26:57,570 --> 00:27:01,790
+صلى على النبي عليه الصلاة والسلام اللهم صلى على
+
+341
+00:27:01,790 --> 00:27:08,890
+سيدنا محمد norm ال T XI 1 XI 2 إلى ما لا نهاية
+
+342
+00:27:08,890 --> 00:27:15,130
+اليد اللي هو جوا من ال X بساوي اللي هو norm T XI 1
+
+343
+00:27:15,130 --> 00:27:20,600
+بساوي 0 XI 1 XI 2 إلى ما لا نهايةوهذا الـ norm هيش
+
+344
+00:27:20,600 --> 00:27:26,320
+فالـ summation لـ XI I سوى summation لـ XI I تربيع
+
+345
+00:27:26,320 --> 00:27:30,760
+I من واحد إلى مالة نهاية الكل أص نص لأنه أول واحد
+
+346
+00:27:30,760 --> 00:27:35,940
+سفر فيها اللي هو عبارة عن مين norm من ال X ماشي
+
+347
+00:27:35,940 --> 00:27:41,780
+إذا صار اللي هو isometric إذا الان إذا T is an
+
+348
+00:27:41,780 --> 00:27:49,070
+isometricBut T is not onto مدام مش onto ده متحكوش
+
+349
+00:27:49,070 --> 00:27:55,530
+عن ال unitary But T is not onto for example خد
+
+350
+00:27:55,530 --> 00:28:01,430
+اللي هو اقصى و اخد و اقولك خد الواحد و السفر و
+
+351
+00:28:01,430 --> 00:28:07,650
+السفر و السفر إلى ما لنهاية element انقلته في TX
+
+352
+00:28:07,650 --> 00:28:13,960
+بتساوي هذالأ يمكن لإن أي و أي TX تبتدأ تكون صورتها
+
+353
+00:28:13,960 --> 00:28:17,400
+أوليش Zero و بعدين نحط اللي بدك هيها و هذا مش Zero
+
+354
+00:28:17,400 --> 00:28:21,160
+إذا مش on to طبعا هو بقولك T is not on to where
+
+355
+00:28:21,160 --> 00:28:25,360
+there is XI واحد و XI اتنين و XI واحد ده ساوي سفر
+
+356
+00:28:25,360 --> 00:28:28,960
+but there is no X element in L2 بحيث أنه TX
+
+357
+00:28:28,960 --> 00:28:32,860
+بالساوي XI واحد لإن هو بعمل shift و بخلي أول واحد
+
+358
+00:28:32,860 --> 00:28:38,050
+اسمه hence we havean isometric which is not onto
+
+359
+00:28:38,050 --> 00:28:41,690
+so it is not unitary لأن ال unitary عشان يكون
+
+360
+00:28:41,690 --> 00:28:47,370
+unitary لازم يكون say adjective و الهو isometric
+
+361
+00:28:47,370 --> 00:28:54,530
+او لو T inverse بسبب T star unitary بتكون
+
+362
+00:28:54,530 --> 00:29:00,670
+اللي هي adjective زي T inverse بسبب T star مبارك
+
+363
+00:29:00,670 --> 00:29:02,290
+الله فيكم و إلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/mlM0h2WP1Sg.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/mlM0h2WP1Sg.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6d6046108ab32b6865860a55ca626b10be5d228a
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/mlM0h2WP1Sg.srt
@@ -0,0 +1,2331 @@
+1
+00:00:05,300 --> 00:00:09,480
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:09,480 --> 00:00:12,680
+والصلاة والسلام على سيدنا محمد وعلى آله وصحبه
+
+3
+00:00:12,680 --> 00:00:17,360
+أجمعين هذه المحاضرة العاشرة مساق تحليل اقتراني أو 
+
+4
+00:00:17,360 --> 00:00:21,380
+تحليل دالي لطلاب وطالبات الجامعة الإسلامية قسم
+
+5
+00:00:21,380 --> 00:00:27,480
+رياضيات لطلاب وطالبات الماجستير، نبدأ اليوم إن شاء
+
+6
+00:00:27,480 --> 00:00:31,520
+الله، أو هناخد اليوم اللي هو 2-4 تحت عنوان
+
+7
+00:00:31,520 --> 00:00:34,540
+اللي هو finite dimensional normed spaces and
+
+8
+00:00:34,540 --> 00:00:38,080
+subspaces يعني اللي هنحكي فيه اللي هو الـ spaces
+
+9
+00:00:38,080 --> 00:00:42,840
+اللي هنحكي فيه أو الـ normed spaces اللي هنحكي فيه
+
+10
+00:00:42,840 --> 00:00:47,320
+اللي هي finite dimensional اللي هي بيكون الـ
+
+11
+00:00:47,320 --> 00:00:51,100
+dimension لها أيش لها finite dimension as a vector
+
+12
+00:00:51,100 --> 00:00:57,760
+space، نأخذ اللمّة ضرورية لإثبات العديد من النظريات
+
+13
+00:00:57,760 --> 00:01:01,580
+في هذا الـ section، اللمّة بتقول ما يليه اللي هو
+
+14
+00:01:01,580 --> 00:01:07,260
+let X1, X2, ..., Xn بيقى linearly independent set of
+
+15
+00:01:07,260 --> 00:01:15,620
+vectors in a normed space X، ثم هناك رقم C أكبر من
+
+16
+00:01:15,620 --> 00:01:20,740
+صفر مثلًا، لأي اختيار من الـ Scalars Alpha 1, Alpha
+
+17
+00:01:20,740 --> 00:01:25,920
+2, ..., Alpha N لدينا دائمًا Norm للـ Linear
+
+18
+00:01:25,920 --> 00:01:29,590
+Combination للألف واحد X واحد ألف اتنين زائد ألف
+
+19
+00:01:29,590 --> 00:01:33,770
+اتنين X اتنين زائد ... + ألف ان X ان هيكون أكبر أو يساوي
+
+20
+00:01:33,770 --> 00:01:39,490
+C في الـ summation للـ scalars اللي أخدتها أي كان الـ
+
+21
+00:01:39,490 --> 00:01:45,130
+scalars اللي أخدتهم بقدر ألاجي C بحيث إنه there
+
+22
+00:01:45,130 --> 00:01:49,490
+exists C بحيث إنه لكل choice يعني الـ C ده بتنفع
+
+23
+00:01:49,490 --> 00:01:53,450
+لكل choices للألف واحد ألف اتنين لعندي ألف N بحيث
+
+24
+00:01:53,450 --> 00:01:56,590
+إنّه يكون الـ norm للألف واحد X1 للألف اتنين X2
+
+25
+00:01:56,590 --> 00:01:59,810
+لعندي الألف N XN أكبر أو يساوي C في الـ summation
+
+26
+00:01:59,810 --> 00:02:05,010
+لمين؟ للـ absolute value للألف I، هذا الكلام إن شاء
+
+27
+00:02:05,010 --> 00:02:09,750
+الله بنشوف كيف وينفعته في خلال اللي هو النظريات
+
+28
+00:02:09,750 --> 00:02:14,920
+اللي هناخدها قدام، خلينا نبرهن هذا البرهان .. نبرهن
+
+29
+00:02:14,920 --> 00:02:20,180
+هذه النظرية، أول شيء أبرهن النظرية أو اللي أبدا
+
+30
+00:02:20,180 --> 00:02:27,200
+أبرهنها اللي هو لـ Beta 1 و Beta 2 و Beta 3 اللي الـ
+
+31
+00:02:27,200 --> 00:02:31,840
+summation لهم بيساوي 1، وبعد هيك هنتقل in general
+
+32
+00:02:31,840 --> 00:02:36,790
+بيصير سهل الانتقال هتشوفوا كيف، الآن أولًا نشهد إن
+
+33
+00:02:36,790 --> 00:02:40,830
+هناك C أكبر من صفر مثل ذلك لأي اختيار من الـ
+
+34
+00:02:40,830 --> 00:02:45,470
+Scalars Beta 1, Beta 2, ..., Beta N، والـ Scalars بس
+
+35
+00:02:45,470 --> 00:02:49,210
+بتحط عليهم شرط، نسمّيها إن هنا أيش بيساوي؟ بيساوي
+
+36
+00:02:49,210 --> 00:02:53,080
+واحد، بعد شوية هذه حاجة حلّتها هتصير سهلة، الآن نحن
+
+37
+00:02:53,080 --> 00:02:56,200
+لدينا Norm بي واحد X واحد بي اتنين X اتنين 
+
+38
+00:02:56,200 --> 00:02:59,440
+زائد ... بي ان X ان، اكبر أو يساوي C، إذا هذه الآن اللي
+
+39
+00:02:59,440 --> 00:03:04,040
+بدأ أثبتها، ماشي الحال، خلينا نثبت هذه ومن ثم ببعدها
+
+40
+00:03:04,040 --> 00:03:08,140
+اللي هو نثبت in general اللي طالبه في الـ M، اطلع
+
+41
+00:03:08,140 --> 00:03:13,100
+على فوق، البرهان قايم على إنه نفترض العكس، نصل لمين؟ لـ
+
+42
+00:03:13,100 --> 00:03:16,360
+contradiction، الآن اللي .. اللي .. اللي .. اللي
+
+43
+00:03:16,360 --> 00:03:21,160
+عندي بيدّقول assume that one does not hold، ماشي
+
+44
+00:03:21,160 --> 00:03:26,340
+الحال، يعني بدي أنفي الجملة الـ there exists such
+
+45
+00:03:26,340 --> 00:03:30,900
+that for any choice of beta 1 عند beta n والاخره 
+
+46
+00:03:31,340 --> 00:03:34,960
+إذا نفيها أكيد إيش بالمّاله بدل اللي هو there exist
+
+47
+00:03:34,960 --> 00:03:40,560
+بده يصير عنده الآن for all، then assume that الآن
+
+48
+00:03:40,560 --> 00:03:47,070
+one does not hold، يعني بده ينفي اللي هو المطلوب،
+
+49
+00:03:47,070 --> 00:03:51,810
+بدي أسأل الـ contradiction مافيه؟ for all M أكبر
+
+50
+00:03:51,810 --> 00:03:55,410
+من 0 بدي أغير بس السياق، سمّيها أيش بقى؟ لأ for all M
+
+51
+00:03:55,410 --> 00:04:00,410
+أكبر من 0 there exist scalars بدل ما هو for all
+
+52
+00:04:00,410 --> 00:04:03,810
+for any choice of scalars، بدي أسيّر أيش ماله؟ there
+
+53
+00:04:03,810 --> 00:04:09,090
+exist scalars Beta واحد خاصة بمين؟ بالـ M هذه، بيتا
+
+54
+00:04:09,090 --> 00:04:13,470
+واحد M بيتا اتنين M بيتا N M بتحت نفس الشروط الـ
+
+55
+00:04:13,470 --> 00:04:17,030
+summation تبحن من واحد عند N مش هو يساوي إيش؟ 
+
+56
+00:04:17,030 --> 00:04:21,310
+واحد وفي نفس الوقت أشماله وهذا ما تتحقق إيش؟ هبدأ
+
+57
+00:04:21,310 --> 00:04:25,470
+بتنفيها إن الـ norm هذا بيتا واحد X واحد زي بيتا
+
+58
+00:04:25,470 --> 00:04:29,730
+اتنين X اتنين زي بيتا M X M اصغر أو ساو مين؟ واحد
+
+59
+00:04:29,730 --> 00:04:34,620
+على M، ماشي الحال، يعني اللي مش عاجبه M اكتب for all
+
+60
+00:04:34,620 --> 00:04:38,020
+أحد على M بنفع نفس الشيء، for all M أو for one أحد
+
+61
+00:04:38,020 --> 00:04:40,880
+على M، يعني الـ C's اللي أنا الـ C اللي بدي أخدها
+
+62
+00:04:40,880 --> 00:04:44,520
+طبعًا صارت for all بدل اللي هي الـ C اللي بدي أسمّيها
+
+63
+00:04:44,520 --> 00:04:49,080
+أشماله واحد على M، لغرض أنا بديّاه، ماشي الحال، لأنّ
+
+64
+00:04:49,080 --> 00:04:54,220
+for all is choice، طيب الآن صار عندي اللي هو اللي
+
+65
+00:04:54,220 --> 00:05:01,100
+هي هذا اللي هو متحقّق، هذا فرضته أنا الآن، طيب يا
+
+66
+00:05:01,100 --> 00:05:04,680
+جماعة الآن
+
+67
+00:05:04,680 --> 00:05:11,020
+بمعنى آخر، لـ M بتساوي واحد انتبهوا، for all M قلنا
+
+68
+00:05:11,020 --> 00:05:15,780
+إذا لـ M بتساوي واحد، for 1 there exist معايا
+
+69
+00:05:15,780 --> 00:05:23,280
+sequence اسمها اللي هي بي واحد واحد بيتا واحد واحد
+
+70
+00:05:23,280 --> 00:05:32,490
+بيتا اتنين واحد، ... بيتا ان واحد، أعداد إن صح ومجموع الـ
+
+71
+00:05:32,490 --> 00:05:38,330
+absolute values له دول إيش بيساوي؟ واحد، for n طبعًا
+
+72
+00:05:38,330 --> 00:05:45,230
+إيش بتحقق؟ الـ norm لـ beta واحد x واحد زائد ... beta n
+
+73
+00:05:45,230 --> 00:05:51,030
+واحد xn إيش ماله؟ اصغر من واحد على واحد اللي هو
+
+74
+00:05:51,030 --> 00:05:57,560
+واحد، اللي بعدها for اللي هو n بتساوي 2 there exist
+
+75
+00:05:57,560 --> 00:06:07,500
+beta 1 2 و beta 2 2 فاهمين عليها؟ لعند beta n 2 ماله؟
+
+76
+00:06:07,500 --> 00:06:10,640
+هذا sequence of scalars، الـ summation اللي بيساوي
+
+77
+00:06:10,640 --> 00:06:16,720
+واحد، absolute value لهن، و Norm هنّ beta 1 2 x 1
+
+78
+00:06:16,720 --> 00:06:27,560
+زائد beta 1 2 2 x 2 زائد ... + beta n 2 x n برضه اصغر من
+
+79
+00:06:27,560 --> 00:06:34,640
+minimum واحد على اتنين، in general for M There
+
+80
+00:06:34,640 --> 00:06:44,340
+exists Beta 1M و Beta 2M لعند Beta nM such that
+
+81
+00:06:44,340 --> 00:06:51,940
+Norm مجموعها بيساوي Absolute Value 1، و Beta 1M في X1
+
+82
+00:06:51,940 --> 00:07:01,280
+زائد ... + Beta nM Xn أصغر من 1 على N، ماشي الحال، هذا
+
+83
+00:07:01,280 --> 00:07:10,180
+الكلام for any M صحيح، طيب شوفوا عليّ الآن، then بناء
+
+84
+00:07:10,180 --> 00:07:12,820
+على الكلام هذا there exist a sequence YM of
+
+85
+00:07:12,820 --> 00:07:18,400
+vectors اللي هو YM بتساوي Beta 1 M X 1 زائد Beta 2
+
+86
+00:07:18,400 --> 00:07:25,020
+M X 2 زائد ... + Beta M X M، ماشي الحال، اللي هي هذه الـ
+
+87
+00:07:25,020 --> 00:07:33,710
+sequence، Y1 هي الأولى، Y1 Beta 1 1 Beta 2 1 إلى عند
+
+88
+00:07:33,710 --> 00:07:38,890
+Beta هي عنصر الآن الأولاني، الـ Y2 العنصر الثاني، الـ
+
+89
+00:07:38,890 --> 00:07:41,510
+Y تلقى نفس الشيء إلى ما نندله، دهانا دي صارت
+
+90
+00:07:41,510 --> 00:07:45,710
+sequence، شوف كيف شكل عناصرها، عناصرها هذوله الـ
+
+91
+00:07:45,710 --> 00:07:50,620
+linear combination من اللي أنا حكيت عنه هنا بحيث إنّ
+
+92
+00:07:50,620 --> 00:07:56,500
+الـ summation لـ الـ absolute value لكل اللي
+
+93
+00:07:56,500 --> 00:08:02,260
+بتتكون منها لكل YM مجموعها إنّه بيساوي واحد، ومش هيك
+
+94
+00:08:02,260 --> 00:08:08,700
+ولو اجيت أخدت Norm الـ YM، هي Norm الـ YM هذا هو من
+
+95
+00:08:08,700 --> 00:08:14,420
+هي هي في الواقع هذا من Norm الـ YM هيساوي الـ Norm
+
+96
+00:08:14,420 --> 00:08:21,470
+لهذه، as M goes to infinity، هذا الـ Norm إيش يشرّ إلى
+
+97
+00:08:21,470 --> 00:08:29,870
+أين؟ نروح إلى Zero، بمعنى آخر صارت عندي اللي هو الـ
+
+98
+00:08:29,870 --> 00:08:34,490
+sequence YM من الـ vectors، هذه الـ Norm تبعها goes
+
+99
+00:08:34,490 --> 00:08:38,930
+to zero as M goes to mean to infinity، خّلوا هذه في
+
+100
+00:08:38,930 --> 00:08:43,850
+الذاكرة، إذا أنت حصلت على sequence YM هي شكل الـ
+
+101
+00:08:43,850 --> 00:08:48,970
+sequence، Normها بيروح لمين؟ للصفر، بدا أصلكم في الآخر
+
+102
+00:08:48,970 --> 00:08:54,810
+لـ contradiction، شوفوا كيف الآن، نتفاجئ إحنا إنّ الـ
+
+103
+00:08:54,810 --> 00:08:59,290
+summation لكل مجموعة من هدولة الـ absolute values
+
+104
+00:08:59,290 --> 00:09:02,650
+لهم، كل مجموعة الـ summation إنّها مش بساوي بساوي
+
+105
+00:09:02,650 --> 00:09:09,190
+واحد، بمعنى بمعنى إن كل واحدة منهم BIM أصغر بساوي
+
+106
+00:09:09,190 --> 00:09:14,350
+واحد لكل I، معايا؟ كلهم دايمًا الـ Norm أشماله أصغر من
+
+107
+00:09:14,350 --> 00:09:17,470
+واحد، ده كل I ولا كل مين؟ واحد، يعني بي واحد واحد
+
+108
+00:09:17,470 --> 00:09:21,430
+أصغر شوي واحد، بي واحد اتنين اصغر .. وهكذا، ماشي
+
+109
+00:09:21,430 --> 00:09:25,230
+الحال .. هذا إيه اللي معناه؟ hence الآن for any
+
+110
+00:09:25,230 --> 00:09:36,330
+fixed I اختارولي BIM اللي هي بي اي واحد، بي اتنين، بي
+
+111
+00:09:36,330 --> 00:09:41,450
+اي تلاتة، بي اي اربعة، بي اي خمسة، يعني بدي أجّي بي اي
+
+112
+00:09:41,450 --> 00:09:52,680
+هنا بي اي واحد بي اي اتنين، BIM in general هذه عبارة
+
+113
+00:09:52,680 --> 00:09:57,660
+عن sequence of numbers، مظبوط ولا لأ؟ كل واحدة منهم
+
+114
+00:09:57,660 --> 00:10:00,200
+هدولة sequence of numbers، وهذه sequence of
+
+115
+00:10:00,200 --> 00:10:04,640
+numbers، وهذه sequence of numbers، عدد من هدولة
+
+116
+00:10:04,640 --> 00:10:07,640
+واحدة اتنين، اتنين تلاتة، أربع إن من اللي من الـ
+
+117
+00:10:07,640 --> 00:10:12,890
+sequences، كل واحدة فيهم is a bounded sequence، لماذا
+
+118
+00:10:12,890 --> 00:10:17,010
+اسمها Sequence؟ لأنّ أي عنكالة الواحدة فيهم أصغر أو
+
+119
+00:10:17,010 --> 00:10:18,550
+يساوي إيش؟ واحد
+
+120
+00:10:21,120 --> 00:10:26,080
+بشرد من الـ space اللي عندي إلى الـ space في R أو
+
+121
+00:10:26,080 --> 00:10:30,420
+في C، أخدتها sequence of main of numbers، بي اي واحد
+
+122
+00:10:30,420 --> 00:10:34,820
+بي اي اتنين، is a bounded sequence، then بي واحد
+
+123
+00:10:34,820 --> 00:10:39,520
+اللي هي M و بي اتنين M، كل هى نفس الشيء sequence of
+
+124
+00:10:39,520 --> 00:10:43,040
+إيش؟ of numbers، و bounded، فبنيجي نشوف العالمين على
+
+125
+00:10:43,040 --> 00:10:48,280
+بي واحد of M، الآن بي واحد of M has مادام sequence
+
+126
+00:10:48,280 --> 00:10:51,580
+of numbers وهي bounded، احنا بنعرف في الـ Real إنّ any
+
+127
+00:10:51,580 --> 00:10:53,860
+bounded sequence has a convergence of a
+
+128
+00:10:53,860 --> 00:11:00,140
+subsequence، بلزانو آه مذاكرين؟ إذا يا جماعة صار
+
+129
+00:11:00,140 --> 00:11:09,900
+عند بي واحد M اللي هيبعد ذلك لديها subsequence
+
+130
+00:11:09,900 --> 00:11:14,920
+بي واحد ام ايش واحد، هذه subsequence من مين؟ من
+
+131
+00:11:14,920 --> 00:11:20,320
+السيكوانس هذه، يعني من السيكوانس بي واحد of ام اللي
+
+132
+00:11:20,320 --> 00:11:25,960
+هي هذه فيها subsequence منها بي ام واحد
+
+133
+00:11:28,760 --> 00:11:33,280
+طيب الآن، مدام converges إذا نقول نسمّيها conversion
+
+134
+00:11:33,280 --> 00:11:38,100
+from mean to beta واحد، يعني الآن فرضنا إنّ الـ beta
+
+135
+00:11:38,100 --> 00:11:40,300
+واحد
+
+136
+00:11:41,560 --> 00:11:53,620
+بواحد of m بواحد
+
+137
+00:11:53,620 --> 00:12:10,920
+of m
+
+138
+00:12:12,230 --> 00:12:16,310
+الآن ما هي الـ .. الـ .. الـ .. الـ .. الـ .. الـ YMs
+
+139
+00:12:16,310 --> 00:12:20,030
+هدولة؟ ما هي sequence بتتكون من اللي بيكونها هي
+
+140
+00:12:20,030 --> 00:12:23,590
+linear combinations بين X1 و X2 و XN، أدات الـ 
+
+141
+00:12:23,590 --> 00:12:26,250
+linear combinations اللي هي الـ scalars هدول ال
+
+142
+00:12:26,250 --> 00:12:30,010
+scalars هدول اللي هي في الأصل من مين جاية من الـ β
+
+143
+00:12:30,010 --> 00:12:34,670
+و .. من β I of M in general ماشي الحالة إذا الآن
+
+144
+00:12:34,670 --> 00:12:40,710
+then عندي Y<sub>1</sub>M
+
+145
+00:12:40,710 --> 00:12:45,090
+بدي أسميها هي الـ subsequence اللي الـ scale
+
+146
+00:12:45,090 --> 00:12:51,690
+الذبعاتها من وين جايت من B و β<sub>1</sub>M لت Y<sub>1</sub>M بي
+
+147
+00:12:51,690 --> 00:12:55,930
+the corresponding sequence which is a subsequence
+
+148
+00:12:55,930 --> 00:13:04,160
+of mean of Y<sub>M</sub>Where Y<sub>1</sub>M بالظبط ايش بتساوي β<sub>1</sub>M<sub>1</sub>
+
+149
+00:13:04,160 --> 00:13:09,580
+X<sub>1</sub> زائد β<sub>2</sub>MX<sub>2</sub> يعني بس أخدت من الأولى مين من
+
+150
+00:13:09,580 --> 00:13:13,980
+الـ β<sub>1</sub> و M هذه و الباقي أخدت من مين من الأصلية
+
+151
+00:13:13,980 --> 00:13:21,380
+تبعت الـ Y<sub>M</sub> β<sub>2</sub>MX<sub>2</sub> زائد β<sub>N</sub>MX<sub>N</sub> هذي
+
+152
+00:13:21,380 --> 00:13:23,500
+اللي هي Y<sub>1</sub>M
+
+153
+00:13:25,220 --> 00:13:29,820
+هذه الآن الـ subsequence برضه اللي عملته على الـ
+
+154
+00:13:29,820 --> 00:13:35,180
+β<sub>1</sub> of M بدي أعمله على مين؟ β<sub>2</sub> of M وهذه
+
+155
+00:13:35,180 --> 00:13:38,640
+اتفاجنة عبارة عن sequence of برضه أيش؟ of numbers
+
+156
+00:13:38,640 --> 00:13:41,380
+which is bounded إذن لها برضه أيش؟ subsequence
+
+157
+00:13:41,730 --> 00:13:46,090
+بالتالي، بما أن β<sub>2</sub> و M هي سيكوانات مرتبطة، فهي
+
+158
+00:13:46,090 --> 00:13:52,410
+تحتوي على سبسيكوانت مرتبطة تسميها β<sub>2</sub>M<sub>2</sub> هذا
+
+159
+00:13:52,410 --> 00:13:54,490
+أيضًا مرتبط إلى B<sub>2</sub>
+
+160
+00:13:58,090 --> 00:14:04,830
+بتكون β<sub>2</sub> of M و 2 converges فرقنا ل مين ل B<sub>2</sub> لأنها
+
+161
+00:14:04,830 --> 00:14:11,070
+sub sequence من bounded sequence يعني بمعنى آخر
+
+162
+00:14:11,070 --> 00:14:13,930
+فما ده في عندي bounded sequence إذا بقدر ألاقي
+
+163
+00:14:13,930 --> 00:14:16,810
+convergent subsequence سميتها اللي قلتها قبل شوية
+
+164
+00:14:16,810 --> 00:14:22,030
+it has a convergent subsequence منها β<sub>2</sub>M that
+
+165
+00:14:22,030 --> 00:14:29,090
+converges to مين to β<sub>2</sub> اطلع لفوقالآن Y<sub>2</sub>M نفس الجثة
+
+166
+00:14:29,090 --> 00:14:33,810
+بدي أخدها الـ Corresponding Sequence المكوّنة من
+
+167
+00:14:33,810 --> 00:14:36,990
+Y<sub>1</sub> .. اللي هي Y<sub>1</sub> .. اللي مكوّنة .. اللي هتكون
+
+168
+00:14:36,990 --> 00:14:41,910
+جزئية من من Y<sub>1</sub> و في M ليش؟ لأن Y<sub>2</sub> و في M على سرها
+
+169
+00:14:41,910 --> 00:14:49,010
+متكونة β<sub>1</sub>M<sub>1</sub> زي اللي هي تمامته الـY<sub>1</sub> و M و β<sub>2</sub> و M<sub>2</sub>
+
+170
+00:14:49,010 --> 00:14:53,790
+جزء من هذيك اللي هي X<sub>2</sub> زاد هذي بتخليهم زي ما هما
+
+171
+00:14:53,790 --> 00:14:57,330
+الأصليات إذا بس اتغيرت هذي إذا صارت هذي Y<sub>2</sub> of M
+
+172
+00:14:57,330 --> 00:15:02,930
+subsequence من مين؟ من Y<sub>1</sub> of M بدي لأنا كموحدة إن
+
+173
+00:15:02,930 --> 00:15:07,210
+هذول أن من العناصر بدي أشتغل على البجيات بنفس
+
+174
+00:15:07,210 --> 00:15:13,640
+الأسلوب we after any steps We get Y<sub>N</sub>M as a
+
+175
+00:15:13,640 --> 00:15:19,540
+subsequence of Y<sub>N</sub> With Y<sub>N</sub>M أيش بتساوي؟ β<sub>1</sub>M<sub>1</sub>
+
+176
+00:15:19,540 --> 00:15:27,400
+β<sub>2</sub>M<sub>2</sub> و β<sub>N</sub> يعني M<sub>N</sub>X<sub>N</sub> هذي و طبعا كل اللي
+
+177
+00:15:27,400 --> 00:15:31,980
+بنشتغل فيه اللي هو الـ absolute values اللي ما له
+
+178
+00:15:31,980 --> 00:15:35,580
+مجموعة بساوي واحد من ضمنه هذول اللي اشتغلت عليه
+
+179
+00:15:35,580 --> 00:15:41,180
+هنا إذا مجموعة دولة بساوي واحد إذا صار عندي β<sub>1</sub>
+
+180
+00:15:41,180 --> 00:15:47,280
+M<sub>1</sub> و β<sub>1</sub> و β<sub>2</sub>M<sub>2</sub> بتروح لـ β<sub>2</sub> و β<sub>N</sub>M<sub>N</sub>
+
+181
+00:15:47,280 --> 00:15:52,600
+بتروح لـ β<sub>N</sub> هذا كله as mean as M الـ goals
+
+182
+00:15:52,600 --> 00:15:57,680
+المعلنة هي لأن M هي اللى بتعمل ال sequence طيب
+
+183
+00:15:57,680 --> 00:16:08,110
+also برضه واحد بيساوي limit Limit اللي هو β<sub>1</sub>M<sub>1</sub>
+
+184
+00:16:08,110 --> 00:16:14,690
+زي β<sub>2</sub>M<sub>2</sub> زي β<sub>N</sub>M<sub>N</sub> مجموح انش هيساوي الآن
+
+185
+00:16:14,690 --> 00:16:21,070
+مجموحين هذولة اللي هو بساوي واحد و limit كل واحدة
+
+186
+00:16:21,070 --> 00:16:26,250
+بتساوي الأولى β<sub>1</sub> والتانية β<sub>2</sub> والتالتة β
+
+187
+00:16:26,250 --> 00:16:32,270
+N إذا limit المجموع بساوي مجموحين هذولة لقيمة ال
+
+188
+00:16:32,270 --> 00:16:35,550
+limits بنوزع ال limit يعني بمعنى آخر بوزع ال limit
+
+189
+00:16:35,550 --> 00:16:39,320
+على مجموع عدد عشر عشرين تلاتين N من ال limits بكون
+
+190
+00:16:39,320 --> 00:16:42,140
+limit الأول زي limit التاني زي limit التالت بساوي
+
+191
+00:16:42,140 --> 00:16:45,420
+summation β<sub>I</sub> وهذا المجموع زي ما قلنا أيش بساوة
+
+192
+00:16:45,420 --> 00:16:51,320
+واحد إذا المجموع هذا النهايات نفسها بساوة واحد إذا
+
+193
+00:16:51,320 --> 00:16:56,220
+حصلت على إن مجموع النهايات بساوة واحد إذا الآن
+
+194
+00:16:56,220 --> 00:17:03,220
+مدان مجموع هذولة، انتبهوا الآن مجموع هذولة بساوة
+
+195
+00:17:03,220 --> 00:17:09,560
+واحد إذا فيه على الأقل، على الأقل واحدة مش صفر هكذا
+
+196
+00:17:09,560 --> 00:17:11,900
+أصبح مجموح من بساوي واحد absolute values هذه
+
+197
+00:17:11,900 --> 00:17:15,280
+absolute values مجموح من إيش بساوي بساوي واحد يعني
+
+198
+00:17:15,280 --> 00:17:18,260
+قيم موجة بأكبر بساوي صفر مجموح من واحد إذا على
+
+199
+00:17:18,260 --> 00:17:21,620
+الأقل أكيد في واحدة يشمالها لا تساوي صفر إذا then
+
+200
+00:17:21,620 --> 00:17:26,200
+there is at least β<sub>I</sub> لا تساوي إيش صفر لكن الـ X
+
+201
+00:17:26,200 --> 00:17:30,660
+واحد والـ X اتنين والـ X unlinearly independent then
+
+202
+00:17:30,660 --> 00:17:36,480
+أكيد الـ Y لا تساوي صفر الـ Y مين هي الـ Y الـ Y هي
+
+203
+00:17:36,480 --> 00:17:46,520
+عبارة الـ Y عبارة عن X<sub>1</sub>β<sub>1</sub> زي X<sub>2</sub>β<sub>2</sub> زي X<sub>N</sub>
+
+204
+00:17:46,520 --> 00:17:55,090
+β<sub>N</sub> هذا أكيد لا تساوي صفر ليش لا تساوي صفر؟ لأن
+
+205
+00:17:55,090 --> 00:18:00,910
+لو كانت صفر لو كانت صفر طبعا في عندي واحدة منهم X<sub>I</sub>
+
+206
+00:18:00,910 --> 00:18:05,570
+β<sub>I</sub> زائد إلى أخير لإن عندك X<sub>n</sub> هذه الـ β<sub>I</sub>
+
+207
+00:18:05,570 --> 00:18:10,370
+تبعتها مش صفر لو بدنا نقول هذه بتساوي صفر معناته
+
+208
+00:18:10,370 --> 00:18:16,120
+صارت الـ X<sub>I</sub> بكتبها على صورة X<sub>1</sub>β<sub>1</sub> على β<sub>I</sub>
+
+209
+00:18:16,120 --> 00:18:22,880
+زائد X<sub>n</sub>β<sub>N</sub> على اليمين β<sub>I</sub> يعني قدرت أكتب X
+
+210
+00:18:22,880 --> 00:18:26,260
+أزالين الـ combination من هذا وهذا أشماله
+
+211
+00:18:26,260 --> 00:18:30,580
+contradiction لأن X<sub>1</sub> و X<sub>2</sub> و X<sub>n</sub> are linearly
+
+212
+00:18:30,580 --> 00:18:36,220
+independent إذن الـ linearly independent هو اللي
+
+213
+00:18:36,220 --> 00:18:43,300
+ضمنلي أن الـ Y هذه أشمالها لاتساوى 0 لكن في الأصل،
+
+214
+00:18:43,300 --> 00:18:47,760
+since the norm is continuous، إذا الـ Normal Y and
+
+215
+00:18:47,760 --> 00:18:53,440
+M بيروح لـ Normal Y مدام ال .. لأنه limit الـ Y<sub>n</sub> و M
+
+216
+00:18:53,440 --> 00:18:57,540
+إيش بيساوي؟ بيساوي الـ Y إذا norm الـ Y<sub>n</sub> و M هيروح
+
+217
+00:18:57,540 --> 00:19:04,080
+لمين؟ لـ norm الـ Y but Y<sub>n</sub> و M اللي ركّبناها .. نرجع
+
+218
+00:19:04,080 --> 00:19:08,700
+لقصتنا الأولى is a subsequence من مين؟ من Y<sub>n</sub>
+
+219
+00:19:08,700 --> 00:19:14,340
+الأصلية Y<sub>n</sub> الأصلية إيش مالها؟ normها راح لمين؟ لل
+
+220
+00:19:14,340 --> 00:19:18,040
+0 .. أو للتركيبة .. أنزل .. أنزل .. أنزل .. هنزل
+
+221
+00:19:18,040 --> 00:19:22,260
+هايو عندنا في واحة اتنين اثبتنا ان normal Y<sub>M</sub> ايش
+
+222
+00:19:22,260 --> 00:19:27,420
+مروح للسفر لازم goes to infinity إذا الآن الآن
+
+223
+00:19:28,880 --> 00:19:32,980
+أثبتنا أن الـ sub-sequence هذه راحت لـ Normal Y و
+
+224
+00:19:32,980 --> 00:19:37,660
+الـ M اللي هي الـ Y and M sub-sequence من Y<sub>M</sub> و
+
+225
+00:19:37,660 --> 00:19:40,520
+Normal Y<sub>M</sub> ما أثبتناه في الأول بيروح لـ Zero إذا
+
+226
+00:19:40,520 --> 00:19:43,400
+الـ Norm هذي إيش بيروح لمين؟ لـ Zero و احنا قلنا
+
+227
+00:19:43,400 --> 00:19:46,860
+هنا الـ Y إيش ما لها؟ لأ تساوي صفر فصار في عندي
+
+228
+00:19:46,860 --> 00:19:51,280
+Contradiction إذا الفرضية الأصلية مش صحيحة Hence
+
+229
+00:19:51,280 --> 00:19:57,600
+اللي هو Therefore واحد is proved بمعنى آخر أنه لكل
+
+230
+00:19:57,600 --> 00:20:02,900
+اللي هي Pfff There exists C such that لكل choice ل
+
+231
+00:20:02,900 --> 00:20:06,300
+β<sub>1</sub> و β<sub>2</sub> المجموحين بيساوي واحد norm اللي هو
+
+232
+00:20:06,300 --> 00:20:12,500
+أكبر أو يساوي C الآن الآن انزل شوية خليني أرجع
+
+233
+00:20:12,500 --> 00:20:16,620
+اللي بس الآن from this and three we have a
+
+234
+00:20:16,620 --> 00:20:21,200
+contradiction therefore one is approved now if ال
+
+235
+00:20:21,200 --> 00:20:24,600
+absolute اللي أثبتناه كله في حالة اللي هو
+
+236
+00:20:24,600 --> 00:20:28,020
+summation للـ β<sub>I</sub>'s بيساوي واحد اللي أنا بتاخده
+
+237
+00:20:28,020 --> 00:20:31,960
+arbitrarily الآن إذا الـ F ألف واحد أفضل قيمة ألف
+
+238
+00:20:31,960 --> 00:20:35,620
+واحد زائد أفضل قيمة ألف اتنين زائد أفضل قيمة ألف ألف
+
+239
+00:20:35,620 --> 00:20:41,540
+ن افترض انه ايش ماله بساوي صفر إذا الف اي صفر لكله
+
+240
+00:20:41,540 --> 00:20:47,040
+مش الحال إذا ال norm للألف واحد X<sub>1</sub> زائد ألف N
+
+241
+00:20:47,040 --> 00:20:53,180
+X<sub>n</sub> اللي هو أكبر أو يساوي C في ال summation hold ايش
+
+242
+00:20:53,180 --> 00:20:55,380
+اللي بده أعمله يا جماعة أنا اللي بده اتبطه الآن
+
+243
+00:20:55,380 --> 00:20:57,080
+انتبهوا
+
+244
+00:20:58,550 --> 00:21:04,790
+اللي بيدثبتلكم إياه الآن الـ arbitrary scalars
+
+245
+00:21:04,790 --> 00:21:10,610
+يعني there exists C أكبر من 0 such that for any
+
+246
+00:21:10,610 --> 00:21:15,010
+choice of α<sub>1</sub>, α<sub>2</sub> لعند α<sub>N</sub> with
+
+247
+00:21:15,010 --> 00:21:21,930
+summation اللي هو such that norm اللي هي الـ α
+
+248
+00:21:21,930 --> 00:21:28,940
+<sub>1</sub>X<sub>1</sub> زي α<sub>N</sub>X<sub>N</sub> اللي هو أكبر أو يساوي C ال
+
+249
+00:21:28,940 --> 00:21:32,520
+summation absolute value of I I من عند واحد لمنين
+
+250
+00:21:32,520 --> 00:21:37,060
+لعندك for any choice لأن بتاخد حالتين الحالة
+
+251
+00:21:37,060 --> 00:21:42,660
+الأولى أن يكون ال summation هذا ال summation α
+
+252
+00:21:42,660 --> 00:21:48,620
+<sub>I</sub> بساوي صفر إذا صفر معناته automatically كل واحدة
+
+253
+00:21:48,620 --> 00:21:51,540
+فيه صفر معناته اللي هو كل الـ C's اللي في الدنيا
+
+254
+00:21:51,540 --> 00:21:55,700
+بتظبط يعني هذا الـ Trivial Case لما نفترض إن الـ
+
+255
+00:21:55,700 --> 00:21:59,020
+summation للأبسوليوت V للألف I أشمالها لا يساوي
+
+256
+00:21:59,020 --> 00:22:04,780
+صفر عشان بتقسم عليها بالعالم طيب طيب finally if S
+
+257
+00:22:04,780 --> 00:22:08,300
+بتساوي ال summation للألف I أشمالها لا تساوي إيش
+
+258
+00:22:08,300 --> 00:22:12,610
+صفر خدوا الـ N أحنا أثبتناها لـ β<sub>I</sub> ال
+
+259
+00:22:12,610 --> 00:22:15,570
+summation اللي بيساوي واحد خدوا β<sub>1</sub> بيساوي
+
+260
+00:22:15,570 --> 00:22:20,090
+α<sub>1</sub> على S β<sub>2</sub> α<sub>2</sub> على S β<sub>N</sub> α<sub>N</sub>
+
+261
+00:22:20,090 --> 00:22:23,730
+على S in general لكل I β<sub>I</sub> بيساوي α<sub>I</sub> على S
+
+262
+00:22:23,730 --> 00:22:28,210
+لـ I بيساوي واحد لعند الـ N حسبولي الآن لـ β<sub>Z</sub>
+
+263
+00:22:28,210 --> 00:22:31,330
+للـ N ال summation لـ β<sub>I</sub> I من عند واحد لـ N
+
+264
+00:22:31,330 --> 00:22:35,750
+بيساوي ال summation بأخد الـ 1 على أسماله عامل
+
+265
+00:22:35,750 --> 00:22:39,050
+مشترك في الـ summation هذا هو هذا فاش بيساوي
+
+266
+00:22:39,050 --> 00:22:42,810
+بيساوي واحد إذا أنا أثبته للي الـ β بيساوي واحد
+
+267
+00:22:42,810 --> 00:22:48,290
+إذا النظرية صحيحة لهذه اه طيب by substituting β
+
+268
+00:22:48,290 --> 00:22:53,110
+<sub>I</sub> بيساوي α<sub>I</sub> على S الواحد اللي أثبتناها we get
+
+269
+00:22:53,110 --> 00:22:58,170
+norm α<sub>1</sub> على S X<sub>1</sub> زائد α<sub>2</sub> على S X<sub>2</sub>
+
+270
+00:22:58,170 --> 00:23:03,400
+زائد α<sub>N</sub> عكس X<sub>N</sub> أكبر بيساوي مين؟ C الآن هناخد الـ
+
+271
+00:23:03,400 --> 00:23:07,360
+C مالها برا عام المشترك اللي هي 1 على ال S فالـ S
+
+272
+00:23:07,360 --> 00:23:10,760
+1 على ال S ناخدها عام المشترك و بعدين نضربها في
+
+273
+00:23:10,760 --> 00:23:14,100
+الطرفين بنكون حصلنا α<sub>1</sub>X<sub>1</sub> α<sub>2</sub>X<sub>2</sub> زائد
+
+274
+00:23:14,100 --> 00:23:18,340
+α X<sub>N</sub> أكبر من مين من C فS اللي هي C بتساوي ال
+
+275
+00:23:18,340 --> 00:23:26,530
+summation this completes the proof أي سؤال طيب نجي
+
+276
+00:23:26,530 --> 00:23:31,770
+لان نظريتنا هذه لما يعني عبارة عن أداء لاللي هو
+
+277
+00:23:31,770 --> 00:23:39,170
+للوصول لإثبات النظريات اللاحقة نجي
+
+278
+00:23:39,170 --> 00:23:42,770
+لان صار النظرية بداخل بيتها لجهة النظرية المهمة
+
+279
+00:23:42,770 --> 00:23:47,630
+هذه المهمة المنيحة و الحلوة هذه صار برهانها سهل
+
+280
+00:23:47,630 --> 00:23:51,010
+الآن أو بسيط بالاستعانة بال .. بال .. بال .. 
+
+281
+00:23:51,420 --> 00:23:55,100
+باللمّة اللي قبلها شوية يعني قد يكون بعض الكتب اللي
+
+282
+00:23:55,100 --> 00:23:59,000
+هي بتثبتها بتثبتش اللمّة فبتروح تثبتها مباشرة و
+
+283
+00:23:59,000 --> 00:24:02,560
+بتبدأ تشتغل شغل طبعا أكثر تعقيدا الآن بعد ما
+
+284
+00:24:02,560 --> 00:24:07,080
+أثبتنا اللمّة بيسير شغلها أكثر سهولة نيجي نشوف أيش
+
+285
+00:24:07,080 --> 00:24:11,900
+اللي بيقوله إعلان هذا theorem every finite
+
+286
+00:24:11,900 --> 00:24:15,420
+dimensional subspace Y of a normed space X أشماله
+
+287
+00:24:15,420 --> 00:24:20,460
+is complete أي في ال finite dimensional space لو
+
+288
+00:24:20,460 --> 00:24:25,920
+أخدنا أو في اللي هو تكون الـ subspace نفسه finite
+
+289
+00:24:25,920 --> 00:24:29,440
+dimensional من space على طول هذا ال subspace بيكون 
+
+290
+00:24:29,440 --> 00:24:34,140
+complete يعني الآن أنا finite dimensional space is
+
+291
+00:24:34,140 --> 00:24:38,020
+complete هذه حالة خاصة بتصير لأن الحالة العامة
+
+292
+00:24:38,020 --> 00:24:43,600
+أن أنا finite dimensional subspace of a normed
+
+293
+00:24:43,600 --> 00:24:49,090
+space must be complete عشان هيك كل اللي بنشتغل فيه
+
+294
+00:24:49,090 --> 00:24:54,410
+R وR تربيع وR تكعيب وR أنه وC وC1 وC2 كلهم finite
+
+295
+00:24:54,410 --> 00:24:58,390
+dimensional spaces هدول كلهم complete metric
+
+296
+00:24:58,390 --> 00:25:04,930
+spaces أو complete normed spaces معين؟ طيب In
+
+297
+00:25:04,930 --> 00:25:08,050
+particular, every finite dimensional normed space
+
+298
+00:25:08,050 --> 00:25:14,030
+كله is complete بدنا نثبت الآن خدوا الآن لثبات سهل
+
+299
+00:25:14,030 --> 00:25:18,070
+let Y be .. عشان نثبت complete ناخد any Cauchy
+
+300
+00:25:18,070 --> 00:25:22,110
+sequence و نثبت انها converged وبس هي كل جثتنا بما
+
+301
+00:25:22,110 --> 00:25:26,170
+يلقم السؤال طبعا let Y be any Cauchy sequence in Y
+
+302
+00:25:27,070 --> 00:25:30,790
+Suppose that the dimension للـ Y إيش بيساوي N هذا
+
+303
+00:25:30,790 --> 00:25:35,070
+الـ Y sub space من a normed space اسمه إيه إيش X
+
+304
+00:25:35,070 --> 00:25:38,530
+ال sub space Y هو اللي ال dimension إيه بيساوي N
+
+305
+00:25:38,530 --> 00:25:42,290
+طيب مدام ال dimension إيه بيساوي N إذا إنه bases
+
+306
+00:25:42,290 --> 00:25:45,830
+ال bases تبع جبل الخطة تبع جبل الخطة زمان اللي أن
+
+307
+00:25:45,830 --> 00:25:49,370
+ال bases إيه نفترض إنه اسمه E1 وE2 وEN بيه any
+
+308
+00:25:49,370 --> 00:25:54,640
+basis forming for Y لأنه finite dimensional مدام
+
+309
+00:25:54,640 --> 00:25:58,980
+اللي هو الـ E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12
+
+310
+00:25:58,980 --> 00:26:04,780
+E13 E14 E14 E15 E16 E17 E18 E19 E21 E21 E21 E21
+
+311
+00:26:04,780 --> 00:26:06,260
+E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21
+
+312
+00:26:06,260 --> 00:26:06,500
+E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21
+
+313
+00:26:06,500 --> 00:26:07,140
+E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21
+
+314
+00:26:07,140 --> 00:26:07,980
+E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21
+
+315
+00:26:07,980 --> 00:26:15,030
+E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 of
+
+316
+00:26:15,030 --> 00:26:18,710
+the form YM بسوء ألف واحد M هذي scalar رمز ال
+
+317
+00:26:18,710 --> 00:26:22,850
+scalar حطيت ال M هنا عشان يشملها بنقول عنها لمين
+
+318
+00:26:22,850 --> 00:26:27,010
+لل YM لو Y واحد هنحط لها واحد عشان تكون لمين لل Y
+
+319
+00:26:27,010 --> 00:26:32,130
+واحد وهكذا لأن YM بتسوء ألف واحد M E واحد زاد ألف
+
+320
+00:26:32,130 --> 00:26:36,790
+اثنين M E اثنين زاد ألف N E M E N اللي هي YM
+
+321
+00:26:36,790 --> 00:26:39,250
+مكتوبة على هذه الصورة لإنه ال E واحد وال E اثنين
+
+322
+00:26:39,250 --> 00:26:43,910
+وال E N are a basis طيب
+
+323
+00:26:44,930 --> 00:26:49,830
+Since YM is Cauchy Sequence إذا لكل Y أكبر من 0
+
+324
+00:26:49,830 --> 00:26:52,930
+there exists K limiting and such that البعد بين أي
+
+325
+00:26:52,930 --> 00:26:59,010
+نقطتين YM نقص YR أصغر من Y لكل R و M أكبر من مين من
+
+326
+00:26:59,010 --> 00:27:03,370
+ال K اللي لجيناها طيب الآن بدي أستخدم اللمّة اللي
+
+327
+00:27:03,370 --> 00:27:07,130
+قابلت بشويها لجيت و بدي أستخدمها دي لإن from this
+
+328
+00:27:07,130 --> 00:27:11,450
+and by لمة 2.4.1 بنقدر نلاقي ال C أكبر
+
+329
+00:27:11,450 --> 00:27:16,990
+من 0 معايا؟ هذا الـ C أكبر من 0 لمين؟ الـ norm اللي
+
+330
+00:27:16,990 --> 00:27:19,870
+هو الـ vector أكبر يساوي C في الصممشي للـ scalar
+
+331
+00:27:19,870 --> 00:27:23,390
+استبعاته، صح؟ هذا اللي قبل شوية اللي ما هو أتعبنا
+
+332
+00:27:23,390 --> 00:27:26,770
+حالنا كلنا أتعب there exists C أكبر من 0 such that
+
+333
+00:27:26,770 --> 00:27:31,270
+YM ناقص YR زي من إبسنون، هي الإبسنون أكبر من YM
+
+334
+00:27:31,270 --> 00:27:36,010
+ناقص YR من إنها قوشي، هي واحد، الآن YM ناقص YR إيش
+
+335
+00:27:36,010 --> 00:27:41,420
+هي؟ الـ YM هي صورتها والـ Yr هي صورتها بس بمشينا
+
+336
+00:27:41,420 --> 00:27:45,640
+الـ M بحط مين؟ R بصير الصممشن لهادي نقصها دي بصير
+
+337
+00:27:45,640 --> 00:27:46,460
+الصممشن لهادي نقصها دي بصير الصممشن لهادي نقصها دي
+
+338
+00:27:46,460 --> 00:27:48,680
+بصير الصممشن لهادي نقصها دي بصير الصممشن لهادي
+
+339
+00:27:48,680 --> 00:27:49,200
+نقصها دي نقصها نقصها نقصها نقصها نقصها نقصها نقصها
+
+340
+00:27:49,200 --> 00:27:51,960
+نقصها نقصها نقصها نقصها نقصها نقصها نقصها نقصها
+
+341
+00:27:51,960 --> 00:27:52,760
+نقصها نقصها نقصها نقصها نقصها نقصها نقصها نقصها
+
+342
+00:27:52,760 --> 00:28:02,190
+نقصها نقصها نقصها نقصها نقصهاأه فاهمين هذا خطها
+
+343
+00:28:02,190 --> 00:28:05,630
+هيك فاهمين ليش اللي بحكيه لأن I من عند واحد لعند
+
+344
+00:28:05,630 --> 00:28:10,870
+مين لعند N هذا الان لل vector اللي هنا هذا اللي
+
+345
+00:28:10,870 --> 00:28:14,970
+هو اللي هو بدي استخدم اللي لمّا اللي قبل شوية أكبر
+
+346
+00:28:14,970 --> 00:28:19,550
+أو يساوي C في الصممش لأبسل يوت values لمين لل
+
+347
+00:28:19,550 --> 00:28:24,410
+scalars هذه اللي عندي هذه صار هذا المقدار هاي و
+
+348
+00:28:24,410 --> 00:28:29,880
+هذا أصغر أو يساوي مين أبسلون this implies that for
+
+349
+00:28:29,880 --> 00:28:32,860
+any fixed I لكل واحدة من هدول مدام ال summation
+
+350
+00:28:32,860 --> 00:28:36,720
+هذا هذا ال summation مضروب في C أصغر من يابسولون
+
+351
+00:28:36,720 --> 00:28:41,620
+إذا كل واحدة منهم absolute value لها هذول أصغر
+
+352
+00:28:41,620 --> 00:28:45,040
+يعني ال summation هذا مضروب في C يعني ال summation
+
+353
+00:28:45,040 --> 00:28:48,460
+هذا لحاله أصغر من يابسولون ع C إذا كل واحدة من
+
+354
+00:28:48,460 --> 00:28:51,360
+اللي جوا أصغر من يابسولون على مين على C
+
+355
+00:28:54,290 --> 00:28:58,890
+then for any fixed I من الـ I هولا واحد و اثنين و
+
+356
+00:28:58,890 --> 00:29:03,630
+إن ال sequence Alpha I M عبارة عن Alpha I واحد
+
+357
+00:29:03,630 --> 00:29:07,370
+Alpha I اثنين Alpha I ثلاثة هتكون أشماله is a
+
+358
+00:29:07,370 --> 00:29:10,190
+Cauchy sequence لإن لجينا كل أبساط أكبر من صفر
+
+359
+00:29:10,190 --> 00:29:17,000
+لجينا K بحيث أن الـ absolute value لهذه أصغر من Y
+
+360
+00:29:17,000 --> 00:29:22,400
+على C for every M وR أكبر من الـ K يعني بمعنى آخر
+
+361
+00:29:22,400 --> 00:29:25,560
+صارت الـ sequence هذه اللي هي هي ال sequence
+
+362
+00:29:25,560 --> 00:29:29,700
+تبعتها هذه اللي هي ال entry تبعت ال sequence مش هده
+
+363
+00:29:29,700 --> 00:29:33,620
+هدى بس بنحكي عن واحدة من الـ sequences الآن مش
+
+364
+00:29:33,620 --> 00:29:37,600
+عندنا للواحد و للتنين و للتلتة اللي عند الآن هدولة
+
+365
+00:29:37,600 --> 00:29:41,580
+sequences هدى لل I in general هدى sequence هدى
+
+366
+00:29:41,580 --> 00:29:44,600
+طلعت كوشي sequence من هن مدام كوشي sequence و هي
+
+367
+00:29:44,600 --> 00:29:48,490
+كوشي sequence و فيها of numbers و لا .. ولا .. ولا
+
+368
+00:29:48,490 --> 00:29:50,970
+real numbers أو ال complex numbers complete إذا
+
+369
+00:29:50,970 --> 00:29:54,310
+أكيد في إلها أشماله اللي هي hence it
+
+370
+00:29:54,310 --> 00:29:59,430
+converges say to alpha I لأنه any Cauchy sequence
+
+371
+00:29:59,430 --> 00:30:03,780
+of real .. of numbers must convergemust converge
+
+372
+00:30:03,780 --> 00:30:10,680
+لأن use these unlimits ألف واحد M بتروح لألف واحد
+
+373
+00:30:10,680 --> 00:30:17,360
+ألف اثنين M لألف اثنين ألف N M بتروح للألف N إذا
+
+374
+00:30:17,360 --> 00:30:20,380
+صارت كل واحدة فيه لها limit لأن use these
+
+375
+00:30:20,380 --> 00:30:24,320
+unlimited to define من هذولة بدي أعرف مين اللي هو
+
+376
+00:30:24,320 --> 00:30:28,020
+Y Y بتساوي ألف واحد E واحد ألف اثنين E اثنين زي
+
+377
+00:30:28,020 --> 00:30:32,120
+ألف N E N اللي هي combination بينهم هذا الـ Y أكيد
+
+378
+00:30:32,120 --> 00:30:37,540
+في الـ space اللي عندي لأن الـ bases إله و هذولا
+
+379
+00:30:37,540 --> 00:30:41,200
+صارت اثنين ال combinations of bases إلا إن استخدمت
+
+380
+00:30:41,200 --> 00:30:44,420
+هذولا ال limits اللي لقيتهم قبل بشوية إذا صارت
+
+381
+00:30:44,420 --> 00:30:49,320
+عندي Y element ومش هيك كمان وخدوا الـ Y أم ناقصوا
+
+382
+00:30:49,320 --> 00:30:55,290
+الـ Y norm الـ YM ناقص نورم الـ Y بيساوي النورم لـ
+
+383
+00:30:55,290 --> 00:30:59,070
+summation هذين هي ال combination من مين Alpha I M
+
+384
+00:30:59,070 --> 00:31:02,870
+مع الـEI وهذه هي ال combination من مين من Alpha I
+
+385
+00:31:02,870 --> 00:31:06,490
+في الـEI نورم هذه ناقص هذه ناقص هذه ناقص هذه ناقص
+
+386
+00:31:06,490 --> 00:31:06,710
+ناقص هذه ناقص هذه ناقص هذه ناقص هذه ناقص هذه ناقص
+
+387
+00:31:06,710 --> 00:31:07,270
+هذه ناقص هذه ناقص هذه ناقص هذه ناقص هذه ناقص هذه
+
+388
+00:31:07,270 --> 00:31:08,550
+ناقص هذه ناقص هذه ناقص هذه ناقص هذه ناقص هذه ناقص
+
+389
+00:31:08,550 --> 00:31:09,490
+هذه ناقص هذه ناقص هذه ناقص هذه ناقص هذه ناقص هذه
+
+390
+00:31:09,490 --> 00:31:14,070
+ناقص هذه
+
+391
+00:31:14,100 --> 00:31:19,360
+الآن صار عندي summation لهذا في هذا however لكل
+
+392
+00:31:19,360 --> 00:31:23,280
+واحدة من هدول Alpha I M بتروح لمين لل Alpha I as M
+
+393
+00:31:23,280 --> 00:31:26,160
+goes to infinity إذا هذا المقدار as M goes to
+
+394
+00:31:26,160 --> 00:31:31,120
+infinity هو إن بدوح لصفر لأن هذه هتروح لهذه as M
+
+395
+00:31:31,120 --> 00:31:33,880
+goes to infinity إذا هذا هيروح لصفر بمعنى آخر
+
+396
+00:31:33,880 --> 00:31:38,920
+Normal YM ناقص ال Y هيروح لصفربمعنى آخر صارت الـ
+
+397
+00:31:38,920 --> 00:31:42,680
+YM converges لمن؟ لـ Y إذن الآن بدأت YM ماكوش
+
+398
+00:31:42,680 --> 00:31:46,900
+sequence و أثبتت أن الـ YM converges لـ Y في ال
+
+399
+00:31:46,900 --> 00:31:53,780
+space نفس Y، therefore Y is complete اللي بعده
+
+400
+00:31:53,780 --> 00:32:00,220
+المادة مفيدة للي بدوا علم منيح مفيدة مفيدة و بتدير
+
+401
+00:32:00,220 --> 00:32:04,860
+بقاكم و أي مكان لو الواحد يعني القدر اللي يكمل
+
+402
+00:32:04,860 --> 00:32:06,960
+كمان و كمان هتلاجوها
+
+403
+00:32:09,310 --> 00:32:13,450
+يستعانى بهوى المكان انه spaces لازم تكون في هال
+
+404
+00:32:13,450 --> 00:32:17,970
+spaces عشان تشتغل أي شغل تشتغل في الاحتمالات تشتغل
+
+405
+00:32:17,970 --> 00:32:23,010
+في الاحصى تشتغل في يعني أنا بتذكر في الاحتمالات
+
+406
+00:32:23,010 --> 00:32:27,610
+أخدنا course كامل بنشتغل فيه في ال LB spaces ال LB
+
+407
+00:32:27,610 --> 00:32:30,370
+طبعا اللي هي مش ال sequences ال functions اللي هي
+
+408
+00:32:30,370 --> 00:32:33,650
+ال .. اللي بيجي integrable functions طب على معناه
+
+409
+00:32:33,650 --> 00:32:36,550
+أنك بدك تسير بتعرف اللي هو اللي هو كل الكلام اللي
+
+410
+00:32:36,550 --> 00:32:43,020
+بنحكيه هذا بيكون مفيد إليك وهكذا طيب theorem every
+
+411
+00:32:43,020 --> 00:32:45,880
+finite dimensional subspace Y of a normed space X
+
+412
+00:32:45,880 --> 00:32:51,080
+إيش ماله is closed طب هو complete و ال complete
+
+413
+00:32:51,080 --> 00:32:55,500
+أكيد إيش ماله closed بتعرفوا تثبتوها أن ال
+
+414
+00:32:55,500 --> 00:33:01,900
+complete space is closed يعني لو كانك X complete
+
+415
+00:33:03,330 --> 00:33:07,890
+بيعطينا انه X اللي هو خلينا نقول Y sub space Y sub
+
+416
+00:33:07,890 --> 00:33:12,210
+space من X و Y complete أكيد ال Y أشماله closed
+
+417
+00:33:12,210 --> 00:33:14,710
+ماحكتش عن ال space اللي كله ال X ما هو ال space
+
+418
+00:33:14,710 --> 00:33:21,090
+دايما اللي هو closed و open فاهمين؟ طيب
+
+419
+00:33:22,590 --> 00:33:26,810
+إذاً أي finite dimensional subspace Y of X is
+
+420
+00:33:26,810 --> 00:33:34,090
+closed لأنه مدام Y subspace من X و finite
+
+421
+00:33:34,090 --> 00:33:37,970
+من X إذاً Y complete مدام complete على
+
+422
+00:33:37,970 --> 00:33:42,270
+طول إشماله closed بتقفل تثبتوها إن الـ close ده قال
+
+423
+00:33:42,270 --> 00:33:47,330
+لو كانت عندي Y complete هتكون closed خد X في الـ Y
+
+424
+00:33:47,330 --> 00:33:53,650
+closure إذاً there exist X<sub>n</sub> in Y such that X<sub>n</sub>
+
+425
+00:33:53,650 --> 00:33:58,490
+converts الـ mean للـ X ماشي الحال طيب الآن صارت
+
+426
+00:33:58,490 --> 00:34:02,850
+عندي الـ X<sub>n</sub> مدينة converts للـ X إذا صارت X<sub>n</sub> كوشي
+
+427
+00:34:02,850 --> 00:34:05,990
+سيكوينس في مين؟ في الـ Y مدينة كوشي سيكوينس في الـ Y
+
+428
+00:34:05,990 --> 00:34:08,710
+و الـ Y complete إذا converts يعني الـ X هذا هتكون
+
+429
+00:34:08,710 --> 00:34:12,550
+وين؟ في الـ Y مدينة X صارت في الـ Y إذا صارت الـ X في
+
+430
+00:34:12,550 --> 00:34:15,370
+الـ Y closure تؤدي الـ X في الـ Y معناته الـ Y closure
+
+431
+00:34:15,370 --> 00:34:19,100
+جزئية من الـ Y و الـ Y جزئية من الـ Y closure معناته
+
+432
+00:34:19,100 --> 00:34:21,880
+صحيح الـ Y بيساوي Y closure معناته الـ Y أشبه لها
+
+433
+00:34:21,880 --> 00:34:31,200
+S closed طيب .. اللي بعده؟ إن قال بجلد الملاحظة
+
+434
+00:34:31,200 --> 00:34:35,560
+التالية Infinite dimensional subspace need not be
+
+435
+00:34:35,560 --> 00:34:38,340
+closed يعني لو كان في عندي infinite dimensional
+
+436
+00:34:38,340 --> 00:34:43,040
+subspace مش شرط closed احنا بنقول عن اللي هو طبعا
+
+437
+00:34:43,040 --> 00:34:46,220
+و اكيد مش شرط ماله complete اكيد مش شرط complete
+
+438
+00:34:46,220 --> 00:34:52,220
+الـ infinite dimensional subspace اللي هو need not 
+
+439
+00:34:52,220 --> 00:34:57,060
+be closed ما حدش قاله closed to see this consider
+
+440
+00:34:57,060 --> 00:35:04,710
+the space C[0,1] الكل continuous functions خد الـ 
+
+441
+00:35:04,710 --> 00:35:10,110
+subspace منها مين؟ Y بتساوي الـ span لـ X<sub>0</sub> X<sub>1</sub> X<sub>2</sub> X<sub>3</sub> X<sub>4</sub> X<sub>5</sub>
+
+442
+00:35:10,110 --> 00:35:11,170
+X<sub>6</sub> X<sub>7</sub> X<sub>8</sub> X<sub>9</sub> X<sub>10</sub> X<sub>11</sub> X<sub>12</sub> X<sub>13</sub> X<sub>12</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub>
+
+443
+00:35:11,170 --> 00:35:11,610
+X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub>
+
+444
+00:35:11,610 --> 00:35:11,830
+X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub>
+
+445
+00:35:11,830 --> 00:35:11,850
+X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub>
+
+446
+00:35:11,850 --> 00:35:14,370
+X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub>
+
+447
+00:35:14,370 --> 00:35:14,390
+X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> X<sub>13</sub> 
+
+448
+00:35:22,100 --> 00:35:28,880
+بس .. اه؟ الان .. الان بدنا نجيبلكم مثال على
+
+449
+00:35:28,880 --> 00:35:32,800
+infinite dimensional subspace ليست closed مش شرط
+
+450
+00:35:32,800 --> 00:35:37,180
+يكون closed الان المثال اللي كان فيه سؤال معاكم في
+
+451
+00:35:37,180 --> 00:35:44,720
+الـ .. في الـ .. في الـ home work هذا .. هذا بيجاوب
+
+452
+00:35:44,720 --> 00:35:49,640
+عليه الان خد الـ space mean C of [0,1] continuous
+
+453
+00:35:49,640 --> 00:35:55,140
+functions انظر من الـ Normal هو الـ Maximum الآن
+
+454
+00:35:55,140 --> 00:35:59,480
+الـ Sub-spacement هو ما يساوي الـ span لـ X<sub>0</sub> X<sub>1</sub> X<sub>2</sub>
+
+455
+00:35:59,480 --> 00:36:03,240
+إلى ما لا نهاية ماشي الحالة طب مين هدول X<sub>0</sub> X<sub>0</sub>
+
+456
+00:36:03,240 --> 00:36:08,000
+بساوي اللي هو واحد X<sub>1</sub> اللي هو بساوي T X<sub>2</sub> بساوي T 
+
+457
+00:36:08,000 --> 00:36:12,300
+تربيع X<sub>3</sub> بساوي T تكعيب وكأنه قاعد بقولي الـ span
+
+458
+00:36:12,300 --> 00:36:16,370
+اللي من الـ Polynomials يعني و كأنه بيقول هذا why
+
+459
+00:36:16,370 --> 00:36:19,150
+is a subspace اللي هو the space they span by this
+
+460
+00:36:19,150 --> 00:36:25,370
+.. this اللي هي terms اللي هو بعملي اللي هو الـ
+
+461
+00:36:25,370 --> 00:36:29,350
+polynomials هذا the space of all polynomials هان
+
+462
+00:36:29,350 --> 00:36:36,130
+is not Closed لأن بلاجة الـ sequence بتروح براته من
+
+463
+00:36:36,130 --> 00:36:40,430
+ضمن الـ mean اللي هو الـ exponential و هكذا و كتير
+
+464
+00:36:40,430 --> 00:36:43,490
+فيه شغلات المهم then why is not closed و why
+
+465
+00:36:43,490 --> 00:36:48,590
+هينجلته و why لكم كمان بتفصلوا أنتم إذا في عندي
+
+466
+00:36:48,590 --> 00:36:51,370
+infinite dimensional spaces need not to be closed
+
+467
+00:36:51,370 --> 00:36:56,070
+طيب نجي الآن في حد اسمها equivalent norms
+
+468
+00:36:58,340 --> 00:37:02,900
+الـ equivalent norms بنقول عن الـ two norms a norm
+
+469
+00:37:02,900 --> 00:37:06,980
+on a vector space X is said to be equivalent to a
+
+470
+00:37:06,980 --> 00:37:11,900
+norm ثاني نسميه norm not on X if there are
+
+471
+00:37:11,900 --> 00:37:16,520
+positive numbers A and B such that for all X
+
+472
+00:37:16,520 --> 00:37:20,560
+element in X لكل X في الـ X هنلاقي اللي هو norm الـ
+
+473
+00:37:20,560 --> 00:37:24,440
+X محصور بين norm الـ X not في constant و بين norm
+
+474
+00:37:24,440 --> 00:37:29,930
+الـ X not برضه في constant آخر إذا لجينا العلاقة هذه
+
+475
+00:37:29,930 --> 00:37:34,030
+موجودة على طول بنقول .. لكل X بنقول إن الـ Normal
+
+476
+00:37:34,030 --> 00:37:38,210
+هذولة الـ Norm هذا و الـ Norm هذا are equivalent
+
+477
+00:37:38,210 --> 00:37:43,630
+بنسميهم إيش مالهين؟ equivalent norms يعني جديتها
+
+478
+00:37:43,630 --> 00:37:46,470
+اللي هو constant في هذه و constant في هذه يحصر
+
+479
+00:37:46,470 --> 00:37:48,670
+اللي هو الـ Norm الأصلي الـ Norm اللي بنحكي عنه
+
+480
+00:37:48,670 --> 00:37:52,590
+بينهم معناته إنه صارت اللي هي .. اللي هي بس اللي
+
+481
+00:37:52,590 --> 00:37:56,430
+هي .. الفرق بينهم constant معناته هيكون are
+
+482
+00:37:56,430 --> 00:38:00,720
+equivalent norms له ما بعده هذا التعريف اللي ما بعده
+
+483
+00:38:00,720 --> 00:38:05,240
+أول واحد هذه equivalent norms on X defines the
+
+484
+00:38:05,240 --> 00:38:09,240
+same topology for X يعني الآن الـ topology اللي
+
+485
+00:38:09,240 --> 00:38:12,380
+هيتولد من هذا الـ norm و من هذا الـ norm are
+
+486
+00:38:12,380 --> 00:38:18,440
+equivalent are equivalent topologies then the
+
+487
+00:38:18,440 --> 00:38:24,560
+proof is left to the reader الموضوع سهل ابتخدوا
+
+488
+00:38:24,560 --> 00:38:29,180
+الآن الـ topology المولد من هنا من هذه و الـ topology
+
+489
+00:38:29,180 --> 00:38:33,920
+المولد من هذه بتقولوا خلّونا ناخد اللي هو a بين 6
+
+490
+00:38:33,920 --> 00:38:37,700
+مولدة من الـ topology هذا و بتثبتوها a بين 6
+
+491
+00:38:37,700 --> 00:38:41,320
+بالنسبة لي مين اللي هي الـ topology الثانية و العكس
+
+492
+00:38:41,320 --> 00:38:44,520
+صحيح اتلاقيها اللي هو سهلة يعني الموضوع بس اللعب
+
+493
+00:38:44,520 --> 00:38:51,920
+في مين في الـ constant اللي موجودة عندنا أي سؤال أو
+
+494
+00:38:51,920 --> 00:38:56,940
+تاخد .. انت بدك تحكي عن الـ open balls و منها تصل
+
+495
+00:38:56,940 --> 00:39:01,280
+طيب اتنين اربعة خمسة theorem تشوفها الـ theorem
+
+496
+00:39:01,280 --> 00:39:09,220
+الحلوة و الجميلة و المفيدة خالص و بتريحنا كثير in
+
+497
+00:39:09,220 --> 00:39:13,860
+a finite dimensional vector space any norm is
+
+498
+00:39:13,860 --> 00:39:21,080
+equivalent to any norm ثاني يعني انت لو جيت و بديت
+
+499
+00:39:21,080 --> 00:39:24,800
+اتفكر في انك تعمل بحكي عن الـ norm مش عن الـ metric
+
+500
+00:39:24,800 --> 00:39:31,860
+لو بتيجي تتفكر تعمل جد ما بدك norms على اللي هو الـ
+
+501
+00:39:31,860 --> 00:39:35,840
+R اعمل norm على الـ R بأي شكل أو على الـ R تربيع أو
+
+502
+00:39:35,840 --> 00:39:39,980
+R تكعيب أو R <sup>n</sup> أو اللي بدك يعمل norms إذا عملت
+
+503
+00:39:39,980 --> 00:39:44,280
+norms اللي هي كل الـ norms اللي بتعملها على R
+
+504
+00:39:44,280 --> 00:39:48,920
+equivalent بولد بس one topology اللي هو اللي بنسميه
+
+505
+00:39:48,920 --> 00:39:53,860
+احنا U Dual Topology اللي هي على الـ R أو R تربيع
+
+506
+00:39:53,860 --> 00:39:57,140
+أو R تكعيب تقول في الـ R تربيع بتدخل مربعات أو
+
+507
+00:39:57,140 --> 00:40:00,560
+بتدخل دوائر أو بتدخل الـ neighbourhood أو بتدخل
+
+508
+00:40:00,560 --> 00:40:05,700
+اللي هي اللي بدكيا في الآخر لما نولد نورم لما نولد
+
+509
+00:40:05,700 --> 00:40:09,660
+نورم كل هدولة أو ولدت من نورم على طول R equivalent
+
+510
+00:40:10,590 --> 00:40:13,610
+لكن انت بتقدر تعمل على الأرض اللي هو metric ثاني
+
+511
+00:40:13,610 --> 00:40:17,230
+الـ discrete metric مش مولد من norm أصلا ماشي
+
+512
+00:40:17,230 --> 00:40:20,210
+الحال لكن الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+513
+00:40:20,210 --> 00:40:23,870
+metricات المولدة من الـ norms أو الـ .. أو الـ
+
+514
+00:40:23,870 --> 00:40:27,070
+topologies .. الـ topologies المولدة من الـ norm على
+
+515
+00:40:27,070 --> 00:40:30,530
+الـ finite dimensional spaces كلهم are equivalent
+
+516
+00:40:30,530 --> 00:40:37,090
+هذا كلام خطير أو كلام كتير مهم لدن الان dimension
+
+517
+00:40:37,090 --> 00:40:39,930
+للـ X أش بساوي n نفترض ان احنا بنشتغل في
+
+518
+00:40:39,930 --> 00:40:43,390
+finite dimensional نفترض ان الـ dimension للـ X أش
+
+519
+00:40:43,390 --> 00:40:47,630
+بساوي n وخد E<sub>1</sub> E<sub>2</sub> E<sub>n</sub> مادام finite
+
+520
+00:40:47,630 --> 00:40:50,890
+dimension لازم بقدر أجواء and bases بيصير E<sub>1</sub> E<sub>2</sub>
+
+521
+00:40:50,890 --> 00:40:54,750
+E<sub>n</sub> بياني bases for mean for X وبنيضيق كمان
+
+522
+00:40:54,750 --> 00:40:55,790
+ومحصورات
+
+523
+00:40:58,070 --> 00:41:01,390
+then ما أقدر أحكي عن finite bases جزيه أما كل الـ
+
+524
+00:41:01,390 --> 00:41:04,670
+vector space فيه له bases ما هو الـ and then every
+
+525
+00:41:04,670 --> 00:41:06,930
+طب ما أنا مش هامش أودر bases أو الاخر هذا الموضوع
+
+526
+00:41:06,930 --> 00:41:11,030
+همل bases الاخرين then every x element in X has a
+
+527
+00:41:11,030 --> 00:41:14,630
+unique representation X بالساوية α<sub>1</sub> E<sub>1</sub>
+
+528
+00:41:14,630 --> 00:41:17,030
+زي α<sub>2</sub> E<sub>2</sub> زي α<sub>n</sub> E<sub>n</sub> و خلاص حطته
+
+529
+00:41:17,030 --> 00:41:19,750
+بني دايم لإن صار فيه عنده اللي هو الـ bases وصار
+
+530
+00:41:19,750 --> 00:41:21,650
+فيه عند الـ scalars والـ X موجودة كده لينا
+
+531
+00:41:21,650 --> 00:41:24,670
+compilation من بينهم a unique representation مظهوط
+
+532
+00:41:24,670 --> 00:41:28,430
+ولا مشاك في الـ vector space؟ طيب و الـ α<sub>1</sub> α<sub>2</sub>
+
+533
+00:41:28,430 --> 00:41:31,570
+α<sub>n</sub> are scalars بيلمّوا 2 4 1
+
+534
+00:41:31,570 --> 00:41:34,450
+اللي غلبتنا هذه في الأول there is a positive
+
+535
+00:41:34,450 --> 00:41:37,990
+constant C such that normal X هذا اللي هو اللي هي
+
+536
+00:41:37,990 --> 00:41:40,550
+ال compilation منهم أكبر أو يساوي C في الـ
+
+537
+00:41:40,550 --> 00:41:44,090
+summation لأ اللي هو الـ scalars سبعته الـ absolute
+
+538
+00:41:44,090 --> 00:41:47,830
+value of scalars سبعته مظبوط؟ طيب on the other hand
+
+539
+00:41:47,830 --> 00:41:50,430
+خلّيها في الذاكرة اللي بنستخدمها بعد شوية on the
+
+540
+00:41:50,430 --> 00:41:54,390
+other hand normal X not أصغر أو ساوى الـ summation
+
+541
+00:41:54,390 --> 00:41:59,950
+للـ α<sub>i</sub> E<sub>i</sub> not هذا .. الآن أنا فا .. الـ .. الـ
+
+542
+00:41:59,950 --> 00:42:00,650
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+543
+00:42:00,650 --> 00:42:01,870
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. ال
+
+544
+00:42:01,870 --> 00:42:03,450
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. ال
+
+545
+00:42:03,450 --> 00:42:03,610
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. ال
+
+546
+00:42:03,610 --> 00:42:04,310
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. ال
+
+547
+00:42:04,310 --> 00:42:04,590
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. ال
+
+548
+00:42:04,590 --> 00:42:07,530
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. ال
+
+549
+00:42:07,530 --> 00:42:08,290
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. ال
+
+550
+00:42:08,290 --> 00:42:08,390
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. ال
+
+551
+00:42:08,390 --> 00:42:10,130
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. ال
+
+552
+00:42:10,130 --> 00:42:13,110
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. ال
+
+553
+00:42:13,110 --> 00:42:13,390
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. ال
+
+554
+00:42:13,390 --> 00:42:16,830
+.. الـ .. الـ .. 
+
+555
+00:42:16,830 --> 00:42:23,070
+الـ .. الـ اللي هو أصغر أو يساوي الـ Summation α<sub>i</sub>
+
+556
+00:42:23,070 --> 00:42:26,530
+نورم الـ E<sub>i</sub> Note Triangling Quality اللي هي نورم
+
+557
+00:42:26,530 --> 00:42:29,870
+الأول زائد نورم التاني زائد نورم التالت زائد نورم
+
+558
+00:42:29,870 --> 00:42:33,730
+الـ N الأخير هذا الـ Triangling Quality أصغر أو
+
+559
+00:42:33,730 --> 00:42:40,650
+يساوي هذا الـ N كيف نورم للـ α<sub>i</sub> كمين هي بتدخل
+
+560
+00:42:40,650 --> 00:42:44,740
+أكبر واحد في هدول و في maximum الهن ليه عشان الواحدة 
+
+561
+00:42:44,740 --> 00:42:47,640
+اتن تان تلاتة إن من الأعداد في الـ maximum إيش
+
+562
+00:42:47,640 --> 00:42:51,540
+تمته بساوة K إذا أصغر أو يساوي K في الـ summation
+
+563
+00:42:51,540 --> 00:42:56,900
+اللي عندي الآن بدي هي عندي حصلت Normal X Note أصغر 
+
+564
+00:42:56,900 --> 00:43:00,760
+أو يساوي K في هذا المقدار وهذا أثبتوا أنه أكبر أو
+
+565
+00:43:00,760 --> 00:43:06,960
+يساوي بده ندمجن مع بعض الآن together بيصير
+
+566
+00:43:06,960 --> 00:43:08,360
+أنه اطلع لفوق بقى شوية
+
+567
+00:43:13,180 --> 00:43:19,020
+Together Normal X Note أصغر أو يساوي K في summation
+
+568
+00:43:19,020 --> 00:43:25,220
+للـ FI هذه وهذه اللي عندي summation أصغر أو يساوي
+
+569
+00:43:25,220 --> 00:43:29,420
+Normal X على C صح؟ هذه بيصير أصغر أو يساوي K على C
+
+570
+00:43:29,420 --> 00:43:32,840
+في Normal X صارت هذه Normal X Note أصغر أو يساوي
+
+571
+00:43:32,840 --> 00:43:38,320
+some number في الـ X إذا صارت اللي هي Hence اللي هو
+
+572
+00:43:38,320 --> 00:43:42,120
+A في Norm الـ X Note أصغر يساوي Norm الـ X جيبت هذا
+
+573
+00:43:42,120 --> 00:43:45,320
+على الجهد أنا عشان يلاقم اللي بدي يعني هي C على K
+
+574
+00:43:45,320 --> 00:43:50,140
+بتصير A بتساوي C على K لأن similarly بنفس الطريقة
+
+575
+00:43:50,140 --> 00:43:54,220
+بدل ما أستخدم للـ X لنورم النوت لنورم أستخدم Norm
+
+576
+00:43:54,220 --> 00:43:56,780
+النوت وبدل Norm النوت أستخدم Norm في الحالتين
+
+577
+00:43:56,780 --> 00:44:00,040
+فبيطلع عندي similarly Norm الـ X أصغر يساوي B في
+
+578
+00:44:00,040 --> 00:44:04,000
+Norm الـ X Note تنتهي المحاضرة مع بعض يظهر Norm X بين
+
+579
+00:44:04,000 --> 00:44:08,060
+Norm X Note و Norm X Note واحدة بسكيلر والثانية 
+
+580
+00:44:08,060 --> 00:44:12,180
+بسيكلر آخر معناته هذا وهذا الـ هن إيه إشمالهن are
+
+581
+00:44:12,180 --> 00:44:15,580
+equivalent norms إذن في الـ finite dimensional
+
+582
+00:44:15,580 --> 00:44:20,720
+spaces كل الـ norms are equivalent وبرك الله فيكم
+
+583
+00:44:20,720 --> 00:44:22,400
+تنتهي المحاضرة العاشرة 
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/mlM0h2WP1Sg_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/mlM0h2WP1Sg_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..39ee3f458f8b34085fc105936efe401d9479738e
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/mlM0h2WP1Sg_postprocess.srt
@@ -0,0 +1,2332 @@
+1
+00:00:05,300 --> 00:00:09,480
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:09,480 --> 00:00:12,680
+والصلاة والسلام على سيدنا محمد وعلى آله وصحبه
+
+3
+00:00:12,680 --> 00:00:17,360
+أجمعين هذه المحاضرة العاشرة مساق تحليل اقتراني أو
+
+4
+00:00:17,360 --> 00:00:21,380
+تحليل دالي طلاب وطالبات الجامعة الإسلامية قسم
+
+5
+00:00:21,380 --> 00:00:27,480
+رياضيات طلاب وطالبات الماجستيرهنبدأ اليوم ان شاء
+
+6
+00:00:27,480 --> 00:00:31,520
+الله او هناخد اليوم اللي هو اتنين اربعة تحت عنوان
+
+7
+00:00:31,520 --> 00:00:34,540
+اللي هو finite dimensional normed spaces and
+
+8
+00:00:34,540 --> 00:00:38,080
+subspaces يعني اللي هنحكي فيه اللي هو ال spaces
+
+9
+00:00:38,080 --> 00:00:42,840
+اللي هنحكي فيه أو ال normed spaces اللي هنحكي فيه
+
+10
+00:00:42,840 --> 00:00:47,320
+اللي هي finite dimensional اللي هي بيكون ال
+
+11
+00:00:47,320 --> 00:00:51,100
+dimension لها أيش لها finite dimension as a vector
+
+12
+00:00:51,100 --> 00:00:57,760
+spaceنأخد اللمّة ضرورية لإثبات العديد من النظريات
+
+13
+00:00:57,760 --> 00:01:01,580
+في هذا الـ section اللمّة بتقول ما يليه اللي هو
+
+14
+00:01:01,580 --> 00:01:07,260
+let X1, X2, Xn بيقى linearly independent set of
+
+15
+00:01:07,260 --> 00:01:15,620
+vectors in a known space Xثم هناك رقم C أكبر من
+
+16
+00:01:15,620 --> 00:01:20,740
+صفر مثلًا، لأي اختار من الـ Scalars Alpha 1, Alpha
+
+17
+00:01:20,740 --> 00:01:25,920
+2, Alpha N لدينا دائمًا نورم للـ Linear
+
+18
+00:01:25,920 --> 00:01:29,590
+Combinationللألف واحد X واحد ألف اتنين زائد ألف
+
+19
+00:01:29,590 --> 00:01:33,770
+اتنين X اتنين زائد ألف ان X ان هيكون أكبر أو يساوي
+
+20
+00:01:33,770 --> 00:01:39,490
+C في ال summation لل scalars اللي أخدتها أي كان ال
+
+21
+00:01:39,490 --> 00:01:45,130
+scalars اللي أخدتهم بقدر ألاجي Cبحيث انه there
+
+22
+00:01:45,130 --> 00:01:49,490
+exists C بحيث انه لكل choice يعني الـC ده بتنفع
+
+23
+00:01:49,490 --> 00:01:53,450
+لكل choices للألف واحد ألف اتنين لعندي ألف N بحيث
+
+24
+00:01:53,450 --> 00:01:56,590
+انه يكون ال norm للألف واحد X2 للألف اتنين X2
+
+25
+00:01:56,590 --> 00:01:59,810
+لعندي الألف N XN أكبر أو يساوي C في ال summation
+
+26
+00:01:59,810 --> 00:02:05,010
+لمين لل absolute value للألف I هذا الكلام ان شاء
+
+27
+00:02:05,010 --> 00:02:09,750
+الله بنشوف كيف وينفعته في خلال اللي هو النظريات
+
+28
+00:02:09,750 --> 00:02:14,920
+اللي هناخدها قدامخلّينا نبرهن هذا البرهان .. نبرهن
+
+29
+00:02:14,920 --> 00:02:20,180
+هذه النظرية أول شيء أبرهن النظرية أو اللي أبدا
+
+30
+00:02:20,180 --> 00:02:27,200
+أبرهنها اللي هو ل Beta 1 و Beta 2 و Beta 3 اللي ال
+
+31
+00:02:27,200 --> 00:02:31,840
+summation لهم بيساوي 1 وبعد هيك هنتقل in general
+
+32
+00:02:31,840 --> 00:02:36,790
+بيصير سهل الانتقال هتشوفوا كيفالان اولا نشهد ان
+
+33
+00:02:36,790 --> 00:02:40,830
+هناك C أكبر من صفر مثل ذلك لأي اختار من الـ
+
+34
+00:02:40,830 --> 00:02:45,470
+Scalars Beta 1, Beta 2, Beta N والـ Scalars بس
+
+35
+00:02:45,470 --> 00:02:49,210
+بتحط عليهم شرط نصممش ان هنا ايش بيساوي، بيساوي
+
+36
+00:02:49,210 --> 00:02:53,080
+واحد، بعد شوية هذه حاجلتها هتصير سهلةالان نحن
+
+37
+00:02:53,080 --> 00:02:56,200
+لدينا نورم بي واحد اكس واحد بي اتنين اكس اتنين
+
+38
+00:02:56,200 --> 00:02:59,440
+زائد بي انكسا ناكوراساوسي فيه C إذا هذه الآن اللي
+
+39
+00:02:59,440 --> 00:03:04,040
+بدأ أثبتها ماشي الحال خلينا نثبت هذه ومن ثم ببعدها
+
+40
+00:03:04,040 --> 00:03:08,140
+اللي هو نثبت in general اللي طالبه في ال M اطلع
+
+41
+00:03:08,140 --> 00:03:13,100
+على فوق البرهان قايم على انه نفترض العكسونصل مين
+
+42
+00:03:13,100 --> 00:03:16,360
+لـ contradiction الان اللي .. اللي .. اللي .. اللي
+
+43
+00:03:16,360 --> 00:03:21,160
+عندي بيدقول assume that one does not hold ماشي
+
+44
+00:03:21,160 --> 00:03:26,340
+الحال يعني بدي أنفي الجملة الو there exists such
+
+45
+00:03:26,340 --> 00:03:30,900
+that for any choice of beta 1 عند beta n و الاخره
+
+46
+00:03:31,340 --> 00:03:34,960
+إذا نفيها أكيد إيش باله بدل اللي هو there exist
+
+47
+00:03:34,960 --> 00:03:40,560
+بده يصير عنده الان for all then assume that الان
+
+48
+00:03:40,560 --> 00:03:47,070
+one does not hold يعني بده أنفل اللي هو المطلوبو
+
+49
+00:03:47,070 --> 00:03:51,810
+بدي أسأل الـ contradiction مافيه؟ for all M أكبر
+
+50
+00:03:51,810 --> 00:03:55,410
+من 0 بدي أغير بس السياق سميها ايش بقى لأ for all M
+
+51
+00:03:55,410 --> 00:04:00,410
+أكبر من 0 there exist scalars بدل ما هو for all
+
+52
+00:04:00,410 --> 00:04:03,810
+for any choice of scalars بدي أسير ايش ماله there
+
+53
+00:04:03,810 --> 00:04:09,090
+exist scalars Beta واحد خاصة بمين؟ بالـ M هذهبيتا
+
+54
+00:04:09,090 --> 00:04:13,470
+واحد M بيتا اتنين M بيتا N M بتحت نفس الشروط الـ
+
+55
+00:04:13,470 --> 00:04:17,030
+Summation تبحن من واحد عند N مش هو يساوي ايه اش
+
+56
+00:04:17,030 --> 00:04:21,310
+واحد وفي نفس الوقت اشمال وهذا ما تتحقق اشها بدأت
+
+57
+00:04:21,310 --> 00:04:25,470
+بتنفيها ان ال norm هذا بيتا واحد X واحد زي بيتا
+
+58
+00:04:25,470 --> 00:04:29,730
+اتنين X اتنين زي بيتا M X M اصغر او ساو مين واحد
+
+59
+00:04:29,730 --> 00:04:34,620
+على Mماشي الحال يعني اللي مش عاجبه M اكتب for all
+
+60
+00:04:34,620 --> 00:04:38,020
+أحد على M بنفع نفس الاشي for all M أو for one أحد
+
+61
+00:04:38,020 --> 00:04:40,880
+على M يعني ال C's اللي أنا ال C اللي بدي أخدها
+
+62
+00:04:40,880 --> 00:04:44,520
+طبعا صارت for all بدل اللي هي ال C اللي بدي أسميها
+
+63
+00:04:44,520 --> 00:04:49,080
+أشمالها واحد على M لغرض أنا بديها ماشي الحال لأن
+
+64
+00:04:49,080 --> 00:04:54,220
+for all is choice طيب الآن صار عندي اللي هو اللي
+
+65
+00:04:54,220 --> 00:05:01,100
+هي هذا اللي هو متحققهذا فرضته انا الان طيب يا
+
+66
+00:05:01,100 --> 00:05:04,680
+جماعة الان
+
+67
+00:05:04,680 --> 00:05:11,020
+بمعنى اخر ل M بتساوي واحد انتبهوا for all M قولنا
+
+68
+00:05:11,020 --> 00:05:15,780
+اذا ل M بتساوي واحد for واحد there exist معايا
+
+69
+00:05:15,780 --> 00:05:23,280
+sequence اسمها اللي هي بي واحد واحد بيتا واحد واحد
+
+70
+00:05:23,280 --> 00:05:32,490
+بيتا اتنين واحدبيتا ان واحد عددين ان صح ومجموع ال
+
+71
+00:05:32,490 --> 00:05:38,330
+absolute values له دول ايش بيساوي واحد for n طبعا
+
+72
+00:05:38,330 --> 00:05:45,230
+ايش بتحقق ال norm ل beta واحد x واحد زائد beta n
+
+73
+00:05:45,230 --> 00:05:51,030
+واحد xn ايش ماله اصغر من واحد على واحد اللي هو
+
+74
+00:05:51,030 --> 00:05:57,560
+واحد اللي بعدها forاللي هو n بتساوي 2 there exist
+
+75
+00:05:57,560 --> 00:06:07,500
+beta 1 2 و beta 2 2 فاهمين عليها لعند beta n 2ماله
+
+76
+00:06:07,500 --> 00:06:10,640
+هذا sequence of scalars الـ summation اللي بيساوي
+
+77
+00:06:10,640 --> 00:06:16,720
+واحد absolute value لهن و norm هن beta 1 2 x 1
+
+78
+00:06:16,720 --> 00:06:27,560
+زائد beta 1 2 2 x 2 زائد beta n 2 x n برضه أصغر من
+
+79
+00:06:27,560 --> 00:06:34,640
+minimum واحد على اتنين in general for MThere
+
+80
+00:06:34,640 --> 00:06:44,340
+exists Beta 1M و Beta 2M لعند Beta nM such that
+
+81
+00:06:44,340 --> 00:06:51,940
+Norمجموح بساوية Absolute Value 1 و Beta 1M في X1
+
+82
+00:06:51,940 --> 00:07:01,280
+زائد Beta nM Xn أصغر من 1 على N ماشي الحالة هذا
+
+83
+00:07:01,280 --> 00:07:10,180
+الكلام for any Mصحيح طيب شوفوا عليا الان then بناء
+
+84
+00:07:10,180 --> 00:07:12,820
+على الكلام هذا there exist a sequence YM of
+
+85
+00:07:12,820 --> 00:07:18,400
+vectors اللي هو YM بتساوي Beta 1 M X 1 زائد Beta 2
+
+86
+00:07:18,400 --> 00:07:25,020
+M X 2 زائد Beta M X M ماشي الحال اللي هي هذه ال
+
+87
+00:07:25,020 --> 00:07:33,710
+sequence Y1هي الأولى Y1 Beta 1 1 Beta 2 1 الى عند
+
+88
+00:07:33,710 --> 00:07:38,890
+Beta هي عنصر الان الأولاني ال Y2 العنصر الثاني ال
+
+89
+00:07:38,890 --> 00:07:41,510
+Y تلقى نفس الاشي إلى ما ندلنا دهانا دي صارت
+
+90
+00:07:41,510 --> 00:07:45,710
+sequence شك كيف شكل عناصرها عناصرها هذوله ال
+
+91
+00:07:45,710 --> 00:07:50,620
+linear combinationمن اللي أنا حكيت عنه هنا بحيث ان
+
+92
+00:07:50,620 --> 00:07:56,500
+الـ summation L الـ absolute value لكل اللي
+
+93
+00:07:56,500 --> 00:08:02,260
+بتتكون منها لكل YM مجبوح ان يش بيساوي واحد ومش هيك
+
+94
+00:08:02,260 --> 00:08:08,700
+ولو اجيت اخدت norm ال YM هي norm ال YM هذا هو من
+
+95
+00:08:08,700 --> 00:08:14,420
+هي هي في الواقع هذا من نورم ال YM هيساوي ال norm
+
+96
+00:08:14,420 --> 00:08:21,470
+لهذهas M goes to infinity هذا الـ norm يشير إلى
+
+97
+00:08:21,470 --> 00:08:29,870
+أين نروح إلى Zero بمعنى آخر صارت عندي اللي هو الـ
+
+98
+00:08:29,870 --> 00:08:34,490
+sequence YM من الـ vectors هذه الـ norm تبعها goes
+
+99
+00:08:34,490 --> 00:08:38,930
+to zero as M goes to mean to infinity خلوا هذه في
+
+100
+00:08:38,930 --> 00:08:43,850
+الذاكرة إذا انت حصلت على sequenceYM هي شكل الـ
+
+101
+00:08:43,850 --> 00:08:48,970
+sequence نورمها بروح لمن؟ للصفر بدا أصلكم في الآخر
+
+102
+00:08:48,970 --> 00:08:54,810
+ل contradiction شوفوا كيف الان نتفجين احنا ان ال
+
+103
+00:08:54,810 --> 00:08:59,290
+summation لكل مجموعة من هدولة ال absolute values
+
+104
+00:08:59,290 --> 00:09:02,650
+لهم كل مجموعة ال summation انهي مش بساوي بساوي
+
+105
+00:09:02,650 --> 00:09:09,190
+واحد بمعنى بمعنى ان كل واحدة منهم BIM أصغر بساوي
+
+106
+00:09:09,190 --> 00:09:14,350
+واحد لكل Iمعايا كلهم دايما ال norm أشماله أصغر من
+
+107
+00:09:14,350 --> 00:09:17,470
+واحد ده كل I ولا كل مين واحد يعني بي واحد واحد
+
+108
+00:09:17,470 --> 00:09:21,430
+أصغر شوي واحد بي واحد اتنين اصغر .. و هكذا ماشي
+
+109
+00:09:21,430 --> 00:09:25,230
+الحال .. هذا إيه اللي معناه hence الآن for any
+
+110
+00:09:25,230 --> 00:09:36,330
+fixed I اختارولي BIM اللي هي بي اي واحدبي اتنين بي
+
+111
+00:09:36,330 --> 00:09:41,450
+اي تلاتة بي اي اربعة بي اي خمسة يعني بدي اجل بي اي
+
+112
+00:09:41,450 --> 00:09:52,680
+هنا بي اي واحد بي اي اتنينbim in general هذه عبارة
+
+113
+00:09:52,680 --> 00:09:57,660
+عن sequence of numbers مظبوط ولا لأ؟ كل واحدة منهم
+
+114
+00:09:57,660 --> 00:10:00,200
+هدولة sequence of numbers و هذه sequence of
+
+115
+00:10:00,200 --> 00:10:04,640
+numbers و هذه sequence of numbers عدد من هدولة
+
+116
+00:10:04,640 --> 00:10:07,640
+واحدة اتنين اتنين تلاتة اربع ان من اللي من ال
+
+117
+00:10:07,640 --> 00:10:12,890
+sequences كل واحدة فيهم is a bounded sequenceلماذا
+
+118
+00:10:12,890 --> 00:10:17,010
+اسمها Sequence؟ لأن اي انكالة الواحدة فيهم اصغر او
+
+119
+00:10:17,010 --> 00:10:18,550
+يساوي ايش واحد
+
+120
+00:10:21,120 --> 00:10:26,080
+بشرد من الـ space اللي عندي إلى الـ space في R أو
+
+121
+00:10:26,080 --> 00:10:30,420
+في C أخدتها sequence of main of numbers بي اي واحد
+
+122
+00:10:30,420 --> 00:10:34,820
+بي اي اتنين is a bounded sequence then بي واحد
+
+123
+00:10:34,820 --> 00:10:39,520
+اللي هي M و بي اتنين M كل هى نفس الشيء sequence of
+
+124
+00:10:39,520 --> 00:10:43,040
+ايش؟ of numbers و bounded فبنيجي نشوف العالمين على
+
+125
+00:10:43,040 --> 00:10:48,280
+بي واحد of Mالأن بي واحد of M has مادام sequence
+
+126
+00:10:48,280 --> 00:10:51,580
+of numbers وهي bounded احنا بنعرف في الريال ان any
+
+127
+00:10:51,580 --> 00:10:53,860
+bounded sequence has a convergence of a
+
+128
+00:10:53,860 --> 00:11:00,140
+subsequence بلزانو اه مذاكرين؟ اذا يا جماعة صار
+
+129
+00:11:00,140 --> 00:11:09,900
+عند بي واحد M اللي هيبعد ذلك لديها سبسيكوانس
+
+130
+00:11:09,900 --> 00:11:14,920
+بي واحد ام ايش واحد هذه سبسيكوانس من مين؟ من
+
+131
+00:11:14,920 --> 00:11:20,320
+السيكوانس هذه يعني من السيكوانس بي واحد of ام اللي
+
+132
+00:11:20,320 --> 00:11:25,960
+هي هذه فيها سبسيكوانس منها بي ام واحد
+
+133
+00:11:28,760 --> 00:11:33,280
+طيب الان مدان converts اذا نقول نسميها conversion
+
+134
+00:11:33,280 --> 00:11:38,100
+from mean to beta واحد يعني الان فرضنا ان ال beta
+
+135
+00:11:38,100 --> 00:11:40,300
+واحد
+
+136
+00:11:41,560 --> 00:11:53,620
+بواحد of m بواحد
+
+137
+00:11:53,620 --> 00:12:10,920
+of m
+
+138
+00:12:12,230 --> 00:12:16,310
+الان ما هي ال .. ال .. ال .. ال .. ال .. الـ YMs
+
+139
+00:12:16,310 --> 00:12:20,030
+هدولة ما هي سيكونس بتتكون من اللي بيكونها هي
+
+140
+00:12:20,030 --> 00:12:23,590
+linear combinations بين X1 و X2 و XN أدات ال
+
+141
+00:12:23,590 --> 00:12:26,250
+linear combinations اللي هي ال scalar هدول ال
+
+142
+00:12:26,250 --> 00:12:30,010
+scalars هدول اللي هي في الأصل من مين جاية من ال بي
+
+143
+00:12:30,010 --> 00:12:34,670
+و .. من بي I of M in general ماشي الحالة إذا الآن
+
+144
+00:12:34,670 --> 00:12:40,710
+thenعندي Y1M
+
+145
+00:12:40,710 --> 00:12:45,090
+بدي أسميها هي الـ subsequence اللي الـ scale
+
+146
+00:12:45,090 --> 00:12:51,690
+الذبعاتها من وين جايت من B و Beta 1 OM لت Y1M بي
+
+147
+00:12:51,690 --> 00:12:55,930
+the corresponding sequence which is a subsequence
+
+148
+00:12:55,930 --> 00:13:04,160
+of mean of YMWhere Y1M بالظبط ايش بتساوي Beta 1 M1
+
+149
+00:13:04,160 --> 00:13:09,580
+X1 زائد Beta 2 M X2 يعني بس أخدت من الأولى مين من
+
+150
+00:13:09,580 --> 00:13:13,980
+ال Beta 1 و M هذه و الباقى أخدت من مين من الأصلية
+
+151
+00:13:13,980 --> 00:13:21,380
+تبعت ال YM Beta 2 M X2 زائد Beta N M X2 XN هذي
+
+152
+00:13:21,380 --> 00:13:23,500
+اللي هي Y1M
+
+153
+00:13:25,220 --> 00:13:29,820
+هذه الآن الـ subsequence برضه اللي عملته على الـ
+
+154
+00:13:29,820 --> 00:13:35,180
+Beta 1 of M بدي اعمله على مين؟ Beta 2 of M وهذه
+
+155
+00:13:35,180 --> 00:13:38,640
+اتفاجنة عبارة عن sequence of برضه أيش؟ of numbers
+
+156
+00:13:38,640 --> 00:13:41,380
+which is bounded إذن لها برضه أيش؟ subsequence
+
+157
+00:13:41,730 --> 00:13:46,090
+بالتالي، بما أن B2 و M هي سيكوانات مرتبطة، فهي
+
+158
+00:13:46,090 --> 00:13:52,410
+تحتوي على سبسيكوانت مرتبطة تسميها Beta 2 M 2 هذا
+
+159
+00:13:52,410 --> 00:13:54,490
+أيضًا مرتبط إلى B2
+
+160
+00:13:58,090 --> 00:14:04,830
+بتكون B2 of M و 2 converges فرقنا ل مين ل B2 لأنها
+
+161
+00:14:04,830 --> 00:14:11,070
+sub sequence من bounded sequence يعني بمعنى أخر
+
+162
+00:14:11,070 --> 00:14:13,930
+فما ده في عندي bounded sequence إذا بقدر ألاقي
+
+163
+00:14:13,930 --> 00:14:16,810
+convergent subsequence سميتها اللي قلتها قبل شوية
+
+164
+00:14:16,810 --> 00:14:22,030
+it has a convergent subsequence منها B2 M that
+
+165
+00:14:22,030 --> 00:14:29,090
+converges to مين to B2 اطلع لفوقالآن Y2M نفس الجثة
+
+166
+00:14:29,090 --> 00:14:33,810
+بدي أخدها الـ Corresponding Sequence المكوّنة من
+
+167
+00:14:33,810 --> 00:14:36,990
+Y1 .. اللي هي Y1 .. اللي مكوّنة .. اللي هتكون
+
+168
+00:14:36,990 --> 00:14:41,910
+جزئية من من Y1 و في M ليش؟ لأن Y2 و في M على سرها
+
+169
+00:14:41,910 --> 00:14:49,010
+متكونة B1M1 زي اللي هي تمامته الـY1و M و B2 و M2
+
+170
+00:14:49,010 --> 00:14:53,790
+جزء من هذيك اللي هي X2 زاد هذي بتخليهم زي ما هما
+
+171
+00:14:53,790 --> 00:14:57,330
+الأصليات إذا بس اتغيرت هذي إذا صارت هذي Y2 of M
+
+172
+00:14:57,330 --> 00:15:02,930
+subsequence من مين؟ من Y1 of M بدي لأنا كموحدة إن
+
+173
+00:15:02,930 --> 00:15:07,210
+هذول أن من العناصر بدي أشتغل على البجيات بنفس
+
+174
+00:15:07,210 --> 00:15:13,640
+الأسلوب we after any stepsWe get YNM as a
+
+175
+00:15:13,640 --> 00:15:19,540
+subsequence of YN With YNM أيش بتساوي؟ Beta 1 M1
+
+176
+00:15:19,540 --> 00:15:27,400
+Beta 2 M2 و Beta N يعني MNXN هذي و طبعا كل اللي
+
+177
+00:15:27,400 --> 00:15:31,980
+بنشتغل فيه اللي هو ال absolute values اللي ما له
+
+178
+00:15:31,980 --> 00:15:35,580
+مجموعة بساوي واحد من ضمنه هذول اللي اشتغلت عليه
+
+179
+00:15:35,580 --> 00:15:41,180
+هنا إذا مجموعة دولة بساوي واحدإذا صار عندى Beta 1
+
+180
+00:15:41,180 --> 00:15:47,280
+M1 و Beta 1 و Beta 2 M2 بتروح ل Beta 2 و Beta N MN
+
+181
+00:15:47,280 --> 00:15:52,600
+بتروح ل Beta N هذا كله as mean as M الـ goals
+
+182
+00:15:52,600 --> 00:15:57,680
+المعلنة هي لأن M هي اللى بتعمل ال sequence طيب
+
+183
+00:15:57,680 --> 00:16:08,110
+also برضه واحد بيساوي limitLimit اللي هو Beta 1 M1
+
+184
+00:16:08,110 --> 00:16:14,690
+زي Beta 2 M2 زي Beta N MN مجموح انش هيساويالان
+
+185
+00:16:14,690 --> 00:16:21,070
+مجموحين هذولة اللي هو بساوي واحد و limit كل واحدة
+
+186
+00:16:21,070 --> 00:16:26,250
+بتساوي الأولى Beta 1 والتانية Beta 2 والتالتة Beta
+
+187
+00:16:26,250 --> 00:16:32,270
+N إذا limit المجموع بساوي مجموحين هذولة لقيمة ال
+
+188
+00:16:32,270 --> 00:16:35,550
+limits بنوزع ال limit يعني بمعنى أخر بوزع ال limit
+
+189
+00:16:35,550 --> 00:16:39,320
+على مجموع عدد عشر عشرين تلاتين N من ال limitsبكون
+
+190
+00:16:39,320 --> 00:16:42,140
+limit الأول زي limit التاني زي limit التالت بساوة
+
+191
+00:16:42,140 --> 00:16:45,420
+summation beta I وهذا المجموع زي ما قلنا أيش بساوة
+
+192
+00:16:45,420 --> 00:16:51,320
+واحد إذا المجموع هذا النهايات نفسها بساوة واحد إذا
+
+193
+00:16:51,320 --> 00:16:56,220
+حصلت على إن مجموع النهايات بساوة واحد إذا الآن
+
+194
+00:16:56,220 --> 00:17:03,220
+مدان مجموع هذولة، انتبهوا الآن مجموع هذولة بساوة
+
+195
+00:17:03,220 --> 00:17:09,560
+واحد إذا فيه على الأقل، على الأقل واحدة مش سفرهكذا
+
+196
+00:17:09,560 --> 00:17:11,900
+أصبح مجموح من بساوي واحد absolute values هذه
+
+197
+00:17:11,900 --> 00:17:15,280
+absolute values مجموح من إيش بساوي بساوي واحد يعني
+
+198
+00:17:15,280 --> 00:17:18,260
+قيم موجة بأكبر بساوي سفر مجموح من واحد إذا على
+
+199
+00:17:18,260 --> 00:17:21,620
+الأقل أكيد في واحدة يشمالها لا تساوي سفر إذا then
+
+200
+00:17:21,620 --> 00:17:26,200
+there is at least beta I لا تساوي إيش سفر لكن ال X
+
+201
+00:17:26,200 --> 00:17:30,660
+واحد وال X اتنين وال X unlinearly independent then
+
+202
+00:17:30,660 --> 00:17:36,480
+أكيد ال Y لا تساوي سفر ال Y مين هي ال Y ال Y هي
+
+203
+00:17:36,480 --> 00:17:46,520
+عبارة ال Yعبارة عن X1 Beta 1 زي X2 Beta 2 زي XN
+
+204
+00:17:46,520 --> 00:17:55,090
+Beta N هذا أكيد لا تساوي سفرليش لا تساوي سفر؟ لأن
+
+205
+00:17:55,090 --> 00:18:00,910
+لو كانت سفر لو كانت سفر طبعا في عندي واحدة منهم XI
+
+206
+00:18:00,910 --> 00:18:05,570
+Beta I زائد إلى أخير لإن عندك Xn هذه ال Beta I
+
+207
+00:18:05,570 --> 00:18:10,370
+تبعتها مش سفر لو بدنا نقول هذه بتساوي سفر معناته
+
+208
+00:18:10,370 --> 00:18:16,120
+صارت ال XIبكتبها على صورة X1 Beta 1 على Beta I
+
+209
+00:18:16,120 --> 00:18:22,880
+زائد Xn Beta N على اليمين Beta I يعني قدرت أكتب X
+
+210
+00:18:22,880 --> 00:18:26,260
+أزالين ال combination من هذا وهذا أشماله
+
+211
+00:18:26,260 --> 00:18:30,580
+contradiction لأن X1 و X2 و Xn are linearly
+
+212
+00:18:30,580 --> 00:18:36,220
+independent إذن ال linearly independent هو اللي
+
+213
+00:18:36,220 --> 00:18:43,300
+ضمنلي أن ال Y هذه أشمالها لاتساوى 0لكن في الأصل،
+
+214
+00:18:43,300 --> 00:18:47,760
+since the norm is continuous، إذا الـ Normal Y and
+
+215
+00:18:47,760 --> 00:18:53,440
+M بيروح لـ Normal Yمدام ال .. لأنه limit ال Yn و M
+
+216
+00:18:53,440 --> 00:18:57,540
+إيش بيساوي؟ بيساوي ال Y إذا norm ال Yn و M هيروح
+
+217
+00:18:57,540 --> 00:19:04,080
+لمين؟ ل norm ال Y but Yn و M اللي ركّبناها .. نرجع
+
+218
+00:19:04,080 --> 00:19:08,700
+لقصتنا الأولى is a subsequence من مين؟ من Yn
+
+219
+00:19:08,700 --> 00:19:14,340
+الأصلية Yn الأصلية إيش مالها؟ normها راح لمين؟ لل
+
+220
+00:19:14,340 --> 00:19:18,040
+0 .. أو للتركيبة .. أنزل .. أنزل .. أنزل ..هنزل
+
+221
+00:19:18,040 --> 00:19:22,260
+هايو عندنا في واحة اتنين اثبتنا ان normal YM ايش
+
+222
+00:19:22,260 --> 00:19:27,420
+مروح للسفر لازم goes to infinity اذا الان الان
+
+223
+00:19:28,880 --> 00:19:32,980
+أثبتنا أن الـ sub-sequence هذه راحت لـ Normal Y و
+
+224
+00:19:32,980 --> 00:19:37,660
+الـ M اللي هي الـ Y and M sub-sequence من YM و
+
+225
+00:19:37,660 --> 00:19:40,520
+Normal YM ما أثبتناه في الأول بيروح لـ Zero إذا
+
+226
+00:19:40,520 --> 00:19:43,400
+الـ Norm هذي إيش بيروح لمين؟ لـ Zero و احنا قلنا
+
+227
+00:19:43,400 --> 00:19:46,860
+هنا الـ Y إيش ما لها؟ لأ تساوي سفر فصار في عندي
+
+228
+00:19:46,860 --> 00:19:51,280
+Contradiction إذا الفرضية الأصلية مش صحيحة Hence
+
+229
+00:19:51,280 --> 00:19:57,600
+اللي هو Therefore واحد is proved بمعنى آخر أنه لكل
+
+230
+00:19:57,600 --> 00:20:02,900
+اللي هيPfffThere exists C such that لكل choice ل
+
+231
+00:20:02,900 --> 00:20:06,300
+Beta 1 و Beta 2 المجموحين بيساوي واحد norm اللي هو
+
+232
+00:20:06,300 --> 00:20:12,500
+أكبر أو يساوي C الان الان انزل شوية خليني أرجع
+
+233
+00:20:12,500 --> 00:20:16,620
+اللي بس الان from this and three we have a
+
+234
+00:20:16,620 --> 00:20:21,200
+contradiction therefore one is approved now if ال
+
+235
+00:20:21,200 --> 00:20:24,600
+absolute اللي أثبتناه كله في حالة اللي هو
+
+236
+00:20:24,600 --> 00:20:28,020
+summation لل Beta I's بيساوي واحد اللي انا بتاخده
+
+237
+00:20:28,020 --> 00:20:31,960
+arbitrarilyالأن اذا الـ F ألف واحد أفضل قيمة ألف
+
+238
+00:20:31,960 --> 00:20:35,620
+واحد زاد أفضل قيمة ألف اتنين زاد أفضل قيمة ألف ألف
+
+239
+00:20:35,620 --> 00:20:41,540
+ن افترض انه ايش ماله بساوء سفر اذا الف اي سفر لكله
+
+240
+00:20:41,540 --> 00:20:47,040
+مش الحال اذا ال norm للألف واحد X واحد زاد ألف ن
+
+241
+00:20:47,040 --> 00:20:53,180
+Xn اللي هو أكبر أو ساوء C في ال summation hold ايش
+
+242
+00:20:53,180 --> 00:20:55,380
+اللي بده اعمله يا جماعة انا اللي بده اتبطه الان
+
+243
+00:20:55,380 --> 00:20:57,080
+انتبهوا
+
+244
+00:20:58,550 --> 00:21:04,790
+اللي بيدثبتلكم إياه الآن الـ arbitrary scalars
+
+245
+00:21:04,790 --> 00:21:10,610
+يعني there exists C أكبر من 0 such that for any
+
+246
+00:21:10,610 --> 00:21:15,010
+choice of Alpha 1, Alpha 2 لعند Alpha N with
+
+247
+00:21:15,010 --> 00:21:21,930
+summation اللي هو such that norm اللي هي الـ Alpha
+
+248
+00:21:21,930 --> 00:21:28,940
+1 X 1 زي Alpha N X Nاللي هو أكبر أو يساوي C ال
+
+249
+00:21:28,940 --> 00:21:32,520
+summation absolute value of I I من عند واحد لمنين
+
+250
+00:21:32,520 --> 00:21:37,060
+لعندك for any choice لأن بتاخد حالتين الحالة
+
+251
+00:21:37,060 --> 00:21:42,660
+الأولى أن يكون ال summation هذا ال summation Alpha
+
+252
+00:21:42,660 --> 00:21:48,620
+I بساوي سفر إذا سفر معناته automatically كل واحدة
+
+253
+00:21:48,620 --> 00:21:51,540
+فيه سفر معناته اللي هو كل ال C's اللي في الدنيا
+
+254
+00:21:51,540 --> 00:21:55,700
+بتظبطيعني هذا الـ Trivial Case لما نفترض إن الـ
+
+255
+00:21:55,700 --> 00:21:59,020
+summation للأبسوليوت V للألف I أشمالها لا يساوي
+
+256
+00:21:59,020 --> 00:22:04,780
+سفر عشان بتقسم عليها بالعالم طيب طيب finally if S
+
+257
+00:22:04,780 --> 00:22:08,300
+بتساوي ال summation للألف I أشمالها لا تساوي إيش
+
+258
+00:22:08,300 --> 00:22:12,610
+سفرخدوا الـ N أحنا أثبتناها لـ Beta I الـ
+
+259
+00:22:12,610 --> 00:22:15,570
+summation اللي بيساوي واحد خدوا Beta 1 بيساوي
+
+260
+00:22:15,570 --> 00:22:20,090
+Alpha 1 على S Beta 2 Alpha 2 على S Beta N Alpha N
+
+261
+00:22:20,090 --> 00:22:23,730
+على S in general لكل I Beta I بيساوي Alpha I على S
+
+262
+00:22:23,730 --> 00:22:28,210
+لـ I بيساوي واحد لعند الـ N حسبولي الآن لـ Beta Z
+
+263
+00:22:28,210 --> 00:22:31,330
+للـ N ال summation لـ Beta I I من عند واحد لـ N
+
+264
+00:22:31,330 --> 00:22:35,750
+بيساوي ال summationباخد الـ 1 على أسماله عامل
+
+265
+00:22:35,750 --> 00:22:39,050
+مشترك في الـ summation هذا هو هذا فاش بيساوي
+
+266
+00:22:39,050 --> 00:22:42,810
+بيساوي واحد إذا أنا أثبته للي ال beta بيساوي واحد
+
+267
+00:22:42,810 --> 00:22:48,290
+إذا النظرية صحيحة لهذه اه طيب by substituting beta
+
+268
+00:22:48,290 --> 00:22:53,110
+I بيساوي Alpha I على S الواحد اللي أثبتناها we get
+
+269
+00:22:53,110 --> 00:22:58,170
+norm Alpha 1 على S Fix 1 زاد Alpha 2 على S Fix 2
+
+270
+00:22:58,170 --> 00:23:03,400
+زاد Alpha N عكس N أكبر بيساوي مين؟ Cالان هناخد الـ
+
+271
+00:23:03,400 --> 00:23:07,360
+C مالها برا عام المشترك اللي هي 1 على ال S فالـ S
+
+272
+00:23:07,360 --> 00:23:10,760
+1 على ال S ناخدها عام المشترك و بعدين نضربها في
+
+273
+00:23:10,760 --> 00:23:14,100
+الطرفين بنكون حصلنا Alpha 1 X 1 Alpha 2 X 2 زاد
+
+274
+00:23:14,100 --> 00:23:18,340
+Alpha X N أكبر من مين من C فS اللي هي C بتساوي ال
+
+275
+00:23:18,340 --> 00:23:26,530
+summation this completes the proof أي سؤالطيب نجي
+
+276
+00:23:26,530 --> 00:23:31,770
+لان نظريتنا هذه لما يعني عبارة عن أداء لاللي هو
+
+277
+00:23:31,770 --> 00:23:39,170
+للوصول لإثبات النظريات اللاحقة نجي
+
+278
+00:23:39,170 --> 00:23:42,770
+لان صار النظرية بداخل بيتها لجهة النظرية المهمة
+
+279
+00:23:42,770 --> 00:23:47,630
+هذه المهمة المنيحة و الحلوة هذه صار برهانها سهل
+
+280
+00:23:47,630 --> 00:23:51,010
+الآن أو بسيط بالاستعانة بال .. بال .. بال ..
+
+281
+00:23:51,420 --> 00:23:55,100
+باللمّة اللي قبله شوية يعني قد يكون بعض الكتب اللي
+
+282
+00:23:55,100 --> 00:23:59,000
+هي بتثبتها بتثبتش اللمّة فبتروح تثبتها مباشرة و
+
+283
+00:23:59,000 --> 00:24:02,560
+بتبدأ تشتغل شغل طبعا أكثر تعقيدا الان بعد ما
+
+284
+00:24:02,560 --> 00:24:07,080
+أثبتنا اللمّة بيسير شغلها أكتر سهولة نيجي نشوف أيش
+
+285
+00:24:07,080 --> 00:24:11,900
+اللي بيقوله إعلان هذا theorem every finite
+
+286
+00:24:11,900 --> 00:24:15,420
+dimensional subspace y of a normed space x أشماله
+
+287
+00:24:15,420 --> 00:24:20,460
+is complete أي في ال finite dimensional spaceلو
+
+288
+00:24:20,460 --> 00:24:25,920
+أخدنا أو في اللي هو تكون الـ subspace نفسه finite
+
+289
+00:24:25,920 --> 00:24:29,440
+dimensional من space على طول هذا ال subspace بيكون
+
+290
+00:24:29,440 --> 00:24:34,140
+complete يعني الآن أنا finite dimensional space is
+
+291
+00:24:34,140 --> 00:24:38,020
+complete هذا الحالة الخاصة بتصير لأن الحالة العامة
+
+292
+00:24:38,020 --> 00:24:43,600
+أن أنا finite dimensional subspace of a normed
+
+293
+00:24:43,600 --> 00:24:49,090
+space must be completeعشان هيك كل اللي بنشتغل فيه
+
+294
+00:24:49,090 --> 00:24:54,410
+R وR تربيع وR تكعيب وR أنه وC وC1 وC2 كلهم finite
+
+295
+00:24:54,410 --> 00:24:58,390
+dimensional spaces هدولة كلهم complete metric
+
+296
+00:24:58,390 --> 00:25:04,930
+spaces أو complete normed spaces معين؟ طيبIn
+
+297
+00:25:04,930 --> 00:25:08,050
+particular, every finite dimensional normed space
+
+298
+00:25:08,050 --> 00:25:14,030
+كله is complete بدنا نثبت الآن خدوا الآن لثبات سهل
+
+299
+00:25:14,030 --> 00:25:18,070
+let Y be .. عشان نثبت complete ناخد any Cauchy
+
+300
+00:25:18,070 --> 00:25:22,110
+sequence و نثبت انها converged وبس هي كل جثتنا بما
+
+301
+00:25:22,110 --> 00:25:26,170
+يلقم السؤال طبعا let Y be any Cauchy sequence in Y
+
+302
+00:25:27,070 --> 00:25:30,790
+Suppose that الـ dimension للـ Y إيش بيساوي N هذا
+
+303
+00:25:30,790 --> 00:25:35,070
+الـ Y sub space من a normed space اسمه إيه إيش X
+
+304
+00:25:35,070 --> 00:25:38,530
+ال sub space Y هو اللي ال dimension إيه بيساوي N
+
+305
+00:25:38,530 --> 00:25:42,290
+طيب مدام ال dimension إيه بيساوي N إذا إنه bases
+
+306
+00:25:42,290 --> 00:25:45,830
+ال bases تبع جبل الخطة تبع جبل الخطة زمان اللي أن
+
+307
+00:25:45,830 --> 00:25:49,370
+ال bases إيه نفترض إنه اسمه E1 وE2 وEN بيه any
+
+308
+00:25:49,370 --> 00:25:54,640
+basis forming for Y لأنه finite dimensionalمدام
+
+309
+00:25:54,640 --> 00:25:58,980
+اللي هو الـ E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12
+
+310
+00:25:58,980 --> 00:26:04,780
+E13 E14 E14 E15 E16 E17 E18 E19 E21 E21 E21 E21
+
+311
+00:26:04,780 --> 00:26:06,260
+E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21
+
+312
+00:26:06,260 --> 00:26:06,500
+E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21
+
+313
+00:26:06,500 --> 00:26:07,140
+E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21
+
+314
+00:26:07,140 --> 00:26:07,980
+E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21
+
+315
+00:26:07,980 --> 00:26:15,030
+E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21of
+
+316
+00:26:15,030 --> 00:26:18,710
+the form YM بسوء ألف واحد M هذي scalar رمز ال
+
+317
+00:26:18,710 --> 00:26:22,850
+scalar حطيت ال M هنا عشان يشملها بنقول عنها لمين
+
+318
+00:26:22,850 --> 00:26:27,010
+لل YM لو Y واحد هنحط لها واحد عشان تكون لمين لل Y
+
+319
+00:26:27,010 --> 00:26:32,130
+واحد وهكذا لأن YM بتسوء ألف واحد M E واحد زاد ألف
+
+320
+00:26:32,130 --> 00:26:36,790
+اتنين M E اتنين زاد ألف N E M E N اللي هي YM
+
+321
+00:26:36,790 --> 00:26:39,250
+مكتوبة على هذه الصورة لإنه ال E واحد وال E اتنين
+
+322
+00:26:39,250 --> 00:26:43,910
+وال E N are a basis طيب
+
+323
+00:26:44,930 --> 00:26:49,830
+Since YM is Cauchy Sequence إذا لكل Y أكبر من 0
+
+324
+00:26:49,830 --> 00:26:52,930
+there exists K limiting and such that البعد بين أي
+
+325
+00:26:52,930 --> 00:26:59,010
+نخطين YM نقص YR أصغر من Y لكل R و M أكبر من مين من
+
+326
+00:26:59,010 --> 00:27:03,370
+ال K اللي لجيناها طيب الآن بدي أستخدم اللمة اللي
+
+327
+00:27:03,370 --> 00:27:07,130
+قابلت بشويها لجيت و بدي أستخدمها دي لإن from this
+
+328
+00:27:07,130 --> 00:27:11,450
+and by لمة اتنين اربعة واحد بنقدر نلاقي ال C أكبر
+
+329
+00:27:11,450 --> 00:27:16,990
+من 0 معايا؟هذا الـ C أكبر من 0 لمين؟ الـ norm اللي
+
+330
+00:27:16,990 --> 00:27:19,870
+هو الـ vector أكبر يساوي C في الصممشي للـ scalar
+
+331
+00:27:19,870 --> 00:27:23,390
+استبعاته، صح؟ هذا اللي قبل شوية اللي ما هو أتعبنا
+
+332
+00:27:23,390 --> 00:27:26,770
+حالنا كلنا أتعب there exists C أكبر من 0 such that
+
+333
+00:27:26,770 --> 00:27:31,270
+YM ناقص YR زي من إبسنون، هي الإبسنون أكبر من YM
+
+334
+00:27:31,270 --> 00:27:36,010
+ناقص YR من إنها قوشي، هي واحد، الآن YM ناقص YR إيش
+
+335
+00:27:36,010 --> 00:27:41,420
+هي؟ الـ YM هي صورتهاوالـ Yr هي صورتها بس بمشينا
+
+336
+00:27:41,420 --> 00:27:45,640
+الـ M بحط مين؟ R بصير الصممشن لهادي نقصها دي بصير
+
+337
+00:27:45,640 --> 00:27:46,460
+الصممشن لهادي نقصها دي بصير الصممشن لهادي نقصها دي
+
+338
+00:27:46,460 --> 00:27:48,680
+بصير الصممشن لهادي نقصها دي بصير الصممشن لهادي
+
+339
+00:27:48,680 --> 00:27:49,200
+نقصها دي نقصها نقصها نقصها نقصها نقصها نقصها نقصها
+
+340
+00:27:49,200 --> 00:27:51,960
+نقصها نقصها نقصها نقصها نقصها نقصها نقصها نقصها
+
+341
+00:27:51,960 --> 00:27:52,760
+نقصها نقصها نقصها نقصها نقصها نقصها نقصها نقصها
+
+342
+00:27:52,760 --> 00:28:02,190
+نقصها نقصها نقصها نقصها نقصهاأه فاهمين هذا خطها
+
+343
+00:28:02,190 --> 00:28:05,630
+هيك فاهمين ليش اللي بحكيه لأن I من عند واحد لعند
+
+344
+00:28:05,630 --> 00:28:10,870
+مين لعند أنا هذا الان لل vector اللي هنا هذا اللي
+
+345
+00:28:10,870 --> 00:28:14,970
+هو اللي هو بدي استخدم اللي لمّا اللي قبل شوية أكبر
+
+346
+00:28:14,970 --> 00:28:19,550
+أو ساوي C في الصممش لأبسل يوت values لمين لل
+
+347
+00:28:19,550 --> 00:28:24,410
+scalars هذه اللي عندي هذه صار هذا المقدار هاي و
+
+348
+00:28:24,410 --> 00:28:29,880
+هذا أصغر أو يساوي مين أبسلونthis implies that for
+
+349
+00:28:29,880 --> 00:28:32,860
+any fixed I لكل واحدة من هدول مدام ال summation
+
+350
+00:28:32,860 --> 00:28:36,720
+هذا هذا ال summation مضروب في C أصغر من يابسولون
+
+351
+00:28:36,720 --> 00:28:41,620
+إذا كل واحدة منهم absolute value لها هذول أصغر
+
+352
+00:28:41,620 --> 00:28:45,040
+يعني ال summation هذا مضروب في C يعني ال summation
+
+353
+00:28:45,040 --> 00:28:48,460
+هذا لحاله أصغر من يابسولون ع C إذا كل واحدة من
+
+354
+00:28:48,460 --> 00:28:51,360
+اللي جوا أصغر من يابسولون على مين على C
+
+355
+00:28:54,290 --> 00:28:58,890
+then for any fixed I من الـ I هولا واحد و اتنين و
+
+356
+00:28:58,890 --> 00:29:03,630
+ان ال sequence Alpha I M عبارة عن Alpha I واحد
+
+357
+00:29:03,630 --> 00:29:07,370
+Alpha I اتنين Alpha I تلاتة هتكون يشمالها is a
+
+358
+00:29:07,370 --> 00:29:10,190
+Cauchy sequence لإن لجينا كل أبساط أكبر من سفر
+
+359
+00:29:10,190 --> 00:29:17,000
+لجينا Kبحيث أن الـ absolute value لهذه أصغر من Y
+
+360
+00:29:17,000 --> 00:29:22,400
+على C for every M وR أكبر من الـ K يعني بمعنى أخر
+
+361
+00:29:22,400 --> 00:29:25,560
+صارت الـ sequence هذه اللي هي هي ال sequence
+
+362
+00:29:25,560 --> 00:29:29,700
+تبعتها هذه اللي هي ال entry تبعت ال sequenceمش هده
+
+363
+00:29:29,700 --> 00:29:33,620
+هدى بس بنحكي عن واحدة من الـ sequences الان مش
+
+364
+00:29:33,620 --> 00:29:37,600
+عندنا للواحد و للتنين و للتلتة اللي عند الان هدولة
+
+365
+00:29:37,600 --> 00:29:41,580
+sequences هدى لل I in general هدى sequence هدى
+
+366
+00:29:41,580 --> 00:29:44,600
+طلعت كوشي sequence من هن مادام كوشي sequence و هي
+
+367
+00:29:44,600 --> 00:29:48,490
+كوشي sequence و فيهاشof numbers و لا .. ولا .. ولا
+
+368
+00:29:48,490 --> 00:29:50,970
+real numbers أو ال complex numbers complete إذا
+
+369
+00:29:50,970 --> 00:29:54,310
+أكيد في إلها إيه أشمالها اللي هي hence it
+
+370
+00:29:54,310 --> 00:29:59,430
+converges say to alpha I لأنه any Cauchy sequence
+
+371
+00:29:59,430 --> 00:30:03,780
+of real .. of numbers must convergemust converge
+
+372
+00:30:03,780 --> 00:30:10,680
+لأن use these unlimits ألف واحد M بتروح لألف واحد
+
+373
+00:30:10,680 --> 00:30:17,360
+ألف اتنين M لألف اتنين ألف N M بتروح للألف N إذا
+
+374
+00:30:17,360 --> 00:30:20,380
+صارت كل واحدة فيه لها limit لأن use these
+
+375
+00:30:20,380 --> 00:30:24,320
+unlimited to define من هذولة بدي أعرف مين اللي هو
+
+376
+00:30:24,320 --> 00:30:28,020
+Y Y بتساوي ألف واحد E واحد ألف اتنين E اتنين زي
+
+377
+00:30:28,020 --> 00:30:32,120
+ألف N E N اللي هي combination بينهمهذا الـ Y أكيد
+
+378
+00:30:32,120 --> 00:30:37,540
+في الـ space اللي عندي لأن الـ bases إله و هذولا
+
+379
+00:30:37,540 --> 00:30:41,200
+صارت إتنين ال combinations of bases إلا إن استخدمت
+
+380
+00:30:41,200 --> 00:30:44,420
+هذولا ال limits اللي لقيتهم قبل بشوية إذا صارت
+
+381
+00:30:44,420 --> 00:30:49,320
+عندي Y element ومش هيك كمان وخدوا الـ Y أم ناقصوا
+
+382
+00:30:49,320 --> 00:30:55,290
+الـ Yنورم الـ YM ناقص نورم الـ Y بساوي النورم لـ
+
+383
+00:30:55,290 --> 00:30:59,070
+summation هذين هي ال combination من مين Alpha I M
+
+384
+00:30:59,070 --> 00:31:02,870
+مع الـEI وهذه هي ال combination من مين من Alpha I
+
+385
+00:31:02,870 --> 00:31:06,490
+في الـEI نورم هذه ناقص هذه ناقص هذه ناقص هذه ناقص
+
+386
+00:31:06,490 --> 00:31:06,710
+ناقص هذه ناقص هذه ناقص هذه ناقص هذه ناقص هذه ناقص
+
+387
+00:31:06,710 --> 00:31:07,270
+هذه ناقص هذه ناقص هذه ناقص هذه ناقص هذه ناقص هذه
+
+388
+00:31:07,270 --> 00:31:08,550
+ناقص هذه ناقص هذه ناقص هذه ناقص هذه ناقص هذه ناقص
+
+389
+00:31:08,550 --> 00:31:09,490
+هذه ناقص هذه ناقص هذه ناقص هذه ناقص هذه ناقص هذه
+
+390
+00:31:09,490 --> 00:31:14,070
+ناقص هذه
+
+391
+00:31:14,100 --> 00:31:19,360
+الان صار عندى summation لهذا في هذا however لكل
+
+392
+00:31:19,360 --> 00:31:23,280
+واحدة من هدول Alpha I M بتروح لمين لل Alpha I as M
+
+393
+00:31:23,280 --> 00:31:26,160
+goes to infinity اذا هذا المقدار as M goes to
+
+394
+00:31:26,160 --> 00:31:31,120
+infinity هو ان بدوح لصفر لأن هذه هتروح لهذه as M
+
+395
+00:31:31,120 --> 00:31:33,880
+goes to infinity اذا هذا هيروح لصفر بمعنى اخر
+
+396
+00:31:33,880 --> 00:31:38,920
+Normal Y M ناقص ال Y هيروح لصفربمعنى أخر صارت الـ
+
+397
+00:31:38,920 --> 00:31:42,680
+Y M converges لمن؟ لـ Y إذن الآن بدأت Y M ماكوش
+
+398
+00:31:42,680 --> 00:31:46,900
+sequence و أثبتت أن الـ Y M converges لـ Y في ال
+
+399
+00:31:46,900 --> 00:31:53,780
+space نفس Y، therefore Y is complete اللي بعده
+
+400
+00:31:53,780 --> 00:32:00,220
+المادة مفيدة للي بدوا علم منيح مفيدة مفيدة و بتدير
+
+401
+00:32:00,220 --> 00:32:04,860
+بقاكم و أي مكان لو الواحد يعني القدر اللي يكمل
+
+402
+00:32:04,860 --> 00:32:06,960
+كمان و كمان هتلاجوها
+
+403
+00:32:09,310 --> 00:32:13,450
+يستعانى بهوى المكان انه spaces لازم تكون في هال
+
+404
+00:32:13,450 --> 00:32:17,970
+spaces عشان تشتغل اي شغل تشتغل في الاحتمالات تشتغل
+
+405
+00:32:17,970 --> 00:32:23,010
+في الاحصة تشتغل في يعني انا بتذكر في الاحتمالات
+
+406
+00:32:23,010 --> 00:32:27,610
+أخدنا course كامل بنشتغل فيه في ال LB spaces ال LB
+
+407
+00:32:27,610 --> 00:32:30,370
+طبعا اللي هي مش ال sequences ال functions اللي هي
+
+408
+00:32:30,370 --> 00:32:33,650
+ال .. اللي بيجي integrable functions طب على معناته
+
+409
+00:32:33,650 --> 00:32:36,550
+انك بدك تسير بتعرف اللي هو اللي هو كل الكلام اللي
+
+410
+00:32:36,550 --> 00:32:43,020
+بنحكيه هذا بيكون مفيد إلىكوهكذا طيب theorem every
+
+411
+00:32:43,020 --> 00:32:45,880
+finite dimensional subspace Y of a normed space X
+
+412
+00:32:45,880 --> 00:32:51,080
+إيش ماله is closed طب هو complete و ال complete
+
+413
+00:32:51,080 --> 00:32:55,500
+أكيد إيش ماله closed بتعرفوا تثبتوها أن ال
+
+414
+00:32:55,500 --> 00:33:01,900
+complete space is closed يعني لو كانك X complete
+
+415
+00:33:03,330 --> 00:33:07,890
+بيعطينا انه X اللي هو خلينا نقول Y sub space Y sub
+
+416
+00:33:07,890 --> 00:33:12,210
+space من X و Y complete اكيد ال Y اشمالها closed
+
+417
+00:33:12,210 --> 00:33:14,710
+ماحكتش عن ال space اللي كله ال X ماهو ال space
+
+418
+00:33:14,710 --> 00:33:21,090
+دايما اللي هو closed و open فاهمين؟ طيب
+
+419
+00:33:22,590 --> 00:33:26,810
+إذاً أي finite dimensional subspace Y of X is
+
+420
+00:33:26,810 --> 00:33:34,090
+closed لأنه مدام Y subspace من X و finite
+
+421
+00:33:34,090 --> 00:33:37,970
+dimensional من X إذاً Y complete مدام complete على
+
+422
+00:33:37,970 --> 00:33:42,270
+طول إشماله closed بتقفل تثبتوها إن ال close ده قال
+
+423
+00:33:42,270 --> 00:33:47,330
+لو كانت عندي Y complete هتكون closed خد X في ال Y
+
+424
+00:33:47,330 --> 00:33:53,650
+closure إذاً there exist XNin Y such that Xn
+
+425
+00:33:53,650 --> 00:33:58,490
+converts الـ mean للـ X ماشي الحال طيب الآن صارت
+
+426
+00:33:58,490 --> 00:34:02,850
+عندي ال Xn مدينة converts لل X إذا صارت Xn كوشي
+
+427
+00:34:02,850 --> 00:34:05,990
+سيكوينس في مين؟ في ال Y مدينة كوشي سيكوينس في ال Y
+
+428
+00:34:05,990 --> 00:34:08,710
+و ال Y complete إذا converts يعني ال X هذا هتكون
+
+429
+00:34:08,710 --> 00:34:12,550
+وين؟ في ال Y مدينة X صارت في ال Y إذا صارت ال X في
+
+430
+00:34:12,550 --> 00:34:15,370
+ال Y closure تؤدي ال X في ال Y معناته ال Y closure
+
+431
+00:34:15,370 --> 00:34:19,100
+جزئية من ال Y و ال Y جزئية من ال Y closureمعناته
+
+432
+00:34:19,100 --> 00:34:21,880
+صحيح الـ Y بيساوي Y closure معناته الـ Y أشبه لها
+
+433
+00:34:21,880 --> 00:34:31,200
+S closed طيب .. اللي بعده؟ ان قال بجلد الملاحظة
+
+434
+00:34:31,200 --> 00:34:35,560
+التالية Infinite dimensional subspaceneed not be
+
+435
+00:34:35,560 --> 00:34:38,340
+closed يعني لو كان في عند infinite dimensional
+
+436
+00:34:38,340 --> 00:34:43,040
+subspace مش شرط closed احنا بنقول عن اللي هو طبعا
+
+437
+00:34:43,040 --> 00:34:46,220
+و اكيد مش شرط ماله complete اكيد مش شرط complete
+
+438
+00:34:46,220 --> 00:34:52,220
+ال infinite dimensional subspace اللي هو need not
+
+439
+00:34:52,220 --> 00:34:57,060
+be closed ماحدش قاله closed to see this consider
+
+440
+00:34:57,060 --> 00:35:04,710
+the space C C01 الكل continuous functionsخُد الـ
+
+441
+00:35:04,710 --> 00:35:10,110
+subspace منها مين؟ Y بتساوي لسبب X0 X1 X2 X3 X4 X5
+
+442
+00:35:10,110 --> 00:35:11,170
+X6 X7 X8 X9 X10 X11 X12 X13 X12 X13 X13 X13 X13
+
+443
+00:35:11,170 --> 00:35:11,610
+X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13
+
+444
+00:35:11,610 --> 00:35:11,830
+X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13
+
+445
+00:35:11,830 --> 00:35:11,850
+X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13
+
+446
+00:35:11,850 --> 00:35:14,370
+X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13
+
+447
+00:35:14,370 --> 00:35:14,390
+X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13
+
+448
+00:35:22,100 --> 00:35:28,880
+بس .. اه؟ الان .. الان بدنا نجيبلكم مثال على
+
+449
+00:35:28,880 --> 00:35:32,800
+infinite dimensional subspace ليست closed مش شرط
+
+450
+00:35:32,800 --> 00:35:37,180
+يكون closed الان المثال اللي كان فيه سؤال معاكم في
+
+451
+00:35:37,180 --> 00:35:44,720
+ال .. في ال .. في ال home work هذا .. هذا بيجاوب
+
+452
+00:35:44,720 --> 00:35:49,640
+عليه الان خد ال space mean C of 0 و 1 continuous
+
+453
+00:35:49,640 --> 00:35:55,140
+functionsانظر من الـ Normal هو الـ Maximum الآن
+
+454
+00:35:55,140 --> 00:35:59,480
+الـ Sub-spacement هو ما يساوي الـ span لـ X0 X1 X2
+
+455
+00:35:59,480 --> 00:36:03,240
+إلى ما لا نهاية ماشي الحالة طب مين هدول X0 X0
+
+456
+00:36:03,240 --> 00:36:08,000
+بساوي اللي هو واحد X1 اللي هو بساوي T X2 بساوي T
+
+457
+00:36:08,000 --> 00:36:12,300
+تربيع X3 بساوي T تكعيب وكأنه قاعد بقولي ال span
+
+458
+00:36:12,300 --> 00:36:16,370
+اللي من الـ Polynomialsيعني و كأنه بيقول هذا why
+
+459
+00:36:16,370 --> 00:36:19,150
+is a subspace اللي هو the space they span by this
+
+460
+00:36:19,150 --> 00:36:25,370
+.. this اللي هي terms اللي هو بعملي اللي هو ال
+
+461
+00:36:25,370 --> 00:36:29,350
+polynomials هذا the space of all polynomials هان
+
+462
+00:36:29,350 --> 00:36:36,130
+is notClosed لأن بلاجة الـ sequence بتروح براته من
+
+463
+00:36:36,130 --> 00:36:40,430
+ضمن الـ mean اللي هو الـ exponential و هكذا و كتير
+
+464
+00:36:40,430 --> 00:36:43,490
+فيه شغلات المهم then why is not closed و why
+
+465
+00:36:43,490 --> 00:36:48,590
+هينجلته و why لكم كمان بتفصلوا أنتوا إذا في عندي
+
+466
+00:36:48,590 --> 00:36:51,370
+infinite dimensional spaces need not to be closed
+
+467
+00:36:51,370 --> 00:36:56,070
+طيب نجي الآن في حد اسمها equivalent norms
+
+468
+00:36:58,340 --> 00:37:02,900
+الـ equivalent norms بنقول عن الـ two norms a norm
+
+469
+00:37:02,900 --> 00:37:06,980
+on a vector space X is said to be equivalent to a
+
+470
+00:37:06,980 --> 00:37:11,900
+norm تاني نسميه norm not on X if there are
+
+471
+00:37:11,900 --> 00:37:16,520
+positive numbers A and B such that for all X
+
+472
+00:37:16,520 --> 00:37:20,560
+element in X لكل X في الـ X هنلاقي اللي هو norm ال
+
+473
+00:37:20,560 --> 00:37:24,440
+X محصور بين norm ال X not في constant و بين norm
+
+474
+00:37:24,440 --> 00:37:29,930
+ال X not برضه في constant آخرإذا لجينا العلاقة هذه
+
+475
+00:37:29,930 --> 00:37:34,030
+موجودة على طول بنقول .. لكل X بنقول إن الـNormal
+
+476
+00:37:34,030 --> 00:37:38,210
+هذولة الـNorm هذا و الـNorm هذا are equivalent
+
+477
+00:37:38,210 --> 00:37:43,630
+بنسميهم إيش مالهين؟ equivalent norms يعني جديتها
+
+478
+00:37:43,630 --> 00:37:46,470
+اللي هو constant في هذه و constant في هذه يحصر
+
+479
+00:37:46,470 --> 00:37:48,670
+اللي هو الـNorm الأصلي الـNorm اللي بنحكي عنه
+
+480
+00:37:48,670 --> 00:37:52,590
+بينهم معناته إنه صارت اللي هي .. اللي هي بس اللي
+
+481
+00:37:52,590 --> 00:37:56,430
+هي .. الفرق بينهم constant معناته هيكون are
+
+482
+00:37:56,430 --> 00:38:00,720
+equivalent normsله مابعده هذا التعريف اللي مابعده
+
+483
+00:38:00,720 --> 00:38:05,240
+أول واحد هذه equivalent norms on X defines the
+
+484
+00:38:05,240 --> 00:38:09,240
+same topology for X يعني الآن ال topology اللي
+
+485
+00:38:09,240 --> 00:38:12,380
+هيتولد من هذا ال norm و من هذا ال norm are
+
+486
+00:38:12,380 --> 00:38:18,440
+equivalent are equivalent topologies then the
+
+487
+00:38:18,440 --> 00:38:24,560
+proof is left to the reader الموضوع سهل ابتخدوا
+
+488
+00:38:24,560 --> 00:38:29,180
+الآن ال topology المولد من هنامن هذه و ال topology
+
+489
+00:38:29,180 --> 00:38:33,920
+المولد من هذه بتقولوا خلّونا ناخد اللي هو a بين 6
+
+490
+00:38:33,920 --> 00:38:37,700
+مولدة من ال topology هذا و بتثبتوها a بين 6
+
+491
+00:38:37,700 --> 00:38:41,320
+بالنسبالي مين اللي هي ال topology التانية و العكس
+
+492
+00:38:41,320 --> 00:38:44,520
+صحيح اتلاقيها اللي هو سهلة يعني الموضوع بس اللعب
+
+493
+00:38:44,520 --> 00:38:51,920
+في مين في ال constant اللي موجودة عندناأي سؤال أو
+
+494
+00:38:51,920 --> 00:38:56,940
+تاخد .. انت بدك تحكي عن ال open balls و منها تصل
+
+495
+00:38:56,940 --> 00:39:01,280
+طيب اتنين اربعة خمسة theorem تشوفها ال theorem
+
+496
+00:39:01,280 --> 00:39:09,220
+الحلوة و الجميلة و المفيدة خالص و بتريحنا كثير in
+
+497
+00:39:09,220 --> 00:39:13,860
+a finite dimensional vector space any norm is
+
+498
+00:39:13,860 --> 00:39:21,080
+equivalent to any norm تاني يعني انت لو جيتوبديت
+
+499
+00:39:21,080 --> 00:39:24,800
+اتفكر في انك تعمل بحكي عن ال norm مش عن ال metric
+
+500
+00:39:24,800 --> 00:39:31,860
+لو بتيجي تتفكر تعمل جد ما بدك norms على اللي هو ال
+
+501
+00:39:31,860 --> 00:39:35,840
+R اعمل norm على ال R بأي شكل أو على ال R تربيع أو
+
+502
+00:39:35,840 --> 00:39:39,980
+R تكعيب أو R unارو اللي بدك يعمل norms إذا عملت
+
+503
+00:39:39,980 --> 00:39:44,280
+norms اللي هي كل ال norms اللي بتعملها R
+
+504
+00:39:44,280 --> 00:39:48,920
+equivalent بولد بس one topologyاللي هو اللي بنسميه
+
+505
+00:39:48,920 --> 00:39:53,860
+احنا U Dual Topology اللي هي على الـ R أو R تربيع
+
+506
+00:39:53,860 --> 00:39:57,140
+أو R تكعيب تقول في الـ R تربيع بتدخل مربعات أو
+
+507
+00:39:57,140 --> 00:40:00,560
+بتدخل دوائر أو بتدخل الـ neighbourhood أو بتدخل
+
+508
+00:40:00,560 --> 00:40:05,700
+اللي هي اللي بدكيا في الآخر لما نولد نورم لما نولد
+
+509
+00:40:05,700 --> 00:40:09,660
+نورم كل هدولة أو ولدت من نورم على طول R equivalent
+
+510
+00:40:10,590 --> 00:40:13,610
+لكن انت بتقدر تعمل على الأرض اللي هو metric تاني
+
+511
+00:40:13,610 --> 00:40:17,230
+الـ discrete metric مش مولد من norm أصلا ماشي
+
+512
+00:40:17,230 --> 00:40:20,210
+الحال لكن ال .. ال .. ال .. ال .. ال .. ال
+
+513
+00:40:20,210 --> 00:40:23,870
+metricات المولدة من ال norms أو ال .. أو ال
+
+514
+00:40:23,870 --> 00:40:27,070
+topologies .. ال topologies المولدة من ال norm على
+
+515
+00:40:27,070 --> 00:40:30,530
+ال finite dimensional spaces كلهم are equivalent
+
+516
+00:40:30,530 --> 00:40:37,090
+هذا كلام خطير أو كلام كتير مهملدت الان dimension
+
+517
+00:40:37,090 --> 00:40:39,930
+للـ X أش بساوي بسوان نفترض ان احنا بنشتغل في
+
+518
+00:40:39,930 --> 00:40:43,390
+finite dimensional نفترض ان ال dimension لل X أش
+
+519
+00:40:43,390 --> 00:40:47,630
+بساوي بسوان وخد E واحد E اتنين E ان مادام finite
+
+520
+00:40:47,630 --> 00:40:50,890
+dimension لازم بقدر أجواء and bases بيصير E واحد E
+
+521
+00:40:50,890 --> 00:40:54,750
+اتنين E ان بياني bases for mean for X وبنيضيق كمان
+
+522
+00:40:54,750 --> 00:40:55,790
+ومحصورات
+
+523
+00:40:58,070 --> 00:41:01,390
+then ماقدر أحكي عن finite bases جزيه أما كل ال
+
+524
+00:41:01,390 --> 00:41:04,670
+vector space فيه له bases ما هو ال and then every
+
+525
+00:41:04,670 --> 00:41:06,930
+طب ما أنا مش هامش أودر bases أو الاخر هذا الموضوع
+
+526
+00:41:06,930 --> 00:41:11,030
+همل bases الاخرين then every x element in X has a
+
+527
+00:41:11,030 --> 00:41:14,630
+unique representation X بالساوية ألف واحد E واحد
+
+528
+00:41:14,630 --> 00:41:17,030
+زي ألف اتنين E اتنين زي ألف and E and خلاص حطته
+
+529
+00:41:17,030 --> 00:41:19,750
+بني دايم لإن صار فيه عنده اللي هو ال bases وصار
+
+530
+00:41:19,750 --> 00:41:21,650
+فيه عند ال scalars وال X موجودة كده لينا
+
+531
+00:41:21,650 --> 00:41:24,670
+compilation من بينهم a unique representation مظهوط
+
+532
+00:41:24,670 --> 00:41:28,430
+ولا مشاك في ال vector space؟طيب و الف واحد الف
+
+533
+00:41:28,430 --> 00:41:31,570
+اتنين الف ان are scalars بيلمّوا اتنين اربع واحد
+
+534
+00:41:31,570 --> 00:41:34,450
+اللي غلبتنا هذه في الأول there is a positive
+
+535
+00:41:34,450 --> 00:41:37,990
+constant C such that normal X هذا اللي هو اللي هي
+
+536
+00:41:37,990 --> 00:41:40,550
+ال compilation منهم أكبر أو يساوي C في ال
+
+537
+00:41:40,550 --> 00:41:44,090
+summation لأ اللي هو ال scalars سبعته ال absolute
+
+538
+00:41:44,090 --> 00:41:47,830
+value of scalars سبعته مظبوط؟طيب on the other hand
+
+539
+00:41:47,830 --> 00:41:50,430
+خلّيها في الذاكرة اللي بنستخدمها بعد شوية on the
+
+540
+00:41:50,430 --> 00:41:54,390
+other hand normal X not أصغر أو ساوى ال summation
+
+541
+00:41:54,390 --> 00:41:59,950
+لل alpha I E I notهذا .. الآن أنا فا .. ال .. ال
+
+542
+00:41:59,950 --> 00:42:00,650
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+543
+00:42:00,650 --> 00:42:01,870
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+544
+00:42:01,870 --> 00:42:03,450
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+545
+00:42:03,450 --> 00:42:03,610
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+546
+00:42:03,610 --> 00:42:04,310
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+547
+00:42:04,310 --> 00:42:04,590
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+548
+00:42:04,590 --> 00:42:07,530
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+549
+00:42:07,530 --> 00:42:08,290
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+550
+00:42:08,290 --> 00:42:08,390
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+551
+00:42:08,390 --> 00:42:10,130
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+552
+00:42:10,130 --> 00:42:13,110
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+553
+00:42:13,110 --> 00:42:13,390
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+554
+00:42:13,390 --> 00:42:16,830
+.. ال .. ال ..
+
+555
+00:42:16,830 --> 00:42:23,070
+ال .. الاللي هو أصغر أو يساوي الـSummation Alpha I
+
+556
+00:42:23,070 --> 00:42:26,530
+نورم الـEI Note Triangling Quality اللي هي نورم
+
+557
+00:42:26,530 --> 00:42:29,870
+الأول زائد نورم التاني زائد نورم التالت زائد نورم
+
+558
+00:42:29,870 --> 00:42:33,730
+الـN الأخير هذا الـTriangling Quality أصغر أو
+
+559
+00:42:33,730 --> 00:42:40,650
+يساوي هذا الـN كيف نورم للـAlpha I كمين هي بتدخل
+
+560
+00:42:40,650 --> 00:42:44,740
+أكبر واحد في هدولوفي maximum الهن ليه عشان الواحدة
+
+561
+00:42:44,740 --> 00:42:47,640
+اتن تان تلاتة ان من الاعداد فى الهن maximum ايش
+
+562
+00:42:47,640 --> 00:42:51,540
+تمته بساوة K اذا اصغر او ساوة K فى ال summation
+
+563
+00:42:51,540 --> 00:42:56,900
+اللى عندى الان بدى هي عندى حصلت Normal X Note اصغر
+
+564
+00:42:56,900 --> 00:43:00,760
+او ساوة K فى هذا المقدار وهذا اثبتوا انه اكبر او
+
+565
+00:43:00,760 --> 00:43:06,960
+ساوة بده ادمجن مع بعض الان together بيصير
+
+566
+00:43:06,960 --> 00:43:08,360
+انه اطلع لفوق بقى شوية
+
+567
+00:43:13,180 --> 00:43:19,020
+Together Normal X Note أصغر أو ساوي K في summation
+
+568
+00:43:19,020 --> 00:43:25,220
+للـ FI هذه وهذه اللي عندي summation أصغر أو ساوي
+
+569
+00:43:25,220 --> 00:43:29,420
+Normal X على C صح؟ هذه بيصير أصغر أو ساوي K على C
+
+570
+00:43:29,420 --> 00:43:32,840
+في Normal X صارت هذه Normal X Note أصغر أو ساوي
+
+571
+00:43:32,840 --> 00:43:38,320
+some number في الـ X إذا صارت اللي هيHence اللي هو
+
+572
+00:43:38,320 --> 00:43:42,120
+A في نورم ال X نوت أصغر يساوي نورم ال X جيبت هذا
+
+573
+00:43:42,120 --> 00:43:45,320
+على الجهد أنا عشان يلاقم اللي بدي يعني هي C على K
+
+574
+00:43:45,320 --> 00:43:50,140
+بتصير A بتساوي C على K لأن similarly بنفس الطريقة
+
+575
+00:43:50,140 --> 00:43:54,220
+بدل ما استخدم لل X لنورم النوت لنورم بستخدم نورم
+
+576
+00:43:54,220 --> 00:43:56,780
+النوت وبدل نورم النوت بستخدم نورم في الحالتين
+
+577
+00:43:56,780 --> 00:44:00,040
+فبطلع عندى similarly نورم ال X أصغر يساوي B في
+
+578
+00:44:00,040 --> 00:44:04,000
+نورم ال X نوتتنتهي المحاضرة مع بعض يظهر نورم X بين
+
+579
+00:44:04,000 --> 00:44:08,060
+نورم X نوت ونورم X نوت واحدة بسكيلر والثانية
+
+580
+00:44:08,060 --> 00:44:12,180
+بسكيلر آخر معناته هذا وهذا الهن إيه اشمالهن are
+
+581
+00:44:12,180 --> 00:44:15,580
+equivalent norms إذن في الـ finite dimensional
+
+582
+00:44:15,580 --> 00:44:20,720
+spaces كل ال norms are equivalent وبرك الله فيكم
+
+583
+00:44:20,720 --> 00:44:22,400
+تنتهي المحاضرة العاشرة
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/oa3DVUxeS2g.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/oa3DVUxeS2g.srt
new file mode 100644
index 0000000000000000000000000000000000000000..969f1fd54b4b6b7121c44ba2a0727f9967e715bf
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/oa3DVUxeS2g.srt
@@ -0,0 +1,1153 @@
+1
+00:00:05,740 --> 00:00:08,400
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,400 --> 00:00:11,260
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:11,260 --> 00:00:16,300
+آله وصحبه أجمعين هذه المحاضرة رقم 28 مساق تحليل 
+
+4
+00:00:16,300 --> 00:00:19,560
+اقتراني أو تحليل دالي طلاب وطالبات الجامعة 
+
+5
+00:00:19,560 --> 00:00:24,820
+الإسلامية قسم الرياضيات للماجستير وصلنا لعند اللي
+
+6
+00:00:24,820 --> 00:00:28,900
+هو ال section الثالث في شبط أربعة اللي هي 4
+
+7
+00:00:28,900 --> 00:00:31,220
+تلاتة اللي هو ال hand-built theorem for complex
+
+8
+00:00:31,220 --> 00:00:34,500
+normed space المرة الفاترة أخذنا ال real vector
+
+9
+00:00:34,500 --> 00:00:38,800
+space وبرهنناه والبرهان كان طويل شوية عند normed
+
+10
+00:00:38,800 --> 00:00:41,660
+spaces وهذه اللي بتهمني أن ال normed spaces فعلا 
+
+11
+00:00:41,660 --> 00:00:44,440
+هي اللي ... اللي أنا ... لأنه أنا شغلي functional
+
+12
+00:00:44,440 --> 00:00:48,140
+analysis بشكل أساسي عند لازم يكون فيه topology و
+
+13
+00:00:48,140 --> 00:00:51,160
+ال topology اللي هو induced by the norm فالآن هاخد
+
+14
+00:00:51,160 --> 00:00:54,760
+.. الآن بنختار المقصود فيها إحدى النظريات الأساسية
+
+15
+00:00:55,080 --> 00:00:59,360
+الأربع أو الخمس اللي موجودة في الـ .. الـ .. الـ
+
+16
+00:00:59,360 --> 00:01:02,580
+الـ .. الـ Function Analysis هي الـ Hahn-Banach
+
+17
+00:01:02,580 --> 00:01:06,120
+theorem for complex ... for normed spaces طبعا احنا
+
+18
+00:01:06,120 --> 00:01:08,440
+عرفناش أن Hahn-Banach theorem بدها الـ Hahn-Banach
+
+19
+00:01:08,440 --> 00:01:11,080
+theorem هي عبارة عن extension يعني بدها توسيع نفوذ
+
+20
+00:01:11,080 --> 00:01:14,940
+يعني هذا الهدف طبعا الهدف الكبير هذا الآن حققنا
+
+21
+00:01:14,940 --> 00:01:17,480
+الهدف هذا في حالة الـ real vector space والآن 
+
+22
+00:01:17,480 --> 00:01:21,200
+هنحققه في حالة ال complex vector space ومش هنبره
+
+23
+00:01:21,200 --> 00:01:25,400
+ن نوع على السريع هنذكر نظرية واللي هنحكي فيه هو
+
+24
+00:01:25,400 --> 00:01:29,620
+توسيع النفوذ هذا في حالة ال normed spaces نيجي 
+
+25
+00:01:29,620 --> 00:01:32,780
+نشوف الـ Hahn-Banach theorem في حالة اللي هي ال complex
+
+26
+00:01:32,780 --> 00:01:39,540
+vector spaces وهي generalization للي فاتت let X be
+
+27
+00:01:39,540 --> 00:01:44,070
+a real or complex لأن real ولا complex vector space
+
+28
+00:01:44,070 --> 00:01:47,410
+and B is a sub-additive real-valued function on X
+
+29
+00:01:47,410 --> 00:01:50,630
+الـ
+
+30
+00:01:50,630 --> 00:01:55,110
+B صارت مالها sub-additive نفسها لكن دلت ليش مالها 
+
+31
+00:01:55,110 --> 00:01:59,410
+real vector اللي هي real-valued function عشان بدها 
+
+32
+00:01:59,410 --> 00:02:02,790
+يصير فيها مقارنة فيها أصغر وأصغر وإذا بتلزم اللي 
+
+33
+00:02:02,790 --> 00:02:07,900
+هو تكون real and for any scalar α عرف P(αx) إيش
+
+34
+00:02:07,900 --> 00:02:11,560
+بيثاور لـ |P(x)| يعني الـ
+
+35
+00:02:11,560 --> 00:02:16,500
+positive homogeneity حيصير عندي لسه بدلنا بمين أنه 
+
+36
+00:02:16,500 --> 00:02:19,600
+يشتغل على كل ألفة ال scalar بما فيه السالب والمدب
+
+37
+00:02:19,600 --> 00:02:23,220
+بس الآن إيش هيطلع P(αx) هيثاور لـ |α|
+
+38
+00:02:23,220 --> 00:02:26,740
+في مين؟ في P(x) الآن هذه الشروط طبعا اللي
+
+39
+00:02:26,740 --> 00:02:30,720
+هي النظرية Furthermore، let F، اللي هي اللي بدنا 
+
+40
+00:02:30,720 --> 00:02:34,340
+نعملها extension، let F be a linear functional،
+
+41
+00:02:34,340 --> 00:02:36,900
+linear functional، complex ولا real، مش مشكلة، 
+
+42
+00:02:36,900 --> 00:02:39,940
+which is defined on subspace Z of subspace 
+
+43
+00:02:39,940 --> 00:02:44,340
+of X، and satisfies، الآن ما بنقدرش نقول F(x) 
+
+44
+00:02:44,340 --> 00:02:47,840
+أصغر أو يساوي، لأ، لأنه F(x) complex ممكن تكون
+
+45
+00:02:48,040 --> 00:02:52,300
+فعشان هيك أخدنا المودولوس له يكون مودولوس ال F(x) أصغر
+
+46
+00:02:52,300 --> 00:02:53,520
+أو يساوي |B(x)| لكل x ∈ Z
+
+47
+00:02:53,520 --> 00:02:54,320
+ 
+48
+00:02:54,320 --> 00:02:54,500
+ 
+49
+00:02:54,500 --> 00:02:55,020
+ 
+
+50
+00:02:55,020 --> 00:02:57,360
+ 
+
+51
+00:02:57,360 --> 00:03:08,500
+ 
+
+52
+00:03:08,500 --> 00:03:14,420
+بما دام فيه جهود معينة هي عملته في حياتها الجهود
+
+53
+00:03:14,420 --> 00:03:17,740
+هذا اللي هو أن هي هتكون أصغر أو يساوي |B(x)| لكل
+
+54
+00:03:17,740 --> 00:03:22,060
+x اللي بتنتمي للـ Z الآن والـ .. والـ .. والـ .. والـ
+
+55
+00:03:22,060 --> 00:03:26,240
+B دي اللي اللي قولنا عنها اللي عندنا الآن فمن 
+
+56
+00:03:26,240 --> 00:03:30,780
+عطاء ربنا نقلها أن هي قدرت تعمل extension هيك الدنيا
+
+57
+00:03:30,780 --> 00:03:35,300
+حتى في الحياة الطبيعية مدام أنت قدمت جهود إذا فيه 
+
+58
+00:03:35,300 --> 00:03:39,200
+إمكانية أنك تعمل لك extension تعمل لك زيادة نفوذ إذا 
+
+59
+00:03:39,200 --> 00:03:44,850
+then there is أو F has a linear extension widetilde{F} 
+
+60
+00:03:44,850 --> 00:03:49,310
+from Z to مين to X وسعت نفوذها من Z على مين على كل
+
+61
+00:03:49,310 --> 00:03:52,890
+X وحافظت على حقوقها الأولى اللي هي أصغر أو يساوي |B| و
+
+62
+00:03:52,890 --> 00:03:56,250
+في x ومدت هذه الحقوق على كل مين أو كل هذا الجود
+
+63
+00:03:56,250 --> 00:03:59,830
+مدته على مين على كل X اللي عندنا اللي هو
+
+64
+00:03:59,830 --> 00:04:02,370
+satisfying |widetilde{F}(x)| أصغر أو يساوي
+
+65
+00:04:02,370 --> 00:04:06,530
+|B(x)| لكل x where موجود في X البرهان بنأشيه
+
+66
+00:04:07,250 --> 00:04:09,550
+في حالة الـ real اللي أثبتناها وطولنا خلّينا نيجي
+
+67
+00:04:09,550 --> 00:04:15,890
+لحالة ال normed space وهو الشغل برهانها طبعا
+
+68
+00:04:15,890 --> 00:04:19,010
+اعتمادا عن البرهان اللي حكيناه هيكون سهل لكن لو
+
+69
+00:04:19,010 --> 00:04:23,930
+بدك تبرهنه من الصفر هيصير برهانه عايش طويل إذن قصر
+
+70
+00:04:23,930 --> 00:04:28,370
+البرهان هنا لأنه إحنا أسسنا في البرهان الأولاني
+
+71
+00:04:28,370 --> 00:04:30,970
+الآن هنأخذ theorem اللي هي normed space اللي هي
+
+72
+00:04:30,970 --> 00:04:34,190
+النظرية اللي بتحكي عنها الآن بتقول لي برضه نفس
+
+73
+00:04:34,190 --> 00:04:37,090
+الفحوى اللي حكيته لأن بس ال extension هيصير من
+
+74
+00:04:37,090 --> 00:04:41,950
+على normed space بدل اللي هي vector space let F be
+
+75
+00:04:41,950 --> 00:04:44,990
+a bounded linear functional على طول ما زي ما بنحكي
+
+76
+00:04:44,990 --> 00:04:48,050
+عن linear functional في حالة ال vector space إذا 
+
+77
+00:04:48,050 --> 00:04:50,890
+إذا بنحكي عن normed بنحكي عن مين؟ عن
+
+78
+00:04:50,890 --> 00:04:55,350
+bounded linear functional ماشي الحال واللي هي
+
+79
+00:04:55,350 --> 00:04:59,350
+برضه على غرار الأول ال linear functional فيه ال
+
+80
+00:04:59,350 --> 00:05:02,490
+extension ال bounded linear functional برضه هيكون 
+
+81
+00:05:02,490 --> 00:05:07,020
+اللي هي إيش أشماله؟ extension بنفس المنطق لأن دع F 
+
+82
+00:05:07,020 --> 00:05:08,620
+يكون مجموعة عامة عامة عامة عامة عامة عامة عامة 
+
+83
+00:05:08,620 --> 00:05:09,340
+عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+84
+00:05:09,340 --> 00:05:13,980
+عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+85
+00:05:13,980 --> 00:05:18,440
+عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+86
+00:05:18,440 --> 00:05:18,820
+عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+87
+00:05:18,820 --> 00:05:24,860
+عامة عامة عامة and has the same norm شوف الآن 
+
+88
+00:05:24,860 --> 00:05:29,500
+الزيادة أن norm هو norm الأصلي بتحافظ على كل
+
+89
+00:05:29,500 --> 00:05:33,420
+حقوقها الأولى مش بتقول لأ زرعت وحصدت إيش أكبر ال
+
+90
+00:05:33,420 --> 00:05:37,100
+norm الـ F(widetilde{F}) إيش بيساوي norm الـ F على الـ Z
+
+91
+00:05:37,100 --> 00:05:41,640
+where norm الـ F(widetilde{F}) إيش بنفسده فيه هو ال supremum
+
+92
+00:05:41,640 --> 00:05:44,880
+لـ F(widetilde{F}) أو |B(x)| للـ Xات اللي في الـ X وnorm هين
+
+93
+00:05:44,880 --> 00:05:48,100
+بيساوي 1 بينما التانية اللي هي على الـ Z اللي هي
+
+94
+00:05:48,100 --> 00:05:52,310
+ال supremum لـ |F(x)| للـ X ∈ Z
+
+95
+00:05:52,310 --> 00:05:55,690
+أن المراتقين أشمالهم بيساوي 1 ماشي الحاجة إذا 
+
+96
+00:05:55,690 --> 00:05:59,510
+هذه Z على الـ .. على Z الـ .. الـ  supremum وهذه 
+
+97
+00:05:59,510 --> 00:06:04,410
+على X الـ supremum هو ||F|| ||Z|| بيساوي 0 في حالة
+
+98
+00:06:04,410 --> 00:06:08,470
+مين الـ trivial case أن Z إيش بيساوي اللي هو مين الـ 
+
+99
+00:06:08,470 --> 00:06:13,050
+zero طيب نيجي الآن نبرهن اطلع البرهان سهل اطلع لفوق
+
+100
+00:06:13,050 --> 00:06:20,290
+F(Z) بتساوي 0 اللي هو 0 0 0 0 Space 
+
+101
+00:06:20,290 --> 00:06:23,970
+يعني then F بتساوي 0 وال extension اللي هيكون 
+
+102
+00:06:23,970 --> 00:06:26,830
+مين F(widetilde{F}) بتساوي 0 خلّيني أقول الـ trivial
+
+103
+00:06:26,830 --> 00:06:30,950
+case قيمتها
+
+104
+00:06:30,950 --> 00:06:36,250
+مش كثيرة إلا للحالات اللي ممكن يعني بدك .. يعني
+
+105
+00:06:36,250 --> 00:06:40,180
+ما نكونش مستثنين الـ zero إنما بتنفع على كل شيء فعشان 
+
+106
+00:06:40,180 --> 00:06:44,380
+إيش؟ خصصنا عليها ليه Z لا تساوي 0 الآن؟ ناخد
+
+107
+00:06:44,380 --> 00:06:49,240
+حالة مين Z لا تساوي 0؟ then for any x element in
+
+108
+00:06:49,240 --> 00:06:54,100
+Z we have فليه F bounded linear functional إذن الـ 
+
+109
+00:06:54,100 --> 00:06:57,200
+|F(x)| أصغر أو يساوي ||F|| ||X||
+
+110
+00:06:57,200 --> 00:07:00,700
+||F|| على مين؟ هي F dismal زي شغالة مين على Z ||F|| 
+
+111
+00:07:00,700 --> 00:07:04,300
+||F|| Z في ||X|| لكل الـ X وين موجودات في Z
+
+112
+00:07:04,300 --> 00:07:10,170
+الآن عرفنا هذه الـ bridge اللي بدنا اللي هو طبيعة .. 
+
+113
+00:07:10,170 --> 00:07:13,150
+اللي هو الـ norm أن هيعمل لي sublinear functional
+
+114
+00:07:13,150 --> 00:07:16,330
+يعني هيعمل .. هيعمل اللي .. اللي .. اللي كانت 
+
+115
+00:07:16,330 --> 00:07:19,350
+المطلوب في معطيات النظريات السابقة هيعملها الـ
+
+116
+00:07:19,350 --> 00:07:22,010
+norm فهيكون automatic تطلع النظرية في extension
+
+117
+00:07:22,010 --> 00:07:27,230
+طيب define P من X ل عند R by P(x) إيش بيساوي ..
+
+118
+00:07:27,230 --> 00:07:32,850
+بيساوي ||F|| Z في ||X|| هي اللي بدي أعرفه حر
+
+119
+00:07:32,850 --> 00:07:36,870
+أنا بدي أعرف الـ P(x) هي عبارة عن مين؟ عن norm
+
+120
+00:07:36,870 --> 00:07:40,390
+الـ Fz اللي أنا عرفتها خلاص norm الـ Fz صار معروف
+
+121
+00:07:40,390 --> 00:07:44,290
+لأنه bounded لأن norm هذا معروف في norm مين الـ X
+
+122
+00:07:44,290 --> 00:07:46,730
+هذه اللي .. اللي .. اللي هدّاك إذا .. إذا هذا هو 
+
+123
+00:07:46,730 --> 00:07:49,970
+كأنه مقدار ثابت بضربه في مين؟ في norm الـ X اللي هي 
+
+124
+00:07:49,970 --> 00:07:54,870
+هذه تتغير بتغير مين؟ X إذا هذا الـ P(x) أكيد
+
+125
+00:07:54,870 --> 00:07:58,950
+هيحقق ضمن الـ |F(x)| اللي هو إيش 
+
+126
+00:07:58,950 --> 00:08:03,660
+إيش ماله؟ اللي هو عبارة عن أصغر من هذا المقدار صح؟ هي 
+
+127
+00:08:03,660 --> 00:08:07,600
+اتلت فاض وهذا المقدار هو اللي أقرفته P(x) إذا
+
+128
+00:08:07,600 --> 00:08:11,480
+صار الـ |F(x)| أصغر أو يساوي P(x)
+
+129
+00:08:11,480 --> 00:08:15,040
+لكل X element in Z إذا هذه أول شرط تحقق من شروط
+
+130
+00:08:15,040 --> 00:08:18,300
+مين النظرية اللي حكينا عنها المرة الماضية تبعت الـ 
+
+131
+00:08:18,300 --> 00:08:20,660
+Hahn-Banach theorem أو اللي حكينا عنها قبل شوية 
+
+132
+00:08:20,660 --> 00:08:29,600
+واضح هذه؟ طيب Furthermore, for any x, y element in X 
+
+133
+00:08:29,600 --> 00:08:34,140
+and any scalar α element in R, we have شغلتين أول 
+
+134
+00:08:34,140 --> 00:08:40,100
+شيء أحسب ليه P(x + y) إيش بيساوي؟ بيساوي ||F||
+
+135
+00:08:40,880 --> 00:08:45,720
+||F|| على Z ||X + Y|| حسب التعريف اللي عرفناه وهذا أصغر أو يساوي 
+
+136
+00:08:45,720 --> 00:08:51,760
+بالـ Triangle Inequality هدي في هدي زائد هدي بفكها
+
+137
+00:08:51,760 --> 00:08:57,280
+هدي في هدي هي P(x) وهدي في هدي اللي هي P(y)
+
+138
+00:08:57,280 --> 00:09:01,660
+إذا صارت عندي P(x + y) أصغر أو يساوي P(x) + P(y)
+
+139
+00:09:01,660 --> 00:09:07,470
+إذا صارت عندي P(x + y) أصغر أو يساوي P(x) +  P(y)
+
+140
+00:09:07,470 --> 00:09:14,110
+الآن P(αx) بيساوي حسب التعريف اللي عندي 
+
+141
+00:09:14,110 --> 00:09:18,430
+عبارة عن حسب التعريف اللي هن عبارة عن norm اللي
+
+142
+00:09:18,430 --> 00:09:25,110
+هي الـ FZ في مين؟ في norm الـ α X بطلع الألفة برا
+
+143
+00:09:25,110 --> 00:09:29,750
+بصير absolute value في هذه في هذه اللي هي مين P of 
+
+144
+00:09:29,750 --> 00:09:33,970
+X إذا برضه اللي هو الشرط الثاني ماله اتحقق إذا
+
+145
+00:09:33,970 --> 00:09:37,930
+hence by theorem أربعة تلاتة .. لأ مش linear hence
+
+146
+00:09:37,930 --> 00:09:43,380
+by theorem أربعة تلاتة واحد اه نعم there exist a
+
+147
+00:09:43,380 --> 00:09:46,380
+linear extension من اللي قبل بشوية اللي حكيناها في
+
+148
+00:09:46,380 --> 00:09:50,840
+حالة الـ vector space إذا صار عندي الآن الشروط
+
+149
+00:09:50,840 --> 00:09:54,740
+النظرية أربعة تلاتة واحد اللي قبل بشوية كلها تحققت
+
+150
+00:09:54,740 --> 00:09:58,700
+إذا في عندي الـ linear extension اسمه f تلدان x
+
+151
+00:09:58,700 --> 00:10:02,720
+which is an extension of f and satisfies كمان ال
+
+152
+00:10:02,720 --> 00:10:07,260
+absolute value لـ f تلدا في x أصغر شو مين بيو في x
+
+153
+00:10:07,650 --> 00:10:10,910
+ماشي الحال لكن الـ P of X بيساوي الـ norm هذا في هذا
+
+154
+00:10:10,910 --> 00:10:16,490
+الآن هذا الكلام لكل mean X limit X إذا هذا إذا 
+
+155
+00:10:16,490 --> 00:10:21,870
+حصلنا على extension ويحقق هذا أصغر يساوي هذا طيب
+
+156
+00:10:21,870 --> 00:10:27,060
+من هذولة مع بعض التنتين هيها هيها هيها الـ Code
+
+157
+00:10:27,060 --> 00:10:29,560
+اللي هو الـ Supremum على النورمات اللي بيساوي صفر
+
+158
+00:10:29,560 --> 00:10:32,400
+الـ Supremum اللي هدي على النورمات اللي بيساوي صفر
+
+159
+00:10:32,400 --> 00:10:36,580
+هو عبارة عن نورم عندي طبعا احنا بنحكي عن الـ Xات
+
+160
+00:10:36,580 --> 00:10:40,400
+اللي وين موجودات في X فبصير نورم الـ F تلدا على الـ X
+
+161
+00:10:40,400 --> 00:10:45,480
+أصغر أو ساوي مين نورم الـ FZ هاي واحدة لكن من جهة
+
+162
+00:10:45,480 --> 00:10:52,180
+أخرى Normal of Z اللي هو supremum على الـ Xات اللي
+
+163
+00:10:52,180 --> 00:10:55,620
+في الـ Z بينما هذا supremum اللي هو نفسه طبعا
+
+164
+00:10:55,620 --> 00:10:59,460
+after ده Z لأن هذا extension بينما هذا supremum
+
+165
+00:10:59,460 --> 00:11:03,550
+على مين؟ على العناصر اللي في الـ X والـ X بتحتوي
+
+166
+00:11:03,550 --> 00:11:07,850
+الـ Z إذا سوبرمام على مجموعة أقل من مجموعة تانية
+
+167
+00:11:07,850 --> 00:11:10,690
+فأكيد السوبرمام هن أصغر يساوي مين؟ السوبرمام هن
+
+168
+00:11:10,690 --> 00:11:15,690
+فهذا أصغر يساوي هذا فبنكون حصلنا على الـ Normal FZ
+
+169
+00:11:15,690 --> 00:11:22,490
+مرة أصغر يساوي ومرة أكبر يساوي من التنتين فيه ايه
+
+170
+00:11:22,490 --> 00:11:25,870
+شماله؟ فيه يساوي إذا أثبتنا الـ Extension و أثبتنا
+
+171
+00:11:25,870 --> 00:11:32,310
+اللي هي الشروط المطلوبة أو خلّيني أقول ما حققته
+
+172
+00:11:32,310 --> 00:11:37,030
+اللي هي النظرية نجلة
+
+173
+00:11:37,030 --> 00:11:42,570
+theorem 433 bounded linear functional انتبهوا ايش
+
+174
+00:11:42,570 --> 00:11:48,650
+هذا اللي بتقول let X be a normed space ركزوا في
+
+175
+00:11:48,650 --> 00:11:54,540
+النص عند X0 لاتساوي 0 بيه any element in X أي
+
+176
+00:11:54,540 --> 00:11:56,980
+element in X أخدناها على البيت الرأي وسميناها X0
+
+177
+00:11:56,980 --> 00:12:01,540
+ماشي الحالة أو X normed space بيقولك then there
+
+178
+00:12:01,540 --> 00:12:06,060
+exists a bounded linear functional F tilde و X
+
+179
+00:12:06,060 --> 00:12:11,700
+such that نورمه بيساوي واحد والـ F tilde و X0 ايش
+
+180
+00:12:11,700 --> 00:12:18,030
+حيسوي نورمين الـ X0 يعني اللي بيحكيلكيا بيقولك انه
+
+181
+00:12:18,030 --> 00:12:22,330
+انت خد أي X note في normed space بقدر ألاجيلك
+
+182
+00:12:22,330 --> 00:12:26,410
+bounded linear functional يحدد بمين بواسطة النقطة
+
+183
+00:12:26,410 --> 00:12:29,590
+هذه اللي أخدتها انت arbitrarily بتفكز بقدر ألاجي
+
+184
+00:12:29,590 --> 00:12:32,330
+bounded linear functional F tilde و X و يقوه normه
+
+185
+00:12:32,330 --> 00:12:36,550
+بساوء واحد و الـ F tilde of X note هذه اللي أخدتها
+
+186
+00:12:36,550 --> 00:12:40,930
+هو ايش هيطلع عنده عبارة عن norm الـ X note خلينا
+
+187
+00:12:40,930 --> 00:12:48,200
+نشوف مع بعض Consider the subspace Z المكوّن من مين؟
+
+188
+00:12:48,200 --> 00:12:54,400
+Alpha X0 هي الـ Span لـ X0 يعني الـ X0 هي النقطة
+
+189
+00:12:54,400 --> 00:12:57,320
+الأربترية اللي أخدناها Alpha is the scalar Define
+
+190
+00:12:57,320 --> 00:13:04,350
+F من Z لعند مين؟ لعند scalar field KF of ZX F of X
+
+191
+00:13:04,350 --> 00:13:11,190
+بيساوي F of Alpha X0 و يساوي Alpha في مين في
+
+192
+00:13:11,190 --> 00:13:17,650
+Normal X0 هذا اللي هو واضح انه Alpha X0 where K is
+
+193
+00:13:17,650 --> 00:13:21,570
+scalar field real or complex it is easy to see
+
+194
+00:13:21,570 --> 00:13:25,840
+that F is linear فها دي ايه عشان إذنها بتعرفوا
+
+195
+00:13:25,840 --> 00:13:34,760
+تثبتوها F of Beta X زائد Y بتساوي كده نفهمها خلاص
+
+196
+00:13:34,760 --> 00:13:38,180
+هي بتعرفوا تثبتوها لأ من التعريف هذا هيه التعريف
+
+197
+00:13:38,180 --> 00:13:42,500
+هيه بتعرفوا تثبتوها على طول مباشرة الان و also f is
+
+198
+00:13:42,500 --> 00:13:45,800
+bounded و الـ boundedness برضه سهل الـ boundedness
+
+199
+00:13:45,800 --> 00:13:50,280
+بيقولك خد ايش معله absolute value of f of x ايش
+
+200
+00:13:50,280 --> 00:13:52,720
+هيساوي؟ بيساوي الـ absolute value هذه بيساوي ال
+
+201
+00:13:52,720 --> 00:13:55,900
+absolute value هذه اللي هو هيطلع alpha mean في x0
+
+202
+00:13:55,900 --> 00:14:00,420
+اللي هو بيساوي mean اللي هو normal x لأن الـ x ايش
+
+203
+00:14:00,420 --> 00:14:05,220
+بتساوي؟ alpha x0 هيك شكل العناصر جوامعايا صار عندى
+
+204
+00:14:05,220 --> 00:14:08,780
+لأن absolute value of f of x ايش بيساوي normal x
+
+205
+00:14:08,780 --> 00:14:12,940
+لكل x و موجودة بيساوي x يعني بمعنى اخر صار عندى
+
+206
+00:14:12,940 --> 00:14:19,260
+اللي هو الـ f is linear و الـ f is bounded ماشي و لو
+
+207
+00:14:19,260 --> 00:14:22,480
+اتطلعت على قِبتها absolute value of f of x بيساوي
+
+208
+00:14:22,480 --> 00:14:29,380
+normal x absolute value لـ الـ f of x بيساوي normal
+
+209
+00:14:29,380 --> 00:14:36,930
+x اذا الـ supremum على الـ norm الـ X أو X ده تساوي
+
+210
+00:14:36,930 --> 00:14:43,270
+شفر هيساوي ايه؟ واحد وهذا عبارة عن norm الـ F over
+
+211
+00:14:43,270 --> 00:14:43,730
+X
+
+212
+00:14:47,220 --> 00:14:50,300
+النظرية اللي قبل بشوية اتحققت
+
+213
+00:15:15,050 --> 00:15:19,210
+الـ X في الـ Z كيف شكل الـ X ألفة في X نور فح؟
+
+214
+00:15:19,210 --> 00:15:23,850
+ألفة scalar أنه scalar لأن طب F of X0 نفسها بساوي
+
+215
+00:15:23,850 --> 00:15:29,650
+اللي هو يعني و كأني بقول F of واحد في X0 حسب
+
+216
+00:15:29,650 --> 00:15:32,850
+القانون اللي هو ايش بيساوي واحد في نورم الـ X0
+
+217
+00:15:32,850 --> 00:15:38,810
+فاهمين؟ بيساوي واحد في نورم الـ X0 بيساوي نورم الـ
+
+218
+00:15:38,810 --> 00:15:45,720
+X0 يعني الف بيساوي واحد اه فبصير عندى f of x0 بساوة
+
+219
+00:15:45,720 --> 00:15:49,280
+.. f .. f tilde of x0 بساوة f of x0 بساوة مين؟
+
+220
+00:15:49,280 --> 00:15:57,680
+نورم الـ x0 أي سؤال؟ اللي بعده؟ Corollary لأن for
+
+221
+00:15:57,680 --> 00:16:02,740
+any x in a normed space X we have لأن احنا كنا
+
+222
+00:16:02,740 --> 00:16:12,190
+نجيب نقول نورم الـ F بساوة supremum للـ f of x
+
+223
+00:16:12,190 --> 00:16:17,990
+absolute value على نورم الـ x الـ x element in x
+
+224
+00:16:17,990 --> 00:16:22,930
+minus mean الـ zero يعني كنا نجيب الـ norm بدلالة
+
+225
+00:16:22,930 --> 00:16:25,310
+mean الـ f و الـ f سبرهما من الـ f على نورم الـ x
+
+226
+00:16:25,310 --> 00:16:31,370
+الآن بده يجيبلك اللي هو نورم الـ x الآن مش نورم
+
+227
+00:16:31,370 --> 00:16:36,770
+الـ f بنضغط بدلالة mean الـ f و الـ f ماشي؟ إذا
+
+228
+00:16:36,770 --> 00:16:42,680
+بقوللي hence نستطيع أن نجد لأي X في عضلة X نستطيع
+
+229
+00:16:42,680 --> 00:16:46,840
+أن نجد X عضلة X بساوية سبريمام للقيم الأبسط F of X
+
+230
+00:16:46,840 --> 00:16:53,300
+عالمي لـ N عن عضلة F فالـ N المتغير بدل ما هو X في X
+
+231
+00:16:53,300 --> 00:16:57,360
+minus Zero هو عبارة عن الـ linear functionals F
+
+232
+00:16:57,360 --> 00:16:59,480
+element in X برايم من X برايم من X برايم من X
+
+233
+00:16:59,480 --> 00:17:01,700
+برايم من X برايم من X برايم من X برايم من X برايم
+
+234
+00:17:01,700 --> 00:17:01,800
+من X برايم من X برايم من X برايم من X برايم من X
+
+235
+00:17:01,800 --> 00:17:01,960
+برايم من X برايم من X برايم من X برايم من X برايم
+
+236
+00:17:01,960 --> 00:17:06,020
+برايم من X برايم من X برايم من X برايم من X برايم
+
+237
+00:17:06,020 --> 00:17:09,360
+من X بأف لا تساوي سفر يعني السبريهم هم عالمين على
+
+238
+00:17:09,360 --> 00:17:14,640
+كل الأفات اللي في الـ X' هنس .. من نتيجة مباشرة
+
+239
+00:17:14,640 --> 00:17:18,060
+هنس if X0 is a .. is such that F of X0 بساوي سفر
+
+240
+00:17:18,060 --> 00:17:22,600
+for all أف اللي متين X' then X' أشبه لها بساوي سفر
+
+241
+00:17:23,840 --> 00:17:27,720
+الان راكزوا الكلام سهل الان عندي من theorem أربعة
+
+242
+00:17:27,720 --> 00:17:30,980
+تلاتة في extension of تل دا element of X prime
+
+243
+00:17:30,980 --> 00:17:35,020
+such that normal of تل دا ايش بيساوي واحد والـ F تل
+
+244
+00:17:35,020 --> 00:17:39,800
+دا of X ايش بيساوي normal X من اللي قبل بشوية
+
+245
+00:17:39,800 --> 00:17:43,820
+theorem أربعة تلاتة تلاتة اللي أثبتناها where الان
+
+246
+00:17:43,820 --> 00:17:49,100
+إذا لجينا Extension F تلدة في الـ X' بحيث نورمه
+
+247
+00:17:49,100 --> 00:17:53,120
+بساوء واحد والـ F تلدة و X له بساوء جداش نورم الـ
+
+248
+00:17:53,120 --> 00:17:56,380
+X اللي كنا بسميه X ناضلة قبل شوية Where X is
+
+249
+00:17:56,380 --> 00:17:59,420
+around zero element in mean in X So that the
+
+250
+00:17:59,420 --> 00:18:02,880
+supremum للـ absolute value F of X على نورم الـ F
+
+251
+00:18:03,560 --> 00:18:06,360
+اللي هي f element in x prime و f أكبر يساوي 0 هذا
+
+252
+00:18:06,360 --> 00:18:09,960
+الـ supremum على الكل ماشي الحال أكيد أكبر أو يساوي
+
+253
+00:18:09,960 --> 00:18:12,800
+واحدة منهم من ضمنهم الواحدة المن هناك اللي اللي
+
+254
+00:18:12,800 --> 00:18:17,320
+أجريها إذا أكبر أو يساوي فاهمين أكبر أو يساوي اللي
+
+255
+00:18:17,320 --> 00:18:23,510
+هو الآن الـ supremum يا جماعة أنا جيت f تل ده فى الـ
+
+256
+00:18:23,510 --> 00:18:29,250
+X' و لجهة F تلدة of X بيساوي الـ X نفسها و نورم
+
+257
+00:18:29,250 --> 00:18:35,510
+الـ F تلدة بيساوي ايش؟ واحد خدوا الآن الـ supremum
+
+258
+00:18:35,510 --> 00:18:40,690
+الـ supremum لـ absolute value of X على نورم الـ F
+
+259
+00:18:40,690 --> 00:18:48,710
+حيث F ويه موجودة فى الـ X' والـ F لا تساوي منين؟ الـ
+
+260
+00:18:48,710 --> 00:18:51,930
+Zero هذه اطلع لفوق أكبر أو يساوي أكيد أي واحدة من
+
+261
+00:18:51,930 --> 00:18:55,530
+هنا أكبر أو يساوي أي واحدة من هنا مين أي واحدة من
+
+262
+00:18:55,530 --> 00:19:04,250
+هنا اللي جايك فوق اللي هي F تلدة of X على norm الـ
+
+263
+00:19:04,250 --> 00:19:09,130
+F تلدة اللي هو بيساوي F تلدة of X ايش بتساوي؟ X
+
+264
+00:19:09,130 --> 00:19:16,350
+صح؟ على اللي هو ايه ايش بتساوي هذه؟ مايساوة نورم الـ
+
+265
+00:19:16,350 --> 00:19:19,690
+X إذا صار عند الـ suprem هذا اللي بقول أكبر أو
+
+266
+00:19:19,690 --> 00:19:24,970
+ساوية مين نورم الـ X واضح اه؟ بالذات بتلك الأن أصغر
+
+267
+00:19:24,970 --> 00:19:27,430
+أو ساوية معناته حدثت المشاوخ خلصت الكورة ده
+
+268
+00:19:27,430 --> 00:19:30,890
+however الـ absolute value of F of X أصغر أو ساوية
+
+269
+00:19:30,890 --> 00:19:34,670
+نورم الـ F و نورم مين؟ الـ X ماشي الحل لأن F is
+
+270
+00:19:34,670 --> 00:19:38,150
+bounded in our functional then الـ suprem على F
+
+271
+00:19:38,150 --> 00:19:42,250
+تلدى على نورم الـ F هيكون أصغر أو ساوية مين نورم الـ
+
+272
+00:19:42,250 --> 00:19:46,470
+X صح؟ إذا من الـ 2 مع بعض الـ Superman بساوي Normal
+
+273
+00:19:46,470 --> 00:19:50,070
+X و هو المطلوب الجزء الثاني من نظرية من الكورولالي
+
+274
+00:19:50,070 --> 00:19:54,210
+و يقولك if X0 is such that F of X0 بساوي 0 لكل ..
+
+275
+00:19:54,210 --> 00:19:58,210
+لو لجأت F of X0 بساوي 0 لكل الـ F اللي هي element
+
+276
+00:19:58,210 --> 00:20:01,370
+in X برايم يعني أي bound linear functional اتلاقي
+
+277
+00:20:01,370 --> 00:20:04,350
+قيمتها عند الـ X0 بساوي 0 أكيد الـ X0 هي السفر
+
+278
+00:20:06,700 --> 00:20:10,180
+معايا F لجينا .. أخدنا أي bounded linear
+
+279
+00:20:10,180 --> 00:20:13,460
+functional F حسبناها عند الـ X0 لجيناها سفر أخدنا
+
+280
+00:20:13,460 --> 00:20:16,100
+التاني لجيناها سفر أخدنا التالت لجيناها سفر يعني 
+
+281
+00:20:16,100 --> 00:20:18,360
+أي bounded linear functional لو جئت حسبتها عند ال
+
+282
+00:20:18,360 --> 00:20:21,820
+X0 هتلاقي صفر هتلاقي ال X0 هي الصفر هذا الكلام سهل
+
+283
+00:20:21,820 --> 00:20:25,560
+الآن اللي هو Norm ال X0 بيساوي الصفر هذا قبل مش
+
+284
+00:20:25,560 --> 00:20:32,550
+أي حد اللي .. اللي فضلناها الآن دي F of X0 معاه؟
+
+285
+00:20:32,550 --> 00:20:36,450
+لأن هذا الكلام .. بقول إنه هذا صفر دائما، هيه، هذا
+
+286
+00:20:36,450 --> 00:20:39,430
+صفر دائما، إذن صار ال Norm عالمي مع Zero إذا Norm
+
+287
+00:20:39,430 --> 00:20:43,610
+الـ X0 إيش حساوية صفر، إذا X0 إيش حساوية صفر، ما
+
+288
+00:20:43,610 --> 00:20:48,470
+هو المطلوب، اللي بعد الله يعطيكم العافية وإلى 
+
+289
+00:20:48,470 --> 00:20:49,790
+لقاء آخر
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/oa3DVUxeS2g_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/oa3DVUxeS2g_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..79f3b258968580bb29032f7523c959d82747e396
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/oa3DVUxeS2g_raw.json
@@ -0,0 +1 @@
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theorem بدها الـ Hahnbenach theorem هي عبارة عن extension يعني بدها توسيع نفوذ يعني هاي الهدف طبعا الهدف الكبير هذا", "tokens": [6027, 9640, 3555, 3615, 34051, 33962, 2304, 3794, 3660, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 39184, 11166, 882, 38172, 39896, 2423, 39184, 45303, 1799, 608, 20904, 337, 2135, 4386, 337, 2107, 7673, 23032, 3555, 3615, 995, 1975, 5016, 8315, 6225, 28480, 8315, 8592, 13672, 1829, 45303, 1799, 608, 20904, 47525, 11296, 2423, 39184, 45303, 1799, 608, 20904, 39896, 6225, 3555, 9640, 3660, 18871, 10320, 37495, 22653, 47525, 11296, 33427, 3794, 40228, 8717, 5172, 2407, 8848, 37495, 22653, 8032, 47302, 2423, 3224, 3215, 5172, 23032, 3555, 3615, 995, 2423, 3224, 3215, 5172, 33251, 3555, 13546, 23758], "avg_logprob": -0.23864976007421063, "compression_ratio": 1.7866666666666666, "no_speech_prob": 3.159046173095703e-06, "words": [{"start": 55.08, "end": 56.08, "word": "الاربع", "probability": 0.7413330078125}, 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0.4541015625}, {"start": 59.4, "end": 59.7, "word": " الـ", "probability": 0.625}, {"start": 59.7, "end": 60.0, "word": " Function", "probability": 0.681640625}, {"start": 60.0, "end": 60.46, "word": " Analysis", "probability": 0.94384765625}, {"start": 60.46, "end": 61.08, "word": " هي", "probability": 0.77734375}, {"start": 61.08, "end": 61.4, "word": " الـ", "probability": 0.8310546875}, {"start": 61.4, "end": 62.58, "word": " Hahnbenach", "probability": 0.47998046875}, {"start": 62.58, "end": 62.86, "word": " theorem", "probability": 0.6044921875}, {"start": 62.86, "end": 63.5, "word": " for", "probability": 0.86865234375}, {"start": 63.5, "end": 63.9, "word": " main", "probability": 0.26123046875}, {"start": 63.9, "end": 64.14, "word": " ..", "probability": 0.2568359375}, {"start": 64.14, "end": 64.32, "word": " for", "probability": 0.890625}, {"start": 64.32, "end": 64.68, "word": " non", "probability": 0.81005859375}, {"start": 64.68, "end": 65.34, "word": " spaces", "probability": 0.138427734375}, {"start": 65.34, "end": 65.94, "word": " طبعا", "probability": 0.932861328125}, {"start": 65.94, "end": 66.12, "word": " احنا", "probability": 0.8331705729166666}, {"start": 66.12, "end": 66.56, "word": " عرفناش", "probability": 0.8284912109375}, {"start": 66.56, "end": 66.66, "word": " اللي", "probability": 0.60980224609375}, {"start": 66.66, "end": 67.06, "word": " Hahnbenach", "probability": 0.9420572916666666}, {"start": 67.06, "end": 67.3, "word": " theorem", "probability": 0.90966796875}, {"start": 67.3, "end": 67.62, "word": " بدها", "probability": 0.935546875}, {"start": 67.62, "end": 68.04, "word": " الـ", "probability": 0.5662841796875}, {"start": 68.04, "end": 68.44, "word": " Hahnbenach", "probability": 0.9671223958333334}, {"start": 68.44, "end": 68.7, "word": " theorem", "probability": 0.93896484375}, {"start": 68.7, "end": 68.84, "word": " هي", "probability": 0.90478515625}, {"start": 68.84, "end": 69.1, "word": " عبارة", "probability": 0.993408203125}, {"start": 69.1, "end": 69.22, "word": " عن", "probability": 0.99560546875}, {"start": 69.22, "end": 69.66, "word": " extension", "probability": 0.79150390625}, {"start": 69.66, "end": 69.98, "word": " يعني", "probability": 0.94384765625}, {"start": 69.98, "end": 70.2, "word": " بدها", "probability": 0.878173828125}, {"start": 70.2, "end": 70.6, "word": " توسيع", "probability": 0.9645182291666666}, {"start": 70.6, "end": 71.08, "word": " نفوذ", "probability": 0.8465576171875}, {"start": 71.08, "end": 71.68, "word": " يعني", "probability": 0.934814453125}, {"start": 71.68, "end": 71.92, "word": " هاي", "probability": 0.648193359375}, {"start": 71.92, "end": 72.26, "word": " الهدف", "probability": 0.993896484375}, {"start": 72.26, "end": 72.5, "word": " طبعا", "probability": 0.9390869140625}, {"start": 72.5, "end": 72.74, "word": " الهدف", "probability": 0.8995361328125}, {"start": 72.74, "end": 73.08, "word": " الكبير", "probability": 0.9571940104166666}, {"start": 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"يعني", "probability": 0.901611328125}, {"start": 735.85, "end": 736.19, "word": " اللي", "probability": 0.91357421875}, {"start": 736.19, "end": 737.03, "word": " بيحكيلكيا", "probability": 0.8603166852678571}, {"start": 737.03, "end": 737.61, "word": " بيقولك", "probability": 0.884033203125}, {"start": 737.61, "end": 738.03, "word": " انه", "probability": 0.7451171875}, {"start": 738.03, "end": 738.59, "word": " انت", "probability": 0.8173828125}, {"start": 738.59, "end": 739.01, "word": " خد", "probability": 0.95166015625}, {"start": 739.01, "end": 739.31, "word": " اي", "probability": 0.820068359375}, {"start": 739.31, "end": 739.55, "word": " X", "probability": 0.68408203125}, {"start": 739.55, "end": 739.77, "word": " note", "probability": 0.189697265625}, {"start": 739.77, "end": 739.93, "word": " في", "probability": 0.8251953125}, {"start": 739.93, "end": 740.27, "word": " normed", "probability": 0.587890625}, {"start": 740.27, "end": 740.79, "word": " space", "probability": 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بيساوي ال absolute value هذه بيساوي ال absolute value هذه اللي هو هيطلع alpha mean في x0 اللي هو بيساوي mean اللي هو normal x لأن ال x ايش بتساوي؟ alpha x0 هيك شكل العناصر جوا", "tokens": [2304, 3555, 33599, 25720, 2423, 7649, 4032, 611, 283, 307, 37498, 4032, 2423, 37498, 1287, 4724, 43042, 3224, 8608, 3224, 1211, 2423, 37498, 1287, 4724, 1829, 39648, 4117, 16490, 3215, 1975, 1829, 8592, 20449, 43761, 8236, 2158, 295, 283, 295, 2031, 1975, 1829, 8592, 39896, 3794, 995, 45865, 22807, 4724, 1829, 3794, 995, 45865, 2423, 8236, 2158, 29538, 4724, 1829, 3794, 995, 45865, 2423, 8236, 2158, 29538, 13672, 1829, 31439, 39896, 9566, 1211, 3615, 8961, 914, 8978, 2031, 15, 13672, 1829, 31439, 4724, 1829, 3794, 995, 45865, 914, 13672, 1829, 31439, 2710, 2031, 5296, 33456, 2423, 2031, 1975, 1829, 8592, 39894, 3794, 995, 45865, 22807, 8961, 2031, 15, 39896, 4117, 13412, 28820, 18863, 1863, 33546, 2288, 10874, 14407], "avg_logprob": -0.2264968439811418, "compression_ratio": 1.912280701754386, 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اللي", "probability": 0.91552734375}, {"start": 834.1, "end": 834.18, "word": " هو", "probability": 0.80859375}, {"start": 834.18, "end": 834.54, "word": " هيطلع", "probability": 0.9053955078125}, {"start": 834.54, "end": 834.86, "word": " alpha", "probability": 0.453369140625}, {"start": 834.86, "end": 835.22, "word": " mean", "probability": 0.65869140625}, {"start": 835.22, "end": 835.44, "word": " في", "probability": 0.95947265625}, {"start": 835.44, "end": 835.9, "word": " x0", "probability": 0.591552734375}, {"start": 835.9, "end": 836.66, "word": " اللي", "probability": 0.983642578125}, {"start": 836.66, "end": 836.78, "word": " هو", "probability": 0.97802734375}, {"start": 836.78, "end": 837.16, "word": " بيساوي", "probability": 0.97861328125}, {"start": 837.16, "end": 837.5, "word": " mean", "probability": 0.70068359375}, {"start": 837.5, "end": 838.12, "word": " اللي", "probability": 0.991455078125}, {"start": 838.12, "end": 838.4, "word": " هو", "probability": 0.98779296875}, 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1239.73, "end": 1239.91, "word": " إيش", "probability": 0.6695149739583334}, {"start": 1239.91, "end": 1240.15, "word": " حساوية", "probability": 0.6884765625}, {"start": 1240.15, "end": 1240.87, "word": " سفر،", "probability": 0.8660888671875}, {"start": 1240.87, "end": 1241.03, "word": " إذا", "probability": 0.89404296875}, {"start": 1241.03, "end": 1241.37, "word": " X0", "probability": 0.778564453125}, {"start": 1241.37, "end": 1241.51, "word": " إيش", "probability": 0.9000651041666666}, {"start": 1241.51, "end": 1242.09, "word": " حساوية", "probability": 0.99384765625}, {"start": 1242.09, "end": 1243.53, "word": " سفر،", "probability": 0.9093017578125}, {"start": 1243.53, "end": 1243.61, "word": " ما", "probability": 0.51806640625}, {"start": 1243.61, "end": 1243.71, "word": " هو", "probability": 0.90625}, {"start": 1243.71, "end": 1244.55, "word": " المطلوب،", "probability": 0.8994140625}, {"start": 1244.55, "end": 1244.73, "word": " اللي", "probability": 0.859130859375}, {"start": 1244.73, "end": 1244.91, "word": " بعد", "probability": 0.92724609375}, {"start": 1244.91, "end": 1247.09, "word": " الله", "probability": 0.377685546875}, {"start": 1247.09, "end": 1247.49, "word": " يعطيكوا", "probability": 0.90625}, {"start": 1247.49, "end": 1247.91, "word": " العافية", "probability": 0.9781901041666666}, {"start": 1247.91, "end": 1248.47, "word": " وإلى", "probability": 0.8497721354166666}, {"start": 1248.47, "end": 1249.21, "word": " لقاء", "probability": 0.97119140625}, {"start": 1249.21, "end": 1249.79, "word": " آخر", "probability": 0.855712890625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1250.04625, "duration_after_vad": 1232.7443749999995}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/uwT2Fp1FRO0.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/uwT2Fp1FRO0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..81fb77221d4cd15db6b72894e9948ff6f655efb2
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/uwT2Fp1FRO0.srt
@@ -0,0 +1,3239 @@
+1
+00:00:05,500 --> 00:00:08,180
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,180 --> 00:00:11,180
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:11,180 --> 00:00:16,340
+آله وصحبه أجمعين هذه المحاضرة السابعة مساق تحليل 
+
+4
+00:00:16,340 --> 00:00:21,900
+اقتراني أو تحليل دالي لطلاب وطالبات الجامعة 
+
+5
+00:00:21,900 --> 00:00:26,820
+الإسلامية كلية العلوم ماجستير رياضيات اليوم إن شاء 
+
+6
+00:00:26,820 --> 00:00:31,640
+الله هنحكي عن موضوع من الموضوعات المهمة واللي شوية 
+
+7
+00:00:31,640 --> 00:00:36,360
+بتغلب لكن إن شاء الله مع بعض بنحاول بقدر الإمكان 
+
+8
+00:00:36,360 --> 00:00:42,000
+أن نوضح الأمور اللي هي تحت عنوان 16 Completion of
+
+9
+00:00:42,000 --> 00:00:46,620
+metric spaces احنا لجينا في spaces عندنا complete
+
+10
+00:00:46,620 --> 00:00:51,770
+spaces وفي spaces إيش مايلها non complete space الـ
+
+11
+00:00:51,770 --> 00:00:54,650
+Complete Space خلاص خلها دي مش هي اللي هنحكي 
+
+12
+00:00:54,650 --> 00:00:57,910
+عليها هنحكي عن الـ Non-Complete Space الـ Non
+
+13
+00:00:57,910 --> 00:01:01,490
+-Complete Space بدي أنا أعملها Completion يعني بدي 
+
+14
+00:01:01,490 --> 00:01:05,290
+أ .. ب .. roughly الكلام إنه إيش اللي خاسس فيها بده 
+
+15
+00:01:05,290 --> 00:01:11,990
+يكملهو Roughly اللي هي وكأنه الـ Sequences اللي 
+
+16
+00:01:11,990 --> 00:01:14,990
+فيها اللي جاية عبالها تروح وتكون Converged وبره 
+
+17
+00:01:14,990 --> 00:01:17,870
+وما بتكونش Converged في الـ Space بدي أجيب هذا 
+
+18
+00:01:17,870 --> 00:01:20,990
+النقطة اللي هي ممكن تروح فيها وأحطها في مين في 
+
+19
+00:01:20,990 --> 00:01:24,250
+الـ Space هذا الكلام Roughly نشوف إيش معنى الكلام 
+
+20
+00:01:24,250 --> 00:01:29,880
+هذا اللي هو بشكل خلينا نقول أطقأولا تعريف let X be
+
+21
+00:01:29,880 --> 00:01:33,980
+let X and و D and Y و D تِلدة بيه metric spaces
+
+22
+00:01:33,980 --> 00:01:39,140
+الآن، ضمن a mapping T من X لعند Y من عند الـ X 
+
+23
+00:01:39,140 --> 00:01:42,700
+لعند Y، بنقول عنها is said to be isometric or
+
+24
+00:01:42,700 --> 00:01:47,500
+isometry يعني بنسمي اللي هي ال space هذا .. ال .. 
+
+25
+00:01:47,500 --> 00:01:50,240
+ال .. ال .. ال function اللي عندي isometry أو
+
+26
+00:01:50,240 --> 00:01:54,620
+isometric اللي هي إذا كان T preserve distances 
+
+27
+00:01:54,620 --> 00:01:59,180
+يعني بمعنى آخر بتنقل المسافة اللي هنا إلى نفس 
+
+28
+00:01:59,180 --> 00:02:03,240
+المسافة اللي هنا بمعنى إنه that is لكل x و y في ال 
+
+29
+00:02:03,240 --> 00:02:10,260
+X ال D تِلدة لل Tx و Ty بساوية D لل X و ال Y يعني 
+
+30
+00:02:10,260 --> 00:02:14,860
+المسافة اللي بين X و Y under D اللي هي في الـ .. في
+
+31
+00:02:14,860 --> 00:02:20,400
+الـ X وD هي نفسها المسافة بين صورها في الأندر 
+
+32
+00:02:20,400 --> 00:02:23,420
+المتريك اللي في مين وفي واي الـ D تِلدة في T X وT Y
+
+33
+00:02:23,420 --> 00:02:27,320
+هذا بنسميه Isometry ومعلومة على جنب إذا كانت الـ T
+
+34
+00:02:27,320 --> 00:02:31,500
+is Isometry اللي هو على طول بتطلع one to one
+
+35
+00:02:31,500 --> 00:02:35,120
+function ماشي الحال وهذا الكلام يعني إثباته اللي 
+
+36
+00:02:35,120 --> 00:02:42,000
+هو سهل بضل معاكم الآن بيجيهذا لما نقول عن الـ T من
+
+37
+00:02:42,000 --> 00:02:45,000
+X لعند Y عزيمتريك أو are the I عزيمتريك، as a
+
+38
+00:02:45,000 --> 00:02:49,940
+function اللي بنقول إن الـ space X is said to be 
+
+39
+00:02:49,940 --> 00:02:56,080
+عزيمتريك كspace والـ space Y إذا بنلاقي if there
+
+40
+00:02:56,080 --> 00:03:00,390
+exists a bijection عزيمتري of X onto Y يعني بنقول 
+
+41
+00:03:00,390 --> 00:03:03,550
+أنه اتنين ال X وال Y are isometric إذا كان في 
+
+42
+00:03:03,550 --> 00:03:07,470
+عندي one to one onto function which is an
+
+43
+00:03:07,470 --> 00:03:11,510
+isometric بنقول عنه إيش ماله The two spaces X and 
+
+44
+00:03:11,510 --> 00:03:16,550
+Y are isometric يعني بمعنى آخر العالم اللي أنا
+
+45
+00:03:16,550 --> 00:03:22,330
+أصلا بشتغل فيه ال metric space X أو D وعندي اللي هو
+
+46
+00:03:22,330 --> 00:03:27,250
+Y وD تِلدة بنقول عنهم إن هدولة isometric ال spaces
+
+47
+00:03:27,250 --> 00:03:32,210
+يعني بمعنى آخر هما نفس الشيء بس اختلفت في الأسماء 
+
+48
+00:03:32,210 --> 00:03:37,050
+هذه الأسانة فيها X وهذه الأسانة فيها اسمها TX لأن
+
+49
+00:03:37,050 --> 00:03:42,370
+المسافة هذه هي نفس المسافة فعشان هيك كل ما يتعلق
+
+50
+00:03:42,370 --> 00:03:45,890
+بالمسافة هنا وهنا نفس الشيء عشان هيك بنقول ال 
+
+51
+00:03:45,890 --> 00:03:49,590
+spaces هنا زي بعض roughly لكن اللي هي اختلافات في
+
+52
+00:03:49,590 --> 00:03:53,490
+مين في الأسماء يعني وكإني بقول ال space اللي 
+
+53
+00:03:53,490 --> 00:03:57,030
+بأثبت إنه isometric بين هنا وبين هنا بنقول عنهم 
+
+54
+00:03:57,030 --> 00:04:01,030
+اللي هم إيه الشمال هم ال two spaces وكإنا بنقول 
+
+55
+00:04:01,030 --> 00:04:04,880
+are equivalent زي ما كنا في الـ Jabra إذا بتذكروا
+
+56
+00:04:04,880 --> 00:04:09,360
+لما نقول اللي هو لما نحكي عن تركيب Jabra نقول X 
+
+57
+00:04:09,360 --> 00:04:14,280
+group و Y group إذا كانت ال X في homomorphism بين
+
+58
+00:04:14,280 --> 00:04:18,200
+التنتين بالإضافة one to one onto function كنا نقول 
+
+59
+00:04:18,200 --> 00:04:22,240
+there are إيش ماله isomorphic يعني العالمين 
+
+60
+00:04:22,240 --> 00:04:25,820
+متكافئان أو هي نفس الشيء بس اختلفت الأسماء وهنا 
+
+61
+00:04:25,820 --> 00:04:30,700
+نفس الشيء عند metric space و metric space بقولش بين 
+
+62
+00:04:30,700 --> 00:04:33,300
+عمليات X عليها وعمليات Y عليها، لأ لأ لأ بس
+
+63
+00:04:33,300 --> 00:04:36,960
+كمتريكي space إذا preserved distances و one to one 
+
+64
+00:04:36,960 --> 00:04:40,300
+نقلت بلاغي function اللي هي one to one نقلت و
+
+65
+00:04:40,300 --> 00:04:42,920
+preserved distances معناته إنه صار the two spaces
+
+66
+00:04:42,920 --> 00:04:47,220
+are the same هذا الكلام مهم لللي بده أحكيه بعد هيك 
+
+67
+00:04:47,220 --> 00:04:51,200
+الآن ندلع ال theorem تبعتنا اللي هي الـ Completion
+
+68
+00:04:51,200 --> 00:04:55,920
+for a metric space الإعلان هذا قلته قبل شوية إنه 
+
+69
+00:04:55,920 --> 00:05:01,440
+أي metric space لو non-complete can be completed
+
+70
+00:05:01,440 --> 00:05:06,860
+اللي هو النظرية بتقول اللي هي ال completion for a
+
+71
+00:05:06,860 --> 00:05:12,550
+metric space X وD اللي هو there exist تفاصيل اللي 
+
+72
+00:05:12,550 --> 00:05:15,710
+قلته a metric space can be completed تفاصيله 
+
+73
+00:05:15,710 --> 00:05:19,910
+كالتالي for a metric space X وD there exist a
+
+74
+00:05:19,910 --> 00:05:26,390
+complete metric space X hat وD hat which has a
+
+75
+00:05:26,390 --> 00:05:34,810
+subspace W that is isometric with X and dense in X 
+
+76
+00:05:34,810 --> 00:05:35,250
+hat
+
+77
+00:05:38,140 --> 00:05:44,460
+لو كان عندي x و d metric space وهذا لو كان مش 
+
+78
+00:05:44,460 --> 00:05:46,500
+complete لو كان complete بيبقى على نفسه مش مشكلة
+
+79
+00:05:46,500 --> 00:05:51,640
+كان non complete اللي هو بقدر ألاقي metric space 
+
+80
+00:05:51,640 --> 00:06:00,240
+اللي هو آخر اسمه x hat و d hat هذا ال metric space
+
+81
+00:06:00,240 --> 00:06:06,380
+complete metric space وإله subspace اسمه main W
+
+82
+00:06:06,380 --> 00:06:15,140
+subspace من main من X hat والـ W اللي هو dense
+
+83
+00:06:15,140 --> 00:06:21,660
+space يعني بمعنى آخر W closure بساوي اللي هو X hat 
+
+84
+00:06:21,660 --> 00:06:25,400
+وال
+
+85
+00:06:25,400 --> 00:06:34,290
+X هذا الـ W isometric للmain لل X نشوف إيش اللي
+
+86
+00:06:34,290 --> 00:06:42,630
+بنقوله اللي بقوله التالت إنه أنا غرضي إن الأجي 
+
+87
+00:06:42,630 --> 00:06:48,190
+اللي هو metric space يكون completion لل X
+
+88
+00:06:50,520 --> 00:06:56,120
+الآن عندي .. بقولكم أكيد هلاقي space اسمه X hat وD
+
+89
+00:06:56,120 --> 00:07:02,400
+hat هذا ال space يتمتع بالآتي اللي فيه W فيه ال
+
+90
+00:07:02,400 --> 00:07:07,250
+closure إيه هي إشبت ثانية؟ X hat والـ W هذه و
+
+91
+00:07:07,250 --> 00:07:12,870
+كأنها هي X لأنها الـ W إيش مايلها؟ Isometric لمين؟ 
+
+92
+00:07:12,870 --> 00:07:19,290
+للـ X وكأنه صار عندي الـ X hat هي عبارة عن اللي 
+
+93
+00:07:19,290 --> 00:07:22,750
+هي الـ X مضافة إلى ال closure اللي خلتها complete
+
+94
+00:07:22,750 --> 00:07:28,700
+مافيه؟ وكأنه صارت X hat complete space اللي هو فيه
+
+95
+00:07:28,700 --> 00:07:32,160
+subspace منه isometric للـ X اللي هو هذا اللي 
+
+96
+00:07:32,160 --> 00:07:38,620
+هنسمي إنه completion لمين للـ X أي سؤال يعني مش
+
+97
+00:07:38,620 --> 00:07:41,580
+شرط إنه احنا يجينا والله نحطنا limit points هنا و
+
+98
+00:07:41,580 --> 00:07:45,520
+هنا نحطناها لأ احنا بنجيب space complete كامل و
+
+99
+00:07:45,520 --> 00:07:51,530
+نclosure ل W هي عبارة عن ال X hat والـ W هي ال X أو
+
+100
+00:07:51,530 --> 00:07:57,390
+بمعنى مش هي هي w isometric لمين لل X واضح طيب هذا 
+
+101
+00:07:57,390 --> 00:08:01,350
+اللي هو خلينا نقول نص نظرية ومش هيك كمان وبيقولك
+
+102
+00:08:01,350 --> 00:08:05,870
+this space X hat راكزوا معايا this space X hat is
+
+103
+00:08:05,870 --> 00:08:09,730
+unique except for isometers يعني هذا ال space X
+
+104
+00:08:09,730 --> 00:08:14,120
+hat إيش ماله وحيد except isometrics يعني لو بتدلج 
+
+105
+00:08:14,120 --> 00:08:19,420
+space تاني مشابه إله هكون isometric إله يعني لو 
+
+106
+00:08:19,420 --> 00:08:24,700
+كان في عند X تِلدة ال complete isometric space و
+
+107
+00:08:24,700 --> 00:08:29,160
+half نفس الخواص تبع X hat يعني having dense
+
+108
+00:08:29,160 --> 00:08:34,210
+subspace W تِلدة و W تِلدة isometric لل X لازم الـ x 
+
+109
+00:08:34,210 --> 00:08:37,630
+تِلدة والـ x هات أشمالين يكون isometric يعني لو 
+
+110
+00:08:37,630 --> 00:08:42,050
+بدنا نلاقي كمان واحد اسمه x تِلدة أو d تِلدة وهذا 
+
+111
+00:08:42,050 --> 00:08:47,390
+اللي هو ال space في w تِلدة sub space منه والـ w
+
+112
+00:08:47,390 --> 00:08:50,450
+تِلدة اللي هي dense فيه وفي نفس الودة isometric
+
+113
+00:08:50,450 --> 00:08:54,210
+للـ x هيطلع اللي هو ال x تِلدة وال x هات are
+
+114
+00:08:54,210 --> 00:09:00,550
+isometric واضح إذا نرخص النظرية there exist a
+
+115
+00:09:00,550 --> 00:09:05,270
+complete metric space أو 
+
+116
+00:09:05,270 --> 00:09:08,250
+a completion metric space لهذا ال space بالمفهوم
+
+117
+00:09:08,250 --> 00:09:14,510
+اللي حكيناه وهذا ال metric واحد except for 
+
+118
+00:09:14,510 --> 00:09:15,530
+isometric
+
+119
+00:09:19,020 --> 00:09:23,740
+طيب نيجي للبرهان البرهان يا جماعة هيتكون من أربع 
+
+120
+00:09:23,740 --> 00:09:28,940
+اللي هو اللي هي أجزاء بتطولوا روحكم عليها الجزء
+
+121
+00:09:28,940 --> 00:09:32,240
+الأول اللي هو constructing X hat وD hat يعني بدي
+
+122
+00:09:32,240 --> 00:09:37,140
+أعملكم construction بدي أركّنكم ل space اللي احنا 
+
+123
+00:09:37,140 --> 00:09:40,900
+بدناه اللي هو اللي متوقعين إن يكون completion 
+
+124
+00:09:40,900 --> 00:09:46,210
+لنهينا ال X وبعد ذلك سأعمل لكم Constructing an
+
+125
+00:09:46,210 --> 00:09:51,310
+Isometry T of X onto W الآن سأعمل لكم ما هو
+
+126
+00:09:51,310 --> 00:09:55,350
+Isometry بين X وبين W اللي يبقى خشوط اللي قبل 
+
+127
+00:09:55,350 --> 00:09:59,590
+شوية الـ W سيكون من مين جزء من الـ X هذا والـ
+
+128
+00:09:59,590 --> 00:10:03,470
+Closure اللي سيكون من مين هو الـ X هذا سيخلصنا 
+
+129
+00:10:03,470 --> 00:10:07,310
+اللي هو الجزء هذا بعد ذلك سأثبت لكم أن الـ X نحن
+
+130
+00:10:07,310 --> 00:10:11,900
+نبحث عنه إيش يكون Complete بدأ أثبت لكم أن الـ space
+
+131
+00:10:11,900 --> 00:10:17,040
+X hat is complete بعد هيك الخطوة الأخيرة بتدابلكم
+
+132
+00:10:17,040 --> 00:10:20,080
+proving the uniqueness of X hat except for 
+
+133
+00:10:20,080 --> 00:10:22,820
+isometries يعني بتدفر الـ XL ده واحد تاني بنفسه 
+
+134
+00:10:22,820 --> 00:10:26,640
+كده كده الاخر شروط ويطلع XL ده يشمله isometric
+
+135
+00:10:26,640 --> 00:10:31,690
+لمين للـ X hat تابعوا معايا بالتفصيل الآن اطلعوا 
+
+136
+00:10:31,690 --> 00:10:35,190
+لفوق خلينا نفصل اللي حكيناها قبل بشوية أول حاجة 
+
+137
+00:10:35,190 --> 00:10:39,490
+اللي هو مين إنها Constructing X هات وD هات بدي أش
+
+138
+00:10:39,490 --> 00:10:47,860
+أسوي بدي أركب ال X هات وأحطه بين اديكم خلينا ناخد 
+
+139
+00:10:47,860 --> 00:10:52,860
+Xn و Zn أني كوشي سيكوانسيز in main in X لأن كوشي 
+
+140
+00:10:52,860 --> 00:10:56,220
+سيكوانسيز ما احنا احنا اصلا من الأول احنا متوقعين 
+
+141
+00:10:56,220 --> 00:11:01,280
+أصلًا إنه الـ X خاسر مين خاسر إنه إنه تروح الـ limits
+
+142
+00:11:01,280 --> 00:11:03,900
+فيه يعني الـ Cauchy sequences دي عبالها تعمل
+
+143
+00:11:03,900 --> 00:11:07,280
+convergence لكن الـ space مافيش فيه لأن الـ limit
+
+144
+00:11:07,280 --> 00:11:10,740
+اللي هو تروح له فعشان ذلك احنا بدأنا بالـ Cauchy
+
+145
+00:11:10,740 --> 00:11:15,360
+sequences let Xn and Zn بيكون Cauchy sequences in X
+
+146
+00:11:16,200 --> 00:11:20,880
+الآن بدنا نعرف xₙ related to zₙ يعني مجرد إيش ما 
+
+147
+00:11:20,880 --> 00:11:26,020
+لها relation الـ relation هذه كيف بدي أعرفها إن الـ
+
+148
+00:11:26,020 --> 00:11:29,940
+limit للـ distance بين xₙ و zₙ إيش سايرة سفر إذا الـ
+
+149
+00:11:29,940 --> 00:11:33,210
+relation العامة اللي بعرفها أخذت أي two sequences
+
+150
+00:11:33,210 --> 00:11:37,250
+Cauchy sequences Xn و Zn بقول إن الـ Cauchy sequences
+
+151
+00:11:37,250 --> 00:11:40,890
+هدول are related إذا كانت الـ limit للمسافات اللي
+
+152
+00:11:40,890 --> 00:11:48,410
+بين X1 و X2 و X3 X2 و Z2 
+
+153
+00:11:48,410 --> 00:11:53,870
+Xn و Zn المسافة is n cos infinity إيش تساوي؟ تساوي
+
+154
+00:11:53,870 --> 00:11:57,560
+صفر هذه is an equivalence relation وكوّن الإنسان
+
+155
+00:11:57,560 --> 00:12:03,220
+عشان نسيّوله عندي أول حاجة الـ Xn related للـ Xn ليه؟
+
+156
+00:12:03,220 --> 00:12:08,120
+لأن المسافة بين Xn و Xn دائمًا مش متساوية فـ limit
+
+157
+00:12:08,120 --> 00:12:12,380
+ها أكيد مش متساوية إذا اللي هو اللي أزال سواها
+
+158
+00:12:12,380 --> 00:12:17,200
+أولًا هي reflexive اثنين الآن symmetric أكيد اللي هو
+
+159
+00:12:17,200 --> 00:12:27,960
+Xn related to Yn معناته limit Xn Yn بساوية 0 و هذه 
+
+160
+00:12:27,960 --> 00:12:36,020
+أكيد limit Yn و xn هيساوي صفر لأن هذه يعني هذه و
+
+161
+00:12:36,020 --> 00:12:42,440
+هذا هيعطيني إنه اللي هو Yn related to xn إذا كانت
+
+162
+00:12:42,440 --> 00:12:47,360
+اللي هو هذه هتكون symmetric برضه الآن تلاتة اللي
+
+163
+00:12:47,360 --> 00:12:51,940
+هي النقطة الأخيرة برضه لو فرضنا إن xn related to
+
+164
+00:12:51,940 --> 00:13:02,830
+Yn و Yn مع Zn مايعطينا هنا limit distance Xn و Yn
+
+165
+00:13:02,830 --> 00:13:10,410
+بساوي 0 والـ Limit للـ Distance بين YN و ZN بساوية
+
+166
+00:13:10,410 --> 00:13:16,310
+0 إذا أنا بدي XN و مين و ZN خذوا Limit الـ
+
+167
+00:13:16,310 --> 00:13:20,330
+Distance بين XN و ZN طبيعي بالطريقة نقول الـ
+
+168
+00:13:20,330 --> 00:13:24,730
+Equality XN و ZN أصغر أو يساوي الـ Distance بين XN
+
+169
+00:13:24,730 --> 00:13:30,470
+و YN زائد الـ Distance بين YN و ZN خذوا الـ limit
+
+170
+00:13:30,470 --> 00:13:35,170
+للجهتين اللي غالب بيصير limit limit as n goes to
+
+171
+00:13:35,170 --> 00:13:37,630
+infinity هذي as n goes to infinity من اللي فوق هذي
+
+172
+00:13:37,630 --> 00:13:41,730
+صفر إذا تطلع وهذا أكبر يساوي صفر إذا هذه هتطلع
+
+173
+00:13:41,730 --> 00:13:48,010
+بتساوي صفر إذا شاملها إذا صارت Zn أو Xn related Zn
+
+174
+00:13:48,010 --> 00:13:51,770
+يعني بمعنى آخر transitive إذا صارت عندي is an
+
+175
+00:13:51,770 --> 00:13:54,770
+equivalence relation إيش بدك في الـ equivalence
+
+176
+00:13:54,770 --> 00:13:57,050
+relation؟ بدي الـ equivalence relation عارفين ليش؟
+
+177
+00:13:58,220 --> 00:14:04,660
+عشان أنا الآن بدي أركب الـ X hat الـ X hat
+
+178
+00:14:04,660 --> 00:14:08,640
+هركبها من الـ equivalence classes للـ relation اللي
+
+179
+00:14:08,640 --> 00:14:14,180
+عندي آه يعني الآن الـ equivalence classes إيش هي
+
+180
+00:14:14,180 --> 00:14:22,100
+مثلًا لو عندي X n عشان X n Cauchy sequence ماشي في
+
+181
+00:14:22,100 --> 00:14:24,940
+الاسم السابع اللي هو main Cauchy sequence in main in
+
+182
+00:14:24,940 --> 00:14:31,000
+X عناصرها من وين جاي من X كل الـ sequences الـ
+
+183
+00:14:31,000 --> 00:14:36,520
+Cauchy اللي related لها يعني IZN related to XN
+
+184
+00:14:36,520 --> 00:14:40,860
+هيكونوا إيش هم كلهم في نفس الـ equivalence class
+
+185
+00:14:40,860 --> 00:14:47,200
+يعني الـ equivalence class للـ XN هذه اللي هي فيها
+
+186
+00:14:47,200 --> 00:14:53,160
+IZN و الـ YN و كل الناس اللي أو الـ sequences اللي 
+
+187
+00:14:53,160 --> 00:14:56,060
+Cauchy sequences و related لهذه عبر الـ relation
+
+188
+00:14:56,060 --> 00:15:02,000
+اللي عندي الآن أنا بدي اسمي الـ X hat بي the set of
+
+189
+00:15:02,000 --> 00:15:05,940
+all equivalence classes اللي بدي اسميها يعني هذه 
+
+190
+00:15:05,940 --> 00:15:08,780
+بدل ما اسميها زي هيك أسهل اللي بدي اسميها X hat
+
+191
+00:15:08,780 --> 00:15:13,480
+ماشي وهكذا واضحيش هذه الـ X hat إيش هي عبارة عن
+
+192
+00:15:13,480 --> 00:15:16,500
+the equivalence class of all اللي هي Cauchy
+
+193
+00:15:16,500 --> 00:15:20,280
+sequences related to بعض ماشي طيب الآن
+
+194
+00:15:22,770 --> 00:15:25,550
+let X hat be the set of all equivalency classes X
+
+195
+00:15:25,550 --> 00:15:29,790
+hat و Y hat و Z hat والأخرى of Cauchy sequences
+
+196
+00:15:29,790 --> 00:15:33,790
+اللي هو rough obtained above اللي هو عن طريق الـ
+
+197
+00:15:33,790 --> 00:15:38,250
+limit distance بين X and Y and يساوي صفر الآن بتعرف
+
+198
+00:15:38,250 --> 00:15:43,130
+الـ d hat إيش الـ d hat بتعرف الـ d hat of x hat و y 
+
+199
+00:15:43,130 --> 00:15:47,910
+hat بساوي الـ limit للـ distance xn yn as n goes to
+
+200
+00:15:47,910 --> 00:15:51,610
+infinity الـ xn مالها كوشي الـ sequences فيها دي و الـ
+
+201
+00:15:51,610 --> 00:15:56,160
+yn كوشي الـ sequences في مين؟ في الثانية فالآن هذا 
+
+202
+00:15:56,160 --> 00:15:59,560
+التعريف اللي هو اللي أمامي بدي أثبت إنه well
+
+203
+00:15:59,560 --> 00:16:04,040
+defined where xn element of x hat and yn element
+
+204
+00:16:04,040 --> 00:16:07,060
+of y hat و الـ x hat و الـ y hat إيش ما اللي موجودات
+
+205
+00:16:07,060 --> 00:16:10,880
+في الـ x hat ليش أثبتوا well defined؟ لحسن مش احنا
+
+206
+00:16:10,880 --> 00:16:13,280
+بنتعامل معاكم equivalency class أنتوا تروحوا
+
+207
+00:16:13,280 --> 00:16:19,020
+تأخذوا ناخذ xn و تأخذوا zn الواحد ياخذ دي يبدو YN و
+
+208
+00:16:19,020 --> 00:16:22,180
+KN و YN و KN أشملين related لبعض في نفس الـ
+
+209
+00:16:22,180 --> 00:16:25,500
+equivalency class خايفين يطلع جواب يعني لما ناخد
+
+210
+00:16:25,500 --> 00:16:28,300
+الـ limit للـ distance بين XN و YN و جوابكم يبدأ الـ
+
+211
+00:16:28,300 --> 00:16:33,040
+limit للـ distance بين ZN و KN يطلع مش زي بعض فلأ
+
+212
+00:16:33,040 --> 00:16:36,880
+بدنا نثبت لكم إنه بيطلع زي بعض دعونا نشوف كيف ..
+
+213
+00:16:36,880 --> 00:16:42,340
+اطلع على فوق to prove that this limit exists we do
+
+214
+00:16:42,340 --> 00:16:45,620
+as follow بدنا نعمل كمان يعني بـ triangling quality
+
+215
+00:16:45,620 --> 00:16:49,220
+سهلة اللي هو distance بين Xm و Ym بـ triangling
+
+216
+00:16:49,220 --> 00:16:54,240
+quality أثر سواء distance بين Xm و Xm ماشي زائد
+
+217
+00:16:54,240 --> 00:16:58,320
+distance بين Xm و Ym زائد الـ distance بين Ym و Ym
+
+218
+00:16:58,320 --> 00:17:04,260
+إنّه un-arbitrary ماشي then جيبولي هذه hand اللي هي
+
+219
+00:17:04,260 --> 00:17:08,000
+الـ Ym و Xm على الجهة دي بيصير عندي distance بين Xm
+
+220
+00:17:08,000 --> 00:17:13,730
+و Ym نقص هذه جبتها هنا الـ distance بين YM و XM و
+
+221
+00:17:13,730 --> 00:17:18,390
+YM أصغر وأصغر اللي بيظل اللي هو هذه وهذه اللي هي
+
+222
+00:17:18,390 --> 00:17:22,430
+الـ distance بين XN و XM و الـ distance بين YM و YN
+
+223
+00:17:22,430 --> 00:17:26,070
+اللي حصلت على هذه similarly بنفس الطريقة بدل ما
+
+224
+00:17:26,070 --> 00:17:29,770
+بدأ بدأ بالـ distance XN و YN ببدأ بالـ distance XM
+
+225
+00:17:29,770 --> 00:17:34,230
+و YM و بعمل نفس الـ triangle inequality بيطلع عندي ..
+
+226
+00:17:34,230 --> 00:17:36,630
+و بجيب هذه اللي .. اللي .. اللي هي في هذه الحالة
+
+227
+00:17:36,630 --> 00:17:41,270
+بتطلع بدل Xm Ym على الجهة هذه بتطلع Xn Yn بجيبها
+
+228
+00:17:41,270 --> 00:17:45,350
+هنا على الجهة هذه بيصير المسافة بين Xm Ym ناقص Xn
+
+229
+00:17:45,350 --> 00:17:49,830
+Yn أصغر أو يساوي نفس الكمية اللي طلعت قبل بشوية و
+
+230
+00:17:49,830 --> 00:17:52,910
+ضربها في سالب حط و .. و .. و .. و .. و .. و .. و ..
+
+231
+00:17:52,910 --> 00:17:53,070
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+232
+00:17:53,070 --> 00:17:54,310
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+233
+00:17:54,310 --> 00:17:55,610
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+234
+00:17:55,610 --> 00:17:56,290
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+235
+00:17:56,290 --> 00:18:01,030
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+236
+00:18:01,030 --> 00:18:02,490
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+237
+00:18:02,490 --> 00:18:04,030
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+238
+00:18:04,030 --> 00:18:08,590
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+239
+00:18:08,590 --> 00:18:08,690
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+240
+00:18:08,690 --> 00:18:16,610
+و .. و .. و .. و
+
+241
+00:18:16,610 --> 00:18:19,840
+..بالرغم من أن Xn وYn هما عاملين عاملين عاملين
+
+242
+00:18:19,840 --> 00:18:20,480
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+243
+00:18:20,480 --> 00:18:21,760
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+244
+00:18:21,760 --> 00:18:29,480
+عاملين عاملين عاملين عاملين عاملين
+
+245
+00:18:29,480 --> 00:18:31,360
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+246
+00:18:31,360 --> 00:18:31,440
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+247
+00:18:31,440 --> 00:18:32,260
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+248
+00:18:32,260 --> 00:18:37,840
+عاملين عاملين
+
+249
+00:18:37,840 --> 00:18:47,260
+عام
+
+250
+00:18:47,280 --> 00:18:52,460
+أصغر من إبسلون لحدها واضح إيش معناه صار عندي اللي
+
+251
+00:18:52,460 --> 00:18:57,980
+هو هذا هذا رقم عدد عدد يعني وكأنه عبارة عن
+
+252
+00:18:57,980 --> 00:19:01,260
+sequence of أعداد وهذا عبارة عن أعداد إذا صارت
+
+253
+00:19:01,260 --> 00:19:06,750
+الـDX and Y and هذه اللي هي عبارة عن sequences of
+
+254
+00:19:06,750 --> 00:19:10,190
+mean of real numbers واحنا بنعرف الـ real number
+
+255
+00:19:10,190 --> 00:19:15,090
+إيش ماله، complete إذا then it converges، thus الـ
+
+256
+00:19:15,090 --> 00:19:19,310
+limit للـ distance xₙ و yₙ إيش ماله exist، exist
+
+257
+00:19:19,310 --> 00:19:25,230
+وكمان وحيد، طيب، طيب، الآن now we show that this
+
+258
+00:19:25,230 --> 00:19:28,710
+limit is إيش، is independent، إذا الأول إشي أثبتنا
+
+259
+00:19:28,710 --> 00:19:32,730
+إنّه الـ limit موجودة، بمعنى آخر الـ d hat اللي عرفناه
+
+260
+00:19:33,450 --> 00:19:38,350
+بين x hat و y hat اللي هو بيساوي الـ limit للـ
+
+261
+00:19:38,350 --> 00:19:42,570
+distance بين x n و y n as n goes to infinity
+
+262
+00:19:42,570 --> 00:19:43,950
+exists
+
+263
+00:19:46,230 --> 00:19:49,910
+هذه واحدة الآن بدأ أثبت لكم إنّه independent of the
+
+264
+00:19:49,910 --> 00:19:55,250
+choice of xn من الـ x hat و الـ y hat من الـ y hat
+
+265
+00:19:55,250 --> 00:19:58,670
+يعني أنت لو اخترت xn في الـ y hat في الـ x hat و
+
+266
+00:19:58,670 --> 00:20:04,710
+اخترت zn في الـ y hat و واحد اختار zkn مثلًا في الـ y
+
+267
+00:20:04,710 --> 00:20:08,330
+hat هيطلع الـ limit بناء على هذا و الـ limit بناء
+
+268
+00:20:08,330 --> 00:20:12,750
+على الـ distance بين zn و kn اللي هو R equivalent
+
+269
+00:20:12,750 --> 00:20:19,140
+تشوف الآن نضرح إن هذا الانتقال مستقل من الاختيار
+
+270
+00:20:19,140 --> 00:20:23,420
+إذا أنا الآن أذكركم ركبت الـ X hat من أين؟ من الـ
+
+271
+00:20:23,420 --> 00:20:27,220
+equivalency classes عرفت الـ D hat اللي هو metric
+
+272
+00:20:27,220 --> 00:20:33,020
+عليه اسمه D hat حسب اللي حكيته فوق، ضال عندي إيش
+
+273
+00:20:33,020 --> 00:20:38,580
+أسوي؟ إن أثبت لكم إن هذا الانتقال مستقل من الاختيار
+
+274
+00:20:38,580 --> 00:20:42,820
+من الاختيارات الخاصة من الاختيارات الخاصة اللي
+
+275
+00:20:42,820 --> 00:20:43,520
+بنحكي عنها
+
+276
+00:20:46,370 --> 00:20:53,830
+لأ سنة خلّيني أنزل بقول لك we show that this limit
+
+277
+00:20:53,830 --> 00:20:56,590
+is independent of the choice of xₙ elemental x hat
+
+278
+00:20:56,590 --> 00:21:00,610
+and yₙ elemental y hat in other words خلّيني نفترض
+
+279
+00:21:00,610 --> 00:21:03,690
+إن xₙ و zₙ من نفس الـ equivalency class تطلع على
+
+280
+00:21:03,690 --> 00:21:07,710
+فوق و نفترض إن الـ yₙ و الـ wₙ من نفس الـ equivalency 
+
+281
+00:21:07,710 --> 00:21:11,440
+class تبعتي اللي هي mean y hat then by one اللي هي
+
+282
+00:21:11,440 --> 00:21:14,660
+قبل شوية اللي عملناها المسافة بين Xn وYn والمسافة 
+
+283
+00:21:14,660 --> 00:21:20,980
+بين Zn وWn أصغر أو يساوي Xn وZn زائد Yn وYn وWn
+
+284
+00:21:20,980 --> 00:21:25,760
+هذي عملناها قبل هيك الآن as n goes to infinityاللي 
+
+285
+00:21:25,760 --> 00:21:29,240
+هي هذا هتروح للصفر وهذا هتروح للصفر ليش؟ لأن Xn
+
+286
+00:21:29,240 --> 00:21:33,240
+وZn ما لهن من نفس ال .. related مدام related على
+
+287
+00:21:33,240 --> 00:21:36,060
+حسب اللي هي Xn related to Zn هيكون ال limit بيساوي
+
+288
+00:21:36,060 --> 00:21:39,220
+صفر وهذا ال limit أيش بيساوي صفر إذا as n goes to
+
+289
+00:21:39,220 --> 00:21:41,780
+infinity هذا هيروح للصفر إذا as n goes to infinity
+
+290
+00:21:41,780 --> 00:21:45,560
+هذا المقطار هيساوي صفر يعني بمعنى آخر limit هذه
+
+291
+00:21:45,560 --> 00:21:49,100
+بيساوي limit التانية إذا limit هذه بيساوي limit
+
+292
+00:21:49,100 --> 00:21:53,660
+هذا إذا يوازي وجوابكم هو نفس الشيء إذا الـD hat
+
+293
+00:21:53,660 --> 00:21:57,660
+الـL على أي كوشي sequence تأخذها من جوا ال
+
+294
+00:21:57,660 --> 00:22:00,800
+equivalency class أي إن كانت اللي إلي واللي إلك وال
+
+295
+00:22:00,800 --> 00:22:04,300
+لي إلي واللي إلك واللي هتطلع نفس الجواب إذا
+
+296
+00:22:04,300 --> 00:22:08,760
+أمورنا تمامة تمام و we prove that الـD hat into is
+
+297
+00:22:08,760 --> 00:22:12,920
+a metric on X hat إذا أثبتنا الخطوة الثانية بعد ما
+
+298
+00:22:12,920 --> 00:22:16,200
+أثبتنا إن exist أثبتنا إنه well defined يعني اللي
+
+299
+00:22:16,200 --> 00:22:20,130
+هو لا يعتمد على ال choice تبع الـ Xn اللي في
+
+300
+00:22:20,130 --> 00:22:24,630
+الـ X hat طيب هبنا نثبت .. ومن ال trick اطلع لفوق
+
+301
+00:22:24,630 --> 00:22:29,610
+طولوا روحكم عليها الآن بدنا نثبت انه هو prove that
+
+302
+00:22:29,610 --> 00:22:33,770
+D hat in two is a metric on X أول شيء it is clear
+
+303
+00:22:33,770 --> 00:22:38,650
+that D hat satisfy M واحد عند M ثلاثة ليش؟ لقيته 
+
+304
+00:22:38,650 --> 00:22:44,120
+هذه أكبر أو يساوي صفر أكيد صح؟مظبوط ولا لأ؟ الآن و
+
+305
+00:22:44,120 --> 00:22:49,440
+لو بدنا نأخذ dy hat وx hat على طول بيصير ال limit
+
+306
+00:22:49,440 --> 00:22:54,680
+بتنقلب فبتطلع نفس الشيء واضح؟ إذا برضه dy hat hat
+
+307
+00:22:54,680 --> 00:23:00,400
+و x hat بيساوي dx hat y hat، مظبوط؟ إذا الشروط هذه
+
+308
+00:23:00,400 --> 00:23:09,150
+سهلة، اللي هي و نجي اللي هو خلاص أنتو بتكمله الآن
+
+309
+00:23:09,150 --> 00:23:11,050
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+310
+00:23:11,050 --> 00:23:11,150
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+311
+00:23:11,150 --> 00:23:11,330
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+312
+00:23:11,330 --> 00:23:12,070
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+313
+00:23:12,070 --> 00:23:12,190
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+314
+00:23:12,190 --> 00:23:14,990
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+315
+00:23:14,990 --> 00:23:19,730
+M M M M M M
+
+316
+00:23:19,730 --> 00:23:20,030
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+317
+00:23:20,030 --> 00:23:22,450
+M M M M M M M M M M M M M M M Mأه then ال limit دي
+
+318
+00:23:22,450 --> 00:23:26,730
+xn و yn بساوة صفر وهذه أيش معناه بساوة صفر إن xn
+
+319
+00:23:26,730 --> 00:23:30,850
+equivalent ل yn hence the equivalence classes x
+
+320
+00:23:30,850 --> 00:23:34,770
+hat and y hat are either equal لأن إحنا عارفين إن 
+
+321
+00:23:34,770 --> 00:23:37,890
+ال equivalence class اللي .. اللي كان فيه عندي 
+
+322
+00:23:37,890 --> 00:23:41,050
+اللي هو ال equivalence classes عارفين يا this
+
+323
+00:23:41,050 --> 00:23:41,810
+joint
+
+324
+00:23:45,020 --> 00:23:48,800
+يا متساوية يا متساوية مدام في عنصر مشترك بينهم
+
+325
+00:23:48,800 --> 00:23:55,440
+مدام Xn و Yn related وال Xn في ال X hat وال Yn في
+
+326
+00:23:55,440 --> 00:23:59,260
+ال Y hat إذا اللي هو أيش مالهن إذا صار في عنصر
+
+327
+00:23:59,260 --> 00:24:01,180
+مشترك إذا التنتين لازم يكون إيه إيه إيه إيه إيه
+
+328
+00:24:01,180 --> 00:24:03,540
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+329
+00:24:03,540 --> 00:24:03,560
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+330
+00:24:03,560 --> 00:24:06,850
+إيه إيه إيه إيه إيه إيه إيه إيه طيب إذا صار عندي لأن
+
+331
+00:24:06,850 --> 00:24:11,290
+hence x and x hat the equivalence class x hat and
+
+332
+00:24:11,290 --> 00:24:15,970
+y hat أيش مالهن متساويتين وهذا بدأنا x d hat لل x
+
+333
+00:24:15,970 --> 00:24:18,890
+hat و y hat بصفر وصلنا ل x hat و y hat أيش بيساوي
+
+334
+00:24:18,890 --> 00:24:26,440
+بيساوى صفر ماهي سؤال الآن conversely اللي هو المسافة
+
+335
+00:24:26,440 --> 00:24:30,060
+بين X hat و Y hat أيش هيساوي صفر لذا خلاص الخاصية 
+
+336
+00:24:30,060 --> 00:24:35,520
+الثانية متحققة تماما to prove M4 اللي عن اتنين هين
+
+337
+00:24:35,520 --> 00:24:40,440
+عملتها اه ال M ثلاثة هذي وهذي اللي هي أكبر يساوي
+
+338
+00:24:40,440 --> 00:24:45,420
+صفر M واحد خلصتها ضال مين اللي هي M4 مستوعبين اه
+
+339
+00:24:47,110 --> 00:24:50,810
+أربعة اطلع فوق أربعة نركز عليها to prove
+
+340
+00:24:50,810 --> 00:24:55,620
+أربعة نركز عليها بس في الهدف هي سهلة برضه Note
+
+341
+00:24:55,620 --> 00:25:01,520
+that for all xₙ in X hat وYₙ in Y hat وZₙ في Z hat
+
+342
+00:25:01,520 --> 00:25:06,580
+والـ X hat وYₙ وZₙ أيش موجودة؟ اللي هي X hat، بتدا
+
+343
+00:25:06,580 --> 00:25:10,560
+وجد ال triangle inequality We have المسافة بين Xₙ
+
+344
+00:25:10,560 --> 00:25:15,920
+وYₙ أصغر بسهولة مسافة بين Xₙ وZₙ وZₙ ومين وYₙ بال
+
+345
+00:25:15,920 --> 00:25:19,640
+triangle inequality لأن الـ D is a metric أنا
+
+346
+00:25:19,640 --> 00:25:24,620
+بتذكر بتمين الآن ال metric الـ D hat الآن d hat لـ
+
+347
+00:25:24,620 --> 00:25:28,700
+x hat و y hat أيش بيساوي ال limit هذا طب ما هو ال
+
+348
+00:25:28,700 --> 00:25:30,820
+limit هذا هيكون أصغر بيساوي ال limit هذا زائد ال
+
+349
+00:25:30,820 --> 00:25:33,840
+limit هذا صح ولا لأ إذا أصغر بيساوي ال limit هذا 
+
+350
+00:25:33,840 --> 00:25:36,820
+زائد ال limit هذا طب ما هو ال limit هذا هو فعلا
+
+351
+00:25:36,820 --> 00:25:40,320
+التعريف التعريف اللي هو ال distance بين x hat و
+
+352
+00:25:40,320 --> 00:25:46,820
+main و z hat وهذا اللي بعده تعريف ال limit هذا
+
+353
+00:25:46,820 --> 00:25:50,460
+تعريف لـ D hat بين XZ hat وY hat
+
+354
+00:26:16,830 --> 00:26:23,270
+بنعمل construction لإيزومتري T من X لعين و لعين W
+
+355
+00:26:23,270 --> 00:26:27,250
+W
+
+356
+00:26:27,250 --> 00:26:34,210
+مين يا جماعة W هتكون لازم تكون W جزء من مين؟ من ال
+
+357
+00:26:34,210 --> 00:26:39,510
+X hat ولازم تكون W closure بسوء ال X hat ولازم
+
+358
+00:26:39,510 --> 00:26:44,810
+يكون عنده يقولوا معايا اللي هو W إيزومتري لمين؟ لل
+
+359
+00:26:44,810 --> 00:26:49,720
+X طيب شوفوا صلّوا على النبي عليه الصلاة والسلام
+
+360
+00:26:49,720 --> 00:26:55,380
+Constructing an isometry T of X onto Y, we have W
+
+361
+00:26:55,380 --> 00:27:00,680
+closure أش بيساوي X hat، هي ما بنعمله، الآن define
+
+362
+00:27:00,680 --> 00:27:07,660
+T من X لعن W subset من X hatإذا بدي أرمي عنصر ال X 
+
+363
+00:27:07,660 --> 00:27:13,160
+في وين في ال W ويكون ال W جزء من من X وكأنني بدي
+
+364
+00:27:13,160 --> 00:27:17,640
+أرميه في equivalency classes طيب، الآن كيف بدي
+
+365
+00:27:17,640 --> 00:27:22,140
+أعرفه طريقة بصراحة يعني رائعة معرفته إياها معرف لك
+
+366
+00:27:22,140 --> 00:27:27,940
+T of any element هنا بيساوي ال B hat طب كده الآن
+
+367
+00:27:27,940 --> 00:27:33,810
+أخذ لك اللي هو إنت بوهان عندي من X لعين W وجالك 
+
+368
+00:27:33,810 --> 00:27:38,410
+هذه W بتأخذها جزء من X هذه هتشوف كم جزء بدي أعرف 
+
+369
+00:27:38,410 --> 00:27:45,470
+لك T of B B المتنوين من X بيساوي الـ B hat طب كيف 
+
+370
+00:27:45,470 --> 00:27:49,350
+هذه الـ B hat عبارة عن equivalence classes صح ولا
+
+371
+00:27:49,350 --> 00:27:55,500
+لأ؟ الآن أيش قال لك أنا بدي آخذ اللي هو الـ B hat
+
+372
+00:27:55,500 --> 00:28:02,360
+اللي بدو يحدد هويتها هي ال sequence B وB وB وB وB
+
+373
+00:28:02,360 --> 00:28:02,840
+وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB
+
+374
+00:28:02,840 --> 00:28:03,960
+وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB
+
+375
+00:28:03,960 --> 00:28:04,180
+وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB
+
+376
+00:28:04,180 --> 00:28:07,540
+وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB
+
+377
+00:28:07,540 --> 00:28:09,560
+وB وB وB وB وB الآن هذه الـ Cauchy Sequence الـ
+
+378
+00:28:09,560 --> 00:28:13,660
+equivalence class لها هي اللي بيسميها أيش ماله؟ B 
+
+379
+00:28:13,660 --> 00:28:19,000
+hat وكل الـ sequences اللي related لها هيكون
+
+380
+00:28:19,000 --> 00:28:22,460
+موجودة في الـ B hat فلاحظوا إن كل عنصر من هان
+
+381
+00:28:22,460 --> 00:28:27,600
+وديته لعنصر اسم بيهتها، ماشي الحال، هذه اللي هي W
+
+382
+00:28:27,600 --> 00:28:33,050
+اللي بتديها جزء من X hat ولا لأ؟ أكيد جزء منها و W
+
+383
+00:28:33,050 --> 00:28:38,790
+في الواقع أنا ماخذها W هأخذها أنا هي عبارة عن T ل
+
+384
+00:28:38,790 --> 00:28:44,030
+X أنا هأخذها هيك يعني هأخذ ال W أيش بتعملها بتقول
+
+385
+00:28:44,030 --> 00:28:49,610
+T of X هي مين هي ال W هال جيت مش عارفة هال جيت T
+
+386
+00:28:49,610 --> 00:28:54,130
+من X لعنده لأ هال جيت عرفت هيك صح؟ عرفتها زهير لأن 
+
+387
+00:28:54,130 --> 00:28:58,030
+هدول موجودة وين في الـ Vها الآن مين اللي بديها 
+
+388
+00:28:58,030 --> 00:29:03,610
+يسميها W؟ بدي أسميها W هي صورة مين الـX إذا إذا 
+
+389
+00:29:03,610 --> 00:29:09,210
+الـW عرفتها أنا هي عبارة عن TX إذا صار الـT عدى 
+
+390
+00:29:09,210 --> 00:29:16,260
+automatic أنا وأنتوا أثبت إنه ايزومتري و أثبت إنه
+
+391
+00:29:16,260 --> 00:29:20,500
+ايزومتري خلص لأن ايزومتري يكون one to one فبيصير
+
+392
+00:29:20,500 --> 00:29:26,740
+عندي الآن T من X لعين W one to one on to function
+
+393
+00:29:26,740 --> 00:29:31,020
+which is ايزومتري إذا دل بس شغل أخرى إن أثبت W
+
+394
+00:29:31,020 --> 00:29:38,670
+closure بيساوي X hat طيب نشوف مع بعض الآن where T
+
+395
+00:29:38,670 --> 00:29:41,790
+بيساوي W بيساوي TX and for B element in X we
+
+396
+00:29:41,790 --> 00:29:45,030
+associate the class B hat element in X which
+
+397
+00:29:45,030 --> 00:29:48,910
+contains the constant Cauchy sequence BBB زي ما
+
+398
+00:29:48,910 --> 00:29:53,070
+حكيته لكم الآن for any A و B element in X hat
+
+399
+00:29:53,070 --> 00:29:57,910
+لاحظوا أن المسافة سهلة هذه بتنهي زيومتري D hat بين 
+
+400
+00:29:57,910 --> 00:30:03,270
+TA و TB بيساوي ال D hat بين A hat و B hat لأن TA
+
+401
+00:30:03,270 --> 00:30:08,350
+أنا هي سمتها A hat و TB أيش بيساوي B hatلكن هذه أيش
+
+402
+00:30:08,350 --> 00:30:12,430
+بتساوي؟ limit للـ distance بين اللي هي الـ Cauchy
+
+403
+00:30:12,430 --> 00:30:15,470
+Sequences اللي فيها من الـ Cauchy Sequences اللي
+
+404
+00:30:15,470 --> 00:30:18,090
+فيها اللي أنا اصلا ركبت هنا عليها اللي هي الـ 
+
+405
+00:30:18,090 --> 00:30:21,230
+constant sequence الـ a, a, a إذا الـ limit للـ d,
+
+406
+00:30:21,310 --> 00:30:24,690
+a ونفس الشيء هدمين اللي هو الـ sequence b, b, b
+
+407
+00:30:24,690 --> 00:30:27,990
+اللي هي d ال distance بين a و b و ال limit اللي 
+
+408
+00:30:27,990 --> 00:30:30,950
+هنا as n goes to infinity اصلا ثبتت هنا بيساوي d, a 
+
+409
+00:30:30,950 --> 00:30:31,290
+و b
+
+410
+00:30:35,330 --> 00:30:40,770
+إذا صار عندي isometry و on to function دل علي بس 
+
+411
+00:30:40,770 --> 00:30:46,730
+أثبت إن الـ W closure بيساوي مين ال X هت however 
+
+412
+00:30:46,730 --> 00:30:51,010
+any isometry is one to one then X and W are
+
+413
+00:30:51,010 --> 00:30:56,570
+isometric we show that W closure بيساوي مين X هت
+
+414
+00:31:01,130 --> 00:31:06,170
+الآن الـ W و الـ W closure أي إن كان ال subset من
+
+415
+00:31:06,170 --> 00:31:09,370
+مين من ال X hat إذا بدي أثبت ال X hat subset من
+
+416
+00:31:09,370 --> 00:31:14,450
+مين من ال W closure يعني بدي آخذ X hat element in 
+
+417
+00:31:14,450 --> 00:31:19,570
+X hat capital و أثبت لك إن ال X hat وين موجودة في
+
+418
+00:31:19,570 --> 00:31:26,630
+ال W closure ماشي الحال؟ طيب الآن عندي
+
+419
+00:31:33,000 --> 00:31:39,360
+متى الـ except في الـ W closure إن لو أخدت أي open
+
+420
+00:31:39,360 --> 00:31:45,930
+ball حوالين ال X hat أي open ball حوالين ال X hat 
+
+421
+00:31:45,930 --> 00:31:51,210
+لازم تتقاطع مع مبتع الأقل من مين؟ من الـ W يعني بمعنى
+
+422
+00:31:51,210 --> 00:31:56,030
+آخر أخد أي ball اللي هو centerها اللي هو X hat ولا
+
+423
+00:31:56,030 --> 00:32:00,830
+أي Y في الدنيا تقطعها مع الـ W أيش معله؟ له يساوي
+
+424
+00:32:00,830 --> 00:32:04,490
+Phi هي اللي بدثبته، بكون خلصت، شوفوا مع بعض، شوفوا
+
+425
+00:32:04,490 --> 00:32:11,790
+الآن We show that W closure is equal to X hat Let X
+
+426
+00:32:11,790 --> 00:32:14,550
+hat element in X hat capital and Xn element in
+
+427
+00:32:14,550 --> 00:32:20,750
+mean in X hat ماشي الحال ملام Xn element in X hat
+
+428
+00:32:20,750 --> 00:32:24,550
+إذا Xn كوشي سيكوينس أكيد كوشي سيكوينس إذا for
+
+429
+00:32:24,550 --> 00:32:28,490
+every Y أكبر من 0 there exists K element in N such
+
+430
+00:32:28,490 --> 00:32:34,870
+that المسافة بين Xn وXk أشمالها أصغر من Y على 2الـ
+
+431
+00:32:34,870 --> 00:32:41,310
+N for all N أكبر من K هذا صحيح الـ N أكبر أو يساوي
+
+432
+00:32:41,310 --> 00:32:46,500
+حتى عشان بتستخدمها أكبر أو يساوي من Kالآن خُدلي
+
+433
+00:32:46,500 --> 00:32:52,880
+الـ sequence xk xk xk الأخيرة أكيد موجودة خارج
+
+434
+00:32:52,880 --> 00:32:56,880
+معناه أدنال أكيد موجودة في مين في الـ xk hat
+
+435
+00:32:56,880 --> 00:32:59,700
+لإن هذه عبارة عن كوشي sequence هذا أخدت الـ xk
+
+436
+00:32:59,700 --> 00:33:03,720
+council يعني اسمه council xk xk xk هذه الكوشي
+
+437
+00:33:03,720 --> 00:33:05,960
+sequence هذه الكوشي sequence موجودة في ال
+
+438
+00:33:05,960 --> 00:33:10,870
+equivalency class سبعتها لـ xk hatإذا XK هتأكيد
+
+439
+00:33:10,870 --> 00:33:14,790
+وين موجودة؟ في الـW لأن الـW هيك اتركبت علي هيك
+
+440
+00:33:14,790 --> 00:33:18,990
+تربط تركبت هذه الـN هذه الـN هي اللي هيلاجيها
+
+441
+00:33:18,990 --> 00:33:24,450
+مشتركة بين الجهتين السر هنا أن المسافة بين XN و XK
+
+442
+00:33:24,450 --> 00:33:27,450
+أصغر من 1 على 2 و يشاوز 1 على 2 لكل N أكبر سواء
+
+443
+00:33:27,450 --> 00:33:33,650
+مين؟ K هذه الـXK هي اللي لاجيتها هنا دير بالكم طيب
+
+444
+00:33:33,650 --> 00:33:38,530
+شوفوا الآنبعيد 2 من اللي قبل بشوية المسافة بين x
+
+445
+00:33:38,530 --> 00:33:42,230
+hat و xk hat أيش بساوي ال limit لل sequence
+
+446
+00:33:42,230 --> 00:33:45,850
+اللي موجودة هنا اسمها xn صح؟ ولل sequence اللي
+
+447
+00:33:45,850 --> 00:33:50,790
+موجودة هنا اللي هي xk xk xk xk xk as n goes to
+
+448
+00:33:50,790 --> 00:33:55,160
+infinityهذه أصلاً أصغر من مين من إبسيلون على اتنين
+
+449
+00:33:55,160 --> 00:34:00,200
+صح لكل اذا اذا انا بصي infinity هذه هتبقى المسافة
+
+450
+00:34:00,200 --> 00:34:03,660
+بين هذه اللي قلتلها أصغر أو يساوي هياش بيصير أصغر
+
+451
+00:34:03,660 --> 00:34:06,560
+أو يساوي مين اتنين اللي هي أصغر من مين من إبسيلون
+
+452
+00:34:06,560 --> 00:34:11,360
+إذا صارت هذه وهذه أصغر من مين من إبسيلون يعني بمعنى
+
+453
+00:34:11,360 --> 00:34:16,380
+أخر في أي إبسيلون في الدنيا طلعت ال XK hat موجودة
+
+454
+00:34:16,380 --> 00:34:21,250
+في الـ ballاللي بين .. اللي هي مركزها X hat ونصف
+
+455
+00:34:21,250 --> 00:34:25,570
+قطرها Y وهي في الأصل الـ X K hat اللي موجودة في
+
+456
+00:34:25,570 --> 00:34:29,750
+الـ W إذا صارت عند الـ ball X hat وY تقاطع و W ليه
+
+457
+00:34:29,750 --> 00:34:34,830
+سوى 5 4 O وY أكبر من 0 إذا صار عندي اللي هو لجينا
+
+458
+00:34:34,830 --> 00:34:39,550
+ال X hat لازم تكون في الـ W closure والآن صارت عند
+
+459
+00:34:39,550 --> 00:34:43,710
+ال X hat جزء من الـ W closure وW closure طبيعي جزء
+
+460
+00:34:43,710 --> 00:34:46,850
+منها إذا صار الحدث تتمين المساواة وهو المطلوب
+
+461
+00:34:49,140 --> 00:34:54,060
+النظرية غزيرة بالمعلومات عشان هيك انا معنى ان
+
+462
+00:34:54,060 --> 00:34:59,700
+ابرهنها طيب اللي بعدها proving the completeness of
+
+463
+00:34:59,700 --> 00:35:04,520
+X hat الآن بدي أركز فيها دي عشان شوية رموز بتلخمكم
+
+464
+00:35:04,520 --> 00:35:08,760
+شوية بضح إن شاء الله بدي اثبت انه اللي هو ال X hat
+
+465
+00:35:08,760 --> 00:35:11,560
+أيش معله complete كيف اثبت انه complete باخد كوشي
+
+466
+00:35:11,560 --> 00:35:18,220
+سيكوانس فيها بدي اسميها X unhatكوشي سيكوانس وين ال
+
+467
+00:35:18,220 --> 00:35:23,920
+X hat وبدأ اثبت لكم ان X un hat هذه لازم تكون
+
+468
+00:35:23,920 --> 00:35:29,630
+convention صميم X برضه موجودة في ال X hatتنسوش ان
+
+469
+00:35:29,630 --> 00:35:34,430
+X1 هات و X2 هات و X3 هات و X4 هات كلهين اصلا
+
+470
+00:35:34,430 --> 00:35:37,190
+equivalency classes يعني كل واحدة فيه في داخلها
+
+471
+00:35:37,190 --> 00:35:42,450
+مين عبارة عن sequences ماشي طيب بدنا نثبت ان
+
+472
+00:35:42,450 --> 00:35:46,750
+الكوشي سيكوانس هذا converse جوا في ال X هات let X
+
+473
+00:35:46,750 --> 00:35:51,520
+انهات بيان الكوشي سيكوانس ال X هاتSince W closure
+
+474
+00:35:51,520 --> 00:35:55,940
+بيساوي X hat لقبل بشوية W closure أيش بيساوي X hat
+
+475
+00:35:55,940 --> 00:35:59,560
+W متوال اللي بنحكي عنها اللي عناصرها بيهات بيهات و
+
+476
+00:35:59,560 --> 00:36:04,300
+إيهات و كده بحيث ان بيهات تحدد من بي بي بي بي as a
+
+477
+00:36:04,300 --> 00:36:09,460
+sequence then for all X unhat element in X hat
+
+478
+00:36:10,850 --> 00:36:16,230
+There is الـ Zn hat element of W such that
+
+479
+00:36:16,230 --> 00:36:20,230
+المسافة بين X N hat و Z N hat أشمالها أصغر من مين
+
+480
+00:36:20,230 --> 00:36:25,810
+من واحد على N لأنه أشمالها لأن الـ W dense في مين؟
+
+481
+00:36:25,810 --> 00:36:29,290
+في الـ X hat فأي element في الـ X hat بلا جيله
+
+482
+00:36:29,290 --> 00:36:33,280
+element هنااللي هو المسافة بينه وبين هذا أصغر من
+
+483
+00:36:33,280 --> 00:36:37,740
+مين من واحد على أن أي ball بالنصف قطر واحد على أن
+
+484
+00:36:37,740 --> 00:36:42,780
+حلاجي اللي هو الموجود
+
+485
+00:36:42,780 --> 00:36:48,340
+فيه عنصر اللي هو في الـZn مشترك في الـW في الـW
+
+486
+00:36:48,340 --> 00:36:53,260
+أسف مشترك بين الـW وبين هذه ال ball يعني بمعنى أخر
+
+487
+00:36:53,260 --> 00:36:57,700
+المسافة بينه بين Xn وZn أصغر من مين من واحد على أن
+
+488
+00:36:57,700 --> 00:37:06,500
+واضحطيب إذا الان خدلي المسافة بين ZM hat و ZN hat
+
+489
+00:37:06,500 --> 00:37:12,980
+لأي M و N اللي هو أصغر أو يساوي اللي هو D hat ZM
+
+490
+00:37:12,980 --> 00:37:19,780
+hat و XM hat زائد D hat XM hat و XN hat تبين ال
+
+491
+00:37:19,780 --> 00:37:24,460
+equality زائد D hat XM hat و ZM hat و ZN hat الآن
+
+492
+00:37:24,460 --> 00:37:31,420
+في اللي فوق لأي XM hat و XM hat ملاجئ ZM hatلـ X M
+
+493
+00:37:31,420 --> 00:37:36,320
+HAT في الـ X HAT نلاقي الـ Z M HAT واضح؟ وهي كذا
+
+494
+00:37:36,320 --> 00:37:39,920
+اللي هو بحيث أنه المسافة أصغر من واحدة لـ M أو
+
+495
+00:37:39,920 --> 00:37:43,480
+المسافة أصغر واحدة لـ M حسب ما سميها أنا متفجين؟
+
+496
+00:37:43,480 --> 00:37:48,090
+هذا الكلام لـ ANطيب أو لأي element x and hat بلاقي
+
+497
+00:37:48,090 --> 00:37:51,610
+اللي هو element z and hat اسمه x and hat أو x and
+
+498
+00:37:51,610 --> 00:37:56,070
+hat أو اللي بدكميه صار عندى الان المسافة بين z and
+
+499
+00:37:56,070 --> 00:38:00,750
+hat و z and hat أصغر و أصغر وهذه زائد هذه زائد هذه
+
+500
+00:38:00,750 --> 00:38:04,550
+هذه حسب الحديث اللي فوق حسب الحديث اللي فوق هذه
+
+501
+00:38:04,550 --> 00:38:09,450
+أشمالها أصغر من واحدة لأن وهذه بنزلها زي ما هي x
+
+502
+00:38:09,450 --> 00:38:13,330
+and hat وx and hat وهذه أصغر من نيل من واحدة لأن
+
+503
+00:38:13,870 --> 00:38:20,270
+لكن أنا ناخد الـ Xm هادهات مادام كوشي سيكوانس
+
+504
+00:38:20,270 --> 00:38:22,450
+مادام كوشي سيكوانس مادام كوشي سيكوانس مادام كوشي
+
+505
+00:38:22,450 --> 00:38:23,610
+سيكوانس مادام كوشي سيكوانس مادام كوشي سيكوانس
+
+506
+00:38:23,610 --> 00:38:24,590
+مادام كوشي سيكوانس مادام كوشي سيكوانس مادام كوشي
+
+507
+00:38:24,590 --> 00:38:25,370
+سيكوانس مادام كوشي سيكوانس مادام كوشي سيكوانس
+
+508
+00:38:25,370 --> 00:38:28,850
+مادام كوشي سيكوانس مادام كوشي سيكوانس مادام كوشي
+
+509
+00:38:28,850 --> 00:38:34,370
+سيكوانس مادام كوشي سيكوانس مادام كوشي سيكوانس ماد
+
+510
+00:38:34,390 --> 00:38:38,050
+However, Xn hat is a Cauchy sequence، إذًا for
+
+511
+00:38:38,050 --> 00:38:42,230
+every Y أكبر من 0، there exists K such that 1 على
+
+512
+00:38:42,230 --> 00:38:48,490
+M زائد هذا المسافة زائد 1 على M أصغر من إبسيلون هذا
+
+513
+00:38:48,490 --> 00:38:53,630
+أيش معناته؟ معناته صارت هذه الآن أصغر من أي إبسيلون
+
+514
+00:38:53,630 --> 00:38:59,190
+في الدنياكل Y أكبر من 0 للي جيت K بحيث لكل N و M
+
+515
+00:38:59,190 --> 00:39:03,850
+أكبر من K المسافة أصغر من مين من Y يعني بمعنى أخر
+
+516
+00:39:03,850 --> 00:39:07,570
+هذه اللي اللي جيتها اللي كل مرة بلاقي اللي هو
+
+517
+00:39:07,570 --> 00:39:13,610
+إليها ZN hat للي هي X1 hat بلاقي Z1 hat ل X2 hat
+
+518
+00:39:13,610 --> 00:39:17,110
+بلاقي Z2 hat ال sequence هذه اللي اللي جيتها اللي
+
+519
+00:39:17,110 --> 00:39:22,410
+هي ZN ZN hat هذه ال sequence اتمتعت بخاصية نقاش
+
+520
+00:39:22,410 --> 00:39:28,040
+Sequencetherefore z unhat is a Cauchy sequence أي
+
+521
+00:39:28,040 --> 00:39:32,720
+سؤال طيب الآن اطلع على فوق خليها في الذاكرة إذا
+
+522
+00:39:32,720 --> 00:39:40,480
+هذه الآن أنا حصلت على ال z unhat ال z unhat حصلت
+
+523
+00:39:40,480 --> 00:39:47,180
+عليها ال z unhat Cauchy sequence خليها في الذاكرة
+
+524
+00:39:47,180 --> 00:39:51,620
+أنا هساخدمها طيب
+
+525
+00:39:53,440 --> 00:39:58,960
+الآن since T من X لعن W إذا كان I جيومتريمظبوط و
+
+526
+00:39:58,960 --> 00:40:04,920
+الـ Z M hat element من الـ W ليش Z M hat element
+
+527
+00:40:04,920 --> 00:40:10,040
+من الـ W لأن فيها اللي هي عندي اللي هي اللي أنا
+
+528
+00:40:10,040 --> 00:40:14,120
+جاتهم ال sequence دي اللي ركّبتها مالها من ال W
+
+529
+00:40:14,120 --> 00:40:18,280
+أصلا ماشي طيب شوفوا صلى على النبي عليه الصلاة
+
+530
+00:40:18,280 --> 00:40:23,360
+والسلام الآن ال sequence Z M hat element من ال W
+
+531
+00:40:23,360 --> 00:40:28,220
+كل واحدة فيه element من ال W إذا ال sequence Z MZM
+
+532
+00:40:28,220 --> 00:40:32,940
+اللي هي موجودة في الـ ZM هات لإن الـ WH مكوّنة
+
+533
+00:40:32,940 --> 00:40:37,440
+مكوّنة اللي هو من اللي هي اللي هي ال equivalency
+
+534
+00:40:37,440 --> 00:40:44,480
+classes اللي هويتها A,A,A,A,A أو B,B,B أو ZM اللي
+
+535
+00:40:44,480 --> 00:40:52,740
+هي ZM,ZM,ZM ماشي الحال الآن بتاخد واحد منهم وعمل
+
+536
+00:40:52,740 --> 00:40:57,660
+منه sequence H مالهازد ام ماشي الحال الان زد ام
+
+537
+00:40:57,660 --> 00:40:59,960
+يعني زد واحد ده اخدوا زد اتنين زد تلتة زد اربعة
+
+538
+00:40:59,960 --> 00:41:04,380
+إلى آخره الآن where زد ام أيش بساوي اللي كيف اللي
+
+539
+00:41:04,380 --> 00:41:10,660
+بدي أركبه بادي أنا عندي أنا T من X لعند Y اتفجنا
+
+540
+00:41:10,660 --> 00:41:17,850
+انه T من X لعند W عيزومترعندى one to one لونتو او
+
+541
+00:41:17,850 --> 00:41:19,030
+أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو
+
+542
+00:41:19,030 --> 00:41:19,530
+أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو
+
+543
+00:41:19,530 --> 00:41:21,790
+أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو
+
+544
+00:41:21,790 --> 00:41:29,190
+أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو
+
+545
+00:41:29,190 --> 00:41:32,610
+أو أو أو الـ T inverse اللي هو موجودة لان وانتوا
+
+546
+00:41:32,610 --> 00:41:38,670
+هم نونتو فانكشن الـ T inverse لـ ZM hat هو الوين
+
+547
+00:41:38,670 --> 00:41:44,970
+وين هيكون flex سمونيها ZM إذا صارت الـ ZM هذه
+
+548
+00:41:44,970 --> 00:41:49,530
+عبارة عن sequence وين موجودة؟ هنا وهذه كوشي إذا
+
+549
+00:41:49,530 --> 00:41:51,990
+اللي هي و preserve distances إذا هتكون هذه برضه
+
+550
+00:41:51,990 --> 00:41:56,580
+أشمالها برضه كوشيمعايا الـ isometric من جل الكوشي
+
+551
+00:41:56,580 --> 00:42:00,020
+لكوشي وبرجع بالكوشي لكوشي ماشي الحال و أثمانه مش
+
+552
+00:42:00,020 --> 00:42:03,240
+صعب لأنه preserve distances هذا اللي بيبقى لها لكم
+
+553
+00:42:03,240 --> 00:42:08,020
+أنه لو كانت اللي هي اللي هنا كوشي sequence هترجع
+
+554
+00:42:08,020 --> 00:42:12,560
+لكوشي ولو كانت كوشي بتروح لكوشي مادام الـ T is
+
+555
+00:42:12,560 --> 00:42:18,920
+isometricو onto طيب صلى على النبي عليه الصلاة
+
+556
+00:42:18,920 --> 00:42:22,440
+والسلام إذا صارت ZM بتساوي T inverse ZM hat is a
+
+557
+00:42:22,440 --> 00:42:28,540
+Cauchy sequence inمين؟ in X الآن شوف كيف بده يركب
+
+558
+00:42:28,540 --> 00:42:34,240
+ال X hat احنا ليش غربنا احنا غربنا انه ناخد اللي
+
+559
+00:42:34,240 --> 00:42:42,620
+هو X M hat هيك عملنا Cauchy sequenceونوصل ال X hat
+
+560
+00:42:42,620 --> 00:42:47,520
+ونوصل إنه في X hat اسمه ال element ال X hat
+
+561
+00:42:47,520 --> 00:42:52,640
+capital such that X unhat converts to X hat
+
+562
+00:42:52,640 --> 00:42:56,560
+شوفوا الآن كيف يتركب لكم الـ X hat اللي هخل الـ X
+
+563
+00:42:56,560 --> 00:43:01,080
+unhat الأصلي تروح to X hat هذه ماشي؟ طيب شوف
+
+564
+00:43:01,080 --> 00:43:07,760
+let X hat element of X كيف يتركبها؟الان let X hat
+
+565
+00:43:07,760 --> 00:43:14,420
+element in X and Z M hat element in X hat صح؟
+
+566
+00:43:14,420 --> 00:43:20,120
+صح؟ ليش Z M element in X hat؟ لأنه الآن الـ Z الـ
+
+567
+00:43:20,120 --> 00:43:25,400
+Z و الـ Z الـ Z M في الأصل من وين جاية؟الاصل ZM من
+
+568
+00:43:25,400 --> 00:43:28,420
+وين جاية؟ ZM hat من وين جاية؟ ZM hat من وين جاية؟
+
+569
+00:43:28,420 --> 00:43:29,560
+ZM hat من وين جاية؟ ZM hat من وين جاية؟ ZM hat من
+
+570
+00:43:29,560 --> 00:43:30,060
+وين جاية؟ ZM hat من وين جاية؟ ZM hat من وين جاية؟
+
+571
+00:43:30,060 --> 00:43:30,200
+ZM hat من وين جاية؟ ZM hat من وين جاية؟ ZM hat من
+
+572
+00:43:30,200 --> 00:43:32,580
+وين جاية؟ ZM hat من وين جاية؟ ZM hat من وين جاية؟
+
+573
+00:43:32,580 --> 00:43:36,040
+ZM
+
+574
+00:43:36,040 --> 00:43:40,000
+hat من وين جاية؟ ZM hat من وين جاية؟ ZM hat من وين
+
+575
+00:43:40,000 --> 00:43:45,380
+جاية؟ ZM
+
+576
+00:43:45,380 --> 00:43:49,520
+hat من وين جاية؟من الـ W واضح كيف اتكونت الآن الـ
+
+577
+00:43:49,520 --> 00:43:53,560
+ZM الـ X hat الـ X hat تكونت من الـ Cauchy
+
+578
+00:43:53,560 --> 00:43:56,320
+sequence يعني عبارة عن الـ equivalence class لهذه
+
+579
+00:43:56,320 --> 00:43:59,320
+الـ Cauchy sequence الـ Cauchy sequence هذه اتكونت
+
+580
+00:43:59,320 --> 00:44:02,880
+من الاصل لـ T inverse الـ ZM hat اللي ZM hat من
+
+581
+00:44:02,880 --> 00:44:08,860
+مين كانت من الـ W خلوها في الذاكرة طيب إذا ال
+
+582
+00:44:08,860 --> 00:44:13,300
+distance بين الـ X un hat و الـ X hat أبدا يتفرج
+
+583
+00:44:13,300 --> 00:44:17,440
+على الـ Y و بيكون خلصةانت فاقتت ان الـ Limit لهذه
+
+584
+00:44:17,440 --> 00:44:21,700
+اللي هو الـ Distance بينها أصغر من Y ممكن خلصت اه
+
+585
+00:44:21,700 --> 00:44:27,020
+الآن أصغر أوي سوى X unhat و Z unhat زاد Z unhat و
+
+586
+00:44:27,020 --> 00:44:30,980
+مين و X hat X unhat و Z unhat تتقبل بشوية عشان
+
+587
+00:44:30,980 --> 00:44:34,820
+عاملنا unhat ولا أصغر من مين من واحدة لأن وهذه Z
+
+588
+00:44:34,820 --> 00:44:40,640
+unhat و X hat أيش معنى؟ زي ما هي الآن عندي الـ Z
+
+589
+00:44:40,640 --> 00:44:46,630
+أموال موجودة في الـ X hat مظبوط ولا لأ؟و الـ ZN hat
+
+590
+00:44:46,630 --> 00:44:51,450
+هو الموجودة في الـ W إذا أكيد الـ ZN و الـ ZN و
+
+591
+00:44:51,450 --> 00:44:57,060
+الـ ZN و الـ ZN هو الموجودة في الـ ZN main hatالان
+
+592
+00:44:57,060 --> 00:45:00,780
+تلاتة بتسير اللي عندى تلاتة هدى بتسير الـ distance
+
+593
+00:45:00,780 --> 00:45:04,640
+بين الـ X hat والـ X hat أصغر من واحد على N زائد
+
+594
+00:45:04,640 --> 00:45:09,860
+هدى اللي هي limit limit لـ sequence من هنا و
+
+595
+00:45:09,860 --> 00:45:13,620
+sequence من هنا الـ sequence من هنا اللي هي ZN ماشي
+
+596
+00:45:13,620 --> 00:45:21,280
+الحال اللي هي عندى ZN ZN ZN ZNأو الـ X hat اللي هي
+
+597
+00:45:21,280 --> 00:45:25,020
+من وين جاية من الـ sequence ZM اللي هي distance
+
+598
+00:45:25,020 --> 00:45:30,000
+بين XN ومين وZM و as N goes to infinity اللي عندي
+
+599
+00:45:30,000 --> 00:45:34,600
+طبعا ZM كوش الـ sequence كلها كوش الـ sequence فال
+
+600
+00:45:34,600 --> 00:45:38,700
+limit لهذه as N goes to infinity طبعا for M أكبر
+
+601
+00:45:38,700 --> 00:45:42,600
+من N بتصير عندي اللي هي هذه بقيت أه زغيرها أه
+
+602
+00:45:42,600 --> 00:45:45,510
+أصغرها Y في الدنياوهذه أزن قصون فيها أصغر من
+
+603
+00:45:45,510 --> 00:45:48,950
+إبسلون في الدنيا إذا دي x unhat وx hat اللي هي
+
+604
+00:45:48,950 --> 00:45:54,490
+أصغر من إبسلون إذا صارت الـ x unhat then for
+
+605
+00:45:54,490 --> 00:45:56,730
+sufficiently for every إبسلون there exists k
+
+606
+00:45:56,730 --> 00:45:59,070
+sufficiently large such that for all أكبر من k ده
+
+607
+00:45:59,070 --> 00:46:01,790
+اللي حكيته المسافة بين هذه و هذه بتكون أصغر من
+
+608
+00:46:01,790 --> 00:46:04,370
+إبسلون إذا صارت الـ x unhat converged to x hat in
+
+609
+00:46:04,370 --> 00:46:10,990
+x therefore x hat is a complete metric space
+
+610
+00:46:19,200 --> 00:46:27,320
+طيب نسرعه الجزء الأخير الجزء الأخير proving the
+
+611
+00:46:27,320 --> 00:46:30,620
+uniqueness of X hat except for isometries خلّيني
+
+612
+00:46:30,620 --> 00:46:36,520
+أركز طويل شوية هذا بس مش صعببدنا نثبت اللي هو الـ
+
+613
+00:46:36,520 --> 00:46:40,240
+uniqueness يعني بمعنى اخر نفترض X ده و D ده ده
+
+614
+00:46:40,240 --> 00:46:45,960
+بنفس مواصفات X hat و D hat
+
+615
+00:46:45,960 --> 00:46:51,100
+و نثبت إن هدول التنين are isometric اللي هو فيه
+
+616
+00:46:51,100 --> 00:46:55,720
+one to one, one to one function بينهم شوفوا
+
+617
+00:46:55,720 --> 00:46:58,680
+Proving the uniqueness of X hat except for
+
+618
+00:46:58,680 --> 00:47:02,220
+isometries يعني اللي بده يعمل زي هيك يكون
+
+619
+00:47:02,220 --> 00:47:08,460
+isometric لهلت X hat و D hat ب another complete
+
+620
+00:47:08,460 --> 00:47:13,000
+metric space واحد تاني completion تاني with a
+
+621
+00:47:13,000 --> 00:47:17,060
+subspace W بنفس المواصفات W tilde دي نصف مين في ال
+
+622
+00:47:17,060 --> 00:47:23,040
+X hat يعني ان انا جيبنا X tilde وD tilde قولنا هذا
+
+623
+00:47:23,040 --> 00:47:28,360
+complete metric space وفي داخله W tilde subset من X
+
+624
+00:47:28,360 --> 00:47:49,840
+tilde حيثحيث و closure بسوء مين اللي هو x tilde عشان
+
+625
+00:47:49,840 --> 00:47:56,960
+نفس المواصفات و tilde ايش ما لهااللي هو فيه عيزومتري
+
+626
+00:47:56,960 --> 00:48:03,800
+بينها عيزومتريك خلّيني أقول معين مع ال X فرضنا هذه
+
+627
+00:48:03,800 --> 00:48:08,260
+كلها وعندنا في الأصل اللي هو طبعنا هذا اللي عملناه
+
+628
+00:48:08,260 --> 00:48:13,460
+ال construction قبل شوية اللي هو W تبعته subset من
+
+629
+00:48:13,460 --> 00:48:19,180
+X hat و W closure بسوء X hat و اللي هي W اللي هي
+
+630
+00:48:19,180 --> 00:48:25,400
+عيزومتريكلمن؟ لـ X بدأ أثبت لك الآن أن الجديد هذا
+
+631
+00:48:25,400 --> 00:48:29,460
+لازم يكون بين هذا وبين هذا أيش فيه؟ عيزومتري بيكون
+
+632
+00:48:29,460 --> 00:48:34,560
+اللي هو يعني بمعنى أخر نفسه اللي هو بس اختلفت
+
+633
+00:48:34,560 --> 00:48:39,240
+الأسماء let X tilde وB tilde وD tilde be another
+
+634
+00:48:39,240 --> 00:48:42,020
+complete metric space with a subspace tilde and
+
+635
+00:48:42,020 --> 00:48:44,980
+عيزومتر tilde then for any X tilde وY tilde element in
+
+636
+00:48:44,980 --> 00:48:45,760
+X tilde
+
+637
+00:48:48,890 --> 00:48:54,430
+Xn tilde سيكوانس وهو احنا بنعرف Y وW tilde ايش ماله
+
+638
+00:48:54,430 --> 00:49:01,030
+اللي هو dense المين X tilde مادام dense وهذه X tilde
+
+639
+00:49:01,030 --> 00:49:04,770
+وY tilde موجودة هنا اذا اكيد في sequence of points
+
+640
+00:49:04,770 --> 00:49:08,950
+converge لهذه وsequence of points converge لهذه من
+
+641
+00:49:08,950 --> 00:49:14,670
+تعريف مين اللي هو ال closure عندى اللي هو هذه ال
+
+642
+00:49:14,670 --> 00:49:19,680
+dense من تعريف انه dense هذه denseانتبهوا هذه
+
+643
+00:49:19,680 --> 00:49:25,160
+dense ان هذه إذا لأي element هنا بقدر ألاقي
+
+644
+00:49:25,160 --> 00:49:29,460
+sequence من هنا converge zero لما يكون يا جماعة
+
+645
+00:49:29,460 --> 00:49:35,400
+الآن أي حاجة في الدنيا y closure اللي هو بيساوي x
+
+646
+00:49:35,400 --> 00:49:41,530
+مثلاو جيت أخدت أي مُخطأ x في الـ x الهادى بقدر
+
+647
+00:49:41,530 --> 00:49:48,090
+ألاقي sequence xn in y such that xn converge لمين
+
+648
+00:49:48,090 --> 00:49:52,390
+للx اللي هو في كل .. لكل واحد .. لكل n بقدر ألاقي
+
+649
+00:49:52,390 --> 00:49:55,950
+ball .. ball المسافة بينهم أصغر من واحد، أصغر من
+
+650
+00:49:55,950 --> 00:49:58,770
+نص، أصغر من تلت، أصغر من كده، بلاقي x واحد أصغر من
+
+651
+00:49:58,770 --> 00:50:04,050
+واحد، x اتنين .. يعني ال .. فاهمين علشه بحكيه؟هذا
+
+652
+00:50:04,050 --> 00:50:09,250
+الكلام معروف إذا لـ gate sequences XN tilde و YN
+
+653
+00:50:09,250 --> 00:50:12,670
+tilde موجودة في الـ W tilde كل واحدة منهم بتروح
+
+654
+00:50:12,670 --> 00:50:19,050
+واحدة لل X واحدة بتروح لمين لل Y tildeSuch that X
+
+655
+00:50:19,050 --> 00:50:22,590
+and tilde تقوم بالإعادة للـ X tilde و Y tilde تقوم
+
+656
+00:50:22,590 --> 00:50:29,770
+بالإعادة للـ Y As in A فوق و
+
+657
+00:50:29,770 --> 00:50:34,890
+نشهد أن الـ absolute value للمسافة بين X tilde و Y
+
+658
+00:50:34,890 --> 00:50:38,370
+tilde نقص المسافة tilde بين X and tilde و Y and tilde
+
+659
+00:50:38,370 --> 00:50:41,550
+أصغر أو سوى اللي هي بالتباين triangle inequality زي ما
+
+660
+00:50:41,550 --> 00:50:46,610
+عملنا قبل شوية X tilde و X and tilde زائد Y tilde و Y
+
+661
+00:50:46,610 --> 00:50:50,620
+and tildeالآن هذه converts صح ولا لأ هذه converts
+
+662
+00:50:50,620 --> 00:50:54,260
+لهذه إذا هذه بتروح للصفر وهذه converts لهذه إذا
+
+663
+00:50:54,260 --> 00:50:58,540
+هذه بتروح للصفر إذا كل هذا هيروح لمين للصفر إذا
+
+664
+00:50:58,540 --> 00:51:03,680
+المقدار هذا هيروح للصفر إذا وكأنه limit هذا هو هذا
+
+665
+00:51:03,680 --> 00:51:09,420
+فبصير D tilde لان X tilde وY tilde بساوة limit D tilde
+
+666
+00:51:09,420 --> 00:51:14,940
+Xn tilde وYn tilde إذا صار عندي اللي هو ال limit هذا
+
+667
+00:51:14,940 --> 00:51:20,720
+بساوة هذاماشي الحال خلّيها ده برضه عندك الان صار
+
+668
+00:51:20,720 --> 00:51:27,140
+عيدي المسافة المسافة بين نقطتين ان تستمتعي مش اللي
+
+669
+00:51:27,140 --> 00:51:33,060
+صار المسافة بين أي نقطين Y tildeأو X tilde و Y tilde هو
+
+670
+00:51:33,060 --> 00:51:36,360
+الموجودة في الـ X tilde أخدتها النقطتين أبتكرانها
+
+671
+00:51:36,360 --> 00:51:41,580
+لجيه من المسافة بينهم بقدر أقول بتساوي ال limit لل
+
+672
+00:51:41,580 --> 00:51:49,480
+D tilde لل X N tilde و Y N tilde as N goes to mean to
+
+673
+00:51:49,480 --> 00:51:55,140
+infinity حيث ال X N tilde و Y N tilde جايات من وين من
+
+674
+00:51:55,140 --> 00:51:57,900
+ال W طيب
+
+675
+00:52:00,450 --> 00:52:07,810
+ماشي حالي الان لل T الان من W تلقاه W اللي هي W
+
+676
+00:52:07,810 --> 00:52:12,570
+subset من ال Xات اللي أصلي اللي ركبناهابـ
+
+677
+00:52:12,570 --> 00:52:15,630
+Abjection Isometry بقدر أقول هيك أه ما أحنا إيش
+
+678
+00:52:15,630 --> 00:52:20,690
+مفترضين ما أحنا مفترضين و tilde dense في ال X
+
+679
+00:52:20,690 --> 00:52:25,570
+عيزومتريك لل X و مفترضين إن و عيزومتريك لل X إذا و
+
+680
+00:52:25,570 --> 00:52:30,530
+tilde و و أشمالين are isometric طيب إذا صارت عندي
+
+681
+00:52:30,530 --> 00:52:36,290
+اللي هو بقدر أقول نفترض إن T من و tilde لW سبس من X
+
+682
+00:52:36,290 --> 00:52:41,930
+hat is Abjection Isometryالان بما ان X tilde ده و
+
+683
+00:52:41,930 --> 00:52:45,750
+Y tilde ده كوشي سيكوانسيز converge اصلا هنا لكن
+
+684
+00:52:45,750 --> 00:52:50,370
+هنا كوشي سيكوانسيز وين في الـ W هي converge وين؟
+
+685
+00:52:50,370 --> 00:52:54,410
+في الـ X tilde converge في ال X tilde لأن ال limit
+
+686
+00:52:54,410 --> 00:52:58,930
+هنا وين موجودة؟ في ال X tilde لكن هنا هما نفس
+
+687
+00:52:58,930 --> 00:53:03,270
+الموجودات في الـ W tilde فهنا في الواقع بقدر اكد ان
+
+688
+00:53:03,270 --> 00:53:07,230
+هنا كوشي سيكوانسيز بس في الـ W tilde اذا صار عندى
+
+689
+00:53:07,230 --> 00:53:15,050
+الانكوشي سيكوانسي و W tilde تتعامل مع X tilde و Y
+
+690
+00:53:15,050 --> 00:53:20,130
+tilde في X tilde وY tilde في X tilde وY tilde في X tilde
+
+691
+00:53:20,130 --> 00:53:20,770
+وY tilde في X tilde وY tilde في X tilde وY tilde في X
+
+692
+00:53:20,770 --> 00:53:21,250
+tilde وY tilde في X tilde وY tilde في X tilde وY tilde
+
+693
+00:53:21,250 --> 00:53:22,790
+في X tilde وY tilde في X tilde وY tilde في X tilde
+
+694
+00:53:22,790 --> 00:53:27,190
+وY tilde في X tilde وY tilde في X tilde وY tilde في X tilde
+
+695
+00:53:27,190 --> 00:53:34,250
+وY tilde في X tilde وY tilde في X
+
+696
+00:53:34,250 --> 00:53:41,510
+tilde وY tilin x hat then they converts in mean in x
+
+697
+00:53:41,510 --> 00:53:46,570
+hat اذا صار عندى لان limit لتى xn tilde موجود فى ال
+
+698
+00:53:46,570 --> 00:53:51,350
+x hat سميه ايش بساوي اذا انا ايش جيت قولت limit
+
+699
+00:53:51,350 --> 00:54:01,020
+لتى xn tilde صح limit لتى xn tilde بساوي x hatas n
+
+700
+00:54:01,020 --> 00:54:06,940
+goes to infinity و limit لتي y n tilde بساوي y hat
+
+701
+00:54:06,940 --> 00:54:11,480
+لاحظوا أنا إيش اللي بسويه أنا بمعنى آخر انتبهوا
+
+702
+00:54:11,480 --> 00:54:19,320
+بالله يا جماعة انتبهوا أنا أجيت أخذت لكم الـ x تيلدا
+
+703
+00:54:19,320 --> 00:54:23,360
+والـ y تيلدا arbitrary points اللي موجودات في الـ
+
+704
+00:54:23,360 --> 00:54:28,560
+x تيلدا وجيت للجسر اللي .. اللي .. اللي .. اللي من
+
+705
+00:54:28,560 --> 00:54:32,820
+خلاله بالدليل إن الـ limit D تيلدا XN تيلدا YN تيلدا
+
+706
+00:54:32,820 --> 00:54:38,060
+هو هذا الـ distance هذول من وين جايات؟ من الـ W تيلدا
+
+707
+00:54:38,060 --> 00:54:45,010
+وأنا بكتب W تيلدا isometric لمين؟ للـ W وجيت صورتها
+
+708
+00:54:45,010 --> 00:54:49,690
+هذه اسمها TX تيلدا وصورة هذه اسمها TY تيلدا
+
+709
+00:54:49,690 --> 00:54:52,670
+طلع ما تكونش Sequences إذا Converse مازال Converse
+
+710
+00:54:52,670 --> 00:54:58,130
+إذا ما بدي أروح لمين؟ لعناصر هدول موجودات في الـ X
+
+711
+00:54:58,130 --> 00:55:02,250
+هذا إذا أنا الجسرين اللي وصلت مني أنا بسأل أنا من
+
+712
+00:55:02,250 --> 00:55:09,240
+وين لوين؟ أنا بسأل إن Xات والـ x تيلدا بدأ أصل M
+
+713
+00:55:09,240 --> 00:55:14,920
+and R isometric بدأت في two elements هنا وهنا وصلت
+
+714
+00:55:14,920 --> 00:55:18,920
+لـ two elements هنا عبر الجسر هذا اللي بدأت يا من
+
+715
+00:55:18,920 --> 00:55:23,200
+خلاله أصل إذا صار عندي الآن الـ limit TXM تيلدا
+
+716
+00:55:23,200 --> 00:55:27,920
+بساوي x هات وTYM تيلدا بساوي y هات وبدأت هنا في الـ
+
+717
+00:55:27,920 --> 00:55:32,060
+x هات إذا كل هذا اللي حكيت عشان أصل أوصل بين x تيلدا
+
+718
+00:55:32,060 --> 00:55:38,660
+وx هات الآن وصلنا
+
+719
+00:55:38,660 --> 00:55:43,160
+لعند الحال ماشي الحال الآن let S be the extension
+
+720
+00:55:43,160 --> 00:55:50,520
+of T to X تيلدا S الآن S الآن عند T تبقى يا جماعة
+
+721
+00:55:50,520 --> 00:56:01,220
+T من وإن وإين؟ من X من W وتيلدا لعين وصح ولا لأ؟ ال
+
+722
+00:56:01,220 --> 00:56:08,920
+بتوسع S S بتخليها تشتغل من X تيلدا لعين 2 ل X
+
+723
+00:56:08,920 --> 00:56:12,690
+هات هذه dense في هذه طبعا وهذه dense في هذه و
+
+724
+00:56:12,690 --> 00:56:17,310
+الأمور بدأت اللي هي إيش؟ اللي هي تتمهد أمامها let
+
+725
+00:56:17,310 --> 00:56:21,270
+us be the extension of T to X تيلدا extension
+
+726
+00:56:21,270 --> 00:56:24,170
+معناته التعريف الأولاني اللي تبعته هيكون زي ما هو
+
+727
+00:56:24,170 --> 00:56:28,250
+بس بده دل التعريف لإنزيد التعريف لمين؟ لباقي النقاط
+
+728
+00:56:28,250 --> 00:56:35,440
+اللي اللي اللي هي X تيلدا ناقص W تيلدا طيب let S be
+
+729
+00:56:35,440 --> 00:56:39,720
+the extension of T to X تيلدا and S من X تيلدا لعند
+
+730
+00:56:39,720 --> 00:56:46,060
+X هات اللي هو defined by S X تيلدا بساوي مين؟ X هات
+
+731
+00:56:46,060 --> 00:56:50,480
+اللي عملناها هو كل الجهد اللي عملناه صارت الآن S
+
+732
+00:56:50,480 --> 00:56:58,000
+X تيلدا اللي بدأنا فيها هتكون يشمين هي X هات اللي
+
+733
+00:56:58,000 --> 00:57:04,080
+هي اللي سيرنا فيها طول الطريق اللي هي الماضية طيب
+
+734
+00:57:04,080 --> 00:57:10,180
+where .. أقول لكم أوضح where TXN تيلدا بساوي X هات
+
+735
+00:57:10,180 --> 00:57:14,480
+يعني X هات مركبة من مين؟ من الـ TXN تيلدا اللي
+
+736
+00:57:14,480 --> 00:57:19,680
+لإجيناها هاد واللي هي and limit XN تيلدا هو مين؟
+
+737
+00:57:19,680 --> 00:57:23,440
+اللي هي الـ X تيلدا الأصلية اللي هي هذا هتكون في الـ
+
+738
+00:57:23,440 --> 00:57:28,860
+W تيلدا وهذا هتكون اللي هي في الـ W نفسها by using
+
+739
+00:57:28,860 --> 00:57:34,470
+the isometry of T we haveD تيلدا of X تيلدا و Y تيلدا
+
+740
+00:57:34,470 --> 00:57:39,590
+تعرفنا الـ Extension D تيلدا X تيلدا و Y تيلدا إيش
+
+741
+00:57:39,590 --> 00:57:45,710
+بيساوي limit D تيلدا X تيلدا و Y تيلدا أكيد هو
+
+742
+00:57:45,710 --> 00:57:48,710
+هيك التعريف مش هيك التعريف الـ D تيلدا مش عرفناه
+
+743
+00:57:48,710 --> 00:57:55,860
+بشكل هذا أثبتناه في الأول Y بساوي هذا عبارة عن قلنا
+
+744
+00:57:55,860 --> 00:58:01,440
+بـ reserve mean T من الـ W لـ W من W تيلدا ل W من W
+
+745
+00:58:01,440 --> 00:58:06,200
+تيلدا ل W بـ reserve ده distance والـ W .. هدول
+
+746
+00:58:06,200 --> 00:58:10,560
+عناصر في الـ W تيلدا وهدول عناصر في مين؟ في الـ W
+
+747
+00:58:10,560 --> 00:58:13,740
+فالـ limit .. فالـ distance بين هدول هي نفس الـ
+
+748
+00:58:13,740 --> 00:58:17,540
+distance بين هدول الأولى تيلدا والتاني مين؟ هات
+
+749
+00:58:17,540 --> 00:58:23,360
+هد في الـ W وهد في الـ W تيلدا طيب ما يساوي هد الآن
+
+750
+00:58:24,120 --> 00:58:28,900
+الـ distance هات بين TXN تيلدا وYN تيلدا الآن
+
+751
+00:58:28,900 --> 00:58:34,180
+limitها limitها limit ال TXN تيلدا هي X هات و
+
+752
+00:58:34,180 --> 00:58:37,880
+limitها دي كإيش بيساوي YN هات إذا الـ limit لهذه D
+
+753
+00:58:37,880 --> 00:58:42,860
+هات هو عبارة عن تدخل جوا اللي هي D هات X هات وY
+
+754
+00:58:42,860 --> 00:58:48,590
+هات ماشي الحال اللي هي الـ D هات من X هات إيش هي
+
+755
+00:58:48,590 --> 00:58:55,790
+اللي عرفناها SX تيلدا وهذا SY تيلدا إذا اللي بدأنا
+
+756
+00:58:55,790 --> 00:59:00,750
+فيه D تيلدا ل X تيلدا وY تيلدا بساوي الـ D هات لل SX
+
+757
+00:59:00,750 --> 00:59:04,550
+تيلدا وSY تيلدا يعني بمعنى آخر اللي هي الـ S ب
+
+758
+00:59:04,550 --> 00:59:06,510
+reserve the distance
+
+759
+00:59:14,080 --> 00:59:18,600
+هذا إذا إنتوا بدي أثبت إن اللي عندي إذا إنتوا بدي
+
+760
+00:59:18,600 --> 00:59:21,780
+آخذ element هنا وأرجع جوا على جيله صورة هنا بحيث
+
+761
+00:59:21,780 --> 00:59:24,200
+أصل هنا بحيث إن صورته هو اللي بدأت فيه
+
+762
+00:59:32,930 --> 00:59:36,850
+النظرية .. النظرية .. النظرية يا جماعة فيها كثير
+
+763
+00:59:36,850 --> 00:59:41,370
+من المعلومات صح هي تركيبتها كبيرة لكن معلوماتها
+
+764
+00:59:41,370 --> 00:59:43,310
+كثيرة ومفيدة
+
+765
+00:59:46,890 --> 00:59:51,010
+طبعا هي أطول نظرية في الكتاب ما في عديق ما في شيء
+
+766
+00:59:51,010 --> 00:59:59,150
+زي هي طيب therefore therefore S is an isometry and
+
+767
+00:59:59,150 --> 01:00:02,250
+so إيش مالها is one to another يعني مروع شعوركم
+
+768
+01:00:02,250 --> 01:00:07,070
+لكن العلم بدهيك يعني let x هات element in x هات
+
+769
+01:00:07,070 --> 01:00:12,130
+capital هذا ما بدأت بتونته بدي آخذ element في الـ
+
+770
+01:00:12,130 --> 01:00:18,030
+co-domain هنا وأقول فيه اللي هو element في ال
+
+771
+01:00:18,030 --> 01:00:20,950
+domain بحيث إن صورة هذا element هو اللي بدأت فيه
+
+772
+01:00:20,950 --> 01:00:26,840
+طيب صلي على النبي عليه الصلاة والسلام ما دام x هات
+
+773
+01:00:26,840 --> 01:00:30,420
+في الـ x هات أنا بدي أروح للجسر، للجسر، الجسر مين؟
+
+774
+01:00:30,420 --> 01:00:34,960
+الجسر W وW تيلدا إني اللي بوصلني لمين؟ لأصل من X
+
+775
+01:00:34,960 --> 01:00:38,800
+هات ل X تيلدا ومن X تيلدا ل X هات let x هات element
+
+776
+01:00:38,800 --> 01:00:42,400
+in X تيلدا then there is a sequence x n هات of
+
+777
+01:00:42,400 --> 01:00:46,460
+elements in W لأنها W dense فيها such that limit x
+
+778
+01:00:46,460 --> 01:00:50,680
+n هات إيش بيساوي الـ x هات اللي عندي لأن since T is
+
+779
+01:00:50,680 --> 01:00:55,800
+onto T نفسها is onto ما هي T isometric isometric و
+
+780
+01:00:55,800 --> 01:01:00,140
+bijection اللي بدأنا فيها مدام T on two إذا هذه
+
+781
+01:01:00,140 --> 01:01:04,120
+اللي لجيهة هناك الواحدة فيه اللي هي إيش؟ أصل then
+
+782
+01:01:04,120 --> 01:01:07,960
+since T is on two then there is a sequence xn تيلدا
+
+783
+01:01:07,960 --> 01:01:11,800
+of elements in Y تيلدا such that T xn تيلدا هذه
+
+784
+01:01:11,800 --> 01:01:17,200
+بساوي مين؟ ال xn head لأن T الأصلية on two for all
+
+785
+01:01:17,200 --> 01:01:23,280
+n then limit هذا بيساوي limit هذا limit TXN تيلدا
+
+786
+01:01:23,280 --> 01:01:28,360
+بيساوي من الـ X هذا بظبط؟ بطبيعي بيساوي limit XN
+
+787
+01:01:28,360 --> 01:01:32,960
+هذه وXN limitها من من هو الـ X هذا الآن إذا صارت
+
+788
+01:01:32,960 --> 01:01:38,360
+ال TXN تيلدا نفسها Cauchy sequence in من W ماشي الحال
+
+789
+01:01:38,360 --> 01:01:45,040
+من تعريف الأصل بين W ومن من من ال .. ال .. ال ..
+
+790
+01:01:45,040 --> 01:01:46,840
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+791
+01:01:46,840 --> 01:01:49,120
+.. ال .. ال .. ال .. ال .. ال .. However, T is an
+
+792
+01:01:49,120 --> 01:01:51,020
+isometry مدينة T هي عبارة عن عبارة عن عبارة عن
+
+793
+01:01:51,020 --> 01:01:53,660
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+794
+01:01:53,660 --> 01:01:56,040
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+795
+01:01:56,040 --> 01:01:56,480
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+796
+01:01:56,480 --> 01:01:57,700
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+797
+01:01:57,700 --> 01:02:04,280
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+798
+01:02:04,280 --> 01:02:06,060
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+799
+01:02:06,060 --> 01:02:14,140
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+800
+01:02:14,140 --> 01:02:21,990
+عن إذا الآن X تيلدا is complete إذا أكيد في X تيلدا
+
+801
+01:02:21,990 --> 01:02:25,690
+في الـ X تيلدا such that x until ده هذي بتروح لمين؟
+
+802
+01:02:25,690 --> 01:02:30,840
+للـ x ماشي إذا نخلص اللي جينا في الآخر مين؟ X تيلدا
+
+803
+01:02:30,840 --> 01:02:34,560
+بدينا ب X هات في الـ X هات واللي جينا X تيلدا
+
+804
+01:02:34,560 --> 01:02:38,760
+موجودة في الـ X تيلدا capital ابحث by the definition
+
+805
+01:02:38,760 --> 01:02:44,200
+of S SX تيلدا هي مين؟ الـ X هات إذا صارت الـ S is
+
+806
+01:02:44,200 --> 01:02:49,400
+onto therefore X تيلدا and X هات are isometric this
+
+807
+01:02:49,400 --> 01:02:56,680
+completes the proof وهي الأسئلة وnote that the
+
+808
+01:02:56,680 --> 01:03:01,120
+space x هات occurring in the above theorem is
+
+809
+01:03:01,120 --> 01:03:05,920
+called the completion of the given space x و الله
+
+810
+01:03:05,920 --> 01:03:09,140
+يعطيكم العافية والسلام عليكم ورحمة الله وبركاته
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/uwT2Fp1FRO0_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/uwT2Fp1FRO0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bc22d8f101b709b8c734eaaec1044307209cc659
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/uwT2Fp1FRO0_postprocess.srt
@@ -0,0 +1,3240 @@
+1
+00:00:05,500 --> 00:00:08,180
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,180 --> 00:00:11,180
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:11,180 --> 00:00:16,340
+آله وصحبه أجمعين هذه المحاضرة السابعة مساق تحليل
+
+4
+00:00:16,340 --> 00:00:21,900
+اقتراني أو تحليل دالي لطلاب وطالبات الجامعة
+
+5
+00:00:21,900 --> 00:00:26,820
+الإسلامية كلية العلوم ماجستير رياضياتاليوم ان شاء
+
+6
+00:00:26,820 --> 00:00:31,640
+الله هنحكي عن موضوع من الموضوعات المهمة واللي شوية
+
+7
+00:00:31,640 --> 00:00:36,360
+بتغلب لكن ان شاء الله مع بعض بنحاول بقدر الإمكان
+
+8
+00:00:36,360 --> 00:00:42,000
+ان نوضح الأمور اللي هي تحت عنوان 16 Completion of
+
+9
+00:00:42,000 --> 00:00:46,620
+metric spaces احنا لجينا في spaces عندنا complete
+
+10
+00:00:46,620 --> 00:00:51,770
+spaces وفي spaces ايش مايلها non complete spaceالـ
+
+11
+00:00:51,770 --> 00:00:54,650
+Complete Space خلاص خلّاها دي مش هي اللي هنحكي
+
+12
+00:00:54,650 --> 00:00:57,910
+عليها هنحكي عن الـ Non-Complete Space الـ Non
+
+13
+00:00:57,910 --> 00:01:01,490
+-Complete Space بدي انا اعملها Completion يعني بدي
+
+14
+00:01:01,490 --> 00:01:05,290
+ا .. ب .. roughly الكلام انه اش اللي خاسس فيها بده
+
+15
+00:01:05,290 --> 00:01:11,990
+اكملههو Roughly اللي هي و كأنه الـ Sequences اللي
+
+16
+00:01:11,990 --> 00:01:14,990
+فيها اللي جاية عبالها تروح و تكون Converged و برة
+
+17
+00:01:14,990 --> 00:01:17,870
+و ما بتكونش Converged في الـ Space بدي أجيب هذا
+
+18
+00:01:17,870 --> 00:01:20,990
+النقطة اللي هي ممكن تروح فيها و أحطها في مين في
+
+19
+00:01:20,990 --> 00:01:24,250
+الـ Space هذا الكلام Roughly نشوف إيش معناة الكلام
+
+20
+00:01:24,250 --> 00:01:29,880
+هذا اللي هو بشكل خلنا نقول أطقأولا تعريف let X be
+
+21
+00:01:29,880 --> 00:01:33,980
+let X and و D and Y و D تلدة بيه metric spaces
+
+22
+00:01:33,980 --> 00:01:39,140
+الآن، ضمن a mapping T من X لعند Y من عند الـ X
+
+23
+00:01:39,140 --> 00:01:42,700
+لعند Y، بنقول عنها is said to be isometric or
+
+24
+00:01:42,700 --> 00:01:47,500
+isometry يعني بنسمي اللي هي ال space هذا .. ال ..
+
+25
+00:01:47,500 --> 00:01:50,240
+ال .. ال .. ال function اللي عندي isometry أو
+
+26
+00:01:50,240 --> 00:01:54,620
+isometric اللي هي إذا كان T preserve distances
+
+27
+00:01:54,620 --> 00:01:59,180
+يعني بمعنى آخربتنقل المسافة اللي هنا إلى نفس
+
+28
+00:01:59,180 --> 00:02:03,240
+المسافة اللي هنا بمعنى انه that is لكل x و y في ال
+
+29
+00:02:03,240 --> 00:02:10,260
+X ال D تلدة لل Tx و Ty بساوية D لل X و ال Y يعني
+
+30
+00:02:10,260 --> 00:02:14,860
+المسافة اللي بين X و Y under Dاللي هي في الـ .. في
+
+31
+00:02:14,860 --> 00:02:20,400
+الـ X وD هي نفسها المسافة بين صورها في الأندر
+
+32
+00:02:20,400 --> 00:02:23,420
+المتريك اللي في مين وفي واي الـ D تلد في T X وT Y
+
+33
+00:02:23,420 --> 00:02:27,320
+هذا بنسميه Isometry ومعلومة على جنب إذا كانت الـ T
+
+34
+00:02:27,320 --> 00:02:31,500
+is Isometry اللي هو على طول بتطلع one to one
+
+35
+00:02:31,500 --> 00:02:35,120
+function ماشي الحال وهذا الكلام يعني إثباته اللي
+
+36
+00:02:35,120 --> 00:02:42,000
+هو سهل بضل معاكم الآن بيجيهذا لما نقول عن الـ T من
+
+37
+00:02:42,000 --> 00:02:45,000
+X لعند Y عزيمتريك أو are the I عزيمتريك، as a
+
+38
+00:02:45,000 --> 00:02:49,940
+function اللي بنقول إن الـ space X is said to be
+
+39
+00:02:49,940 --> 00:02:56,080
+عزيمتريك كspace و الـ space Y إذا بنلاقي if there
+
+40
+00:02:56,080 --> 00:03:00,390
+exists a bijection عزيمتري of X onto Yيعني بنقول
+
+41
+00:03:00,390 --> 00:03:03,550
+أنه اتنين ال X و ال Y are isometric إذا كان في
+
+42
+00:03:03,550 --> 00:03:07,470
+عندي one to one onto function which is an
+
+43
+00:03:07,470 --> 00:03:11,510
+isometric بنقول عنه إيش ماله The two spaces X and
+
+44
+00:03:11,510 --> 00:03:16,550
+Y are isometric يعني بمعنى آخر العالم اللي أنا
+
+45
+00:03:16,550 --> 00:03:22,330
+أصلا بشتغل فيه ال metric space X أو Dوعندي اللي هو
+
+46
+00:03:22,330 --> 00:03:27,250
+Y وD تلدة بنقول عنهم ان هدولة isometric ال spaces
+
+47
+00:03:27,250 --> 00:03:32,210
+يعني بمعنى اخر هما نفس الاشي بس اختلفت في الأسماء
+
+48
+00:03:32,210 --> 00:03:37,050
+هذه الأسانة فيها X وهذه الأسانة فيها اسمها TXلأن
+
+49
+00:03:37,050 --> 00:03:42,370
+المسافة هذه هي نفس المسافة فعشان هيك كل ما يتعلق
+
+50
+00:03:42,370 --> 00:03:45,890
+بالمسافة هنا و هنا نفس الاشي عشان هيك بنقول ال
+
+51
+00:03:45,890 --> 00:03:49,590
+spaces هنا زي بعض roughly لكن اللي هي اختلافات في
+
+52
+00:03:49,590 --> 00:03:53,490
+مين في الأسماء يعني و كإني بقول ال space اللي
+
+53
+00:03:53,490 --> 00:03:57,030
+بأثبت أنه isometric بين هنا و بين هنا بنقول عنهم
+
+54
+00:03:57,030 --> 00:04:01,030
+اللي هم إيه الشمال هم ال two spaces و كإنا بنقول
+
+55
+00:04:01,030 --> 00:04:04,880
+are equivalentزي ما كنا في الـ Jabra إذا بتذكروا
+
+56
+00:04:04,880 --> 00:04:09,360
+لما نقول اللي هو لما نحكي عن تركيب Jabra نقول X
+
+57
+00:04:09,360 --> 00:04:14,280
+group و Y group إذا كانت ال X في homomorphism بين
+
+58
+00:04:14,280 --> 00:04:18,200
+التنتين بالإضافة one to one onto function كنا نقول
+
+59
+00:04:18,200 --> 00:04:22,240
+there are أيش ما له isomorphic يعني العالمين
+
+60
+00:04:22,240 --> 00:04:25,820
+متكافئان أو هي نفس الأشي بس اختلفت الأسماء وهنا
+
+61
+00:04:25,820 --> 00:04:30,700
+نفس الأشي عند metric space و metric spaceبقولش بين
+
+62
+00:04:30,700 --> 00:04:33,300
+عمليات X عليها وعمليات Y عليها، لأ لأ لأ بس
+
+63
+00:04:33,300 --> 00:04:36,960
+كمتريكي space إذا preserved distances و one to one
+
+64
+00:04:36,960 --> 00:04:40,300
+نقلت بلاغي function اللي هي one to one نقلت و
+
+65
+00:04:40,300 --> 00:04:42,920
+preserved distances معناته إنه صار the two spaces
+
+66
+00:04:42,920 --> 00:04:47,220
+are the same هذا الكلام مهم لللي بده أحكيه بعد هيك
+
+67
+00:04:47,220 --> 00:04:51,200
+الآن ندلع ال theorem تبعتنااللي هي الـ Completion
+
+68
+00:04:51,200 --> 00:04:55,920
+for a metric space الإعلان هذا قلته قبل شوية أنه
+
+69
+00:04:55,920 --> 00:05:01,440
+أي metric space لو non-complete can be completed
+
+70
+00:05:01,440 --> 00:05:06,860
+اللي هو النظرية بتقول اللي هي ال completion for a
+
+71
+00:05:06,860 --> 00:05:12,550
+metric space X وDاللي هو there exist تفاصيل اللي
+
+72
+00:05:12,550 --> 00:05:15,710
+قلته a metric space can be completed تفاصيله
+
+73
+00:05:15,710 --> 00:05:19,910
+كالتالي for a metric space X وD there exist a
+
+74
+00:05:19,910 --> 00:05:26,390
+complete metric space X hat وD hat which has a
+
+75
+00:05:26,390 --> 00:05:34,810
+subspace W that is isometric with X and dense in X
+
+76
+00:05:34,810 --> 00:05:35,250
+hat
+
+77
+00:05:38,140 --> 00:05:44,460
+لو كان عندى x و d metric space و هذا لو كان مش
+
+78
+00:05:44,460 --> 00:05:46,500
+complete لو كان complete بيبقى على نفسه مش مشكلة
+
+79
+00:05:46,500 --> 00:05:51,640
+كان non complete اللي هو بقدر ألاقي metric space
+
+80
+00:05:51,640 --> 00:06:00,240
+اللي هو آخر اسمه x hat و d hat هذا ال metric space
+
+81
+00:06:00,240 --> 00:06:06,380
+complete metric spaceوإله subspace اسمه main W
+
+82
+00:06:06,380 --> 00:06:15,140
+subspace من main من X hat و الـ W اللي هو dense
+
+83
+00:06:15,140 --> 00:06:21,660
+space يعني بمعنى أخر W closure بساوي اللي هو X hat
+
+84
+00:06:21,660 --> 00:06:25,400
+وال
+
+85
+00:06:25,400 --> 00:06:34,290
+X هذا الـ W isometric للmain لل Xنشوف ايش اللي
+
+86
+00:06:34,290 --> 00:06:42,630
+بنقوله اللي بقوله التالت انه انا غرضي ان الاجي
+
+87
+00:06:42,630 --> 00:06:48,190
+اللي هو metric space يكون completion لل X
+
+88
+00:06:50,520 --> 00:06:56,120
+الان عندى .. بقولكم أكيد هلاقي space اسمه X hat وD
+
+89
+00:06:56,120 --> 00:07:02,400
+hat هذا ال space يتمتع بالآتى اللى فيه W فيه ال
+
+90
+00:07:02,400 --> 00:07:07,250
+closure إيه هي أشبت ثانية؟ X hatو الـ W هذه و
+
+91
+00:07:07,250 --> 00:07:12,870
+كأنها هي X لإنها الـ W إيش مانها؟ Isometric لمين؟
+
+92
+00:07:12,870 --> 00:07:19,290
+للـ X و كأنه صار عندي الـ X hat هي عبارة عن اللي
+
+93
+00:07:19,290 --> 00:07:22,750
+هي الـ X مضافة إلى ال closure اللي خلاها complete
+
+94
+00:07:22,750 --> 00:07:28,700
+مافيه؟ و كأنه صارت X hat complete space اللي هوفي
+
+95
+00:07:28,700 --> 00:07:32,160
+subspace منه isometric للـ X اللي هو هذا اللي
+
+96
+00:07:32,160 --> 00:07:38,620
+هنسمي انه completion لمين للـ X أي سؤال يعني مش
+
+97
+00:07:38,620 --> 00:07:41,580
+شرط انه احنا يجينا و الله نحطنا limit points هنا و
+
+98
+00:07:41,580 --> 00:07:45,520
+هنا نحطناها لأ احنا بنجيب space complete كامل و
+
+99
+00:07:45,520 --> 00:07:51,530
+نclosure ل W هي عبارة عن ال X hat و ال W هي ال Xأو
+
+100
+00:07:51,530 --> 00:07:57,390
+بمعنى مش هي هي w isometric لمين لل X واضح طيب هذا
+
+101
+00:07:57,390 --> 00:08:01,350
+اللي هو خلينا نقول نص نظريه ومش هيك كمان وبيقولك
+
+102
+00:08:01,350 --> 00:08:05,870
+this space X hat راقزوا معايا this space X hat is
+
+103
+00:08:05,870 --> 00:08:09,730
+unique except for isometers يعني هذا ال space X
+
+104
+00:08:09,730 --> 00:08:14,120
+hat إيش ماله وحيدexcept isometrics يعني لو بتدلج
+
+105
+00:08:14,120 --> 00:08:19,420
+space تاني مشابه إله هكون isometric إله يعني لو
+
+106
+00:08:19,420 --> 00:08:24,700
+كان في عند X تلدة ال complete isometric space و
+
+107
+00:08:24,700 --> 00:08:29,160
+half نفس الخواص تبع X hat يعني having dense
+
+108
+00:08:29,160 --> 00:08:34,210
+subspace W تلدة و W تلدة isometric لل Xلازم الـ x
+
+109
+00:08:34,210 --> 00:08:37,630
+تلدة و الـ x هات أشمالين يكون isometric يعني لو
+
+110
+00:08:37,630 --> 00:08:42,050
+بدنا نلاقي كمان واحد اسمه x تلدة أو d تلدة و هذا
+
+111
+00:08:42,050 --> 00:08:47,390
+اللي هو ال space في w تلدة sub space منه و الـ w
+
+112
+00:08:47,390 --> 00:08:50,450
+تلدة اللي هي dense فيه و في نفس الودة isometric
+
+113
+00:08:50,450 --> 00:08:54,210
+للـ x هيطلع اللي هو ال x تلدة و ال x هات are
+
+114
+00:08:54,210 --> 00:09:00,550
+isometricواضح اذا نرخص النظرية there exist a
+
+115
+00:09:00,550 --> 00:09:05,270
+complete metric space او
+
+116
+00:09:05,270 --> 00:09:08,250
+a completion metric space لهذا ال space بالمفهوم
+
+117
+00:09:08,250 --> 00:09:14,510
+اللي حكيناه وهذا ال metric واحد except for
+
+118
+00:09:14,510 --> 00:09:15,530
+isometric
+
+119
+00:09:19,020 --> 00:09:23,740
+طيب نيجي البرهان البرهان يا جماعة هيتكون من أربع
+
+120
+00:09:23,740 --> 00:09:28,940
+اللي هو اللي هي أجزاء بتطولوا روحكم عليها الجزء
+
+121
+00:09:28,940 --> 00:09:32,240
+الأول اللي هو constructing X hat وD hat يعني بدي
+
+122
+00:09:32,240 --> 00:09:37,140
+أعملكم construction بدي أركّنكم ل space اللي احنا
+
+123
+00:09:37,140 --> 00:09:40,900
+بدناه اللي هو اللي متوقعين ان يكون completion
+
+124
+00:09:40,900 --> 00:09:46,210
+لنهينا ال Xوبعد ذلك سأعمل لكم Constructing an
+
+125
+00:09:46,210 --> 00:09:51,310
+Isometry T of X onto W الأن سأعمل لكم ما هو
+
+126
+00:09:51,310 --> 00:09:55,350
+Isometry بين X و بين W اللي يبقى خشوط اللي قبل
+
+127
+00:09:55,350 --> 00:09:59,590
+شوية الـ W سيكون من مين جزء من الـ X هذا و الـ
+
+128
+00:09:59,590 --> 00:10:03,470
+Closure اللي سيكون من مين هو الـ X هذا سيخلصنا
+
+129
+00:10:03,470 --> 00:10:07,310
+اللي هو الجزء هذا بعد ذلك سأثبت لكم أن الـ X نحن
+
+130
+00:10:07,310 --> 00:10:11,900
+نبحث عنه أشيكون Completeبدأ أثبت لكم أن الـ space
+
+131
+00:10:11,900 --> 00:10:17,040
+X hat is complete بعد هيك الخطوة الأخيرة بتدابلكم
+
+132
+00:10:17,040 --> 00:10:20,080
+proving the uniqueness of X hat except for
+
+133
+00:10:20,080 --> 00:10:22,820
+isometries يعني بتدفر الـ XL ده واحد تاني بنفسه
+
+134
+00:10:22,820 --> 00:10:26,640
+كده كده الاخر شروط ويطلع XL ده يشمله isometric
+
+135
+00:10:26,640 --> 00:10:31,690
+لمين للـ X hatتابعوا معايا بالتفصيل الآن اطلعوا
+
+136
+00:10:31,690 --> 00:10:35,190
+لفوق خلّينا نفصل اللي حكيناها قبل بشوية اول حاجة
+
+137
+00:10:35,190 --> 00:10:39,490
+اللي هو مين انها Constructing X هات وD هات بدي اش
+
+138
+00:10:39,490 --> 00:10:47,860
+اسوي بدي اركب ال X هات و احطه بين اديكمخلّينا ناخد
+
+139
+00:10:47,860 --> 00:10:52,860
+Xn و Zn أني كوشي سيكوانسيز in main in X لإن كوشي
+
+140
+00:10:52,860 --> 00:10:56,220
+سيكوانسيز ما احنا احنا اصلا من الأول احنا متوقعين
+
+141
+00:10:56,220 --> 00:11:01,280
+اصلا انه ال X خاسس مين خاسس انه انه تروح ال limits
+
+142
+00:11:01,280 --> 00:11:03,900
+فيه يعني الكوشي سيكوانسيز دي عبالها تعمل
+
+143
+00:11:03,900 --> 00:11:07,280
+convergence لكن ال space مافيش فيه لأن ال limit
+
+144
+00:11:07,280 --> 00:11:10,740
+اللي هو تروح له فعشان ذلك احنا بدّينا بالكوشي
+
+145
+00:11:10,740 --> 00:11:15,360
+سيكوانسيز let Xn and Zn بيكون كوشي سيكوانسيز in X
+
+146
+00:11:16,200 --> 00:11:20,880
+الان بدنا نعرف xₙ related to zₙ يعني مجرد ايش ما
+
+147
+00:11:20,880 --> 00:11:26,020
+لها relation ال relation هذه كيف بدى اعرفها ان ال
+
+148
+00:11:26,020 --> 00:11:29,940
+limit لل distance بين xₙ و zₙ ايش ساية سفر اذا ال
+
+149
+00:11:29,940 --> 00:11:33,210
+relation العامة اللي بعرفهاأخدت اي two sequences
+
+150
+00:11:33,210 --> 00:11:37,250
+كوشي sequences Xn و Zn بقول ان الكوشي sequences
+
+151
+00:11:37,250 --> 00:11:40,890
+هدولة are related إذا كانت ال limit للمسافات اللي
+
+152
+00:11:40,890 --> 00:11:48,410
+بين X1 و X2 و X3 X2 و Z2
+
+153
+00:11:48,410 --> 00:11:53,870
+Xn و Zn المسافة is n cos infinity ايش تساوي؟ ساوي
+
+154
+00:11:53,870 --> 00:11:57,560
+صفر هذه is an equivalence relationوكوف الانسان
+
+155
+00:11:57,560 --> 00:12:03,220
+عشان نسيوله عندى اول حاجة ال Xn related لل Xn ليه؟
+
+156
+00:12:03,220 --> 00:12:08,120
+لأن المسافة بين Xn و Xn دايما مش متساوية ف limit
+
+157
+00:12:08,120 --> 00:12:12,380
+ها اكيد مش متساوية اذا اللي هو اللي ازال سواها
+
+158
+00:12:12,380 --> 00:12:17,200
+اولاشه reflexive اتنين الان symmetric اكيد اللي هو
+
+159
+00:12:17,200 --> 00:12:27,960
+Xn related to Yn معناتها limit Xn Yn بساوية0 و هذي
+
+160
+00:12:27,960 --> 00:12:36,020
+اكيد limit dyn و xn هيساوي سفر لأن هذي يعني هذي و
+
+161
+00:12:36,020 --> 00:12:42,440
+هذا هيعطيني انه اللي هو yn related to xn إذا كانت
+
+162
+00:12:42,440 --> 00:12:47,360
+اللي هو هذي هتكون symmetric برضه الان تلاتة اللي
+
+163
+00:12:47,360 --> 00:12:51,940
+هي النقطة الأخيرة برضه لو فرضنا ان xn related to
+
+164
+00:12:51,940 --> 00:13:02,830
+yn و ynمع Zn مايعطينا هنا limit distance Xn و Yn
+
+165
+00:13:02,830 --> 00:13:10,410
+بساوي0 والـ Limit للـ Distance بين YN و ZN بساوية
+
+166
+00:13:10,410 --> 00:13:16,310
+0 إذا أنا بدي XN و مين و ZN خدوا Limit الـ
+
+167
+00:13:16,310 --> 00:13:20,330
+Distance بين XN و ZN طبيعي بالطريقة نقول الـ
+
+168
+00:13:20,330 --> 00:13:24,730
+Equality XN و ZN أصغر أو شاوي الـ Distance بين XN
+
+169
+00:13:24,730 --> 00:13:30,470
+و YN زائد الـ Distance بين YN و ZNخُدوا الـ limit
+
+170
+00:13:30,470 --> 00:13:35,170
+للجهتين اللي غالب بيصير limit limit as n goes to
+
+171
+00:13:35,170 --> 00:13:37,630
+infinity هذي as n goes to infinity من اللي فوق هذي
+
+172
+00:13:37,630 --> 00:13:41,730
+سفر إذا تطلع وهذا أكبر ساو سفر إذا هذي هتطلع
+
+173
+00:13:41,730 --> 00:13:48,010
+بتساوي سفر إذا أشملها إذا صارت Zn أو Xn related Zn
+
+174
+00:13:48,010 --> 00:13:51,770
+يعني بمعنى أخر transitive إذا صارت عندي is an
+
+175
+00:13:51,770 --> 00:13:54,770
+equivalence relation إيش بدك في ال equivalence
+
+176
+00:13:54,770 --> 00:13:57,050
+relation؟ بد ال equivalence relation عارفين ليش؟
+
+177
+00:13:58,220 --> 00:14:04,660
+عشان أنا الآن بدي أركّب الـ X hat الـ X hat
+
+178
+00:14:04,660 --> 00:14:08,640
+هركّبها من ال equivalence classes لل relation اللي
+
+179
+00:14:08,640 --> 00:14:14,180
+عندي اه يعني الآن ال equivalence classes ايش هي
+
+180
+00:14:14,180 --> 00:14:22,100
+مثلا لو عندي X n عشان X n قوشي sequence ماشي في
+
+181
+00:14:22,100 --> 00:14:24,940
+الاسم السابع اللي هو main قوشي sequence in main in
+
+182
+00:14:24,940 --> 00:14:31,000
+X عناصره من وين جاي من Xكل الـ sequences الـ
+
+183
+00:14:31,000 --> 00:14:36,520
+Cauchy اللي related لها يعني IZN related to XN
+
+184
+00:14:36,520 --> 00:14:40,860
+هيكونوا إيش مانوا كلهم في نفس ال equivalence class
+
+185
+00:14:40,860 --> 00:14:47,200
+يعني ال equivalence class لل XN هذه اللي هي فيها
+
+186
+00:14:47,200 --> 00:14:53,160
+IZN و ال YN و كل الناس اللي او ال sequences اللي
+
+187
+00:14:53,160 --> 00:14:56,060
+Cauchy sequences و related لهذه عبر ال relation
+
+188
+00:14:56,060 --> 00:15:02,000
+اللي عنديالان انا بدي اسمي ال X hat بي the set of
+
+189
+00:15:02,000 --> 00:15:05,940
+all equivalence classes اللي بدي اسميها يعني هذه
+
+190
+00:15:05,940 --> 00:15:08,780
+بدل ما اسميها زي هيك اسهل اللي بدي اسميها X hat
+
+191
+00:15:08,780 --> 00:15:13,480
+ماشي و هكذا واضحيش هذه ال X hat ايش هي عبارة عن
+
+192
+00:15:13,480 --> 00:15:16,500
+the equivalence class of all اللي هي كوشي
+
+193
+00:15:16,500 --> 00:15:20,280
+sequences related to بعض ماشي طيب الان
+
+194
+00:15:22,770 --> 00:15:25,550
+لت X hat be the set of all equivalency classes X
+
+195
+00:15:25,550 --> 00:15:29,790
+hat و Y hat و Z hat الاخره of Cauchy sequences
+
+196
+00:15:29,790 --> 00:15:33,790
+اللي هو rough obtained above اللي هو عن طريق ال
+
+197
+00:15:33,790 --> 00:15:38,250
+limit distance بين X and Y and ساوة سفرالان بتدعرف
+
+198
+00:15:38,250 --> 00:15:43,130
+ال d hat ايش ال d hat بتدعرف ال d hat of x hat و y
+
+199
+00:15:43,130 --> 00:15:47,910
+hat بساوى ال limit لل distance xn yn as n goes to
+
+200
+00:15:47,910 --> 00:15:51,610
+infinity ال xn مالها كوش ال sequences فيها دي و ال
+
+201
+00:15:51,610 --> 00:15:56,160
+yn كوش ال sequences في مين؟ في التانيةفالان هذا
+
+202
+00:15:56,160 --> 00:15:59,560
+التعريف اللي هو اللي أمامي بدي أثبت انه well
+
+203
+00:15:59,560 --> 00:16:04,040
+defined where xn element of x hat and yn element
+
+204
+00:16:04,040 --> 00:16:07,060
+of y hat و ال x hat و ال y hat ايش ما اللي موجودات
+
+205
+00:16:07,060 --> 00:16:10,880
+في ال x hat ليش اثبتوا well defined؟ لحسن مش احنا
+
+206
+00:16:10,880 --> 00:16:13,280
+بنتعامل معاكوا equivalency class انتوا تروحوا
+
+207
+00:16:13,280 --> 00:16:19,020
+تاخدوا ناخد xn و تاخدوا zالواحد ياخد دي يبدو YN و
+
+208
+00:16:19,020 --> 00:16:22,180
+KN و YN و KN أشمالين related لبعض في نفس ال
+
+209
+00:16:22,180 --> 00:16:25,500
+equivalency class خايفين يطلع جواب يعني لما ناخد
+
+210
+00:16:25,500 --> 00:16:28,300
+ال limit لل distance بين XN و YN و جوابكم يبدأ ال
+
+211
+00:16:28,300 --> 00:16:33,040
+limit لل distance بين ZN و KN يطلع مش زي بعض فلأ
+
+212
+00:16:33,040 --> 00:16:36,880
+بدنا نثبت لكم أنه بطلع زي بعض دعونا نشوف كيف ..
+
+213
+00:16:36,880 --> 00:16:42,340
+اطلع على فوقto prove that this limit exists we do
+
+214
+00:16:42,340 --> 00:16:45,620
+as follow بدنا نعمل كمان يعني ب triangling quality
+
+215
+00:16:45,620 --> 00:16:49,220
+سهلة اللي هو distance بين Xm و Ym ب triangling
+
+216
+00:16:49,220 --> 00:16:54,240
+quality أثر سواء distance بين Xm و Xm ماشي زاد
+
+217
+00:16:54,240 --> 00:16:58,320
+distance بين Xm و Ym زاد ال distance بين Ym و Ym
+
+218
+00:16:58,320 --> 00:17:04,260
+انه un-arbitrary ماشي then جيبولي هذه hand اللي هي
+
+219
+00:17:04,260 --> 00:17:08,000
+ال Ym و Xm على الجهة دي بيصير عندى distance بين Xm
+
+220
+00:17:08,000 --> 00:17:13,730
+و Ymنقص هذه جيبتها هنا ال distance بين YM و XM و
+
+221
+00:17:13,730 --> 00:17:18,390
+YM أصغر و أصغر اللي بيظل اللي هو هذه و هذه اللي هي
+
+222
+00:17:18,390 --> 00:17:22,430
+ال distance بين XN و XM و ال distance بين YM و YN
+
+223
+00:17:22,430 --> 00:17:26,070
+اللي حصلت على هذه similarly بنفس الطريقة بدل ما
+
+224
+00:17:26,070 --> 00:17:29,770
+بدأ بدأ بال distance XN و YN ببدأ بال distance XM
+
+225
+00:17:29,770 --> 00:17:34,230
+و YMو بعمل نفس ال triangle inequality بطلع عندى ..
+
+226
+00:17:34,230 --> 00:17:36,630
+و بجيب هذه اللي .. اللي .. اللي هي في هذه الحالة
+
+227
+00:17:36,630 --> 00:17:41,270
+بتطلع بدل Xm Ym على الجهة هذه بتطلع Xn Yn بجيبها
+
+228
+00:17:41,270 --> 00:17:45,350
+هنا على الجهة هذه بصير المسافة بين Xm Ym ناقص Xn
+
+229
+00:17:45,350 --> 00:17:49,830
+Yn أصغر أو يساوي نفس الكمية اللي طلعت قبل بشوية و
+
+230
+00:17:49,830 --> 00:17:52,910
+ضربها في سالبحط و .. و .. و .. و .. و .. و .. و ..
+
+231
+00:17:52,910 --> 00:17:53,070
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+232
+00:17:53,070 --> 00:17:54,310
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+233
+00:17:54,310 --> 00:17:55,610
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+234
+00:17:55,610 --> 00:17:56,290
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+235
+00:17:56,290 --> 00:18:01,030
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+236
+00:18:01,030 --> 00:18:02,490
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+237
+00:18:02,490 --> 00:18:04,030
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+238
+00:18:04,030 --> 00:18:08,590
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+239
+00:18:08,590 --> 00:18:08,690
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+240
+00:18:08,690 --> 00:18:16,610
+و .. و .. و .. و
+
+241
+00:18:16,610 --> 00:18:19,840
+..بالرغم من أن Xn وYn هما عاملين عاملين عاملين
+
+242
+00:18:19,840 --> 00:18:20,480
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+243
+00:18:20,480 --> 00:18:21,760
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+244
+00:18:21,760 --> 00:18:29,480
+عاملين عاملين عاملين عاملين عاملين
+
+245
+00:18:29,480 --> 00:18:31,360
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+246
+00:18:31,360 --> 00:18:31,440
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+247
+00:18:31,440 --> 00:18:32,260
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+248
+00:18:32,260 --> 00:18:37,840
+عاملين عاملين
+
+249
+00:18:37,840 --> 00:18:47,260
+عام
+
+250
+00:18:47,280 --> 00:18:52,460
+أصغر من إبسلون لحدها واضح إيش معناته صار عندي اللي
+
+251
+00:18:52,460 --> 00:18:57,980
+هو هذا هذا رقم عدد عدد يعني وكأنه عبارة عن
+
+252
+00:18:57,980 --> 00:19:01,260
+sequence of أعداد وهذا عبارة عن أعداد إذا صارت
+
+253
+00:19:01,260 --> 00:19:06,750
+الـDX and Y and هذهاللي هي عبارة عن sequences of
+
+254
+00:19:06,750 --> 00:19:10,190
+mean of real numbers واحنا بنعرف الـ real number
+
+255
+00:19:10,190 --> 00:19:15,090
+إيش ماله، complete إذا then it converges، thus ال
+
+256
+00:19:15,090 --> 00:19:19,310
+limit لل distance xₙ و yₙ إيش ماله exist، exist
+
+257
+00:19:19,310 --> 00:19:25,230
+وكمان وحيد، طيب، طيب، الآن now we show that this
+
+258
+00:19:25,230 --> 00:19:28,710
+limit is إيش، is independent، إذا الأول إشي أثبتنا
+
+259
+00:19:28,710 --> 00:19:32,730
+إنه ال limit موجودة، بمعنى آخر الديهات اللي عرفته
+
+260
+00:19:33,450 --> 00:19:38,350
+بين x hat و y hat اللي هو بيساوي ال limit لل
+
+261
+00:19:38,350 --> 00:19:42,570
+distance بين x n و y n as n goes to infinity
+
+262
+00:19:42,570 --> 00:19:43,950
+exists
+
+263
+00:19:46,230 --> 00:19:49,910
+هذه واحدة الان بدأ اثبت لكم انه independent of the
+
+264
+00:19:49,910 --> 00:19:55,250
+choice of xn من ال x hat و ال y hat من ال y hat
+
+265
+00:19:55,250 --> 00:19:58,670
+يعني انت لو اخترت xn في ال y hat في ال x hat و
+
+266
+00:19:58,670 --> 00:20:04,710
+اخترت zn في ال y hat و واحد اختار zkn مثلا في ال y
+
+267
+00:20:04,710 --> 00:20:08,330
+hat هيطلع ال limit بناء على هذا و ال limit بناء
+
+268
+00:20:08,330 --> 00:20:12,750
+على ال distance بين zn و kn اللي هو R equivalent
+
+269
+00:20:12,750 --> 00:20:19,140
+تنشوفالان نظرح ان هذا الانتقال مستقل من الاختيار
+
+270
+00:20:19,140 --> 00:20:23,420
+اذا انا الآن اذكركم ركبت ال X hat من اين؟ من ال
+
+271
+00:20:23,420 --> 00:20:27,220
+equivalency classes عرفت ال D hat اللي هو metric
+
+272
+00:20:27,220 --> 00:20:33,020
+عليها اسمه D hat حسب اللي حكيته فوق، ضال عندي ايش
+
+273
+00:20:33,020 --> 00:20:38,580
+اسوي؟ ان اثبتلكم ان هذا الانتقال مستقل من الاختيار
+
+274
+00:20:38,580 --> 00:20:42,820
+من الاختيارات الخاصة من الاختيارات الخاصة اللي
+
+275
+00:20:42,820 --> 00:20:43,520
+بنحكي عنها
+
+276
+00:20:46,370 --> 00:20:53,830
+لأ سنة خلّيني أنزل بقول لك we show that this limit
+
+277
+00:20:53,830 --> 00:20:56,590
+is independent of the choice of xₙ elemental x hat
+
+278
+00:20:56,590 --> 00:21:00,610
+and yₙ elemental y hat in other words خلّيني نفترض
+
+279
+00:21:00,610 --> 00:21:03,690
+أن xₙ و zₙ من نفس ال equivalency class تطلع على
+
+280
+00:21:03,690 --> 00:21:07,710
+فوق و نفترض أن ال yₙ و ال wₙ من نفس ال equivalency
+
+281
+00:21:07,710 --> 00:21:11,440
+class تبعتي اللي هي mean y hatthen by one اللي هي
+
+282
+00:21:11,440 --> 00:21:14,660
+قبل شوية اللي عملناها المسافة بين Xn وYn والمسافة
+
+283
+00:21:14,660 --> 00:21:20,980
+بين Zn وWn أصغر أو يساوي Xn وZn زائد Yn وMain وWn
+
+284
+00:21:20,980 --> 00:21:25,760
+هذي عملناها قبل هيك الان as n goes to infinityاللي
+
+285
+00:21:25,760 --> 00:21:29,240
+هي هذا هتروح للصفر وهذا هتروح للصفر ليش؟ لأن Xn
+
+286
+00:21:29,240 --> 00:21:33,240
+وZn مالهن من نفس ال .. related مدام related على
+
+287
+00:21:33,240 --> 00:21:36,060
+حسب اللي هي Xn related to Zn هيكون ال limit بيساوي
+
+288
+00:21:36,060 --> 00:21:39,220
+صفر وهذا ال limit أيش بيساوي صفر إذا as n goes to
+
+289
+00:21:39,220 --> 00:21:41,780
+infinity هذا هيروح للصفر إذا as n goes to infinity
+
+290
+00:21:41,780 --> 00:21:45,560
+هذا المقطار هيساوي صفر يعني بمعنى آخر limit هذه
+
+291
+00:21:45,560 --> 00:21:49,100
+بيساوي limit التانية إذا limit هذه بيساوي limit
+
+292
+00:21:49,100 --> 00:21:53,660
+هذا إذايوابي وجوابكم هو نفس الشيء إذا الـD hat
+
+293
+00:21:53,660 --> 00:21:57,660
+الـL على أي كوشي sequence تاخدها من جوا ال
+
+294
+00:21:57,660 --> 00:22:00,800
+equivalency class أي إن كانت اللي إلي و اللي إلك و
+
+295
+00:22:00,800 --> 00:22:04,300
+اللي إلي و اللي إلك و اللي هتطلع نفس الجواب إذا
+
+296
+00:22:04,300 --> 00:22:08,760
+أمورنا تمامة تمام و we prove that الـD hat into is
+
+297
+00:22:08,760 --> 00:22:12,920
+a metric on X hat إذا أثبتنا الخطوة التانية بعد ما
+
+298
+00:22:12,920 --> 00:22:16,200
+أثبتنا إن exist أثبتنا إنه well defined يعني اللي
+
+299
+00:22:16,200 --> 00:22:20,130
+هو لا يعتمد على ال choice تبع ال Xالـ Xn اللي في
+
+300
+00:22:20,130 --> 00:22:24,630
+الـ X hat طيب هبنا نثبت .. و من ال trick اطلع لفوق
+
+301
+00:22:24,630 --> 00:22:29,610
+طولوا روحكم عليها الان بدنا نثبت انه هو prove that
+
+302
+00:22:29,610 --> 00:22:33,770
+D hat in two is a metric on X اول اشي it is clear
+
+303
+00:22:33,770 --> 00:22:38,650
+that D hat satisfy M واحد عند M تلاتة ليش؟ لقيتها
+
+304
+00:22:38,650 --> 00:22:44,120
+هذه أكبر أو سوء سفر أكيد صح؟مظبوط ولا لأ؟ الان و
+
+305
+00:22:44,120 --> 00:22:49,440
+لو بدنا ناخد dy hat و x hat على طول بيصير ال limit
+
+306
+00:22:49,440 --> 00:22:54,680
+بتنقلب فبتطلع نفس الاشي واضح؟ اذا برضه dy hat hat
+
+307
+00:22:54,680 --> 00:23:00,400
+و x hat بيساوي dx hat y hat، مظبوط؟ اذا الشروط هذه
+
+308
+00:23:00,400 --> 00:23:09,150
+سهلة، اللي هي و نيجي اللي هو خلاص انتوا بتكملهالان
+
+309
+00:23:09,150 --> 00:23:11,050
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+310
+00:23:11,050 --> 00:23:11,150
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+311
+00:23:11,150 --> 00:23:11,330
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+312
+00:23:11,330 --> 00:23:12,070
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+313
+00:23:12,070 --> 00:23:12,190
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+314
+00:23:12,190 --> 00:23:14,990
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+315
+00:23:14,990 --> 00:23:19,730
+M M M M M M
+
+316
+00:23:19,730 --> 00:23:20,030
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+317
+00:23:20,030 --> 00:23:22,450
+M M M M M M M M M M M M M M M Mأه then ال limit دي
+
+318
+00:23:22,450 --> 00:23:26,730
+xn و yn بساوة سفر وهذه ايش معناه بساوة سفر ان xn
+
+319
+00:23:26,730 --> 00:23:30,850
+equivalent ل yn hence the equivalence classes x
+
+320
+00:23:30,850 --> 00:23:34,770
+hat and y hat are either equal لأن احنا عارفين ان
+
+321
+00:23:34,770 --> 00:23:37,890
+ال equivalence class اللي .. اللي كان فيه عندى
+
+322
+00:23:37,890 --> 00:23:41,050
+اللي هو ال equivalence classes عارفين يا this
+
+323
+00:23:41,050 --> 00:23:41,810
+joint
+
+324
+00:23:45,020 --> 00:23:48,800
+يا متسوية يا متسوية مادام في عنصر مشترك بينهم
+
+325
+00:23:48,800 --> 00:23:55,440
+مادام Xn و Yn related وال Xn في ال X hat وال Yn في
+
+326
+00:23:55,440 --> 00:23:59,260
+ال Y hat إذا اللي هو إيش مالهن إذا صار في عنصر
+
+327
+00:23:59,260 --> 00:24:01,180
+مشترك إذا التنتين لازم يكون إيه إيه إيه إيه إيه
+
+328
+00:24:01,180 --> 00:24:03,540
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+329
+00:24:03,540 --> 00:24:03,560
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+330
+00:24:03,560 --> 00:24:06,850
+إيه إيه إيه إيه إيه إيه إيه إيطيب إذا صار عندى لان
+
+331
+00:24:06,850 --> 00:24:11,290
+hence x and x hat the equivalence class x hat and
+
+332
+00:24:11,290 --> 00:24:15,970
+y hat ايش بالي متساويتين وهذا بدأنا x d hat لل x
+
+333
+00:24:15,970 --> 00:24:18,890
+hat و y hat بصفر وصلنا ل x hat و y hat ايش بيساوي
+
+334
+00:24:18,890 --> 00:24:26,440
+بساوى صفر ماهي سؤالالان conversely اللي هو المسافة
+
+335
+00:24:26,440 --> 00:24:30,060
+بين X hat و Y hat ايش هيساوي صفر لذا خلاص الخاصية
+
+336
+00:24:30,060 --> 00:24:35,520
+التانية متحققة تماما to prove M4 اللي عن اتنين هين
+
+337
+00:24:35,520 --> 00:24:40,440
+عملتها اه ال M تلاتة هذي و هذي اللي هي أكبر يساوي
+
+338
+00:24:40,440 --> 00:24:45,420
+صفر M واحد خلصتها ضال مين اللي هي M4 مستوعبين اه
+
+339
+00:24:47,110 --> 00:24:50,810
+أما اربعة اطلع فوق اما اربعة نركز عليها to prove
+
+340
+00:24:50,810 --> 00:24:55,620
+اما اربعة نركز عليها بس في الهدف هي سهلة برضهNote
+
+341
+00:24:55,620 --> 00:25:01,520
+that for all xₙ in X hat وYₙ in Y hat وZₙ في Z hat
+
+342
+00:25:01,520 --> 00:25:06,580
+والـ X hat وYₙ وZₙ إيش موجودة؟ اللي هي X hat، بتدا
+
+343
+00:25:06,580 --> 00:25:10,560
+وجد ال triangle inequality We have المسافة بين Xₙ
+
+344
+00:25:10,560 --> 00:25:15,920
+وYₙ أصغر بسهول مسافة بين Xₙ وZₙ وZₙ ومين وYₙ بال
+
+345
+00:25:15,920 --> 00:25:19,640
+triangle inequality لإن الـ D is a metric أنا
+
+346
+00:25:19,640 --> 00:25:24,620
+بتذكر بتمين الآن ال metric الـ D hatالان d hat لـ
+
+347
+00:25:24,620 --> 00:25:28,700
+x hat و y hat ايش بيساوي ال limit هذا طب ما هو ال
+
+348
+00:25:28,700 --> 00:25:30,820
+limit هذا هيكون أصغر بيساوي ال limit هذا زاد ال
+
+349
+00:25:30,820 --> 00:25:33,840
+limit هذا صح ولا لأ اذا أصغر بيساوي ال limit هذا
+
+350
+00:25:33,840 --> 00:25:36,820
+زاد ال limit هذا طب ما هو ال limit هذا هو فعلا
+
+351
+00:25:36,820 --> 00:25:40,320
+التعريف التعريف اللي هو ال distance بين x hat و
+
+352
+00:25:40,320 --> 00:25:46,820
+main و z hat وهذا اللي بعده تعريف ال limitهذا
+
+353
+00:25:46,820 --> 00:25:50,460
+تعريف لـ D hat بين XZ hat وY hat
+
+354
+00:26:16,830 --> 00:26:23,270
+بنعمل construction لإيزومتري T من X لعين و لعين W
+
+355
+00:26:23,270 --> 00:26:27,250
+W
+
+356
+00:26:27,250 --> 00:26:34,210
+مين يا جماعة W هتكون لازم تكون W جزء من مين؟ من ال
+
+357
+00:26:34,210 --> 00:26:39,510
+X hat و لازم تكون W closure بسوء ال X hat و لازم
+
+358
+00:26:39,510 --> 00:26:44,810
+يكون عنده يقولوا معايا اللي هو W إيزومتري لمين؟ لل
+
+359
+00:26:44,810 --> 00:26:49,720
+Xطيب شوفوا صلّوا على النبي عليه الصلاة والسلام
+
+360
+00:26:49,720 --> 00:26:55,380
+Constructing an isometry T of X onto Y, we have W
+
+361
+00:26:55,380 --> 00:27:00,680
+closure أش بساوي X hat، هي ما بنعمله، الآن define
+
+362
+00:27:00,680 --> 00:27:07,660
+T من X لعن W subset من X hatأذا بدي أرمي عنصر ال X
+
+363
+00:27:07,660 --> 00:27:13,160
+في وين في ال W ويكون ال W جزء من من X وكأنني بدي
+
+364
+00:27:13,160 --> 00:27:17,640
+أرميه في equivalency classes طيب، الان كيف بدي
+
+365
+00:27:17,640 --> 00:27:22,140
+أعرفه طريقة بصراحة يعني رائعة معرفته إياها معرف لك
+
+366
+00:27:22,140 --> 00:27:27,940
+T of any element هنا بساوي ال B hat طب كده الآن
+
+367
+00:27:27,940 --> 00:27:33,810
+أخد لك اللي هو انت بوهان عندىمن X لعين W و جالك
+
+368
+00:27:33,810 --> 00:27:38,410
+هذه W بتاخدها جزء من X هذه هتشوف كم جزء بدي أعرف
+
+369
+00:27:38,410 --> 00:27:45,470
+لك T of B B المتنوين من X بساوي الـ B hat طب كيف
+
+370
+00:27:45,470 --> 00:27:49,350
+هذه الـ B hat عبارة عن equivalence classes صح ولا
+
+371
+00:27:49,350 --> 00:27:55,500
+لأ؟الان ايش قال لك انا بدي اخد اللي هو الـ B hat
+
+372
+00:27:55,500 --> 00:28:02,360
+اللي بدو حدد هويتها هي ال sequence B وB وB وB وB
+
+373
+00:28:02,360 --> 00:28:02,840
+وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB
+
+374
+00:28:02,840 --> 00:28:03,960
+وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB
+
+375
+00:28:03,960 --> 00:28:04,180
+وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB
+
+376
+00:28:04,180 --> 00:28:07,540
+وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB
+
+377
+00:28:07,540 --> 00:28:09,560
+وB وB وB وB وBالأن هذه الـ Cauchy Sequence الـ
+
+378
+00:28:09,560 --> 00:28:13,660
+equivalence class لها هي اللي بيسميها إيش مالها؟ B
+
+379
+00:28:13,660 --> 00:28:19,000
+hat وكل الـ sequences اللي related لها هيكون
+
+380
+00:28:19,000 --> 00:28:22,460
+موجودات في الـ B hat فراحظوا إن كل عوصر من هان
+
+381
+00:28:22,460 --> 00:28:27,600
+وديته لعوصر اسم بيهتها، ماشي الحال، هذه اللي هي W
+
+382
+00:28:27,600 --> 00:28:33,050
+اللي بتديها جزء من X hat ولا لأ؟ أكيد جزء منهاو W
+
+383
+00:28:33,050 --> 00:28:38,790
+في الواقع أنا ماخدها W هاخدها انا هي عبارة عن T ل
+
+384
+00:28:38,790 --> 00:28:44,030
+X انا هاخدها هيك يعني هاخد ال W ايش بتعملها بتقول
+
+385
+00:28:44,030 --> 00:28:49,610
+T of X هي مين هي ال W هال جيت مش عارفت هال جيت T
+
+386
+00:28:49,610 --> 00:28:54,130
+من X ل عنده لأ هال جيت عرفت هيك صح؟عرفتها زهير لإن
+
+387
+00:28:54,130 --> 00:28:58,030
+هدولة موجودة وين في الـVها الآن مين اللي بديها
+
+388
+00:28:58,030 --> 00:29:03,610
+يسميها W؟ بدي أسميها W هي صور مين الـX إذا إذا
+
+389
+00:29:03,610 --> 00:29:09,210
+الـW عرفتها أنا هي عبارة عن TX إذا صار الـT عدى
+
+390
+00:29:09,210 --> 00:29:16,260
+automatic أنا وأنتواأثبت انه ايزومتري و اثبت انه
+
+391
+00:29:16,260 --> 00:29:20,500
+ايزومتري خلص لان ايزومتري يكون one to one فبصير
+
+392
+00:29:20,500 --> 00:29:26,740
+عندى الان T من X لعين W one to one on to function
+
+393
+00:29:26,740 --> 00:29:31,020
+which is ايزومتري اذا دل بس شغل اخرى ان اثبت W
+
+394
+00:29:31,020 --> 00:29:38,670
+closure بساوة X hat طيب نشوف مع بعضالان where T
+
+395
+00:29:38,670 --> 00:29:41,790
+بيساوي W بيساوي TX and for B element in X we
+
+396
+00:29:41,790 --> 00:29:45,030
+associate the class B hat element in X which
+
+397
+00:29:45,030 --> 00:29:48,910
+contains the constant Cauchy sequence BBB زي ما
+
+398
+00:29:48,910 --> 00:29:53,070
+حكيته لكم الان for any A و B element in X hat
+
+399
+00:29:53,070 --> 00:29:57,910
+لاحظوا أن المسافة سهلة هذه بتنهي زيومتري D hat بين
+
+400
+00:29:57,910 --> 00:30:03,270
+TA و TB بيساوي ال D hat بين A hat و B hat لأن TA
+
+401
+00:30:03,270 --> 00:30:08,350
+انا هي أسميتها A hat وTBاش بيساوي B hatلكن هذه ايش
+
+402
+00:30:08,350 --> 00:30:12,430
+بتساوي؟ limit للـ distance بين اللي هي الـ Cauchy
+
+403
+00:30:12,430 --> 00:30:15,470
+Sequences اللي فيها من الـ Cauchy Sequences اللي
+
+404
+00:30:15,470 --> 00:30:18,090
+فيها اللي انا اصلا ركبت هنا عليها اللي هي الـ
+
+405
+00:30:18,090 --> 00:30:21,230
+constant sequence الـ a, a, a إذا الـ limit للـ d,
+
+406
+00:30:21,310 --> 00:30:24,690
+a ونفس الاشي هدمين اللي هو الـ sequence b, b, b
+
+407
+00:30:24,690 --> 00:30:27,990
+اللي هي d ال distance بين a و b و ال limit اللي
+
+408
+00:30:27,990 --> 00:30:30,950
+هنا as n goes to infinity أصلا ثبتت هنا بساوي d, a
+
+409
+00:30:30,950 --> 00:30:31,290
+و b
+
+410
+00:30:35,330 --> 00:30:40,770
+إذا صار عندى isometry و on to function دل علي بس
+
+411
+00:30:40,770 --> 00:30:46,730
+أثبت ان الـ W closure بساوة مين ال X هت however
+
+412
+00:30:46,730 --> 00:30:51,010
+any isometry is one to one then X and W are
+
+413
+00:30:51,010 --> 00:30:56,570
+isometric we show that W closure بساوة مين X هت
+
+414
+00:31:01,130 --> 00:31:06,170
+الان الـ W و الـ W closure أي إن كان ال subset من
+
+415
+00:31:06,170 --> 00:31:09,370
+مين من ال X hat إذا بدي أثبت ال X hat subset من
+
+416
+00:31:09,370 --> 00:31:14,450
+مين من ال W closure يعني بدي أاخد X hat element in
+
+417
+00:31:14,450 --> 00:31:19,570
+X hat capital و أثبتلك إن ال X hat وين موجودة في
+
+418
+00:31:19,570 --> 00:31:26,630
+ال W closure ماشي الحال؟ طيب الآن عندي
+
+419
+00:31:33,000 --> 00:31:39,360
+متى الـ except في الـ W closure ان لو أخدت اي open
+
+420
+00:31:39,360 --> 00:31:45,930
+ballحوالين ال X hat أي open ball حوالين ال X hat
+
+421
+00:31:45,930 --> 00:31:51,210
+لازم تتقاطع مع مبتع الأقل من مين؟ من W يعني بمعنى
+
+422
+00:31:51,210 --> 00:31:56,030
+أخر أخد أي ball اللي هو centerها اللي هو X hat ولا
+
+423
+00:31:56,030 --> 00:32:00,830
+أي Y في الدنيا تقطحها مع ال W أيش مهله؟ له يساوي
+
+424
+00:32:00,830 --> 00:32:04,490
+Phi هي اللي بدثبته، بكون خلصت، شوفوا مع بعض، شوفوا
+
+425
+00:32:04,490 --> 00:32:11,790
+الانWe show that W closure is equal to X hat Let X
+
+426
+00:32:11,790 --> 00:32:14,550
+hat element in X hat capital and Xn element in
+
+427
+00:32:14,550 --> 00:32:20,750
+mean in X hat ماشي الحال ملام Xn element in X hat
+
+428
+00:32:20,750 --> 00:32:24,550
+إذا Xn كوشي سيكوينس أكيد كوشي سيكوينس إذا for
+
+429
+00:32:24,550 --> 00:32:28,490
+every Y أكبر من 0 there exists K element in N such
+
+430
+00:32:28,490 --> 00:32:34,870
+that المسافة بين Xn وXk أشمالها أصغر من Y على 2الـ
+
+431
+00:32:34,870 --> 00:32:41,310
+N for all N أكبر من K هذا صحيح الـ N أكبر أو يساوي
+
+432
+00:32:41,310 --> 00:32:46,500
+حتى عشان بتستخدمها أكبر أو يساوي من Kالآن خُدلي
+
+433
+00:32:46,500 --> 00:32:52,880
+الـ sequence xk xk xk الاخره أكيد موجودة خارج
+
+434
+00:32:52,880 --> 00:32:56,880
+معناه أدنال أكيد موجودة في مين في الـ xk إيش hat
+
+435
+00:32:56,880 --> 00:32:59,700
+لإن هذه عبارة عن كوشي sequence هذا أخدت الـ xk
+
+436
+00:32:59,700 --> 00:33:03,720
+council يعني اسمه council xk xk xk هذه الكوشي
+
+437
+00:33:03,720 --> 00:33:05,960
+sequence هذه الكوشي sequence موجودة في ال
+
+438
+00:33:05,960 --> 00:33:10,870
+equivalency class سبعتها لـ xk hatإذا XK هتأكيد
+
+439
+00:33:10,870 --> 00:33:14,790
+وين موجودة؟ في الـW لأن الـW هيك اتركبت علي هيك
+
+440
+00:33:14,790 --> 00:33:18,990
+تربط تركبت هذه الـN هذه الـN هي اللي هيلاجيها
+
+441
+00:33:18,990 --> 00:33:24,450
+مشتركة بين الجهتين السر هنا أن المسافة بين XN و XK
+
+442
+00:33:24,450 --> 00:33:27,450
+أزهر من 1 على 2 و يشاوز 1 على 2 لكل N أكبر سواء
+
+443
+00:33:27,450 --> 00:33:33,650
+مين؟ K هذه الـXK هي اللي لاجيتها هنا دير بالكم طيب
+
+444
+00:33:33,650 --> 00:33:38,530
+شوفوا الآنبعيد 2 من اللي قبل بشوية المسافة بين x
+
+445
+00:33:38,530 --> 00:33:42,230
+hat و xk hat ايش بالساوية ال limit لل sequence
+
+446
+00:33:42,230 --> 00:33:45,850
+اللي موجودة هنا اسمها xn صح؟ ولل sequence اللي
+
+447
+00:33:45,850 --> 00:33:50,790
+موجودة هنا اللي هي xk xk xk xk xk as n goes to
+
+448
+00:33:50,790 --> 00:33:55,160
+infinityهذه أصلاً أصغر من مين من يبسلون على اتنين
+
+449
+00:33:55,160 --> 00:34:00,200
+صح لكل اذا اذا انا بصي infinity هذه هتبقى المسافة
+
+450
+00:34:00,200 --> 00:34:03,660
+بين هذه اللي قلتلها أصغر أو يساوي هياش بيصير أصغر
+
+451
+00:34:03,660 --> 00:34:06,560
+أو يساوي مين اتنين اللي هي أصغر من مين من يبسلون
+
+452
+00:34:06,560 --> 00:34:11,360
+إذا صارت هذه وهذه أصغر من مين من يبسلون يعني بمعنى
+
+453
+00:34:11,360 --> 00:34:16,380
+أخر في أي يبسلون في الدنيا طلعت ال XK hat موجودة
+
+454
+00:34:16,380 --> 00:34:21,250
+في ال ballاللي بين .. اللي هي مركزها X hat ونصف
+
+455
+00:34:21,250 --> 00:34:25,570
+قطرها Y وهي في الأصل الـ X K hat اللي موجودة في
+
+456
+00:34:25,570 --> 00:34:29,750
+الـ W إذا صارت عند الـ ball X hat وY تقاطع و W ليه
+
+457
+00:34:29,750 --> 00:34:34,830
+سوى 5 4 O وY أكبر من 0 إذا صار عندي اللي هو لجينا
+
+458
+00:34:34,830 --> 00:34:39,550
+ال X hat لازم تكون في الـ W closure والآن صارت عند
+
+459
+00:34:39,550 --> 00:34:43,710
+ال X hat جزء من الـ W closure وW closure طبيعي جزء
+
+460
+00:34:43,710 --> 00:34:46,850
+منها إذا صار الحدث تتمين المساواة وهو المطلوب
+
+461
+00:34:49,140 --> 00:34:54,060
+النظرية غزيرة بالمعلومات عشان هيك انا معنى ان
+
+462
+00:34:54,060 --> 00:34:59,700
+ابرهنها طيب اللي بعدها proving the completeness of
+
+463
+00:34:59,700 --> 00:35:04,520
+X hat الان بدي اركز فيها دي عشان شوية رموز بتلخمكم
+
+464
+00:35:04,520 --> 00:35:08,760
+شوية بضح ان شاء الله بدي اثبت انه اللي هو ال X hat
+
+465
+00:35:08,760 --> 00:35:11,560
+ايش معله complete كيف اثبت انه complete باخد كوشي
+
+466
+00:35:11,560 --> 00:35:18,220
+سيكوانس فيها بدي اسميها X unhatكوشي سيكوانس وين ال
+
+467
+00:35:18,220 --> 00:35:23,920
+X hat وبدأ اثبت لكم ان X un hat هذه لازم تكون
+
+468
+00:35:23,920 --> 00:35:29,630
+convention صميم X برضه موجودة في ال X hatتنسوش ان
+
+469
+00:35:29,630 --> 00:35:34,430
+X1 هات و X2 هات و X3 هات و X4 هات كلهين اصلا
+
+470
+00:35:34,430 --> 00:35:37,190
+equivalency classes يعني كل واحدة فيه في داخلها
+
+471
+00:35:37,190 --> 00:35:42,450
+مين عبارة عن sequences ماشي طيب بدنا نثبت ان
+
+472
+00:35:42,450 --> 00:35:46,750
+الكوشي سيكوانس هذا converse جوا في ال X هات let X
+
+473
+00:35:46,750 --> 00:35:51,520
+انهات بيان الكوشي سيكوانس ال X هاتSince W closure
+
+474
+00:35:51,520 --> 00:35:55,940
+بيساوي X hat لقبل بشوية W closure أش بيساوي X hat
+
+475
+00:35:55,940 --> 00:35:59,560
+W متوال اللي بنحكي عنها اللي عناصرها بيهات بيهات و
+
+476
+00:35:59,560 --> 00:36:04,300
+إيهات و كده بحيث ان بيهات تحدد من بي بي بي بي as a
+
+477
+00:36:04,300 --> 00:36:09,460
+sequence then for all X unhat element in X hat
+
+478
+00:36:10,850 --> 00:36:16,230
+There is الوزج N hat element of W such that
+
+479
+00:36:16,230 --> 00:36:20,230
+المسافة بين X N hat و Z N hat اشمالها أصغر من مين
+
+480
+00:36:20,230 --> 00:36:25,810
+من واحد على N لأنه اشمالها لأن الـ W dense في مين؟
+
+481
+00:36:25,810 --> 00:36:29,290
+في الـ X hat فأي element في الـ X hat بلا جيله
+
+482
+00:36:29,290 --> 00:36:33,280
+element هنااللي هو المسافة بينه وبين هذا أصغر من
+
+483
+00:36:33,280 --> 00:36:37,740
+مين من واحد على أن أي ball بالنصف خطر واحد على أن
+
+484
+00:36:37,740 --> 00:36:42,780
+حلاجي اللي هو الموجود
+
+485
+00:36:42,780 --> 00:36:48,340
+فيه عنصر اللي هو في الـZn مشترك في الـW في الـW
+
+486
+00:36:48,340 --> 00:36:53,260
+أسف مشترك بين الـW وبين هذه ال ball يعني بمعنى أخر
+
+487
+00:36:53,260 --> 00:36:57,700
+المسافة بينه بين Xn وZn أصغر من مين من واحد على أن
+
+488
+00:36:57,700 --> 00:37:06,500
+واضحطيب إذا الان خدلي المسافة بين ZM hat و ZN hat
+
+489
+00:37:06,500 --> 00:37:12,980
+لأي M و N اللي هو أصغر أو يساوي اللي هو D hat ZM
+
+490
+00:37:12,980 --> 00:37:19,780
+hat و XM hat زائد D hat XM hat و XN hat تبين ال
+
+491
+00:37:19,780 --> 00:37:24,460
+equality زائد D hat XM hat و ZM hat و ZN hat الآن
+
+492
+00:37:24,460 --> 00:37:31,420
+في اللي فوق لأي XM hat و XM hat ملاجئ ZM hatلـ X M
+
+493
+00:37:31,420 --> 00:37:36,320
+HAT في الـ X HAT نلاقي الـ Z M HAT واضح؟ وهي كذا
+
+494
+00:37:36,320 --> 00:37:39,920
+اللي هو بحيث أنه المسافة أصغر من واحدة لـ M أو
+
+495
+00:37:39,920 --> 00:37:43,480
+المسافة أصغر واحدة لـ M حسب ما سميها أنا متفجين؟
+
+496
+00:37:43,480 --> 00:37:48,090
+هذا الكلام لـ ANطيب او لأي element x and hat بلاقي
+
+497
+00:37:48,090 --> 00:37:51,610
+اللي هو element z and hat اسمه x and hat او x and
+
+498
+00:37:51,610 --> 00:37:56,070
+hat او اللي بدكميه صار عندى الان المسافة بين z and
+
+499
+00:37:56,070 --> 00:38:00,750
+hat و z and hat اصغر و اصغر وهذه زائد هذه زائد هذه
+
+500
+00:38:00,750 --> 00:38:04,550
+هذه حسب الحديث اللى فوق حسب الحديث اللى فوق هذه
+
+501
+00:38:04,550 --> 00:38:09,450
+اشمالها اصغر من واحدة لان وهذه بنزلها زي ما هي x
+
+502
+00:38:09,450 --> 00:38:13,330
+and hat وx and hat وهذه اصغر من نيل من واحدة لان
+
+503
+00:38:13,870 --> 00:38:20,270
+لكن أنا ناخد الـ Xm هادهات مادان كوشي سيكوانس
+
+504
+00:38:20,270 --> 00:38:22,450
+مادان كوشي سيكوانس مادان كوشي سيكوانس مادان كوشي
+
+505
+00:38:22,450 --> 00:38:23,610
+سيكوانس مادان كوشي سيكوانس مادان كوشي سيكوانس
+
+506
+00:38:23,610 --> 00:38:24,590
+مادان كوشي سيكوانس مادان كوشي سيكوانس مادان كوشي
+
+507
+00:38:24,590 --> 00:38:25,370
+سيكوانس مادان كوشي سيكوانس مادان كوشي سيكوانس
+
+508
+00:38:25,370 --> 00:38:28,850
+مادان كوشي سيكوانس مادان كوشي سيكوانس مادان كوشي
+
+509
+00:38:28,850 --> 00:38:34,370
+سيكوانس مادان كوشي سيكوانس مادان كوشي سيكوانس ماد
+
+510
+00:38:34,390 --> 00:38:38,050
+However, Xn hat is a Cauchy sequence، إذاً for
+
+511
+00:38:38,050 --> 00:38:42,230
+every Y أكبر من 0، there exists K such that 1 على
+
+512
+00:38:42,230 --> 00:38:48,490
+M زائد هذا المسافة زائد 1 على M أصغر من إبسلون هذا
+
+513
+00:38:48,490 --> 00:38:53,630
+إيش معناته؟ معناته صارت هذه الآن أصغر من أي إبسلون
+
+514
+00:38:53,630 --> 00:38:59,190
+في الدنيالكل Y أكبر من 0 للي جيت K بحيث لكل N و M
+
+515
+00:38:59,190 --> 00:39:03,850
+أكبر من K البسافة أصغر من مين من Y يعني بمعنى أخر
+
+516
+00:39:03,850 --> 00:39:07,570
+هذه اللي اللي جيتها اللي كل مرة بلاقي اللي هو
+
+517
+00:39:07,570 --> 00:39:13,610
+إليها ZN hat للي هي X1 hat بلاقي Z1 hat ل X2 hat
+
+518
+00:39:13,610 --> 00:39:17,110
+بلاقي Z2 hat ال sequence هذه اللي اللي جيتها اللي
+
+519
+00:39:17,110 --> 00:39:22,410
+هي ZN ZN hat هذه ال sequence اتمتعت بخاصية نقاش
+
+520
+00:39:22,410 --> 00:39:28,040
+Sequencetherefore z unhat is a Cauchy sequence أي
+
+521
+00:39:28,040 --> 00:39:32,720
+سؤال طيب الان اطلع على فوق خليها في الذاكرة اذا
+
+522
+00:39:32,720 --> 00:39:40,480
+هذه الان انا حصلت على ال z unhat ال z unhat حصلت
+
+523
+00:39:40,480 --> 00:39:47,180
+عليها ال z unhat Cauchy sequence خليها في الذاكرة
+
+524
+00:39:47,180 --> 00:39:51,620
+انا هساخدمها طيب
+
+525
+00:39:53,440 --> 00:39:58,960
+الآن since T من X لعن W إذا كان I جيومتريمظبوط و
+
+526
+00:39:58,960 --> 00:40:04,920
+الـ Z M hat element من الـ W ليش Z M hat element
+
+527
+00:40:04,920 --> 00:40:10,040
+من الـ W لأن فيها اللي هي عندي اللي هي اللي أنا
+
+528
+00:40:10,040 --> 00:40:14,120
+جاتهم ال sequence دي اللي ركّبتها مالها من ال W
+
+529
+00:40:14,120 --> 00:40:18,280
+أصلا ماشي طيب شوفوا صلى على النبي عليه الصلاة
+
+530
+00:40:18,280 --> 00:40:23,360
+والسلام الآن ال sequence Z M hat element من ال W
+
+531
+00:40:23,360 --> 00:40:28,220
+كل واحدة فيه element من ال W إذا ال sequence Z MZM
+
+532
+00:40:28,220 --> 00:40:32,940
+اللي هي موجودة في الـ ZM هات لإن الـ WH مكوّنة
+
+533
+00:40:32,940 --> 00:40:37,440
+مكوّنة اللي هو من اللي هي اللي هي ال equivalency
+
+534
+00:40:37,440 --> 00:40:44,480
+classes اللي هويتها A,A,A,A,A أو B,B,B أو ZM اللي
+
+535
+00:40:44,480 --> 00:40:52,740
+هي ZM,ZM,ZM ماشي الحال الآن بتاخد واحد منهم وعمل
+
+536
+00:40:52,740 --> 00:40:57,660
+منه sequence H مالهازد ام ماشي الحال الان زد ام
+
+537
+00:40:57,660 --> 00:40:59,960
+يعني زد واحد ده اخدوا زد اتنين زد تلتة زد اربعة
+
+538
+00:40:59,960 --> 00:41:04,380
+الى اخرين الان where زد ام ايش بساوي اللي كيف اللي
+
+539
+00:41:04,380 --> 00:41:10,660
+بدي أركبه بادي انا عندي انا T من X لعند Y اتفجنا
+
+540
+00:41:10,660 --> 00:41:17,850
+انه T من X لعند W عيزومتريعندى one to one لونتو او
+
+541
+00:41:17,850 --> 00:41:19,030
+او او او او او او او او او او او او او او او او او
+
+542
+00:41:19,030 --> 00:41:19,530
+او او او او او او او او او او او او او او او او او
+
+543
+00:41:19,530 --> 00:41:21,790
+او او او او او او او او او او او او او او او او او
+
+544
+00:41:21,790 --> 00:41:29,190
+او او او او او او او او او او او او او او او او او
+
+545
+00:41:29,190 --> 00:41:32,610
+او او او اوالـ T inverse اللي هو موجودة لان وانتوا
+
+546
+00:41:32,610 --> 00:41:38,670
+هم نونتو فانكشن الـ T inverse لـ ZM hat هو الوين
+
+547
+00:41:38,670 --> 00:41:44,970
+وين هيكون flex سمونيها ZM إذا صارت الـ ZM هذه
+
+548
+00:41:44,970 --> 00:41:49,530
+عبارة عن sequence وين موجودة؟ هنا و هذه كوشي إذا
+
+549
+00:41:49,530 --> 00:41:51,990
+اللي هي و preserve distances إذا هتكون هذه برضه
+
+550
+00:41:51,990 --> 00:41:56,580
+أشمالها برضه كوشيمعايا الـ isometric من جل الكوشي
+
+551
+00:41:56,580 --> 00:42:00,020
+لكوشي وبرجع بالكوشي لكوشي ماشي الحال و أثمانه مش
+
+552
+00:42:00,020 --> 00:42:03,240
+صعب لأنه preserve distances هذا اللي بيبقى لها لكم
+
+553
+00:42:03,240 --> 00:42:08,020
+أنه لو كانت اللي هي اللي هنا كوشي sequence هترجع
+
+554
+00:42:08,020 --> 00:42:12,560
+لكوشي و لو كانت كوشي بتروح لكوشي مادام الـ T is
+
+555
+00:42:12,560 --> 00:42:18,920
+isometricو onto طيب صلى على النبي عليه الصلاة
+
+556
+00:42:18,920 --> 00:42:22,440
+والسلام إذا صارت ZM بتساوي T inverse ZM hat is a
+
+557
+00:42:22,440 --> 00:42:28,540
+Cauchy sequence inين؟ in X الان شوف كيف بده يركب
+
+558
+00:42:28,540 --> 00:42:34,240
+ال X hat احنا ليش غربنا احنا غربنا انه ناخد اللي
+
+559
+00:42:34,240 --> 00:42:42,620
+هو X M hat هيك عملنا Cauchy sequenceونوصل ال X hat
+
+560
+00:42:42,620 --> 00:42:47,520
+ونوصل إنه في X hat اسمه ال element ال X hat
+
+561
+00:42:47,520 --> 00:42:52,640
+capital such that X unhat converts نمين لل X hat
+
+562
+00:42:52,640 --> 00:42:56,560
+شوفوا الآن كيف يتركب لكم ال X hat اللي هخل ال X
+
+563
+00:42:56,560 --> 00:43:01,080
+unhat الأصلي تروح نمين لل X hat هذه ماشي؟ طيب شوف
+
+564
+00:43:01,080 --> 00:43:07,760
+let X hat element X كيف يتركبها؟الان let X hat
+
+565
+00:43:07,760 --> 00:43:14,420
+element in X and Z M hat element in X hat صح؟
+
+566
+00:43:14,420 --> 00:43:20,120
+صح؟ ليش Z M element in X hat؟ لأنه الآن الـ Z الـ
+
+567
+00:43:20,120 --> 00:43:25,400
+Z و الـ Z الـ Z M في الأصل من وين جاية؟الاصل ZM من
+
+568
+00:43:25,400 --> 00:43:28,420
+وين جاية؟ ZM hat من وين جاية؟ ZM hat من وين جاية؟
+
+569
+00:43:28,420 --> 00:43:29,560
+ZM hat من وين جاية؟ ZM hat من وين جاية؟ ZM hat من
+
+570
+00:43:29,560 --> 00:43:30,060
+وين جاية؟ ZM hat من وين جاية؟ ZM hat من وين جاية؟
+
+571
+00:43:30,060 --> 00:43:30,200
+ZM hat من وين جاية؟ ZM hat من وين جاية؟ ZM hat من
+
+572
+00:43:30,200 --> 00:43:32,580
+وين جاية؟ ZM hat من وين جاية؟ ZM hat من وين جاية؟
+
+573
+00:43:32,580 --> 00:43:36,040
+ZM
+
+574
+00:43:36,040 --> 00:43:40,000
+hat من وين جاية؟ ZM hat من وين جاية؟ ZM hat من وين
+
+575
+00:43:40,000 --> 00:43:45,380
+جاية؟ ZM
+
+576
+00:43:45,380 --> 00:43:49,520
+hat من وين جاية؟من الـ W واضح كيف اتكونت الآن الـ
+
+577
+00:43:49,520 --> 00:43:53,560
+ZM الـ X hat الـ X hat تكونت من الـ Cauchy
+
+578
+00:43:53,560 --> 00:43:56,320
+sequence يعني عبارة عن ال equivalence class لهذه
+
+579
+00:43:56,320 --> 00:43:59,320
+الـ Cauchy sequence الـ Cauchy sequence هذه اتكونت
+
+580
+00:43:59,320 --> 00:44:02,880
+من الاصل لـ T inverse الـ ZM hat اللي ZM hat من
+
+581
+00:44:02,880 --> 00:44:08,860
+مين كانت من الـ W خلوها في الذاكرة طيب إذا ال
+
+582
+00:44:08,860 --> 00:44:13,300
+distance بين الـ X un hat و الـ X hat أبدا يتفرج
+
+583
+00:44:13,300 --> 00:44:17,440
+على الـ Y و بيكون خلصةانت فاقتت ان الـ Limit لهذه
+
+584
+00:44:17,440 --> 00:44:21,700
+اللي هو الـ Distance بينها أصغر من Y ممكن خلصت اه
+
+585
+00:44:21,700 --> 00:44:27,020
+الآن أصغر أوي سوى X أنهات و Z أنهات زاد Z أنهات و
+
+586
+00:44:27,020 --> 00:44:30,980
+مين و X هات X أنهات و Z أنهات تتقبل بشوية عشان
+
+587
+00:44:30,980 --> 00:44:34,820
+عاملنا أنهات ولا أصغر من مين من واحدة لأن وهذه Z
+
+588
+00:44:34,820 --> 00:44:40,640
+أنهات و X هات أيش معنى؟ زي ما هي الآن عندي الـ Z
+
+589
+00:44:40,640 --> 00:44:46,630
+أموال موجودة في ال X هات مظبوط ولا لأ؟و الـ ZN hat
+
+590
+00:44:46,630 --> 00:44:51,450
+هو الموجودة في الـ W إذا أكيد الـ ZN و الـ ZN و
+
+591
+00:44:51,450 --> 00:44:57,060
+الـ ZN و الـ ZN هو الموجودة في الـ ZN main hatالان
+
+592
+00:44:57,060 --> 00:45:00,780
+تلاتة بتسير اللي عندى تلاتة هدى بتسير ال distance
+
+593
+00:45:00,780 --> 00:45:04,640
+بين ال X and هت وال X هت أصغر من واحد على N زائد
+
+594
+00:45:04,640 --> 00:45:09,860
+هدى اللي هي limit limit ل sequence من هنا و
+
+595
+00:45:09,860 --> 00:45:13,620
+sequence من هنا ال sequence من هنا اللي هي ZN ماشي
+
+596
+00:45:13,620 --> 00:45:21,280
+الحال اللي هي عندى ZN ZN ZN ZNأو الـ X hat اللي هي
+
+597
+00:45:21,280 --> 00:45:25,020
+من وين جاية من الـ sequence ZM اللي هي distance
+
+598
+00:45:25,020 --> 00:45:30,000
+بين XN ومين وZM و as N goes to infinity اللي عندي
+
+599
+00:45:30,000 --> 00:45:34,600
+طبعا ZM كوش ال sequence كلها كوش ال sequence فال
+
+600
+00:45:34,600 --> 00:45:38,700
+limit لهذه as N goes to infinity طبعا for M أكبر
+
+601
+00:45:38,700 --> 00:45:42,600
+من N بتصير عندي اللي هي هذه بقيت أه زغيرها أه
+
+602
+00:45:42,600 --> 00:45:45,510
+أصغرها Y في الدنياوهذه أزن قصون فيها أصغر من
+
+603
+00:45:45,510 --> 00:45:48,950
+إبسلون في الدنيا إذا دي x أن هات وx هات اللي هي
+
+604
+00:45:48,950 --> 00:45:54,490
+أصغر من إبسلون إذا صارت ال x أن هات then for
+
+605
+00:45:54,490 --> 00:45:56,730
+sufficiently for every إبسلون there exists k
+
+606
+00:45:56,730 --> 00:45:59,070
+sufficiently large such that for all أكبر من k ده
+
+607
+00:45:59,070 --> 00:46:01,790
+اللي حكيته المسافة بين هذه و هذه بتكون أصغر من
+
+608
+00:46:01,790 --> 00:46:04,370
+إبسلون إذا صارت ال x أن هات converged to x hat in
+
+609
+00:46:04,370 --> 00:46:10,990
+x therefore x hat is a complete metric space
+
+610
+00:46:19,200 --> 00:46:27,320
+طيب نسرعه الجزء الأخير الجزء الأخير proving the
+
+611
+00:46:27,320 --> 00:46:30,620
+uniqueness of X hat except for isometries خلّيني
+
+612
+00:46:30,620 --> 00:46:36,520
+أركز طويل شوية هذا بس مش صعببدنا نثبت اللي هو الـ
+
+613
+00:46:36,520 --> 00:46:40,240
+uniqueness يعني بمعنى اخر نفترض X ده و D ده ده
+
+614
+00:46:40,240 --> 00:46:45,960
+بنفس مواصفات X hat و D hat
+
+615
+00:46:45,960 --> 00:46:51,100
+و نثبت إن هدول التنين are isometric اللي هو فيه
+
+616
+00:46:51,100 --> 00:46:55,720
+one to one, one to one function بينهم شوفوا
+
+617
+00:46:55,720 --> 00:46:58,680
+Proving the uniqueness of X hat except for
+
+618
+00:46:58,680 --> 00:47:02,220
+isometries يعني اللي بده يعمل زي هيك يكون
+
+619
+00:47:02,220 --> 00:47:08,460
+isometric لهلت X hat و D hat ب another complete
+
+620
+00:47:08,460 --> 00:47:13,000
+metric space واحد تاني completion تاني with a
+
+621
+00:47:13,000 --> 00:47:17,060
+subspace W بنفس المواصفات W تلدة دي نصف مين في ال
+
+622
+00:47:17,060 --> 00:47:23,040
+X hat يعني ان انا جيبنا X تلدة وD تلدة قولنا هذا
+
+623
+00:47:23,040 --> 00:47:28,360
+complete metric space وفي داخله W تلدة subset من X
+
+624
+00:47:28,360 --> 00:47:49,840
+تلدة حيثحيث و closure بسوء مين اللي هو x تلده عشان
+
+625
+00:47:49,840 --> 00:47:56,960
+نفس المواصفات و تلد ايش ما لهااللي هو فيه عيزومتري
+
+626
+00:47:56,960 --> 00:48:03,800
+بينها عيزومتريك خلّيني أقول معين مع ال X فرضنا هذه
+
+627
+00:48:03,800 --> 00:48:08,260
+كلها وعندنا في الأصل اللي هو طبعنا هذا اللي عملناه
+
+628
+00:48:08,260 --> 00:48:13,460
+ال construction قبل شوية اللي هو W تبعته subset من
+
+629
+00:48:13,460 --> 00:48:19,180
+X hat و W closure بسوء X hat و اللي هي W اللي هي
+
+630
+00:48:19,180 --> 00:48:25,400
+عيزومتريكلمن؟ لـ X بدأ أثبت لك الآن أن الجديد هذا
+
+631
+00:48:25,400 --> 00:48:29,460
+لازم يكون بين هذا وبين هذا أيش فيه؟ عيزومتري بيكون
+
+632
+00:48:29,460 --> 00:48:34,560
+اللي هو يعني بمعنى أخر نفسه اللي هو بس اختلفت
+
+633
+00:48:34,560 --> 00:48:39,240
+الأسماء let X تلده وB تلده وD تلده be another
+
+634
+00:48:39,240 --> 00:48:42,020
+complete metric space with a subspace كده and
+
+635
+00:48:42,020 --> 00:48:44,980
+عيزومتر كده then for any X تلده وY تلده element in
+
+636
+00:48:44,980 --> 00:48:45,760
+X تلده
+
+637
+00:48:48,890 --> 00:48:54,430
+Xn تلدة سيكوانس وهو احنا بنعرف Y وW تلدة ايش ماله
+
+638
+00:48:54,430 --> 00:49:01,030
+اللي هو dense المين X تلدة مادام dense وهذه X تلدة
+
+639
+00:49:01,030 --> 00:49:04,770
+وY تلدة موجودة هنا اذا اكيد في sequence of points
+
+640
+00:49:04,770 --> 00:49:08,950
+converge لهذه وsequence of points converge لهذه من
+
+641
+00:49:08,950 --> 00:49:14,670
+تعريف مين اللي هو ال closure عندى اللي هو هذه ال
+
+642
+00:49:14,670 --> 00:49:19,680
+dense من تعريف انه dense هذه denseانتبهوا هذه
+
+643
+00:49:19,680 --> 00:49:25,160
+dense ان هذه إذا لأي element هنا بقدر ألاقي
+
+644
+00:49:25,160 --> 00:49:29,460
+sequence من هنا converge zero لما يكون يا جماعة
+
+645
+00:49:29,460 --> 00:49:35,400
+الآن أي حاجة في الدنيا y closure اللي هو بيساوي x
+
+646
+00:49:35,400 --> 00:49:41,530
+مثلاو جيت أخدت أي مُخطأ x في الـ x الهادى بقدر
+
+647
+00:49:41,530 --> 00:49:48,090
+ألاقي sequence xn in y such that xn converge لمين
+
+648
+00:49:48,090 --> 00:49:52,390
+للx اللي هو في كل .. لكل واحد .. لكل n بقدر ألاقي
+
+649
+00:49:52,390 --> 00:49:55,950
+ball .. ball المسافة بينهم أصغر من واحد، أصغر من
+
+650
+00:49:55,950 --> 00:49:58,770
+نص، أصغر من تلت، أصغر من كده، بلاقي x واحد أصغر من
+
+651
+00:49:58,770 --> 00:50:04,050
+واحد، x اتنين .. يعني ال .. فاهمين علشه بحكيه؟هذا
+
+652
+00:50:04,050 --> 00:50:09,250
+الكلام معروف إذا لـ gate sequences XN تلدة و YN
+
+653
+00:50:09,250 --> 00:50:12,670
+تلدة موجودة في الـ W تلدة كل واحدة منهم بتروح
+
+654
+00:50:12,670 --> 00:50:19,050
+واحدة لل X واحدة بتروح لمين لل Y تلدةSuch that X
+
+655
+00:50:19,050 --> 00:50:22,590
+and تلدة تقوم بالإعادة للـ X تلدة و Y تلدة تقوم
+
+656
+00:50:22,590 --> 00:50:29,770
+بالإعادة للـ Y As in A فوق و
+
+657
+00:50:29,770 --> 00:50:34,890
+نشهد أن الـ absolute value للمسافة بين X تلدة و Y
+
+658
+00:50:34,890 --> 00:50:38,370
+تلدة نقص المسافة تلدة بين X and تلدة و Y and تلدة
+
+659
+00:50:38,370 --> 00:50:41,550
+أصغر أو سوى اللي هي بالتباين green quality زي ما
+
+660
+00:50:41,550 --> 00:50:46,610
+عملنا قبل شوية X تلدة و X and تلدة زائد Y تلدة و Y
+
+661
+00:50:46,610 --> 00:50:50,620
+and تلدةالآن هذه converts صح ولا لأ هذه converts
+
+662
+00:50:50,620 --> 00:50:54,260
+لهذه إذا هذه بتروح للصفر وهذه converts لهذه إذا
+
+663
+00:50:54,260 --> 00:50:58,540
+هذه بتروح للصفر إذا كل هذا هيروح لمين للصفر إذا
+
+664
+00:50:58,540 --> 00:51:03,680
+المقدار هذا هيروح للصفر إذا وكأنه limit هذا هو هذا
+
+665
+00:51:03,680 --> 00:51:09,420
+فبصير D تلدة لان X تلدة وY تلدة بساوة limit D تلدة
+
+666
+00:51:09,420 --> 00:51:14,940
+Xn تلدة وYn تلدة إذا صار عندي اللي هو ال limit هذا
+
+667
+00:51:14,940 --> 00:51:20,720
+بساوة هذاماشي الحال خلّيها ده برضه عندك الان صار
+
+668
+00:51:20,720 --> 00:51:27,140
+عيدي المسافة المسافة بين نقطتين ان تستمتعي مش اللي
+
+669
+00:51:27,140 --> 00:51:33,060
+صار المسافة بين أي نقطين Y تلدهأو X تلد و Y تلد هو
+
+670
+00:51:33,060 --> 00:51:36,360
+الموجودة في الـ X تلد أخدتها النقطتين أبتكرانها
+
+671
+00:51:36,360 --> 00:51:41,580
+لجيه من المسافة بينهم بقدر أقول بتساوي ال limit لل
+
+672
+00:51:41,580 --> 00:51:49,480
+D تلد لل X N تلد و Y N تلد as N goes to mean to
+
+673
+00:51:49,480 --> 00:51:55,140
+infinity حيث ال X N تلد و Y N تلد جايات من وين من
+
+674
+00:51:55,140 --> 00:51:57,900
+ال W طيب
+
+675
+00:52:00,450 --> 00:52:07,810
+ماشي حالي الان لل T الان من W تلقاه W اللي هي W
+
+676
+00:52:07,810 --> 00:52:12,570
+subset من ال Xات اللي أصلي اللي ركبناهابـ
+
+677
+00:52:12,570 --> 00:52:15,630
+Abjection Isometry بقدر أقول هيك أه ما أحنا إيش
+
+678
+00:52:15,630 --> 00:52:20,690
+مفترضين ما أحنا مفترضين و تلدة dense في ال X
+
+679
+00:52:20,690 --> 00:52:25,570
+عيزومتريك لل X و مفترضين إن و عيزومتريك لل X إذا و
+
+680
+00:52:25,570 --> 00:52:30,530
+تلدة و و أشمالين are isometric طيب إذا صارت عندي
+
+681
+00:52:30,530 --> 00:52:36,290
+اللي هو بقدر أقول نفترض إن T من و تلدة لW سبس من X
+
+682
+00:52:36,290 --> 00:52:41,930
+hat is Abjection Isometryالان بما ان X until ده و
+
+683
+00:52:41,930 --> 00:52:45,750
+Y until ده كوشي سيكوانسيز converge اصلا هنا لكن
+
+684
+00:52:45,750 --> 00:52:50,370
+هنا كوشي سيكوانسيز وين في الـ W هي converge وين؟
+
+685
+00:52:50,370 --> 00:52:54,410
+في الـ X تلده converge في ال X تلده لأن ال limit
+
+686
+00:52:54,410 --> 00:52:58,930
+هنا وين موجودة؟ في ال X تلده لكن هنا هما نفس
+
+687
+00:52:58,930 --> 00:53:03,270
+الموجودات في الـ W تلده فهنا في الواقع بقدر اكد ان
+
+688
+00:53:03,270 --> 00:53:07,230
+هنا كوشي سيكوانسيز بس في الـ W تلده اذا صار عندى
+
+689
+00:53:07,230 --> 00:53:15,050
+الانكوشي سيكوانسي و W تلدة تتعامل مع X تلدة و Y
+
+690
+00:53:15,050 --> 00:53:20,130
+تلدة في X تلدة وY تلدة في X تلدة وY تلدة في X تلدة
+
+691
+00:53:20,130 --> 00:53:20,770
+وY تلدة في X تلدة وY تلدة في X تلدة وY تلدة في X
+
+692
+00:53:20,770 --> 00:53:21,250
+تلدة وY تلدة في X تلدة وY تلدة في X تلدة وY تلدة
+
+693
+00:53:21,250 --> 00:53:22,790
+في X تلدة وY تلدة في X تلدة وY تلدة في X تلدة وY
+
+694
+00:53:22,790 --> 00:53:27,190
+تلدة في X تلدة وY تلدة في X تلدة وY تلدة في X تلدة
+
+695
+00:53:27,190 --> 00:53:34,250
+وY تلدة في X تلدة وY تلدة في X
+
+696
+00:53:34,250 --> 00:53:41,510
+تلدة وY تلin x hat then they converts in mean in x
+
+697
+00:53:41,510 --> 00:53:46,570
+hat اذا صار عندى لان limit لتى xn تلدى موجود فى ال
+
+698
+00:53:46,570 --> 00:53:51,350
+x hat سميه ايش بساوي اذا انا ايش جيت قولت limit
+
+699
+00:53:51,350 --> 00:54:01,020
+لتى xn تلدى صح limit لتى xn تلدى بساوي x hatas n
+
+700
+00:54:01,020 --> 00:54:06,940
+goes to infinity و limit لتي y n تلده بساوي y hat
+
+701
+00:54:06,940 --> 00:54:11,480
+لاحظوا انا ايش اللي بسويه انا بمعنى اخر انتبهوا
+
+702
+00:54:11,480 --> 00:54:19,320
+بالله يا جماعة انتبهوا انا اجيت اخدتلكم ال x تلده
+
+703
+00:54:19,320 --> 00:54:23,360
+و ال y تلده ال arbitrary points اللي موجودات في ال
+
+704
+00:54:23,360 --> 00:54:28,560
+x تلدهو جيت للجسر اللي .. اللي .. اللي .. اللي من
+
+705
+00:54:28,560 --> 00:54:32,820
+خلاله بالدسال ان ال limit D تلده XN تلده YN تلده
+
+706
+00:54:32,820 --> 00:54:38,060
+هو هذا ال distance هذوله من وين جيات؟ من ال W تلده
+
+707
+00:54:38,060 --> 00:54:45,010
+و انا بكتب W تلده isometric لمين؟ لل Wفجيت صورة
+
+708
+00:54:45,010 --> 00:54:49,690
+هذه اسمها TX انتل ده وصورة هذه اسمها TY انتل ده
+
+709
+00:54:49,690 --> 00:54:52,670
+طلع مكونش Sequences اذا Converse مازال Converse
+
+710
+00:54:52,670 --> 00:54:58,130
+اذا مابدي نروح لمين لأ عناصر هدولة موجودات في ال X
+
+711
+00:54:58,130 --> 00:55:02,250
+هذا اذا انا الجسرين اللي صلت مني انا بتسأل انا من
+
+712
+00:55:02,250 --> 00:55:09,240
+وين لوين انا بتسأل ان Xهات والـ x تل ده بدأ أصل M
+
+713
+00:55:09,240 --> 00:55:14,920
+and R isometric بدأت في two elements هنا وهين وصلت
+
+714
+00:55:14,920 --> 00:55:18,920
+ل two elements هنا عبر الجسر هذا اللي بدأويا من
+
+715
+00:55:18,920 --> 00:55:23,200
+خلاله أصل إذا صار عندي الآن ال limit T x M تل ده
+
+716
+00:55:23,200 --> 00:55:27,920
+بسوء x hat وT y M تل ده بسوء y hat وبدأت هنا في ال
+
+717
+00:55:27,920 --> 00:55:32,060
+x hat إذا كل هذا اللي حكي عشان أصل أوصل بين x تل
+
+718
+00:55:32,060 --> 00:55:38,660
+ده وx hatالان وصلنا
+
+719
+00:55:38,660 --> 00:55:43,160
+لعند الحال ماشي الحال الان let S be the extension
+
+720
+00:55:43,160 --> 00:55:50,520
+of T to X tilde S الان S الان عند T تبقى يا جماعة
+
+721
+00:55:50,520 --> 00:56:01,220
+T من وإن وإين من X من Wو تل ده لعين و صح ولا لأ ال
+
+722
+00:56:01,220 --> 00:56:08,920
+بتوسع S S بتخليها تشتغل من X till ده لعين 2 ل X
+
+723
+00:56:08,920 --> 00:56:12,690
+hatهذه dense في هذه طبعا وهذه dense في هذه و
+
+724
+00:56:12,690 --> 00:56:17,310
+الأمور بدأت اللي هي أياش اللي هي تتمهد أمامها let
+
+725
+00:56:17,310 --> 00:56:21,270
+us be the extension of T to X تلدة extension
+
+726
+00:56:21,270 --> 00:56:24,170
+معناته التعريف الأولان اللي تبعته هيكون زي ما هو
+
+727
+00:56:24,170 --> 00:56:28,250
+بس بده دل التعريف لإنزيد التعريف لمين لباقى النقاط
+
+728
+00:56:28,250 --> 00:56:35,440
+اللي اللي اللي هي X تلدة ناقص W تلدةطيب let S be
+
+729
+00:56:35,440 --> 00:56:39,720
+the extension of T to X تلدى and S من X تلدى لعند
+
+730
+00:56:39,720 --> 00:56:46,060
+X hat اللي هو defined by S X تلدى بساومين X hat
+
+731
+00:56:46,060 --> 00:56:50,480
+اللي عملناها هو كل الجثة اللي عملناها صارت الآن S
+
+732
+00:56:50,480 --> 00:56:58,000
+X تلدى اللي بدأنا فيها هتكون يشمين هي X hat اللي
+
+733
+00:56:58,000 --> 00:57:04,080
+هي اللي سيرنا فيها طول الطريق اللي هي الماضيةطيب
+
+734
+00:57:04,080 --> 00:57:10,180
+where .. أقولكم أوضح where T X N تلده بسوء X hat
+
+735
+00:57:10,180 --> 00:57:14,480
+يعني X hat مركبة من مين؟ من ال T X N تلده اللي
+
+736
+00:57:14,480 --> 00:57:19,680
+لاجيناها هاد و اللي هي and limit X N تلده هو مين
+
+737
+00:57:19,680 --> 00:57:23,440
+اللي هي ال X تلده الأصلية اللي هي هذا هتكون في ال
+
+738
+00:57:23,440 --> 00:57:28,860
+W تلده و هذا هتكون اللي هي في ال W نفسها by using
+
+739
+00:57:28,860 --> 00:57:34,470
+the isometry of T we haveD تلدة of X تلدة و Y تلدة
+
+740
+00:57:34,470 --> 00:57:39,590
+اتعرفنا الـ Extension D تلدة X تلدة و Y تلدة ايش
+
+741
+00:57:39,590 --> 00:57:45,710
+بيساوي limit D تلدة X انتلدة و Y انتلدة أكيد هو
+
+742
+00:57:45,710 --> 00:57:48,710
+هيك التعريف مش هيك التعريف الـ D تلدة مش عرفناه
+
+743
+00:57:48,710 --> 00:57:55,860
+بشكل هذا أثبتناه في الأول Y ساوي هذا عبارة عنقلنا
+
+744
+00:57:55,860 --> 00:58:01,440
+بـ reserve mean T من الـ W لـ W من W تلدة ل W من W
+
+745
+00:58:01,440 --> 00:58:06,200
+تلدة ل W بـ reserve ده distance و الـ W .. هدول
+
+746
+00:58:06,200 --> 00:58:10,560
+عناصر في الـ W تلدة و هدول عناصر في مين؟ في الـ W
+
+747
+00:58:10,560 --> 00:58:13,740
+فال limit .. فال distance بين هدولة هي نفس ال
+
+748
+00:58:13,740 --> 00:58:17,540
+distance بين هدولة الأولى تلدة و التاني مين؟ hat
+
+749
+00:58:17,540 --> 00:58:23,360
+هد في الـ W و هد في الـ W تلدة طيب مايساوي هد الآن
+
+750
+00:58:24,120 --> 00:58:28,900
+الـ distance هات بين TXN تلده و YN تلده الان
+
+751
+00:58:28,900 --> 00:58:34,180
+limitها limitها limit ال TXN تلده هي X hat و
+
+752
+00:58:34,180 --> 00:58:37,880
+limitها دي كإيش بيساوي YN hat إذا ال limit لهذه D
+
+753
+00:58:37,880 --> 00:58:42,860
+hat هو عبارة عن تدخل جوا اللي هي D hat X hat و Y
+
+754
+00:58:42,860 --> 00:58:48,590
+hatماشي الحال اللي هي ال D hat من X hat ايش هي
+
+755
+00:58:48,590 --> 00:58:55,790
+اللي عرفناها S X تلده وهذا S Y تلده إذا اللي بدأنا
+
+756
+00:58:55,790 --> 00:59:00,750
+فيه D تلده ل X تلده وY تلده بساوي ال D hat لل S X
+
+757
+00:59:00,750 --> 00:59:04,550
+تلده وS Y تلده يعني بمعنى آخر اللي هي ال S ب
+
+758
+00:59:04,550 --> 00:59:06,510
+reserve the distance
+
+759
+00:59:14,080 --> 00:59:18,600
+هذا اذا انتوا بدي اثبت انه اللي عندى اذا انتوا بدي
+
+760
+00:59:18,600 --> 00:59:21,780
+اخد element هنا و ارجع جوه على جيله صورة هنا بحيث
+
+761
+00:59:21,780 --> 00:59:24,200
+اصل هنا بحيث ان صورته هو اللي بدأت فيه
+
+762
+00:59:32,930 --> 00:59:36,850
+النظرية .. النظرية .. النظرية يا جماعة فيها كثير
+
+763
+00:59:36,850 --> 00:59:41,370
+من المعلومات صح هي تركبتها كبيرة لكن معلوماتها
+
+764
+00:59:41,370 --> 00:59:43,310
+كثيرة ومفيدة
+
+765
+00:59:46,890 --> 00:59:51,010
+طبعا هي أطول نظرية في الكتاب مافيش عديق مافيش اشي
+
+766
+00:59:51,010 --> 00:59:59,150
+زي هي طيب therefore therefore S is an isometry and
+
+767
+00:59:59,150 --> 01:00:02,250
+so ايش مالها is one to another يعني مروع شعوركم
+
+768
+01:00:02,250 --> 01:00:07,070
+لكن العلم بدهيك يعنيlet x hat element in x hat
+
+769
+01:00:07,070 --> 01:00:12,130
+capital هذا ما بدأت بتونته بدي أخد element في ال
+
+770
+01:00:12,130 --> 01:00:18,030
+code domain هنا و أقول فيه اللي هو element في ال
+
+771
+01:00:18,030 --> 01:00:20,950
+domain بحيث ان صورة هذا element هو اللي بدأت فيه
+
+772
+01:00:20,950 --> 01:00:26,840
+طيب صلى على النبي عليه الصلاة والسلامما دام x hat
+
+773
+01:00:26,840 --> 01:00:30,420
+في الـ x hat أنا بدي أروح للجسر، للجسر، الجسر مين؟
+
+774
+01:00:30,420 --> 01:00:34,960
+الجسر w و w تلدة اني اللي بوصلني لمين؟ لأصل من x
+
+775
+01:00:34,960 --> 01:00:38,800
+hat ل x تلدة و من x تلدة ل x hat let x hat element
+
+776
+01:00:38,800 --> 01:00:42,400
+in x تلدة then there is a sequence x unhat of
+
+777
+01:00:42,400 --> 01:00:46,460
+elements in w لأنها w dense فيها such that limit x
+
+778
+01:00:46,460 --> 01:00:50,680
+unhat إيش بيساوي ال x hat اللي عندي لأن since T is
+
+779
+01:00:50,680 --> 01:00:55,800
+onto T نفسها is ontoما هي تي ازومتريك ازومتريك و
+
+780
+01:00:55,800 --> 01:01:00,140
+bijection اللي بدأنا فيها مدام تي on two إذا هذه
+
+781
+01:01:00,140 --> 01:01:04,120
+اللي لجيهت هناك الواحدة فيه اللي هي إيش أصل then
+
+782
+01:01:04,120 --> 01:01:07,960
+since T is on two then there is a sequence xn تلدة
+
+783
+01:01:07,960 --> 01:01:11,800
+of elements in y تلدة such that T xn تلدة هذه
+
+784
+01:01:11,800 --> 01:01:17,200
+بتساومين ال xn head لإن تي الأصلية on two for all
+
+785
+01:01:17,200 --> 01:01:23,280
+nthen limit هذا بيساوي limit هذا limit TXN تلده
+
+786
+01:01:23,280 --> 01:01:28,360
+بيساوي من ال X هذا بظبط؟ بطبيعي بيساوي limit XN
+
+787
+01:01:28,360 --> 01:01:32,960
+هذه و XN limitها من من هو ال X هذا الآن إذا صارت
+
+788
+01:01:32,960 --> 01:01:38,360
+ال TXN تلده نفسها كوشي sequence in من W ماعش الحال
+
+789
+01:01:38,360 --> 01:01:45,040
+من تعريف الأصل بين W ومن من من ال .. ال .. ال ..
+
+790
+01:01:45,040 --> 01:01:46,840
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+791
+01:01:46,840 --> 01:01:49,120
+.. ال .. ال .. ال .. ال .. ال ..However, T is an
+
+792
+01:01:49,120 --> 01:01:51,020
+isometry مدينة T هي عبارة عن عبارة عن عبارة عن
+
+793
+01:01:51,020 --> 01:01:53,660
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+794
+01:01:53,660 --> 01:01:56,040
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+795
+01:01:56,040 --> 01:01:56,480
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+796
+01:01:56,480 --> 01:01:57,700
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+797
+01:01:57,700 --> 01:02:04,280
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+798
+01:02:04,280 --> 01:02:06,060
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+799
+01:02:06,060 --> 01:02:14,140
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+800
+01:02:14,140 --> 01:02:21,990
+عنإذا الان x تلده is complete إذا أكيد في x تلده
+
+801
+01:02:21,990 --> 01:02:25,690
+في ال x تلده such that x until ده هذي بتروح لمين
+
+802
+01:02:25,690 --> 01:02:30,840
+لل x ماشيإذا نخلص اللي جينا في الآخر مين X تلده
+
+803
+01:02:30,840 --> 01:02:34,560
+بدينا ب X hat في ال X hat و اللي جينا X تلده
+
+804
+01:02:34,560 --> 01:02:38,760
+موجودة في ال X تلده capital ابحث by the definition
+
+805
+01:02:38,760 --> 01:02:44,200
+of S S X تلده هي مين ال X hat إذا صارت ال S is
+
+806
+01:02:44,200 --> 01:02:49,400
+onto therefore X تلده and X hat are isometric this
+
+807
+01:02:49,400 --> 01:02:56,680
+completes the proofوهي الأسئلة وnote that the
+
+808
+01:02:56,680 --> 01:03:01,120
+space x hat occurring in the above theorem is
+
+809
+01:03:01,120 --> 01:03:05,920
+called the completion of the given space x و الله
+
+810
+01:03:05,920 --> 01:03:09,140
+يعطيكم العافية والسلام عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/uwT2Fp1FRO0_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/uwT2Fp1FRO0_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..ccbfa52e4f2ed0a2050801752380d588d694008e
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+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/uwT2Fp1FRO0_raw.json
@@ -0,0 +1 @@
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بنلاقي if there exists a bijection عزيمتري of X onto Y", "tokens": [3224, 15730, 5296, 15042, 8717, 39648, 18871, 2423, 39184, 314, 9154, 1783, 5296, 3615, 41260, 398, 6225, 11622, 32640, 2655, 16572, 4117, 34051, 366, 264, 286, 6225, 11622, 32640, 2655, 16572, 4117, 12399, 382, 257, 2445, 13672, 1829, 4724, 1863, 39648, 36145, 2423, 39184, 1901, 1783, 307, 848, 281, 312, 6225, 11622, 32640, 2655, 16572, 4117, 9122, 24824, 4032, 2423, 39184, 1901, 398, 11933, 15730, 4724, 1863, 15040, 38436, 498, 456, 8198, 257, 3228, 1020, 313, 6225, 11622, 32640, 2655, 16572, 295, 1783, 3911, 398], "avg_logprob": -0.30123546373012455, "compression_ratio": 1.6166666666666667, "no_speech_prob": 7.152557373046875e-07, "words": [{"start": 159.92, "end": 160.28, "word": "هذا", "probability": 0.791259765625}, {"start": 160.28, "end": 160.46, "word": " لما", "probability": 0.6373291015625}, {"start": 160.46, "end": 160.82, "word": " نقول", "probability": 0.97802734375}, {"start": 160.82, "end": 161.18, 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"probability": 0.98076171875}, {"start": 197.35, "end": 197.63, "word": " فيه", "probability": 0.994384765625}, {"start": 197.63, "end": 197.71, "word": " ال", "probability": 0.74365234375}, {"start": 197.71, "end": 197.99, "word": " metric", "probability": 0.90478515625}, {"start": 197.99, "end": 198.65, "word": " space", "probability": 0.94873046875}, {"start": 198.65, "end": 199.49, "word": " X", "probability": 0.93505859375}, {"start": 199.49, "end": 200.27, "word": " أو", "probability": 0.391845703125}, {"start": 200.27, "end": 200.51, "word": " D", "probability": 0.943359375}], "temperature": 1.0}, {"id": 10, "seek": 21627, "start": 201.23, "end": 216.27, "text": "وعندي اللي هو Y وD تلدة بنقول عنهم ان هدولة isometric ال spaces يعني بمعنى اخر هما نفس الاشي بس اختلفت في الأسماء هذه الأسانة فيها X وهذه الأسانة فيها اسمها TX", "tokens": [2407, 3615, 1863, 16254, 13672, 1829, 31439, 398, 4032, 35, 6055, 1211, 3215, 3660, 44945, 39648, 18871, 16095, 16472, 8032, 3215, 12610, 3660, 307, 29470, 2423, 7673, 37495, 22653, 4724, 2304, 3615, 1863, 7578, 1975, 34740, 8032, 15042, 8717, 36178, 2423, 33599, 1829, 4724, 3794, 1975, 46456, 46538, 2655, 8978, 16247, 38251, 16606, 29538, 16247, 3794, 7649, 3660, 8978, 11296, 1783, 37037, 24192, 16247, 3794, 7649, 3660, 8978, 11296, 24525, 2304, 11296, 314, 55], "avg_logprob": -0.2306249976158142, "compression_ratio": 1.5798816568047338, "no_speech_prob": 5.4836273193359375e-06, "words": [{"start": 201.23, "end": 201.89, "word": "وعندي", "probability": 0.66607666015625}, {"start": 201.89, "end": 202.09, "word": " اللي", "probability": 0.587646484375}, {"start": 202.09, "end": 202.33, "word": " هو", "probability": 0.93212890625}, {"start": 202.33, "end": 202.67, "word": " Y", "probability": 0.5166015625}, {"start": 202.67, "end": 203.21, "word": " وD", "probability": 0.695068359375}, {"start": 203.21, "end": 204.05, "word": " تلدة", "probability": 0.654296875}, {"start": 204.05, "end": 204.83, "word": " بنقول", "probability": 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{"start": 210.15, "end": 210.35, "word": " بس", "probability": 0.96337890625}, {"start": 210.35, "end": 210.87, "word": " اختلفت", "probability": 0.9515380859375}, {"start": 210.87, "end": 211.73, "word": " في", "probability": 0.814453125}, {"start": 211.73, "end": 212.21, "word": " الأسماء", "probability": 0.8636067708333334}, {"start": 212.21, "end": 212.51, "word": " هذه", "probability": 0.490234375}, {"start": 212.51, "end": 213.39, "word": " الأسانة", "probability": 0.7991943359375}, {"start": 213.39, "end": 213.63, "word": " فيها", "probability": 0.9755859375}, {"start": 213.63, "end": 214.01, "word": " X", "probability": 0.93115234375}, {"start": 214.01, "end": 214.61, "word": " وهذه", "probability": 0.82958984375}, {"start": 214.61, "end": 215.03, "word": " الأسانة", "probability": 0.98583984375}, {"start": 215.03, "end": 215.27, "word": " فيها", "probability": 0.969482421875}, {"start": 215.27, "end": 215.63, "word": " اسمها", "probability": 0.8937174479166666}, {"start": 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0.6936848958333334}, {"start": 393.97, "end": 394.19, "word": " ايش", "probability": 0.7125651041666666}, {"start": 394.19, "end": 394.29, "word": " اللي", "probability": 0.958984375}, {"start": 394.29, "end": 395.25, "word": " بنقوله", "probability": 0.91845703125}, {"start": 395.25, "end": 396.19, "word": " اللي", "probability": 0.92529296875}, {"start": 396.19, "end": 396.69, "word": " بقوله", "probability": 0.97314453125}, {"start": 396.69, "end": 397.29, "word": " التالت", "probability": 0.9441731770833334}, {"start": 397.29, "end": 398.89, "word": " انه", "probability": 0.79541015625}, {"start": 398.89, "end": 400.81, "word": " انا", "probability": 0.7880859375}, {"start": 400.81, "end": 401.39, "word": " غرضي", "probability": 0.9287109375}, {"start": 401.39, "end": 401.83, "word": " ان", "probability": 0.89208984375}, {"start": 401.83, "end": 402.63, "word": " الاجي", "probability": 0.67669677734375}, {"start": 402.63, "end": 402.89, "word": " اللي", "probability": 0.922607421875}, {"start": 402.89, "end": 403.19, "word": " هو", "probability": 0.95458984375}, {"start": 403.19, "end": 403.69, "word": " metric", "probability": 0.884765625}, {"start": 403.69, "end": 404.51, "word": " space", "probability": 0.9326171875}, {"start": 404.51, "end": 405.85, "word": " يكون", "probability": 0.97412109375}, {"start": 405.85, "end": 406.53, "word": " completion", "probability": 0.68505859375}, {"start": 406.53, "end": 407.25, "word": " لل", "probability": 0.173583984375}, {"start": 407.25, "end": 408.19, "word": " X", "probability": 0.474365234375}], "temperature": 1.0}, {"id": 19, "seek": 42504, "start": 410.52, "end": 425.04, "text": "الان عندى .. بقولكم أكيد هلاقي space اسمه X hat وD hat هذا ال space يتمتع بالآتى اللى فيه W فيه ال closure إيه هي أشبت ثانية؟ X hat", "tokens": [6027, 7649, 43242, 7578, 4386, 4724, 39648, 24793, 5551, 4117, 25708, 8032, 15040, 38436, 1901, 24525, 2304, 3224, 1783, 2385, 4032, 35, 2385, 23758, 2423, 1901, 7251, 39237, 2655, 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415.5, "word": " X", "probability": 0.488525390625}, {"start": 415.5, "end": 415.82, "word": " hat", "probability": 0.479736328125}, {"start": 415.82, "end": 416.12, "word": " وD", "probability": 0.7568359375}, {"start": 416.12, "end": 416.46, "word": " hat", "probability": 0.96728515625}, {"start": 416.46, "end": 417.32, "word": " هذا", "probability": 0.7783203125}, {"start": 417.32, "end": 417.48, "word": " ال", "probability": 0.99267578125}, {"start": 417.48, "end": 418.04, "word": " space", "probability": 0.81005859375}, {"start": 418.04, "end": 419.22, "word": " يتمتع", "probability": 0.987060546875}, {"start": 419.22, "end": 420.04, "word": " بالآتى", "probability": 0.675048828125}, {"start": 420.04, "end": 420.58, "word": " اللى", "probability": 0.880615234375}, {"start": 420.58, "end": 420.88, "word": " فيه", "probability": 0.870849609375}, {"start": 420.88, "end": 421.12, "word": " W", "probability": 0.431884765625}, {"start": 421.12, "end": 422.02, "word": " فيه", 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444.75, "word": " صارت", "probability": 0.98779296875}, {"start": 444.75, "end": 445.01, "word": " X", "probability": 0.9091796875}, {"start": 445.01, "end": 445.35, "word": " hat", "probability": 0.9638671875}, {"start": 445.35, "end": 445.75, "word": " complete", "probability": 0.837890625}, {"start": 445.75, "end": 446.51, "word": " space", "probability": 0.93310546875}, {"start": 446.51, "end": 447.23, "word": " اللي", "probability": 0.977294921875}, {"start": 447.23, "end": 447.53, "word": " هو", "probability": 0.9912109375}], "temperature": 1.0}, {"id": 21, "seek": 47066, "start": 448.3, "end": 470.66, "text": "في subspace منه isometric للـ X اللي هو هذا اللي هنسمي انه completion لمين للـ X أي سؤال يعني مش شرط انه احنا يجينا و الله نحطنا limit points هنا و هنا نحطناها لأ احنا بنجيب space complete كامل و نclosure ل W هي عبارة عن ال X hat و ال W هي ال X", "tokens": [41185, 2090, 17940, 9154, 3224, 307, 29470, 24976, 39184, 1783, 13672, 1829, 31439, 23758, 13672, 1829, 8032, 1863, 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" للـ", "probability": 0.6396484375}, {"start": 450.78, "end": 451.0, "word": " X", "probability": 0.57958984375}, {"start": 451.0, "end": 451.64, "word": " اللي", "probability": 0.52294921875}, {"start": 451.64, "end": 451.72, "word": " هو", "probability": 0.57568359375}, {"start": 451.72, "end": 451.96, "word": " هذا", "probability": 0.748046875}, {"start": 451.96, "end": 452.16, "word": " اللي", "probability": 0.971435546875}, {"start": 452.16, "end": 452.9, "word": " هنسمي", "probability": 0.8033447265625}, {"start": 452.9, "end": 453.38, "word": " انه", "probability": 0.5977783203125}, {"start": 453.38, "end": 454.36, "word": " completion", "probability": 0.609375}, {"start": 454.36, "end": 455.46, "word": " لمين", "probability": 0.599609375}, {"start": 455.46, "end": 456.14, "word": " للـ", "probability": 0.6192626953125}, {"start": 456.14, "end": 456.44, "word": " X", "probability": 0.91259765625}, {"start": 456.44, "end": 457.22, "word": " أي", "probability": 0.427978515625}, {"start": 457.22, "end": 457.66, "word": " سؤال", "probability": 0.994140625}, {"start": 457.66, "end": 458.24, "word": " يعني", "probability": 0.850830078125}, {"start": 458.24, "end": 458.62, "word": " مش", "probability": 0.9091796875}, {"start": 458.62, "end": 458.9, "word": " شرط", "probability": 0.978515625}, {"start": 458.9, "end": 459.1, "word": " انه", "probability": 0.633544921875}, {"start": 459.1, "end": 459.28, "word": " احنا", "probability": 0.9344075520833334}, {"start": 459.28, "end": 459.62, "word": " يجينا", "probability": 0.8370361328125}, {"start": 459.62, "end": 459.74, "word": " و", "probability": 0.64501953125}, {"start": 459.74, "end": 459.86, "word": " الله", "probability": 0.87744140625}, {"start": 459.86, "end": 460.36, "word": " نحطنا", "probability": 0.916748046875}, {"start": 460.36, "end": 460.64, "word": " limit", "probability": 0.84130859375}, {"start": 460.64, "end": 461.06, "word": " points", "probability": 0.307373046875}, {"start": 461.06, "end": 461.36, "word": " هنا", "probability": 0.73193359375}, {"start": 461.36, "end": 461.58, "word": " و", "probability": 0.5185546875}, {"start": 461.58, "end": 461.58, "word": " هنا", "probability": 0.95654296875}, {"start": 461.58, "end": 462.04, "word": " نحطناها", "probability": 0.800341796875}, {"start": 462.04, "end": 462.26, "word": " لأ", "probability": 0.7724609375}, {"start": 462.26, "end": 462.88, "word": " احنا", "probability": 0.9137369791666666}, {"start": 462.88, "end": 463.4, "word": " بنجيب", "probability": 0.9613037109375}, {"start": 463.4, "end": 463.7, "word": " space", "probability": 0.87841796875}, {"start": 463.7, "end": 464.3, "word": " complete", "probability": 0.87841796875}, {"start": 464.3, "end": 464.94, "word": " كامل", "probability": 0.9879557291666666}, {"start": 464.94, "end": 465.52, "word": " و", "probability": 0.810546875}, {"start": 465.52, "end": 466.16, "word": " نclosure", "probability": 0.47705078125}, {"start": 466.16, "end": 466.4, "word": " ل", "probability": 0.89990234375}, {"start": 466.4, "end": 466.78, "word": " W", "probability": 0.40869140625}, {"start": 466.78, "end": 467.18, "word": " هي", "probability": 0.93017578125}, {"start": 467.18, "end": 468.24, "word": " عبارة", "probability": 0.934326171875}, {"start": 468.24, "end": 468.42, "word": " عن", "probability": 0.99169921875}, {"start": 468.42, "end": 468.54, "word": " ال", "probability": 0.84814453125}, {"start": 468.54, "end": 468.72, "word": " X", "probability": 0.67529296875}, {"start": 468.72, "end": 469.16, "word": " hat", "probability": 0.66552734375}, {"start": 469.16, "end": 469.62, "word": " و", "probability": 0.59619140625}, {"start": 469.62, "end": 469.72, "word": " ال", "probability": 0.56298828125}, {"start": 469.72, "end": 470.04, "word": " W", "probability": 0.560546875}, {"start": 470.04, "end": 470.3, "word": " هي", "probability": 0.7734375}, {"start": 470.3, "end": 470.42, "word": " ال", "probability": 0.58544921875}, {"start": 470.42, "end": 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هكون isometric إله يعني لو كان في عند X تلدة ال complete isometric space و half نفس الخواص تبع X hat يعني having dense subspace W تلدة و W تلدة isometric لل X", "tokens": [3121, 1336, 307, 649, 10716, 37495, 22653, 45164, 39894, 3215, 1211, 7435, 1901, 6055, 7649, 1829, 37893, 16758, 3224, 11933, 43761, 8032, 30544, 307, 29470, 11933, 43761, 37495, 22653, 45164, 25961, 8978, 43242, 1783, 6055, 1211, 3215, 3660, 2423, 3566, 307, 29470, 1901, 4032, 1922, 8717, 36178, 33962, 14407, 9381, 6055, 3555, 3615, 1783, 2385, 37495, 22653, 1419, 18011, 2090, 17940, 343, 6055, 1211, 3215, 3660, 4032, 343, 6055, 1211, 3215, 3660, 307, 29470, 24976, 1783], "avg_logprob": -0.3364448160320133, "compression_ratio": 1.6145251396648044, "no_speech_prob": 1.3709068298339844e-06, "words": [{"start": 492.02, "end": 492.46, "word": "except", "probability": 0.620849609375}, {"start": 492.46, "end": 493.06, "word": " isometrics", "probability": 0.5638020833333334}, {"start": 493.06, "end": 493.28, "word": " 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0.990234375}, {"start": 499.7, "end": 499.86, "word": " في", "probability": 0.90380859375}, {"start": 499.86, "end": 500.14, "word": " عند", "probability": 0.85498046875}, {"start": 500.14, "end": 500.52, "word": " X", "probability": 0.398193359375}, {"start": 500.52, "end": 501.46, "word": " تلدة", "probability": 0.682373046875}, {"start": 501.46, "end": 502.22, "word": " ال", "probability": 0.472900390625}, {"start": 502.22, "end": 502.88, "word": " complete", "probability": 0.779296875}, {"start": 502.88, "end": 503.48, "word": " isometric", "probability": 0.768310546875}, {"start": 503.48, "end": 504.16, "word": " space", "probability": 0.9580078125}, {"start": 504.16, "end": 504.7, "word": " و", "probability": 0.89892578125}, {"start": 504.7, "end": 505.1, "word": " half", "probability": 0.365234375}, {"start": 505.1, "end": 505.52, "word": " نفس", "probability": 0.970947265625}, {"start": 505.52, "end": 506.2, "word": " الخواص", "probability": 0.4947102864583333}, {"start": 506.2, "end": 506.42, "word": " تبع", "probability": 0.7115071614583334}, {"start": 506.42, "end": 506.74, "word": " X", "probability": 0.70654296875}, {"start": 506.74, "end": 507.12, "word": " hat", "probability": 0.7734375}, {"start": 507.12, "end": 507.7, "word": " يعني", "probability": 0.8837890625}, {"start": 507.7, "end": 508.2, "word": " having", "probability": 0.498779296875}, {"start": 508.2, "end": 509.16, "word": " dense", "probability": 0.1903076171875}, {"start": 509.16, "end": 509.92, "word": " subspace", "probability": 0.926513671875}, {"start": 509.92, "end": 510.4, "word": " W", "probability": 0.8681640625}, {"start": 510.4, "end": 511.24, "word": " تلدة", "probability": 0.8734130859375}, {"start": 511.24, "end": 511.62, "word": " و", "probability": 0.9248046875}, {"start": 511.62, "end": 512.02, "word": " W", "probability": 0.619140625}, {"start": 512.02, "end": 512.4, "word": " تلدة", "probability": 0.9532470703125}, {"start": 512.4, "end": 512.92, "word": " isometric", "probability": 0.9453125}, {"start": 512.92, "end": 513.18, "word": " لل", "probability": 0.64892578125}, {"start": 513.18, "end": 513.48, "word": " X", "probability": 0.9150390625}], "temperature": 1.0}, {"id": 24, "seek": 53504, "start": 513.59, "end": 535.05, "text": "لازم الـ x تلدة و الـ x هات أشمالين يكون isometric يعني لو بدنا نلاقي كمان واحد اسمه x تلدة أو d تلدة و هذا اللي هو ال space في w تلدة sub space منه و الـ w تلدة اللي هي dense فيه و في نفس الودة isometric للـ x هيطلع اللي هو ال x تلدة و ال x هات are isometric", "tokens": [1211, 31377, 2304, 2423, 39184, 2031, 6055, 1211, 3215, 3660, 4032, 2423, 39184, 2031, 8032, 9307, 5551, 8592, 2304, 6027, 9957, 7251, 30544, 307, 29470, 37495, 22653, 45164, 47525, 8315, 8717, 15040, 38436, 9122, 2304, 7649, 36764, 24401, 24525, 2304, 3224, 2031, 6055, 1211, 3215, 3660, 34051, 274, 6055, 1211, 3215, 3660, 4032, 23758, 13672, 1829, 31439, 2423, 1901, 8978, 261, 6055, 1211, 3215, 3660, 1422, 1901, 9154, 3224, 4032, 2423, 39184, 261, 6055, 1211, 3215, 3660, 13672, 1829, 39896, 18011, 8978, 3224, 4032, 8978, 8717, 36178, 2423, 23328, 3660, 307, 29470, 24976, 39184, 2031, 39896, 9566, 1211, 3615, 13672, 1829, 31439, 2423, 2031, 6055, 1211, 3215, 3660, 4032, 2423, 2031, 8032, 9307, 366, 307, 29470], "avg_logprob": -0.25614316544981086, "compression_ratio": 1.9801980198019802, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 513.59, "end": 514.01, "word": "لازم", "probability": 0.7843424479166666}, {"start": 514.01, "end": 514.11, "word": " الـ", "probability": 0.69580078125}, {"start": 514.11, "end": 514.21, "word": " x", "probability": 0.37109375}, {"start": 514.21, "end": 514.51, "word": " تلدة", "probability": 0.64990234375}, {"start": 514.51, "end": 514.61, "word": " و", "probability": 0.671875}, {"start": 514.61, "end": 514.75, "word": " الـ", "probability": 0.593994140625}, {"start": 514.75, "end": 514.97, "word": " x", "probability": 0.955078125}, {"start": 514.97, "end": 515.19, "word": " هات", "probability": 0.335205078125}, {"start": 515.19, "end": 515.83, "word": " أشمالين", "probability": 0.80029296875}, {"start": 515.83, "end": 516.57, "word": " يكون", "probability": 0.951416015625}, {"start": 516.57, "end": 517.13, "word": " isometric", "probability": 0.5968017578125}, {"start": 517.13, "end": 517.47, "word": " يعني", "probability": 0.78564453125}, {"start": 517.47, "end": 517.63, "word": " لو", "probability": 0.96484375}, {"start": 517.63, "end": 517.91, "word": " بدنا", "probability": 0.978759765625}, {"start": 517.91, "end": 518.19, "word": " نلاقي", "probability": 0.9523111979166666}, {"start": 518.19, "end": 518.61, "word": " كمان", "probability": 0.92333984375}, {"start": 518.61, "end": 518.97, "word": " واحد", "probability": 0.994873046875}, {"start": 518.97, "end": 519.29, "word": " اسمه", "probability": 0.9685872395833334}, {"start": 519.29, "end": 519.51, "word": " x", "probability": 0.89599609375}, {"start": 519.51, "end": 520.13, "word": " تلدة", "probability": 0.8302001953125}, {"start": 520.13, "end": 520.49, "word": " أو", "probability": 0.5986328125}, {"start": 520.49, "end": 520.71, "word": " d", "probability": 0.82763671875}, {"start": 520.71, "end": 521.29, "word": " تلدة", "probability": 0.93603515625}, {"start": 521.29, "end": 521.61, "word": " و", "probability": 0.33447265625}, {"start": 521.61, "end": 522.05, "word": " هذا", "probability": 0.91796875}, {"start": 522.05, "end": 522.41, "word": " اللي", "probability": 0.978759765625}, {"start": 522.41, "end": 522.65, "word": " هو", "probability": 0.98974609375}, {"start": 522.65, "end": 522.81, "word": " ال", "probability": 0.98193359375}, {"start": 522.81, "end": 523.25, "word": " space", "probability": 0.75}, {"start": 523.25, "end": 523.67, "word": " في", "probability": 0.94384765625}, {"start": 523.67, "end": 524.19, "word": " w", "probability": 0.52783203125}, {"start": 524.19, "end": 524.91, "word": " تلدة", "probability": 0.90576171875}, {"start": 524.91, "end": 525.33, "word": " sub", "probability": 0.2197265625}, {"start": 525.33, "end": 526.07, "word": " space", "probability": 0.6943359375}, {"start": 526.07, "end": 526.63, "word": " منه", "probability": 0.978271484375}, {"start": 526.63, "end": 526.95, "word": " و", "probability": 0.84033203125}, {"start": 526.95, "end": 527.23, "word": " الـ", "probability": 0.7568359375}, {"start": 527.23, "end": 527.39, "word": " w", "probability": 0.6494140625}, {"start": 527.39, "end": 527.87, "word": " تلدة", "probability": 0.919189453125}, {"start": 527.87, "end": 528.05, "word": " اللي", "probability": 0.95166015625}, {"start": 528.05, "end": 528.21, "word": " هي", "probability": 0.91015625}, {"start": 528.21, "end": 528.55, "word": " dense", "probability": 0.54541015625}, {"start": 528.55, "end": 529.05, "word": " فيه", "probability": 0.975341796875}, {"start": 529.05, "end": 529.23, "word": " و", "probability": 0.59423828125}, {"start": 529.23, "end": 529.33, "word": " في", "probability": 0.8388671875}, {"start": 529.33, "end": 529.55, "word": " نفس", "probability": 0.997314453125}, {"start": 529.55, "end": 529.89, "word": " الودة", "probability": 0.5927734375}, {"start": 529.89, "end": 530.45, "word": " isometric", "probability": 0.7215576171875}, {"start": 530.45, "end": 530.81, "word": " للـ", "probability": 0.5272216796875}, {"start": 530.81, "end": 530.97, "word": " x", "probability": 0.4736328125}, {"start": 530.97, "end": 531.97, "word": " هيطلع", "probability": 0.8636474609375}, {"start": 531.97, "end": 532.13, "word": " اللي", "probability": 0.986083984375}, {"start": 532.13, "end": 532.27, "word": " هو", "probability": 0.98095703125}, {"start": 532.27, "end": 532.43, "word": " ال", "probability": 0.96044921875}, {"start": 532.43, "end": 532.67, "word": " x", "probability": 0.3701171875}, {"start": 532.67, "end": 533.11, "word": " تلدة", "probability": 0.959716796875}, {"start": 533.11, "end": 533.19, "word": " و", "probability": 0.84912109375}, {"start": 533.19, "end": 533.29, "word": " ال", "probability": 0.9619140625}, {"start": 533.29, "end": 533.47, "word": " x", "probability": 0.46923828125}, {"start": 533.47, "end": 533.77, "word": " هات", "probability": 0.931396484375}, {"start": 533.77, "end": 534.21, "word": " are", "probability": 0.71044921875}, {"start": 534.21, "end": 535.05, "word": " isometric", "probability": 0.9560546875}], "temperature": 1.0}, {"id": 25, "seek": 55553, "start": 535.51, "end": 555.53, "text": "واضح اذا نرخص النظرية there exist a complete metric space او a completion metric space لهذا ال space بالمفهوم اللي حكيناه وهذا ال metric واحد except for isometric", "tokens": [2407, 46958, 5016, 1975, 15730, 8717, 2288, 9778, 9381, 28239, 19913, 2288, 10632, 456, 2514, 257, 3566, 20678, 1901, 1975, 2407, 257, 19372, 20678, 1901, 46740, 15730, 2423, 1901, 20666, 2304, 5172, 3224, 20498, 13672, 1829, 11331, 4117, 1829, 8315, 3224, 37037, 15730, 2423, 20678, 36764, 24401, 3993, 337, 307, 29470], "avg_logprob": 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بساوى ال limit لل distance xn yn as n goes to infinity ال xn مالها كوش ال sequences فيها دي و ال yn كوش ال sequences في مين؟ في التانية", "tokens": [6027, 7649, 39894, 3215, 3615, 28480, 2423, 274, 2385, 1975, 1829, 8592, 2423, 274, 2385, 39894, 3215, 3615, 28480, 2423, 274, 2385, 295, 2031, 2385, 4032, 288, 2385, 4724, 3794, 995, 2407, 7578, 2423, 4948, 24976, 4560, 2031, 77, 17861, 382, 297, 1709, 281, 13202, 2423, 2031, 77, 3714, 6027, 11296, 9122, 2407, 8592, 2423, 22978, 8978, 11296, 11778, 1829, 4032, 2423, 17861, 9122, 2407, 8592, 2423, 22978, 8978, 3714, 9957, 22807, 8978, 16712, 7649, 10632], "avg_logprob": -0.33116883271700376, "compression_ratio": 1.6746987951807228, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 937.05, "end": 937.65, "word": "الان", "probability": 0.759765625}, {"start": 937.65, "end": 938.25, "word": " بتدعرف", "probability": 0.7095947265625}, {"start": 938.25, "end": 938.49, "word": " ال", "probability": 0.89453125}, {"start": 938.49, 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{"start": 972.34, "end": 973.0, "word": " انتوا", "probability": 0.8116861979166666}, {"start": 973.0, "end": 973.28, "word": " تروحوا", "probability": 0.9869384765625}, {"start": 973.28, "end": 973.68, "word": " تاخدوا", "probability": 0.9691162109375}, {"start": 973.68, "end": 974.58, "word": " ناخد", "probability": 0.6790364583333334}, {"start": 974.58, "end": 974.96, "word": " xn", "probability": 0.861572265625}, {"start": 974.96, "end": 975.14, "word": " و", "probability": 0.66796875}, {"start": 975.14, "end": 975.48, "word": " تاخدوا", "probability": 0.9302978515625}, {"start": 975.48, "end": 975.64, "word": " z", "probability": 0.7412109375}], "temperature": 1.0}, {"id": 44, "seek": 99754, "start": 977.1, "end": 997.54, "text": "الواحد ياخد دي يبدو YN و KN و YN و KN أشمالين related لبعض في نفس ال equivalency class خايفين يطلع جواب يعني لما ناخد ال limit لل distance بين XN و YN و جوابكم يبدأ ال limit لل distance بين ZN و KN يطلع مش زي بعض فلأ بدنا نثبت لكم أنه بطلع زي بعض دعونا 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" limit", "probability": 0.9453125}, {"start": 988.52, "end": 988.74, "word": " لل", "probability": 0.89111328125}, {"start": 988.74, "end": 989.24, "word": " distance", "probability": 0.96826171875}, {"start": 989.24, "end": 989.54, "word": " بين", "probability": 0.9111328125}, {"start": 989.54, "end": 990.42, "word": " ZN", "probability": 0.96533203125}, {"start": 990.42, "end": 990.52, "word": " و", "probability": 0.99462890625}, {"start": 990.52, "end": 990.96, "word": " KN", "probability": 0.81591796875}, {"start": 990.96, "end": 991.28, "word": " يطلع", "probability": 0.933837890625}, {"start": 991.28, "end": 991.44, "word": " مش", "probability": 0.68701171875}, {"start": 991.44, "end": 991.56, "word": " زي", "probability": 0.71533203125}, {"start": 991.56, "end": 991.96, "word": " بعض", "probability": 0.96484375}, {"start": 991.96, "end": 993.04, "word": " فلأ", "probability": 0.9537760416666666}, {"start": 993.04, "end": 993.38, "word": " بدنا", "probability": 0.851806640625}, {"start": 993.38, "end": 993.74, "word": " نثبت", "probability": 0.9925537109375}, {"start": 993.74, "end": 993.98, "word": " لكم", "probability": 0.754150390625}, {"start": 993.98, "end": 994.26, "word": " أنه", "probability": 0.7296142578125}, {"start": 994.26, "end": 994.64, "word": " بطلع", "probability": 0.845947265625}, {"start": 994.64, "end": 995.24, "word": " زي", "probability": 0.983154296875}, {"start": 995.24, "end": 995.92, "word": " بعض", "probability": 0.99072265625}, {"start": 995.92, "end": 996.22, "word": " دعونا", "probability": 0.68157958984375}, {"start": 996.22, "end": 996.4, "word": " نشوف", "probability": 0.9972330729166666}, {"start": 996.4, "end": 996.64, "word": " كيف", "probability": 0.82421875}, {"start": 996.64, "end": 996.88, "word": " ..", "probability": 0.1468505859375}, {"start": 996.88, "end": 997.14, "word": " اطلع", "probability": 0.95703125}, {"start": 997.14, "end": 997.24, "word": " على", "probability": 0.4755859375}, {"start": 997.24, "end": 997.54, "word": " فوق", "probability": 0.93603515625}], "temperature": 1.0}, {"id": 45, "seek": 102848, "start": 999.42, "end": 1028.48, "text": "to prove that this limit exists we do as follow بدنا نعمل كمان يعني ب triangling quality سهلة اللي هو distance بين Xm و Ym ب triangling quality أثر سواء distance بين Xm و Xm ماشي زاد distance بين Xm و Ym زاد ال distance بين Ym و Ym انه un-arbitrary ماشي then جيبولي هذه hand اللي هي ال Ym و Xm على الجهة دي بيصير عندى distance بين Xm و Ym", "tokens": [1353, 7081, 300, 341, 4948, 8198, 321, 360, 382, 1524, 4724, 3215, 8315, 8717, 25957, 1211, 9122, 2304, 7649, 37495, 22653, 4724, 19335, 1688, 3125, 8608, 3224, 37977, 13672, 1829, 31439, 4560, 49374, 1783, 76, 4032, 398, 76, 4724, 19335, 1688, 3125, 5551, 49115, 8608, 2407, 16606, 4560, 49374, 1783, 76, 4032, 1783, 76, 3714, 33599, 1829, 30767, 18513, 4560, 49374, 1783, 76, 4032, 398, 76, 30767, 18513, 2423, 4560, 49374, 398, 76, 4032, 398, 76, 16472, 3224, 517, 12, 289, 5260, 81, 822, 3714, 33599, 1829, 550, 10874, 1829, 3555, 12610, 1829, 29538, 1011, 13672, 1829, 39896, 2423, 398, 76, 4032, 1783, 76, 15844, 25724, 3224, 3660, 11778, 1829, 4724, 1829, 9381, 13546, 43242, 7578, 4560, 49374, 1783, 76, 4032, 398, 76], "avg_logprob": -0.2951109012769115, "compression_ratio": 1.8178137651821862, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 999.42, "end": 999.6, "word": "to", "probability": 0.1624755859375}, {"start": 999.6, "end": 999.96, "word": " prove", "probability": 0.931640625}, {"start": 999.96, "end": 1000.24, "word": " that", "probability": 0.90283203125}, {"start": 1000.24, "end": 1000.56, "word": " this", "probability": 0.9189453125}, {"start": 1000.56, "end": 1000.9, "word": " limit", "probability": 0.92236328125}, {"start": 1000.9, "end": 1001.42, "word": " exists", "probability": 0.51708984375}, {"start": 1001.42, "end": 1001.86, "word": " we", "probability": 0.609375}, {"start": 1001.86, "end": 1002.34, "word": " do", "probability": 0.89111328125}, {"start": 1002.34, "end": 1002.82, "word": " as", "probability": 0.94189453125}, {"start": 1002.82, "end": 1003.22, "word": " follow", "probability": 0.609375}, {"start": 1003.22, "end": 1003.64, "word": " بدنا", "probability": 0.580322265625}, {"start": 1003.64, "end": 1003.92, "word": " نعمل", "probability": 0.9930013020833334}, {"start": 1003.92, "end": 1004.22, "word": " كمان", "probability": 0.634521484375}, {"start": 1004.22, "end": 1004.42, "word": " يعني", "probability": 0.6015625}, {"start": 1004.42, "end": 1004.66, "word": " ب", "probability": 0.385009765625}, {"start": 1004.66, "end": 1005.3, "word": " triangling", "probability": 0.51513671875}, {"start": 1005.3, "end": 1005.62, "word": " quality", "probability": 0.75927734375}, {"start": 1005.62, "end": 1006.02, "word": " سهلة", "probability": 0.9376627604166666}, {"start": 1006.02, "end": 1006.66, "word": " اللي", "probability": 0.876953125}, {"start": 1006.66, "end": 1006.86, "word": " هو", "probability": 0.9560546875}, {"start": 1006.86, "end": 1007.28, "word": " distance", "probability": 0.7998046875}, {"start": 1007.28, "end": 1007.52, "word": " بين", "probability": 0.8125}, {"start": 1007.52, "end": 1007.86, "word": " Xm", "probability": 0.412109375}, {"start": 1007.86, "end": 1008.02, "word": " و", "probability": 0.9765625}, {"start": 1008.02, "end": 1008.4, "word": " Ym", "probability": 0.702392578125}, {"start": 1008.4, "end": 1008.7, "word": " ب", "probability": 0.572265625}, {"start": 1008.7, "end": 1009.22, "word": " triangling", "probability": 0.71923828125}, {"start": 1009.22, "end": 1009.6, "word": " quality", "probability": 0.880859375}, {"start": 1009.6, "end": 1010.06, "word": " أثر", "probability": 0.35595703125}, {"start": 1010.06, "end": 1010.36, "word": " سواء", "probability": 0.6795247395833334}, {"start": 1010.36, "end": 1010.72, "word": " distance", "probability": 0.97119140625}, {"start": 1010.72, "end": 1010.9, "word": " بين", "probability": 0.9443359375}, {"start": 1010.9, "end": 1011.38, "word": " Xm", "probability": 0.884033203125}, {"start": 1011.38, "end": 1011.88, "word": " و", "probability": 0.94091796875}, {"start": 1011.88, "end": 1012.34, "word": " Xm", "probability": 0.884765625}, {"start": 1012.34, "end": 1013.58, "word": " ماشي", "probability": 0.7499186197916666}, {"start": 1013.58, "end": 1014.24, "word": " زاد", "probability": 0.73828125}, {"start": 1014.24, "end": 1014.62, "word": " distance", "probability": 0.8525390625}, {"start": 1014.62, "end": 1014.8, "word": " بين", "probability": 0.90625}, {"start": 1014.8, "end": 1015.2, "word": " Xm", "probability": 0.965576171875}, {"start": 1015.2, "end": 1015.5, "word": " و", "probability": 0.99267578125}, {"start": 1015.5, "end": 1015.92, "word": " Ym", "probability": 0.90576171875}, {"start": 1015.92, "end": 1016.76, "word": " زاد", "probability": 0.853271484375}, {"start": 1016.76, "end": 1016.84, "word": " ال", "probability": 0.383056640625}, {"start": 1016.84, "end": 1017.1, "word": " distance", "probability": 0.98486328125}, {"start": 1017.1, "end": 1017.32, "word": " بين", "probability": 0.86181640625}, {"start": 1017.32, "end": 1017.68, "word": " Ym", "probability": 0.959228515625}, {"start": 1017.68, "end": 1017.92, "word": " و", "probability": 0.99609375}, {"start": 1017.92, "end": 1018.32, "word": " Ym", "probability": 0.882080078125}, {"start": 1018.32, "end": 1019.22, "word": " انه", "probability": 0.325286865234375}, {"start": 1019.22, "end": 1019.36, "word": " un", "probability": 0.544921875}, {"start": 1019.36, "end": 1019.9, "word": "-arbitrary", "probability": 0.7835693359375}, {"start": 1019.9, "end": 1020.48, "word": " ماشي", "probability": 0.9239908854166666}, {"start": 1020.48, "end": 1021.24, "word": " then", "probability": 0.8017578125}, {"start": 1021.24, "end": 1022.24, "word": " جيبولي", "probability": 0.92666015625}, {"start": 1022.24, "end": 1022.5, "word": " هذه", "probability": 0.7841796875}, {"start": 1022.5, "end": 1022.8, "word": " hand", "probability": 0.270263671875}, {"start": 1022.8, "end": 1023.94, "word": " اللي", "probability": 0.9560546875}, {"start": 1023.94, "end": 1024.26, "word": " هي", "probability": 0.94140625}, {"start": 1024.26, "end": 1024.78, "word": " ال", "probability": 0.9208984375}, {"start": 1024.78, "end": 1025.14, "word": " Ym", "probability": 0.90087890625}, {"start": 1025.14, "end": 1025.24, "word": " و", "probability": 0.92333984375}, {"start": 1025.24, "end": 1025.6, "word": " Xm", "probability": 0.898681640625}, {"start": 1025.6, "end": 1025.72, "word": " على", "probability": 0.5625}, {"start": 1025.72, "end": 1025.96, "word": " الجهة", "probability": 0.9619140625}, {"start": 1025.96, "end": 1026.26, "word": " دي", "probability": 0.79248046875}, {"start": 1026.26, "end": 1026.92, "word": " بيصير", "probability": 0.8929443359375}, {"start": 1026.92, "end": 1027.16, "word": " عندى", "probability": 0.5936279296875}, {"start": 1027.16, "end": 1027.48, "word": " distance", "probability": 0.97216796875}, {"start": 1027.48, "end": 1027.68, "word": " بين", "probability": 0.83740234375}, {"start": 1027.68, "end": 1028.0, "word": " Xm", "probability": 0.986328125}, {"start": 1028.0, "end": 1028.12, "word": " و", "probability": 0.99755859375}, {"start": 1028.12, "end": 1028.48, "word": " Ym", "probability": 0.92138671875}], "temperature": 1.0}, {"id": 46, "seek": 105051, "start": 1029.49, "end": 1050.51, "text": "نقص هذه جيبتها هنا ال distance بين YM و XM و YM أصغر و أصغر اللي بيظل اللي هو هذه و هذه اللي هي ال distance بين XN و XM و ال distance بين YM و YN اللي حصلت على هذه similarly بنفس الطريقة بدل ما بدأ بدأ بال distance XN و YN ببدأ بال distance XM و YM", "tokens": [1863, 4587, 9381, 29538, 10874, 1829, 3555, 2655, 11296, 34105, 2423, 4560, 49374, 398, 44, 4032, 1783, 44, 4032, 398, 44, 5551, 9381, 17082, 2288, 4032, 5551, 9381, 17082, 2288, 13672, 1829, 4724, 1829, 19913, 1211, 13672, 1829, 31439, 29538, 4032, 29538, 13672, 1829, 39896, 2423, 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"probability": 0.6748046875}, {"start": 1032.65, "end": 1032.99, "word": " YM", "probability": 0.425537109375}, {"start": 1032.99, "end": 1033.17, "word": " و", "probability": 0.91845703125}, {"start": 1033.17, "end": 1033.65, "word": " XM", "probability": 0.856201171875}, {"start": 1033.65, "end": 1033.73, "word": " و", "probability": 0.84423828125}, {"start": 1033.73, "end": 1034.13, "word": " YM", "probability": 0.90625}, {"start": 1034.13, "end": 1034.75, "word": " أصغر", "probability": 0.906494140625}, {"start": 1034.75, "end": 1034.85, "word": " و", "probability": 0.255126953125}, {"start": 1034.85, "end": 1035.01, "word": " أصغر", "probability": 0.77703857421875}, {"start": 1035.01, "end": 1035.15, "word": " اللي", "probability": 0.936767578125}, {"start": 1035.15, "end": 1035.87, "word": " بيظل", "probability": 0.759033203125}, {"start": 1035.87, "end": 1036.07, "word": " اللي", "probability": 0.8681640625}, {"start": 1036.07, "end": 1036.23, "word": " هو", "probability": 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1040.71, "word": " ال", "probability": 0.6064453125}, {"start": 1040.71, "end": 1041.01, "word": " distance", "probability": 0.97412109375}, {"start": 1041.01, "end": 1041.23, "word": " بين", "probability": 0.87646484375}, {"start": 1041.23, "end": 1041.71, "word": " YM", "probability": 0.98388671875}, {"start": 1041.71, "end": 1041.99, "word": " و", "probability": 0.994140625}, {"start": 1041.99, "end": 1042.43, "word": " YN", "probability": 0.767333984375}, {"start": 1042.43, "end": 1043.13, "word": " اللي", "probability": 0.9326171875}, {"start": 1043.13, "end": 1043.73, "word": " حصلت", "probability": 0.7339274088541666}, {"start": 1043.73, "end": 1043.87, "word": " على", "probability": 0.71875}, {"start": 1043.87, "end": 1044.11, "word": " هذه", "probability": 0.9228515625}, {"start": 1044.11, "end": 1044.61, "word": " similarly", "probability": 0.359619140625}, {"start": 1044.61, "end": 1045.17, "word": " بنفس", "probability": 0.968994140625}, {"start": 1045.17, "end": 1045.63, 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"start": 1651.45, "end": 1669.71, "text": "من X لعين W و جالك هذه W بتاخدها جزء من X هذه هتشوف كم جزء بدي أعرف لك T of B B المتنوين من X بساوي الـ B hat طب كيف هذه الـ B hat عبارة عن equivalence classes صح ولا لأ؟", "tokens": [27842, 1783, 5296, 3615, 9957, 343, 4032, 10874, 6027, 4117, 29538, 343, 39894, 47283, 3215, 11296, 10874, 11622, 38207, 9154, 1783, 29538, 8032, 2655, 8592, 38688, 9122, 2304, 10874, 11622, 38207, 4724, 16254, 5551, 3615, 28480, 5296, 4117, 314, 295, 363, 363, 9673, 2655, 1863, 2407, 9957, 9154, 1783, 4724, 3794, 995, 45865, 2423, 39184, 363, 2385, 23032, 3555, 9122, 33911, 29538, 2423, 39184, 363, 2385, 6225, 3555, 9640, 3660, 18871, 9052, 655, 5359, 20328, 5016, 49429, 5296, 10721, 22807], "avg_logprob": -0.32445987065633136, "compression_ratio": 1.423913043478261, "no_speech_prob": 1.3589859008789062e-05, "words": [{"start": 1651.45, "end": 1651.79, "word": "من", "probability": 0.76318359375}, {"start": 1651.79, "end": 1652.23, "word": " X", "probability": 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1952.59, "text": "We show that W closure is equal to X hat Let X hat element in X hat capital and Xn element in mean in X hat ماشي الحال ملام Xn element in X hat إذا Xn كوشي سيكوينس أكيد كوشي سيكوينس إذا for every Y أكبر من 0 there exists K element in N such that المسافة بين Xn وXk أشمالها أصغر من Y على 2", "tokens": [4360, 855, 300, 343, 24653, 307, 2681, 281, 1783, 2385, 961, 1783, 2385, 4478, 294, 1783, 2385, 4238, 293, 1783, 77, 4478, 294, 914, 294, 1783, 2385, 3714, 33599, 1829, 21542, 6027, 3714, 37440, 1783, 77, 4478, 294, 1783, 2385, 11933, 15730, 1783, 77, 9122, 2407, 8592, 1829, 8608, 1829, 4117, 2407, 9957, 3794, 5551, 4117, 25708, 9122, 2407, 8592, 1829, 8608, 1829, 4117, 2407, 9957, 3794, 11933, 15730, 337, 633, 398, 5551, 4117, 26890, 9154, 1958, 456, 8198, 591, 4478, 294, 426, 1270, 300, 9673, 3794, 31845, 3660, 49374, 1783, 77, 4032, 55, 74, 5551, 8592, 2304, 6027, 11296, 5551, 9381, 17082, 2288, 9154, 398, 15844, 568], "avg_logprob": -0.2938646799927458, 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{"start": 1931.51, "end": 1931.79, "word": " X", "probability": 0.94384765625}, {"start": 1931.79, "end": 1932.05, "word": " hat", "probability": 0.958984375}, {"start": 1932.05, "end": 1932.29, "word": " element", "probability": 0.89404296875}, {"start": 1932.29, "end": 1932.53, "word": " in", "probability": 0.9072265625}, {"start": 1932.53, "end": 1932.67, "word": " X", "probability": 0.98974609375}, {"start": 1932.67, "end": 1932.83, "word": " hat", "probability": 0.984375}, {"start": 1932.83, "end": 1933.19, "word": " capital", "probability": 0.86279296875}, {"start": 1933.19, "end": 1933.53, "word": " and", "probability": 0.73828125}, {"start": 1933.53, "end": 1933.99, "word": " Xn", "probability": 0.6175537109375}, {"start": 1933.99, "end": 1934.31, "word": " element", "probability": 0.94970703125}, {"start": 1934.31, "end": 1934.55, "word": " in", "probability": 0.92236328125}, {"start": 1934.55, "end": 1934.87, "word": " mean", "probability": 0.328369140625}, {"start": 1934.87, "end": 1935.61, "word": " in", "probability": 0.8759765625}, {"start": 1935.61, "end": 1936.17, "word": " X", "probability": 0.9775390625}, {"start": 1936.17, "end": 1936.85, "word": " hat", "probability": 0.955078125}, {"start": 1936.85, "end": 1937.27, "word": " ماشي", "probability": 0.7698567708333334}, {"start": 1937.27, "end": 1937.61, "word": " الحال", "probability": 0.970947265625}, {"start": 1937.61, "end": 1938.79, "word": " ملام", "probability": 0.44287109375}, {"start": 1938.79, "end": 1939.95, "word": " Xn", "probability": 0.77880859375}, {"start": 1939.95, "end": 1940.13, "word": " element", "probability": 0.912109375}, {"start": 1940.13, "end": 1940.43, "word": " in", "probability": 0.93115234375}, {"start": 1940.43, "end": 1940.57, "word": " X", "probability": 0.99072265625}, {"start": 1940.57, "end": 1940.75, "word": " hat", "probability": 0.96728515625}, {"start": 1940.75, "end": 1940.93, "word": " إذا", "probability": 0.4515380859375}, {"start": 1940.93, "end": 1941.49, "word": " Xn", "probability": 0.899169921875}, {"start": 1941.49, "end": 1941.81, "word": " كوشي", "probability": 0.73077392578125}, {"start": 1941.81, "end": 1942.37, "word": " سيكوينس", "probability": 0.7294514973958334}, {"start": 1942.37, "end": 1943.03, "word": " أكيد", "probability": 0.89208984375}, {"start": 1943.03, "end": 1943.33, "word": " كوشي", "probability": 0.9276123046875}, {"start": 1943.33, "end": 1943.85, "word": " سيكوينس", "probability": 0.9641927083333334}, {"start": 1943.85, "end": 1944.29, "word": " إذا", "probability": 0.7978515625}, {"start": 1944.29, "end": 1944.55, "word": " for", "probability": 0.93408203125}, {"start": 1944.55, "end": 1944.83, "word": " every", "probability": 0.8154296875}, {"start": 1944.83, "end": 1945.07, "word": " Y", "probability": 0.41015625}, {"start": 1945.07, "end": 1945.41, "word": " أكبر", "probability": 0.9783528645833334}, {"start": 1945.41, "end": 1945.57, "word": " من", "probability": 0.998046875}, {"start": 1945.57, "end": 1945.83, "word": " 0", "probability": 0.48681640625}, {"start": 1945.83, "end": 1946.55, "word": " there", "probability": 0.497802734375}, {"start": 1946.55, "end": 1947.11, "word": " exists", "probability": 0.486328125}, {"start": 1947.11, "end": 1947.47, "word": " K", "probability": 0.50830078125}, {"start": 1947.47, "end": 1947.85, "word": " element", "probability": 0.9501953125}, {"start": 1947.85, "end": 1948.11, "word": " in", "probability": 0.943359375}, {"start": 1948.11, "end": 1948.25, "word": " N", "probability": 0.85400390625}, {"start": 1948.25, "end": 1948.49, "word": " such", "probability": 0.9208984375}, {"start": 1948.49, "end": 1948.73, "word": " that", "probability": 0.9521484375}, {"start": 1948.73, "end": 1949.23, "word": " المسافة", "probability": 0.972412109375}, {"start": 1949.23, "end": 1949.41, "word": " بين", "probability": 0.94970703125}, {"start": 1949.41, "end": 1949.75, "word": " Xn", "probability": 0.79638671875}, {"start": 1949.75, "end": 1950.13, "word": " وXk", "probability": 0.7174479166666666}, {"start": 1950.13, "end": 1950.75, "word": " أشمالها", "probability": 0.815966796875}, {"start": 1950.75, "end": 1951.65, "word": " أصغر", "probability": 0.9931640625}, {"start": 1951.65, "end": 1951.79, "word": " من", "probability": 0.99560546875}, {"start": 1951.79, "end": 1952.09, "word": " Y", "probability": 0.88671875}, {"start": 1952.09, "end": 1952.41, "word": " على", "probability": 0.60205078125}, {"start": 1952.41, "end": 1952.59, "word": " 2", "probability": 0.76611328125}], "temperature": 1.0}, {"id": 86, "seek": 196413, "start": 1954.51, "end": 1964.13, "text": "الـ N for all N أكبر من K هذا صحيح الـ N أكبر أو يساوي حتى عشان بتستخدمها أكبر أو يساوي من K", "tokens": [6027, 39184, 426, 337, 439, 426, 5551, 4117, 26890, 9154, 591, 23758, 20328, 5016, 1829, 5016, 2423, 39184, 426, 5551, 4117, 26890, 34051, 7251, 3794, 995, 45865, 11331, 49975, 6225, 8592, 7649, 39894, 14851, 9778, 40448, 11296, 5551, 4117, 26890, 34051, 7251, 3794, 995, 45865, 9154, 591], "avg_logprob": -0.1915690085540215, "compression_ratio": 1.3727272727272728, "no_speech_prob": 1.1920928955078125e-06, "words": [{"start": 1954.51, "end": 1954.87, "word": "الـ", "probability": 0.65869140625}, {"start": 1954.87, "end": 1954.99, "word": " N", "probability": 0.4228515625}, {"start": 1954.99, "end": 1955.51, "word": " for", "probability": 0.79541015625}, {"start": 1955.51, "end": 1955.97, "word": " all", "probability": 0.90380859375}, {"start": 1955.97, "end": 1956.23, "word": " N", "probability": 0.49267578125}, {"start": 1956.23, "end": 1956.55, "word": " أكبر", "probability": 0.9156901041666666}, {"start": 1956.55, "end": 1956.71, "word": " من", "probability": 0.880859375}, {"start": 1956.71, "end": 1956.99, "word": " K", "probability": 0.419189453125}, {"start": 1956.99, "end": 1957.55, "word": " هذا", "probability": 0.423828125}, {"start": 1957.55, "end": 1958.15, "word": " صحيح", "probability": 0.990478515625}, {"start": 1958.15, "end": 1959.81, "word": " الـ", "probability": 0.679443359375}, {"start": 1959.81, "end": 1959.89, "word": " N", "probability": 0.91650390625}, {"start": 1959.89, "end": 1960.73, "word": " أكبر", "probability": 0.96044921875}, {"start": 1960.73, "end": 1960.87, "word": " أو", "probability": 0.9609375}, {"start": 1960.87, "end": 1961.31, "word": " يساوي", "probability": 0.9705810546875}, {"start": 1961.31, "end": 1961.73, "word": " حتى", "probability": 0.88720703125}, {"start": 1961.73, "end": 1962.47, "word": " عشان", "probability": 0.8582356770833334}, {"start": 1962.47, "end": 1963.05, "word": " بتستخدمها", "probability": 0.867236328125}, {"start": 1963.05, "end": 1963.35, "word": " أكبر", "probability": 0.9620768229166666}, {"start": 1963.35, "end": 1963.41, "word": " أو", "probability": 0.82861328125}, {"start": 1963.41, "end": 1963.63, "word": " يساوي", "probability": 0.97216796875}, {"start": 1963.63, "end": 1963.75, "word": " من", "probability": 0.92431640625}, {"start": 1963.75, "end": 1964.13, "word": " K", "probability": 0.7109375}], "temperature": 1.0}, {"id": 87, "seek": 198850, "start": 1964.84, "end": 1988.5, "text": "الآن خُدلي الـ sequence xk xk xk الاخره أكيد موجودة خارج معناه أدنال أكيد موجودة في مين في الـ xk إيش hat لإن هذه عبارة عن كوشي sequence هذا أخدت الـ xk council يعني اسمه council xk xk xk هذه الكوشي sequence هذه الكوشي sequence موجودة في ال equivalency class سبعتها لـ xk hat", "tokens": [6027, 148, 48506, 16490, 10859, 3215, 20292, 2423, 39184, 8310, 2031, 74, 2031, 74, 2031, 74, 2423, 47283, 2288, 3224, 5551, 4117, 25708, 3714, 29245, 23328, 3660, 16490, 9640, 7435, 20449, 8315, 3224, 5551, 3215, 1863, 6027, 5551, 4117, 25708, 3714, 29245, 23328, 3660, 8978, 3714, 9957, 8978, 2423, 39184, 2031, 74, 11933, 1829, 8592, 2385, 5296, 28814, 1863, 29538, 6225, 3555, 9640, 3660, 18871, 9122, 2407, 8592, 1829, 8310, 23758, 5551, 9778, 3215, 2655, 2423, 39184, 2031, 74, 9209, 37495, 22653, 24525, 2304, 3224, 9209, 2031, 74, 2031, 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"probability": 0.881103515625}, {"start": 1975.84, "end": 1976.36, "word": " إيش", "probability": 0.7777506510416666}, {"start": 1976.36, "end": 1976.88, "word": " hat", "probability": 0.50341796875}, {"start": 1976.88, "end": 1977.18, "word": " لإن", "probability": 0.7350260416666666}, {"start": 1977.18, "end": 1977.48, "word": " هذه", "probability": 0.322998046875}, {"start": 1977.48, "end": 1977.84, "word": " عبارة", "probability": 0.9599609375}, {"start": 1977.84, "end": 1977.98, "word": " عن", "probability": 0.9921875}, {"start": 1977.98, "end": 1978.2, "word": " كوشي", "probability": 0.763519287109375}, {"start": 1978.2, "end": 1978.48, "word": " sequence", "probability": 0.68212890625}, {"start": 1978.48, "end": 1978.7, "word": " هذا", "probability": 0.231689453125}, {"start": 1978.7, "end": 1979.3, "word": " أخدت", "probability": 0.911376953125}, {"start": 1979.3, "end": 1979.44, "word": " الـ", "probability": 0.86474609375}, {"start": 1979.44, "end": 1979.7, "word": " xk", "probability": 0.954833984375}, {"start": 1979.7, "end": 1980.16, "word": " council", "probability": 0.270263671875}, {"start": 1980.16, "end": 1980.46, "word": " يعني", "probability": 0.915283203125}, {"start": 1980.46, "end": 1980.78, "word": " اسمه", "probability": 0.9226888020833334}, {"start": 1980.78, "end": 1981.66, "word": " council", "probability": 0.6904296875}, {"start": 1981.66, "end": 1982.04, "word": " xk", "probability": 0.95556640625}, {"start": 1982.04, "end": 1982.44, "word": " xk", "probability": 0.990966796875}, {"start": 1982.44, "end": 1982.9, "word": " xk", "probability": 0.98876953125}, {"start": 1982.9, "end": 1983.36, "word": " هذه", "probability": 0.52294921875}, {"start": 1983.36, "end": 1983.72, "word": " الكوشي", "probability": 0.741162109375}, {"start": 1983.72, "end": 1984.12, "word": " sequence", "probability": 0.96484375}, {"start": 1984.12, "end": 1984.42, "word": " هذه", "probability": 0.5458984375}, {"start": 1984.42, "end": 1984.76, "word": " الكوشي", "probability": 0.91669921875}, {"start": 1984.76, "end": 1985.16, "word": " sequence", "probability": 0.98779296875}, {"start": 1985.16, "end": 1985.84, "word": " موجودة", "probability": 0.96826171875}, {"start": 1985.84, "end": 1985.92, "word": " في", "probability": 0.98193359375}, {"start": 1985.92, "end": 1985.96, "word": " ال", "probability": 0.93701171875}, {"start": 1985.96, "end": 1986.38, "word": " equivalency", "probability": 0.793701171875}, {"start": 1986.38, "end": 1986.64, "word": " class", "probability": 0.9775390625}, {"start": 1986.64, "end": 1987.12, "word": " سبعتها", "probability": 0.8709716796875}, {"start": 1987.12, "end": 1987.68, "word": " لـ", "probability": 0.6722412109375}, {"start": 1987.68, "end": 1988.14, "word": " xk", "probability": 0.9052734375}, {"start": 1988.14, "end": 1988.5, "word": " hat", "probability": 0.970703125}], "temperature": 1.0}, {"id": 88, "seek": 201421, "start": 1988.97, "end": 2014.21, "text": "إذا XK هتأكيد وين موجودة؟ في الـW لأن الـW هيك اتركبت علي هيك تربط تركبت هذه الـN هذه الـN هي اللي هيلاجيها مشتركة بين الجهتين السر هنا أن المسافة بين XN و XK أزهر من 1 على 2 و يشاوز 1 على 2 لكل N أكبر سواء مين؟ K هذه الـXK هي اللي لاجيتها هنا دير بالكم طيب شوفوا الآن", "tokens": [28814, 15730, 1783, 42, 8032, 2655, 10721, 4117, 25708, 4032, 9957, 3714, 29245, 23328, 3660, 22807, 8978, 2423, 39184, 54, 5296, 33456, 2423, 39184, 54, 39896, 4117, 1975, 2655, 31747, 3555, 2655, 25894, 39896, 4117, 6055, 25513, 9566, 6055, 31747, 3555, 2655, 29538, 2423, 39184, 45, 29538, 2423, 39184, 45, 39896, 13672, 1829, 39896, 15040, 7435, 1829, 11296, 37893, 2655, 31747, 3660, 49374, 25724, 3224, 2655, 9957, 21136, 2288, 34105, 14739, 9673, 3794, 31845, 3660, 49374, 1783, 45, 4032, 1783, 42, 5551, 11622, 3224, 2288, 9154, 502, 15844, 568, 4032, 7251, 8592, 995, 2407, 11622, 502, 15844, 568, 5296, 28820, 426, 5551, 4117, 26890, 8608, 2407, 16606, 3714, 9957, 22807, 591, 29538, 2423, 39184, 55, 42, 39896, 13672, 1829, 5296, 26108, 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"probability": 0.29345703125}, {"start": 2322.23, "end": 2322.51, "word": " M", "probability": 0.89892578125}, {"start": 2322.51, "end": 2322.87, "word": " زائد", "probability": 0.696044921875}, {"start": 2322.87, "end": 2323.69, "word": " هذا", "probability": 0.5458984375}, {"start": 2323.69, "end": 2324.43, "word": " المسافة", "probability": 0.9871826171875}, {"start": 2324.43, "end": 2324.95, "word": " زائد", "probability": 0.8072916666666666}, {"start": 2324.95, "end": 2325.17, "word": " 1", "probability": 0.892578125}, {"start": 2325.17, "end": 2325.37, "word": " على", "probability": 0.80615234375}, {"start": 2325.37, "end": 2325.51, "word": " M", "probability": 0.94677734375}, {"start": 2325.51, "end": 2325.89, "word": " أصغر", "probability": 0.9808349609375}, {"start": 2325.89, "end": 2326.07, "word": " من", "probability": 0.994140625}, {"start": 2326.07, "end": 2328.01, "word": " إبسلون", "probability": 0.745556640625}, {"start": 2328.01, "end": 2328.49, "word": " هذا", "probability": 0.255126953125}, {"start": 2328.49, "end": 2328.75, "word": " إيش", "probability": 0.8072102864583334}, {"start": 2328.75, "end": 2329.59, "word": " معناته؟", "probability": 0.9525146484375}, {"start": 2329.59, "end": 2330.09, "word": " معناته", "probability": 0.9651692708333334}, {"start": 2330.09, "end": 2330.59, "word": " صارت", "probability": 0.7526041666666666}, {"start": 2330.59, "end": 2331.09, "word": " هذه", "probability": 0.75}, {"start": 2331.09, "end": 2332.21, "word": " الآن", "probability": 0.6395263671875}, {"start": 2332.21, "end": 2332.83, "word": " أصغر", "probability": 0.9942626953125}, {"start": 2332.83, "end": 2332.99, "word": " من", "probability": 0.99365234375}, {"start": 2332.99, "end": 2333.21, "word": " أي", "probability": 0.93603515625}, {"start": 2333.21, "end": 2333.63, "word": " إبسلون", "probability": 0.95703125}, {"start": 2333.63, "end": 2333.77, "word": " في", "probability": 0.990234375}, {"start": 2333.77, "end": 2334.21, "word": " الدنيا", "probability": 0.9871419270833334}], "temperature": 1.0}, {"id": 103, "seek": 236323, "start": 2334.43, "end": 2363.23, "text": "لكل Y أكبر من 0 للي جيت K بحيث لكل N و M أكبر من K البسافة أصغر من مين من Y يعني بمعنى أخر هذه اللي اللي جيتها اللي كل مرة بلاقي اللي هو إليها ZN hat للي هي X1 hat بلاقي Z1 hat ل X2 hat بلاقي Z2 hat ال sequence هذه اللي اللي جيتها اللي هي ZN ZN hat هذه ال sequence اتمتعت بخاصية نقاش Sequence", "tokens": [1211, 28820, 398, 5551, 4117, 26890, 9154, 1958, 5296, 20292, 10874, 36081, 591, 4724, 5016, 1829, 12984, 5296, 28820, 426, 4032, 376, 5551, 4117, 26890, 9154, 591, 29739, 3794, 31845, 3660, 5551, 9381, 17082, 2288, 9154, 3714, 9957, 9154, 398, 37495, 22653, 4724, 2304, 3615, 1863, 7578, 5551, 34740, 29538, 13672, 1829, 13672, 1829, 10874, 36081, 11296, 13672, 1829, 28242, 3714, 25720, 4724, 15040, 38436, 13672, 1829, 31439, 11933, 20292, 11296, 1176, 45, 2385, 5296, 20292, 39896, 1783, 16, 2385, 4724, 15040, 38436, 1176, 16, 2385, 5296, 1783, 17, 2385, 4724, 15040, 38436, 1176, 17, 2385, 2423, 8310, 29538, 13672, 1829, 13672, 1829, 10874, 36081, 11296, 13672, 1829, 39896, 1176, 45, 1176, 45, 2385, 29538, 2423, 8310, 1975, 39237, 2655, 34268, 4724, 9778, 33546, 10632, 8717, 4587, 33599, 46859, 655], "avg_logprob": -0.19465649173459934, "compression_ratio": 2.031390134529148, "no_speech_prob": 1.2159347534179688e-05, "words": [{"start": 2334.43, "end": 2335.05, "word": "لكل", "probability": 0.77392578125}, {"start": 2335.05, "end": 2335.73, "word": " Y", "probability": 0.08795166015625}, {"start": 2335.73, "end": 2336.07, "word": " أكبر", "probability": 0.8929036458333334}, {"start": 2336.07, "end": 2336.25, "word": " من", "probability": 0.99267578125}, {"start": 2336.25, "end": 2336.55, "word": " 0", "probability": 0.6767578125}, {"start": 2336.55, "end": 2337.07, "word": " للي", "probability": 0.47222900390625}, {"start": 2337.07, "end": 2337.29, "word": " جيت", "probability": 0.85693359375}, {"start": 2337.29, "end": 2337.61, 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"probability": 0.9931640625}, {"start": 2346.45, "end": 2347.23, "word": " بلاقي", "probability": 0.8557942708333334}, {"start": 2347.23, "end": 2347.41, "word": " اللي", "probability": 0.83251953125}, {"start": 2347.41, "end": 2347.57, "word": " هو", "probability": 0.65673828125}, {"start": 2347.57, "end": 2347.87, "word": " إليها", "probability": 0.62890625}, {"start": 2347.87, "end": 2348.37, "word": " ZN", "probability": 0.55078125}, {"start": 2348.37, "end": 2348.83, "word": " hat", "probability": 0.54248046875}, {"start": 2348.83, "end": 2349.65, "word": " للي", "probability": 0.6224365234375}, {"start": 2349.65, "end": 2349.85, "word": " هي", "probability": 0.68505859375}, {"start": 2349.85, "end": 2350.51, "word": " X1", "probability": 0.92529296875}, {"start": 2350.51, "end": 2350.87, "word": " hat", "probability": 0.97119140625}, {"start": 2350.87, "end": 2351.23, "word": " بلاقي", "probability": 0.9410807291666666}, {"start": 2351.23, "end": 2351.89, "word": " Z1", "probability": 0.94482421875}, {"start": 2351.89, "end": 2352.43, "word": " hat", "probability": 0.9853515625}, {"start": 2352.43, "end": 2352.75, "word": " ل", "probability": 0.87939453125}, {"start": 2352.75, "end": 2353.31, "word": " X2", "probability": 0.7169189453125}, {"start": 2353.31, "end": 2353.61, "word": " hat", "probability": 0.97509765625}, {"start": 2353.61, "end": 2353.97, "word": " بلاقي", "probability": 0.9319661458333334}, {"start": 2353.97, "end": 2354.53, "word": " Z2", "probability": 0.991455078125}, {"start": 2354.53, "end": 2354.97, "word": " hat", "probability": 0.98046875}, {"start": 2354.97, "end": 2355.39, "word": " ال", "probability": 0.720703125}, {"start": 2355.39, "end": 2355.87, "word": " sequence", "probability": 0.88671875}, {"start": 2355.87, "end": 2356.19, "word": " هذه", "probability": 0.8076171875}, {"start": 2356.19, "end": 2356.37, "word": " اللي", "probability": 0.99267578125}, {"start": 2356.37, "end": 2356.49, "word": " اللي", "probability": 0.7861328125}, {"start": 2356.49, "end": 2356.95, "word": " جيتها", "probability": 0.9915364583333334}, {"start": 2356.95, "end": 2357.11, "word": " اللي", "probability": 0.933349609375}, {"start": 2357.11, "end": 2357.23, "word": " هي", "probability": 0.85302734375}, {"start": 2357.23, "end": 2357.95, "word": " ZN", "probability": 0.969970703125}, {"start": 2357.95, "end": 2358.85, "word": " ZN", "probability": 0.82177734375}, {"start": 2358.85, "end": 2359.17, "word": " hat", "probability": 0.96728515625}, {"start": 2359.17, "end": 2359.37, "word": " هذه", "probability": 0.78369140625}, {"start": 2359.37, "end": 2359.51, "word": " ال", "probability": 0.96044921875}, {"start": 2359.51, "end": 2360.05, "word": " sequence", "probability": 0.94189453125}, {"start": 2360.05, "end": 2361.15, "word": " اتمتعت", "probability": 0.8656005859375}, {"start": 2361.15, "end": 2361.93, "word": " بخاصية", "probability": 0.98193359375}, {"start": 2361.93, "end": 2362.41, "word": " نقاش", "probability": 0.6629231770833334}, {"start": 2362.41, "end": 2363.23, "word": " Sequence", "probability": 0.61395263671875}], "temperature": 1.0}, {"id": 104, "seek": 239162, "start": 2363.66, "end": 2391.62, "text": "therefore z unhat is a Cauchy sequence أي سؤال طيب الان اطلع على فوق خليها في الذاكرة اذا هذه الان انا حصلت على ال z unhat ال z unhat حصلت عليها ال z unhat Cauchy sequence خليها في الذاكرة انا هساخدمها طيب", "tokens": [15456, 845, 710, 517, 15178, 307, 257, 7544, 625, 88, 8310, 36632, 8608, 33604, 6027, 23032, 1829, 3555, 2423, 7649, 1975, 9566, 1211, 3615, 15844, 6156, 30543, 16490, 20292, 11296, 8978, 32545, 995, 4117, 25720, 1975, 15730, 29538, 2423, 7649, 1975, 8315, 11331, 36520, 2655, 15844, 2423, 710, 517, 15178, 2423, 710, 517, 15178, 11331, 36520, 2655, 25894, 11296, 2423, 710, 517, 15178, 7544, 625, 88, 8310, 16490, 20292, 11296, 8978, 32545, 995, 4117, 25720, 1975, 8315, 8032, 3794, 995, 9778, 40448, 11296, 23032, 1829, 3555], "avg_logprob": -0.2593390715533289, "compression_ratio": 1.8047337278106508, "no_speech_prob": 1.8537044525146484e-05, "words": [{"start": 2363.66, "end": 2364.46, "word": "therefore", "probability": 0.481231689453125}, {"start": 2364.46, "end": 2364.74, "word": " z", "probability": 0.34375}, {"start": 2364.74, "end": 2365.34, "word": " unhat", "probability": 0.45013427734375}, {"start": 2365.34, "end": 2365.62, "word": " is", "probability": 0.83251953125}, {"start": 2365.62, "end": 2365.84, "word": " a", "probability": 0.92919921875}, {"start": 2365.84, "end": 2366.14, "word": " Cauchy", "probability": 0.8590494791666666}, {"start": 2366.14, "end": 2366.82, "word": " sequence", "probability": 0.92138671875}, {"start": 2366.82, "end": 2368.04, "word": " أي", "probability": 0.5244140625}, {"start": 2368.04, "end": 2368.48, "word": " سؤال", "probability": 0.9847005208333334}, {"start": 2368.48, "end": 2369.24, "word": " طيب", "probability": 0.7522786458333334}, {"start": 2369.24, "end": 2370.28, "word": " الان", "probability": 0.6419677734375}, {"start": 2370.28, "end": 2370.66, "word": " اطلع", "probability": 0.9417724609375}, {"start": 2370.66, "end": 2370.78, "word": " على", "probability": 0.444091796875}, {"start": 2370.78, "end": 2371.06, "word": " فوق", "probability": 0.97216796875}, {"start": 2371.06, "end": 2371.94, "word": " خليها", "probability": 0.7884114583333334}, {"start": 2371.94, "end": 2372.1, "word": " في", "probability": 0.828125}, {"start": 2372.1, "end": 2372.52, "word": " الذاكرة", "probability": 0.946533203125}, {"start": 2372.52, "end": 2372.72, "word": " اذا", "probability": 0.7252197265625}, {"start": 2372.72, "end": 2373.04, "word": " هذه", "probability": 0.52978515625}, {"start": 2373.04, "end": 2373.48, "word": " الان", "probability": 0.6884765625}, {"start": 2373.48, "end": 2374.08, "word": " انا", "probability": 0.916748046875}, {"start": 2374.08, "end": 2374.68, "word": " حصلت", "probability": 0.9378255208333334}, {"start": 2374.68, "end": 2374.92, "word": " على", "probability": 0.78564453125}, {"start": 2374.92, "end": 2375.14, "word": " ال", "probability": 0.2445068359375}, {"start": 2375.14, "end": 2375.38, "word": " z", "probability": 0.73974609375}, {"start": 2375.38, "end": 2376.54, "word": " unhat", "probability": 0.9013671875}, {"start": 2376.54, "end": 2378.02, "word": " ال", "probability": 0.74267578125}, {"start": 2378.02, "end": 2378.18, "word": " z", "probability": 0.94189453125}, {"start": 2378.18, "end": 2379.06, "word": " unhat", "probability": 0.947509765625}, {"start": 2379.06, "end": 2380.48, "word": " حصلت", "probability": 0.9422200520833334}, {"start": 2380.48, "end": 2381.04, "word": " عليها", "probability": 0.9755859375}, {"start": 2381.04, "end": 2381.48, "word": " ال", "probability": 0.90869140625}, {"start": 2381.48, "end": 2381.7, "word": " z", "probability": 0.9814453125}, {"start": 2381.7, "end": 2382.46, "word": " unhat", "probability": 0.95849609375}, {"start": 2382.46, "end": 2384.72, "word": " Cauchy", "probability": 0.92041015625}, {"start": 2384.72, "end": 2386.36, "word": " sequence", "probability": 0.93505859375}, {"start": 2386.36, "end": 2386.82, "word": " خليها", "probability": 0.8369140625}, {"start": 2386.82, "end": 2386.96, "word": " في", "probability": 0.97314453125}, {"start": 2386.96, "end": 2387.18, "word": " الذاكرة", "probability": 0.9044189453125}, {"start": 2387.18, "end": 2387.34, "word": " انا", "probability": 0.6109619140625}, {"start": 2387.34, "end": 2388.06, "word": " هساخدمها", "probability": 0.7044270833333334}, {"start": 2388.06, "end": 2391.62, "word": " طيب", "probability": 0.9405924479166666}], "temperature": 1.0}, {"id": 105, "seek": 239676, "start": 2393.44, "end": 2396.76, "text": "الآن since T من X لعن W إذا كان I جيومتري", "tokens": [6027, 148, 48506, 1670, 314, 9154, 1783, 5296, 3615, 1863, 343, 11933, 15730, 25961, 286, 10874, 1829, 20498, 2655, 16572], "avg_logprob": -0.5531993934086391, "compression_ratio": 0.9130434782608695, 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2397.5, "end": 2426.72, "text": "مظبوط و الـ Z M hat element من الـ W ليش Z M hat element من الـ W لأن فيها اللي هي عندي اللي هي اللي أنا جاتهم ال sequence دي اللي ركّبتها مالها من ال W أصلا ماشي طيب شوفوا صلى على النبي عليه الصلاة والسلام الآن ال sequence Z M hat element من ال W كل واحدة فيه element من ال W إذا ال sequence Z M", "tokens": [2304, 19913, 3555, 2407, 9566, 4032, 2423, 39184, 1176, 376, 2385, 4478, 9154, 2423, 39184, 343, 32239, 8592, 1176, 376, 2385, 4478, 9154, 2423, 39184, 343, 5296, 33456, 8978, 11296, 13672, 1829, 39896, 43242, 1829, 13672, 1829, 39896, 13672, 1829, 41850, 10874, 9307, 16095, 2423, 8310, 11778, 1829, 13672, 1829, 12602, 4117, 11703, 3555, 2655, 11296, 3714, 6027, 11296, 9154, 2423, 343, 5551, 9381, 15040, 3714, 33599, 1829, 23032, 1829, 3555, 13412, 38688, 14407, 20328, 23942, 15844, 28239, 21292, 47356, 31767, 15040, 3660, 16070, 3794, 37440, 6024, 48506, 2423, 8310, 1176, 376, 2385, 4478, 9154, 2423, 343, 28242, 36764, 24401, 3660, 8978, 3224, 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"word": " Y", "probability": 0.2337646484375}, {"start": 2932.97, "end": 2933.41, "word": " وW", "probability": 0.4815673828125}, {"start": 2933.41, "end": 2933.79, "word": " تلدة", "probability": 0.7864990234375}, {"start": 2933.79, "end": 2933.95, "word": " ايش", "probability": 0.7112630208333334}, {"start": 2933.95, "end": 2934.43, "word": " ماله", "probability": 0.845703125}, {"start": 2934.43, "end": 2935.43, "word": " اللي", "probability": 0.831787109375}, {"start": 2935.43, "end": 2935.89, "word": " هو", "probability": 0.958984375}, {"start": 2935.89, "end": 2936.61, "word": " dense", "probability": 0.55029296875}, {"start": 2936.61, "end": 2937.53, "word": " المين", "probability": 0.35516357421875}, {"start": 2937.53, "end": 2937.99, "word": " X", "probability": 0.48486328125}, {"start": 2937.99, "end": 2938.49, "word": " تلدة", "probability": 0.7913818359375}, {"start": 2938.49, "end": 2939.13, "word": " مادام", "probability": 0.6949055989583334}, {"start": 2939.13, "end": 2939.59, "word": " dense", "probability": 0.81640625}, {"start": 2939.59, "end": 2940.45, "word": " وهذه", "probability": 0.6015625}, {"start": 2940.45, "end": 2940.71, "word": " X", "probability": 0.94873046875}, {"start": 2940.71, "end": 2941.03, "word": " تلدة", "probability": 0.846435546875}, {"start": 2941.03, "end": 2941.23, "word": " وY", "probability": 0.864990234375}, {"start": 2941.23, "end": 2941.55, "word": " تلدة", "probability": 0.9273681640625}, {"start": 2941.55, "end": 2941.93, "word": " موجودة", "probability": 0.919189453125}, {"start": 2941.93, "end": 2942.09, "word": " هنا", "probability": 0.47265625}, {"start": 2942.09, "end": 2942.33, "word": " اذا", "probability": 0.68798828125}, {"start": 2942.33, "end": 2942.81, "word": " اكيد", "probability": 0.9375}, {"start": 2942.81, "end": 2943.05, "word": " في", "probability": 0.94482421875}, {"start": 2943.05, "end": 2943.89, "word": " sequence", "probability": 0.69189453125}, {"start": 2943.89, "end": 2944.23, "word": " of", "probability": 0.94873046875}, {"start": 2944.23, "end": 2944.77, "word": " points", "probability": 0.91650390625}, {"start": 2944.77, "end": 2945.25, "word": " converge", "probability": 0.529296875}, {"start": 2945.25, "end": 2945.73, "word": " لهذه", "probability": 0.95068359375}, {"start": 2945.73, "end": 2946.81, "word": " وsequence", "probability": 0.6688639322916666}, {"start": 2946.81, "end": 2947.01, "word": " of", "probability": 0.9697265625}, {"start": 2947.01, "end": 2947.37, "word": " points", "probability": 0.94970703125}, {"start": 2947.37, "end": 2947.85, "word": " converge", "probability": 0.90966796875}, {"start": 2947.85, "end": 2948.81, "word": " لهذه", "probability": 0.969970703125}, {"start": 2948.81, "end": 2948.95, "word": " من", "probability": 0.40771484375}, {"start": 2948.95, "end": 2949.35, "word": " تعريف", "probability": 0.986328125}, {"start": 2949.35, "end": 2949.73, "word": " مين", "probability": 0.962890625}, {"start": 2949.73, "end": 2950.07, "word": " اللي", "probability": 0.892578125}, {"start": 2950.07, "end": 2950.47, "word": " هو", "probability": 0.98486328125}, {"start": 2950.47, "end": 2950.75, "word": " ال", "probability": 0.8662109375}, {"start": 2950.75, "end": 2951.11, "word": " closure", "probability": 0.9111328125}, {"start": 2951.11, "end": 2952.37, "word": " عندى", "probability": 0.58154296875}, {"start": 2952.37, "end": 2952.79, "word": " اللي", "probability": 0.987060546875}, {"start": 2952.79, "end": 2953.19, "word": " هو", "probability": 0.98388671875}, {"start": 2953.19, "end": 2954.31, "word": " هذه", "probability": 0.439208984375}, {"start": 2954.31, "end": 2954.67, "word": " ال", "probability": 0.72802734375}, {"start": 2954.67, "end": 2955.91, "word": " dense", "probability": 0.77392578125}, {"start": 2955.91, "end": 2956.15, "word": " من", "probability": 0.912109375}, {"start": 2956.15, "end": 2956.45, "word": " تعريف", "probability": 0.9845377604166666}, {"start": 2956.45, "end": 2956.65, "word": " انه", "probability": 0.7158203125}, {"start": 2956.65, "end": 2957.01, "word": " dense", "probability": 0.9375}, {"start": 2957.01, "end": 2957.29, "word": " هذه", "probability": 0.62158203125}, {"start": 2957.29, "end": 2957.75, "word": " dense", "probability": 0.9013671875}], "temperature": 1.0}, {"id": 129, "seek": 297586, "start": 2958.42, "end": 2975.86, "text": "انتبهوا هذه dense ان هذه إذا لأي element هنا بقدر ألاقي sequence من هنا converge zero لما يكون يا جماعة الآن أي حاجة في الدنيا y closure اللي هو بيساوي x مثلا", "tokens": [7649, 2655, 3555, 3224, 14407, 29538, 18011, 16472, 29538, 11933, 15730, 5296, 10721, 1829, 4478, 34105, 4724, 28543, 2288, 5551, 15040, 38436, 8310, 9154, 34105, 41881, 4018, 5296, 15042, 7251, 30544, 35186, 10874, 15042, 27884, 6024, 48506, 36632, 11331, 26108, 3660, 8978, 32748, 22653, 995, 288, 24653, 13672, 1829, 31439, 4724, 1829, 3794, 995, 45865, 2031, 50113, 15040], "avg_logprob": -0.22219279357942484, "compression_ratio": 1.4269005847953216, 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من تلت، أصغر من كده، بلاقي x واحد أصغر من واحد، x اتنين .. يعني ال .. فاهمين علشه بحكيه؟", "tokens": [2407, 10874, 36081, 5551, 9778, 3215, 2655, 36632, 3714, 10859, 9778, 9566, 10721, 2031, 8978, 2423, 39184, 2031, 2423, 3224, 18513, 7578, 4724, 28543, 2288, 5551, 15040, 38436, 8310, 2031, 77, 294, 288, 1270, 300, 2031, 77, 41881, 32767, 9957, 24976, 87, 13672, 1829, 31439, 8978, 28242, 4386, 5296, 28820, 36764, 24401, 4386, 5296, 28820, 297, 4724, 28543, 2288, 5551, 15040, 38436, 2594, 4386, 2594, 9673, 3794, 31845, 3660, 49374, 16095, 5551, 9381, 17082, 2288, 9154, 36764, 24401, 12399, 5551, 9381, 17082, 2288, 9154, 8717, 9381, 12399, 5551, 9381, 17082, 2288, 9154, 6055, 1211, 2655, 12399, 5551, 9381, 17082, 2288, 9154, 9122, 3215, 3224, 12399, 4724, 15040, 38436, 2031, 36764, 24401, 5551, 9381, 17082, 2288, 9154, 36764, 24401, 12399, 2031, 1975, 2655, 1863, 9957, 4386, 37495, 22653, 2423, 4386, 6156, 995, 16095, 9957, 11203, 8592, 3224, 4724, 5016, 4117, 1829, 3224, 22807], 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من", "probability": 0.998046875}, {"start": 2996.57, "end": 2996.87, "word": " تلت،", "probability": 0.92578125}, {"start": 2996.87, "end": 2997.07, "word": " أصغر", "probability": 0.9735107421875}, {"start": 2997.07, "end": 2997.17, "word": " من", "probability": 0.98779296875}, {"start": 2997.17, "end": 2997.43, "word": " كده،", "probability": 0.83544921875}, {"start": 2997.43, "end": 2997.73, "word": " بلاقي", "probability": 0.6710611979166666}, {"start": 2997.73, "end": 2997.87, "word": " x", "probability": 0.94580078125}, {"start": 2997.87, "end": 2998.19, "word": " واحد", "probability": 0.9609375}, {"start": 2998.19, "end": 2998.71, "word": " أصغر", "probability": 0.963623046875}, {"start": 2998.71, "end": 2998.77, "word": " من", "probability": 0.98388671875}, {"start": 2998.77, "end": 2999.03, "word": " واحد،", "probability": 0.97314453125}, {"start": 2999.03, "end": 2999.25, "word": " x", "probability": 0.8798828125}, {"start": 2999.25, "end": 2999.55, "word": " اتنين", 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n تلده بساوي y hat لاحظوا انا ايش اللي بسويه انا بمعنى اخر انتبهوا بالله يا جماعة انتبهوا انا اجيت اخدتلكم ال x تلده و ال y تلده ال arbitrary points اللي موجودات في ال x تلده", "tokens": [296, 297, 1709, 281, 13202, 4032, 4948, 5296, 2655, 1829, 288, 297, 6055, 1211, 3215, 3224, 4724, 3794, 995, 45865, 288, 2385, 20193, 5016, 19913, 14407, 1975, 8315, 1975, 1829, 8592, 13672, 1829, 4724, 3794, 45865, 3224, 1975, 8315, 4724, 2304, 3615, 1863, 7578, 1975, 34740, 16472, 2655, 3555, 3224, 14407, 20666, 43761, 35186, 10874, 15042, 27884, 16472, 2655, 3555, 3224, 14407, 1975, 8315, 1975, 7435, 36081, 1975, 9778, 3215, 2655, 23275, 2304, 2423, 2031, 6055, 1211, 3215, 3224, 4032, 2423, 288, 6055, 1211, 3215, 3224, 2423, 23211, 2793, 13672, 1829, 3714, 29245, 23328, 9307, 8978, 2423, 2031, 6055, 1211, 3215, 3224], "avg_logprob": -0.24590412216279114, "compression_ratio": 1.7046632124352332, "no_speech_prob": 1.7583370208740234e-05, "words": [{"start": 3240.5, "end": 3240.82, "word": "as", 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"word": " النظرية", "probability": 0.9677734375}, {"start": 3574.37, "end": 3574.47, "word": " ..", "probability": 0.56884765625}, {"start": 3574.47, "end": 3575.05, "word": " النظرية", "probability": 0.968994140625}, {"start": 3575.05, "end": 3575.21, "word": " يا", "probability": 0.97119140625}, {"start": 3575.21, "end": 3575.69, "word": " جماعة", "probability": 0.9943033854166666}, {"start": 3575.69, "end": 3576.45, "word": " فيها", "probability": 0.905029296875}, {"start": 3576.45, "end": 3576.85, "word": " كثير", "probability": 0.9903971354166666}, {"start": 3576.85, "end": 3576.95, "word": " من", "probability": 0.9404296875}, {"start": 3576.95, "end": 3577.65, "word": " المعلومات", "probability": 0.9925537109375}, {"start": 3577.65, "end": 3579.03, "word": " صح", "probability": 0.948486328125}, {"start": 3579.03, "end": 3579.21, "word": " هي", "probability": 0.94091796875}, {"start": 3579.21, "end": 3579.83, "word": " تركبتها", "probability": 0.92451171875}, {"start": 3579.83, "end": 3580.17, "word": " كبيرة", "probability": 0.9783528645833334}, {"start": 3580.17, "end": 3580.51, "word": " لكن", "probability": 0.86181640625}, {"start": 3580.51, "end": 3581.37, "word": " معلوماتها", "probability": 0.89033203125}, {"start": 3581.37, "end": 3581.81, "word": " كثيرة", "probability": 0.9534505208333334}, {"start": 3581.81, "end": 3583.31, "word": " ومفيدة", "probability": 0.9365234375}], "temperature": 1.0}, {"id": 156, "seek": 360409, "start": 3586.89, "end": 3604.09, "text": "طبعا هي أطول نظرية في الكتاب مافيش عديق مافيش اشي زي هي طيب therefore therefore S is an isometry and so ايش مالها is one to another يعني مروع شعوركم لكن العلم بدهيك يعني", "tokens": [9566, 3555, 3615, 995, 39896, 5551, 9566, 12610, 8717, 19913, 2288, 10632, 8978, 33251, 2655, 16758, 19446, 41185, 8592, 6225, 16254, 4587, 19446, 41185, 8592, 1975, 8592, 1829, 30767, 1829, 39896, 23032, 1829, 3555, 4412, 4412, 318, 307, 364, 307, 34730, 293, 370, 1975, 1829, 8592, 19446, 1211, 11296, 307, 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من x تلدة ل x hat let x hat element in x تلدة then there is a sequence x unhat of elements in w لأنها w dense فيها such that limit x unhat إيش بيساوي ال x hat اللي عندي لأن since T is onto T نفسها is onto", "tokens": [15042, 11778, 10943, 2031, 2385, 8978, 2423, 39184, 2031, 2385, 41850, 4724, 16254, 5551, 32887, 5016, 24976, 7435, 3794, 2288, 12399, 24976, 7435, 3794, 2288, 12399, 2423, 7435, 3794, 2288, 3714, 9957, 22807, 25724, 3794, 2288, 261, 4032, 261, 6055, 1211, 3215, 3660, 16472, 1829, 13672, 1829, 4724, 2407, 36520, 22653, 32767, 9957, 22807, 5296, 10721, 36520, 9154, 2031, 2385, 5296, 2031, 6055, 1211, 3215, 3660, 4032, 9154, 2031, 6055, 1211, 3215, 3660, 5296, 2031, 2385, 718, 2031, 2385, 4478, 294, 2031, 6055, 1211, 3215, 3660, 550, 456, 307, 257, 8310, 2031, 517, 15178, 295, 4959, 294, 261, 5296, 33456, 11296, 261, 18011, 8978, 11296, 1270, 300, 4948, 2031, 517, 15178, 11933, 1829, 8592, 4724, 1829, 3794, 995, 45865, 2423, 2031, 2385, 13672, 1829, 18871, 16254, 5296, 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3648.58, "end": 3648.94, "word": " عندي", "probability": 0.851806640625}, {"start": 3648.94, "end": 3649.82, "word": " لأن", "probability": 0.76953125}, {"start": 3649.82, "end": 3650.24, "word": " since", "probability": 0.865234375}, {"start": 3650.24, "end": 3650.5, "word": " T", "probability": 0.7626953125}, {"start": 3650.5, "end": 3650.68, "word": " is", "probability": 0.468994140625}, {"start": 3650.68, "end": 3651.06, "word": " onto", "probability": 0.376708984375}, {"start": 3651.06, "end": 3651.92, "word": " T", "probability": 0.365478515625}, {"start": 3651.92, "end": 3652.3, "word": " نفسها", "probability": 0.99462890625}, {"start": 3652.3, "end": 3652.48, "word": " is", "probability": 0.9541015625}, {"start": 3652.48, "end": 3652.8, "word": " onto", "probability": 0.890625}], "temperature": 1.0}, {"id": 159, "seek": 367748, "start": 3653.54, "end": 3677.48, "text": "ما هي تي ازومتريك ازومتريك و bijection اللي بدأنا فيها مدام تي on two إذا هذه اللي لجيهت هناك الواحدة فيه اللي هي إيش أصل then since T is on two then there is a sequence xn تلدة of elements in y تلدة such that T xn تلدة هذه بتساومين ال xn head لإن تي الأصلية on two for all n", "tokens": [15042, 39896, 6055, 1829, 1975, 11622, 20498, 2655, 16572, 4117, 1975, 11622, 20498, 2655, 16572, 4117, 4032, 3228, 1020, 313, 13672, 1829, 47525, 10721, 8315, 8978, 11296, 3714, 3215, 10943, 6055, 1829, 322, 732, 11933, 15730, 29538, 13672, 1829, 5296, 7435, 1829, 3224, 2655, 34105, 4117, 2423, 14407, 24401, 3660, 8978, 3224, 13672, 1829, 39896, 11933, 1829, 8592, 5551, 36520, 550, 1670, 314, 307, 322, 732, 550, 456, 307, 257, 8310, 2031, 77, 6055, 1211, 41891, 295, 4959, 294, 288, 6055, 1211, 41891, 1270, 300, 314, 2031, 77, 6055, 1211, 41891, 29538, 39894, 3794, 995, 20498, 9957, 2423, 2031, 77, 1378, 5296, 28814, 1863, 6055, 1829, 16247, 36520, 10632, 322, 732, 337, 439, 297], "avg_logprob": -0.34592392289120216, "compression_ratio": 1.6666666666666667, "no_speech_prob": 2.9206275939941406e-06, 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ال X تلده capital ابحث by the definition of S S X تلده هي مين ال X hat إذا صارت ال S is onto therefore X تلده and X hat are isometric this completes the proof", "tokens": [28814, 15730, 8717, 9778, 1211, 9381, 13672, 1829, 10874, 1829, 8315, 8978, 6024, 95, 34740, 3714, 9957, 1783, 6055, 1211, 3215, 3224, 4724, 16254, 8315, 4724, 1783, 2385, 8978, 2423, 1783, 2385, 4032, 13672, 1829, 10874, 1829, 8315, 1783, 6055, 1211, 3215, 3224, 3714, 29245, 23328, 3660, 8978, 2423, 1783, 6055, 1211, 3215, 3224, 4238, 48127, 5016, 12984, 538, 264, 7123, 295, 318, 318, 1783, 6055, 1211, 3215, 3224, 39896, 3714, 9957, 2423, 1783, 2385, 11933, 15730, 20328, 9640, 2655, 2423, 318, 307, 3911, 4412, 1783, 6055, 1211, 3215, 3224, 293, 1783, 2385, 366, 307, 29470, 341, 36362, 264, 8177], "avg_logprob": -0.24999999763942002, "compression_ratio": 1.7386934673366834, "no_speech_prob": 1.2516975402832031e-06, "words": [{"start": 3747.92, "end": 3748.2, "word": "إذا", "probability": 0.52606201171875}, {"start": 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"end": 3751.92, "word": " في", "probability": 0.6796875}, {"start": 3751.92, "end": 3752.02, "word": " ال", "probability": 0.74169921875}, {"start": 3752.02, "end": 3752.2, "word": " X", "probability": 0.83349609375}, {"start": 3752.2, "end": 3752.54, "word": " hat", "probability": 0.87158203125}, {"start": 3752.54, "end": 3753.02, "word": " و", "probability": 0.56640625}, {"start": 3753.02, "end": 3753.12, "word": " اللي", "probability": 0.8056640625}, {"start": 3753.12, "end": 3753.82, "word": " جينا", "probability": 0.8795572916666666}, {"start": 3753.82, "end": 3754.08, "word": " X", "probability": 0.87939453125}, {"start": 3754.08, "end": 3754.56, "word": " تلده", "probability": 0.9193115234375}, {"start": 3754.56, "end": 3755.22, "word": " موجودة", "probability": 0.96435546875}, {"start": 3755.22, "end": 3755.38, "word": " في", "probability": 0.9296875}, {"start": 3755.38, "end": 3755.56, "word": " ال", "probability": 0.489990234375}, {"start": 3755.56, "end": 3755.82, "word": " X", "probability": 0.96484375}, {"start": 3755.82, "end": 3756.4, "word": " تلده", "probability": 0.9549560546875}, {"start": 3756.4, "end": 3756.92, "word": " capital", "probability": 0.65966796875}, {"start": 3756.92, "end": 3757.96, "word": " ابحث", "probability": 0.7593587239583334}, {"start": 3757.96, "end": 3758.16, "word": " by", "probability": 0.603515625}, {"start": 3758.16, "end": 3758.32, "word": " the", "probability": 0.87255859375}, {"start": 3758.32, "end": 3758.76, "word": " definition", "probability": 0.9287109375}, {"start": 3758.76, "end": 3759.0, "word": " of", "probability": 0.9716796875}, {"start": 3759.0, "end": 3759.2, "word": " S", "probability": 0.82275390625}, {"start": 3759.2, "end": 3759.6, "word": " S", "probability": 0.1785888671875}, {"start": 3759.6, "end": 3760.04, "word": " X", "probability": 0.9482421875}, {"start": 3760.04, "end": 3760.56, "word": " تلده", "probability": 0.9522705078125}, {"start": 3760.56, "end": 3760.76, "word": " هي", "probability": 0.869140625}, {"start": 3760.76, "end": 3761.3, "word": " مين", "probability": 0.976318359375}, {"start": 3761.3, "end": 3761.98, "word": " ال", "probability": 0.662109375}, {"start": 3761.98, "end": 3762.22, "word": " X", "probability": 0.974609375}, {"start": 3762.22, "end": 3762.52, "word": " hat", "probability": 0.94873046875}, {"start": 3762.52, "end": 3763.14, "word": " إذا", "probability": 0.9072265625}, {"start": 3763.14, "end": 3763.62, "word": " صارت", "probability": 0.7791341145833334}, {"start": 3763.62, "end": 3763.76, "word": " ال", "probability": 0.9052734375}, {"start": 3763.76, "end": 3764.0, "word": " S", "probability": 0.92138671875}, {"start": 3764.0, "end": 3764.2, "word": " is", "probability": 0.85595703125}, {"start": 3764.2, "end": 3764.56, "word": " onto", "probability": 0.5595703125}, {"start": 3764.56, "end": 3765.36, "word": " therefore", "probability": 0.52978515625}, {"start": 3765.36, "end": 3766.12, "word": " X", "probability": 0.98193359375}, {"start": 3766.12, "end": 3766.56, "word": " تلده", "probability": 0.9761962890625}, {"start": 3766.56, "end": 3766.8, "word": " and", "probability": 0.70751953125}, {"start": 3766.8, "end": 3767.0, "word": " X", "probability": 0.9873046875}, {"start": 3767.0, "end": 3767.22, "word": " hat", "probability": 0.9638671875}, {"start": 3767.22, "end": 3767.54, "word": " are", "probability": 0.9248046875}, {"start": 3767.54, "end": 3768.14, "word": " isometric", "probability": 0.95166015625}, {"start": 3768.14, "end": 3769.4, "word": " this", "probability": 0.8037109375}, {"start": 3769.4, "end": 3770.54, "word": " completes", "probability": 0.9306640625}, {"start": 3770.54, "end": 3771.06, "word": " the", "probability": 0.9072265625}, {"start": 3771.06, "end": 3771.84, "word": " proof", "probability": 0.9638671875}], "temperature": 1.0}, {"id": 164, "seek": 378914, "start": 3772.52, "end": 3789.14, "text": "وهي الأسئلة وnote that the space x hat occurring in the above theorem is called the completion of the given space x و الله يعطيكم العافية والسلام عليكم ورحمة الله وبركاته", "tokens": [2407, 3224, 1829, 16247, 3794, 19986, 37977, 4032, 22178, 300, 264, 1901, 2031, 2385, 18386, 294, 264, 3673, 20904, 307, 1219, 264, 19372, 295, 264, 2212, 1901, 2031, 4032, 21984, 37495, 9566, 1829, 24793, 18863, 31845, 10632, 16070, 3794, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224], "avg_logprob": -0.2163915161816579, "compression_ratio": 1.3841463414634145, "no_speech_prob": 2.1457672119140625e-06, "words": [{"start": 3772.52, "end": 3773.48, "word": "وهي", "probability": 0.6351725260416666}, {"start": 3773.48, "end": 3774.18, "word": " الأسئلة", "probability": 0.9761962890625}, {"start": 3774.18, "end": 3776.06, "word": " وnote", "probability": 0.183685302734375}, {"start": 3776.06, "end": 3776.46, "word": " that", "probability": 0.9189453125}, {"start": 3776.46, "end": 3776.68, "word": " the", "probability": 0.701171875}, {"start": 3776.68, "end": 3777.04, "word": " space", "probability": 0.82373046875}, {"start": 3777.04, "end": 3777.36, "word": " x", "probability": 0.4990234375}, {"start": 3777.36, "end": 3777.68, "word": " hat", "probability": 0.720703125}, {"start": 3777.68, "end": 3778.72, "word": " occurring", "probability": 0.87060546875}, {"start": 3778.72, "end": 3779.26, "word": " in", "probability": 0.95947265625}, {"start": 3779.26, "end": 3779.42, "word": " the", "probability": 0.89501953125}, {"start": 3779.42, "end": 3779.88, "word": " above", "probability": 0.93994140625}, {"start": 3779.88, "end": 3780.58, "word": " theorem", "probability": 0.892578125}, {"start": 3780.58, "end": 3781.12, "word": " is", "probability": 0.95556640625}, {"start": 3781.12, "end": 3781.6, "word": " called", "probability": 0.89697265625}, {"start": 3781.6, "end": 3781.84, "word": " the", "probability": 0.7841796875}, {"start": 3781.84, "end": 3782.46, "word": " completion", "probability": 0.82666015625}, {"start": 3782.46, "end": 3783.36, "word": " of", "probability": 0.97607421875}, {"start": 3783.36, "end": 3783.58, "word": " the", "probability": 0.8740234375}, {"start": 3783.58, "end": 3783.82, "word": " given", "probability": 0.91748046875}, {"start": 3783.82, "end": 3784.24, "word": " space", "probability": 0.91455078125}, {"start": 3784.24, "end": 3784.68, "word": " x", "probability": 0.91015625}, {"start": 3784.68, "end": 3785.52, "word": " و", "probability": 0.49755859375}, {"start": 3785.52, "end": 3785.92, "word": " الله", "probability": 0.73828125}, {"start": 3785.92, "end": 3786.8, "word": " يعطيكم", "probability": 0.97021484375}, {"start": 3786.8, "end": 3787.44, "word": " العافية", "probability": 0.9788411458333334}, {"start": 3787.44, "end": 3788.16, "word": " والسلام", "probability": 0.767822265625}, {"start": 3788.16, "end": 3788.48, "word": " عليكم", "probability": 0.91943359375}, {"start": 3788.48, "end": 3788.7, "word": " ورحمة", "probability": 0.9000244140625}, {"start": 3788.7, "end": 3788.82, "word": " الله", "probability": 0.95458984375}, {"start": 3788.82, "end": 3789.14, "word": " وبركاته", "probability": 0.96875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3789.40375, "duration_after_vad": 3696.754374999988}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/uwT2Fp1FRO0_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/uwT2Fp1FRO0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fa64a771239916a2070e9647f1ab8f8c78e006af
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/uwT2Fp1FRO0_raw.srt
@@ -0,0 +1,3268 @@
+1
+00:00:05,500 --> 00:00:08,180
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,180 --> 00:00:11,180
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:11,180 --> 00:00:16,340
+آله وصحبه أجمعين هذه المحاضرة السابعة مساق تحليل
+
+4
+00:00:16,340 --> 00:00:21,900
+اقتراني أو تحليل دالي لطلاب وطالبات الجامعة
+
+5
+00:00:21,900 --> 00:00:26,820
+الإسلامية كلية العلوم ماجستير رياضياتاليوم ان شاء
+
+6
+00:00:26,820 --> 00:00:31,640
+الله هنحكي عن موضوع من الموضوعات المهمة واللي شوية
+
+7
+00:00:31,640 --> 00:00:36,360
+بتغلب لكن ان شاء الله مع بعض بنحاول بقدر الإمكان
+
+8
+00:00:36,360 --> 00:00:42,000
+ان نوضح الأمور اللي هي تحت عنوان 16 Completion of
+
+9
+00:00:42,000 --> 00:00:46,620
+metric spaces احنا لجينا في spaces عندنا complete
+
+10
+00:00:46,620 --> 00:00:51,770
+spaces وفي spaces ايش مايلها non complete spaceالـ
+
+11
+00:00:51,770 --> 00:00:54,650
+Complete Space خلاص خلّاها دي مش هي اللي هنحكي
+
+12
+00:00:54,650 --> 00:00:57,910
+عليها هنحكي عن الـ Non-Complete Space الـ Non
+
+13
+00:00:57,910 --> 00:01:01,490
+-Complete Space بدي انا اعملها Completion يعني بدي
+
+14
+00:01:01,490 --> 00:01:05,290
+ا .. ب .. roughly الكلام انه اش اللي خاسس فيها بده
+
+15
+00:01:05,290 --> 00:01:11,990
+اكملههو Roughly اللي هي و كأنه الـ Sequences اللي
+
+16
+00:01:11,990 --> 00:01:14,990
+فيها اللي جاية عبالها تروح و تكون Converged و برة
+
+17
+00:01:14,990 --> 00:01:17,870
+و ما بتكونش Converged في الـ Space بدي أجيب هذا
+
+18
+00:01:17,870 --> 00:01:20,990
+النقطة اللي هي ممكن تروح فيها و أحطها في مين في
+
+19
+00:01:20,990 --> 00:01:24,250
+الـ Space هذا الكلام Roughly نشوف إيش معناة الكلام
+
+20
+00:01:24,250 --> 00:01:29,880
+هذا اللي هو بشكل خلنا نقول أطقأولا تعريف let X be
+
+21
+00:01:29,880 --> 00:01:33,980
+let X and و D and Y و D تلدة بيه metric spaces
+
+22
+00:01:33,980 --> 00:01:39,140
+الآن، ضمن a mapping T من X لعند Y من عند الـ X
+
+23
+00:01:39,140 --> 00:01:42,700
+لعند Y، بنقول عنها is said to be isometric or
+
+24
+00:01:42,700 --> 00:01:47,500
+isometry يعني بنسمي اللي هي ال space هذا .. ال ..
+
+25
+00:01:47,500 --> 00:01:50,240
+ال .. ال .. ال function اللي عندي isometry أو
+
+26
+00:01:50,240 --> 00:01:54,620
+isometric اللي هي إذا كان T preserve distances
+
+27
+00:01:54,620 --> 00:01:59,180
+يعني بمعنى آخربتنقل المسافة اللي هنا إلى نفس
+
+28
+00:01:59,180 --> 00:02:03,240
+المسافة اللي هنا بمعنى انه that is لكل x و y في ال
+
+29
+00:02:03,240 --> 00:02:10,260
+X ال D تلدة لل Tx و Ty بساوية D لل X و ال Y يعني
+
+30
+00:02:10,260 --> 00:02:14,860
+المسافة اللي بين X و Y under Dاللي هي في الـ .. في
+
+31
+00:02:14,860 --> 00:02:20,400
+الـ X وD هي نفسها المسافة بين صورها في الأندر
+
+32
+00:02:20,400 --> 00:02:23,420
+المتريك اللي في مين وفي واي الـ D تلد في T X وT Y
+
+33
+00:02:23,420 --> 00:02:27,320
+هذا بنسميه Isometry ومعلومة على جنب إذا كانت الـ T
+
+34
+00:02:27,320 --> 00:02:31,500
+is Isometry اللي هو على طول بتطلع one to one
+
+35
+00:02:31,500 --> 00:02:35,120
+function ماشي الحال وهذا الكلام يعني إثباته اللي
+
+36
+00:02:35,120 --> 00:02:42,000
+هو سهل بضل معاكم الآن بيجيهذا لما نقول عن الـ T من
+
+37
+00:02:42,000 --> 00:02:45,000
+X لعند Y عزيمتريك أو are the I عزيمتريك، as a
+
+38
+00:02:45,000 --> 00:02:49,940
+function اللي بنقول إن الـ space X is said to be
+
+39
+00:02:49,940 --> 00:02:56,080
+عزيمتريك كspace و الـ space Y إذا بنلاقي if there
+
+40
+00:02:56,080 --> 00:03:00,390
+exists a bijection عزيمتري of X onto Yيعني بنقول
+
+41
+00:03:00,390 --> 00:03:03,550
+أنه اتنين ال X و ال Y are isometric إذا كان في
+
+42
+00:03:03,550 --> 00:03:07,470
+عندي one to one onto function which is an
+
+43
+00:03:07,470 --> 00:03:11,510
+isometric بنقول عنه إيش ماله The two spaces X and
+
+44
+00:03:11,510 --> 00:03:16,550
+Y are isometric يعني بمعنى آخر العالم اللي أنا
+
+45
+00:03:16,550 --> 00:03:22,330
+أصلا بشتغل فيه ال metric space X أو Dوعندي اللي هو
+
+46
+00:03:22,330 --> 00:03:27,250
+Y وD تلدة بنقول عنهم ان هدولة isometric ال spaces
+
+47
+00:03:27,250 --> 00:03:32,210
+يعني بمعنى اخر هما نفس الاشي بس اختلفت في الأسماء
+
+48
+00:03:32,210 --> 00:03:37,050
+هذه الأسانة فيها X وهذه الأسانة فيها اسمها TXلأن
+
+49
+00:03:37,050 --> 00:03:42,370
+المسافة هذه هي نفس المسافة فعشان هيك كل ما يتعلق
+
+50
+00:03:42,370 --> 00:03:45,890
+بالمسافة هنا و هنا نفس الاشي عشان هيك بنقول ال
+
+51
+00:03:45,890 --> 00:03:49,590
+spaces هنا زي بعض roughly لكن اللي هي اختلافات في
+
+52
+00:03:49,590 --> 00:03:53,490
+مين في الأسماء يعني و كإني بقول ال space اللي
+
+53
+00:03:53,490 --> 00:03:57,030
+بأثبت أنه isometric بين هنا و بين هنا بنقول عنهم
+
+54
+00:03:57,030 --> 00:04:01,030
+اللي هم إيه الشمال هم ال two spaces و كإنا بنقول
+
+55
+00:04:01,030 --> 00:04:04,880
+are equivalentزي ما كنا في الـ Jabra إذا بتذكروا
+
+56
+00:04:04,880 --> 00:04:09,360
+لما نقول اللي هو لما نحكي عن تركيب Jabra نقول X
+
+57
+00:04:09,360 --> 00:04:14,280
+group و Y group إذا كانت ال X في homomorphism بين
+
+58
+00:04:14,280 --> 00:04:18,200
+التنتين بالإضافة one to one onto function كنا نقول
+
+59
+00:04:18,200 --> 00:04:22,240
+there are أيش ما له isomorphic يعني العالمين
+
+60
+00:04:22,240 --> 00:04:25,820
+متكافئان أو هي نفس الأشي بس اختلفت الأسماء وهنا
+
+61
+00:04:25,820 --> 00:04:30,700
+نفس الأشي عند metric space و metric spaceبقولش بين
+
+62
+00:04:30,700 --> 00:04:33,300
+عمليات X عليها وعمليات Y عليها، لأ لأ لأ بس
+
+63
+00:04:33,300 --> 00:04:36,960
+كمتريكي space إذا preserved distances و one to one
+
+64
+00:04:36,960 --> 00:04:40,300
+نقلت بلاغي function اللي هي one to one نقلت و
+
+65
+00:04:40,300 --> 00:04:42,920
+preserved distances معناته إنه صار the two spaces
+
+66
+00:04:42,920 --> 00:04:47,220
+are the same هذا الكلام مهم لللي بده أحكيه بعد هيك
+
+67
+00:04:47,220 --> 00:04:51,200
+الآن ندلع ال theorem تبعتنااللي هي الـ Completion
+
+68
+00:04:51,200 --> 00:04:55,920
+for a metric space الإعلان هذا قلته قبل شوية أنه
+
+69
+00:04:55,920 --> 00:05:01,440
+أي metric space لو non-complete can be completed
+
+70
+00:05:01,440 --> 00:05:06,860
+اللي هو النظرية بتقول اللي هي ال completion for a
+
+71
+00:05:06,860 --> 00:05:12,550
+metric space X وDاللي هو there exist تفاصيل اللي
+
+72
+00:05:12,550 --> 00:05:15,710
+قلته a metric space can be completed تفاصيله
+
+73
+00:05:15,710 --> 00:05:19,910
+كالتالي for a metric space X وD there exist a
+
+74
+00:05:19,910 --> 00:05:26,390
+complete metric space X hat وD hat which has a
+
+75
+00:05:26,390 --> 00:05:34,810
+subspace W that is isometric with X and dense in X
+
+76
+00:05:34,810 --> 00:05:35,250
+hat
+
+77
+00:05:38,140 --> 00:05:44,460
+لو كان عندى x و d metric space و هذا لو كان مش
+
+78
+00:05:44,460 --> 00:05:46,500
+complete لو كان complete بيبقى على نفسه مش مشكلة
+
+79
+00:05:46,500 --> 00:05:51,640
+كان non complete اللي هو بقدر ألاقي metric space
+
+80
+00:05:51,640 --> 00:06:00,240
+اللي هو آخر اسمه x hat و d hat هذا ال metric space
+
+81
+00:06:00,240 --> 00:06:06,380
+complete metric spaceوإله subspace اسمه main W
+
+82
+00:06:06,380 --> 00:06:15,140
+subspace من main من X hat و الـ W اللي هو dense
+
+83
+00:06:15,140 --> 00:06:21,660
+space يعني بمعنى أخر W closure بساوي اللي هو X hat
+
+84
+00:06:21,660 --> 00:06:25,400
+وال
+
+85
+00:06:25,400 --> 00:06:34,290
+X هذا الـ W isometric للmain لل Xنشوف ايش اللي
+
+86
+00:06:34,290 --> 00:06:42,630
+بنقوله اللي بقوله التالت انه انا غرضي ان الاجي
+
+87
+00:06:42,630 --> 00:06:48,190
+اللي هو metric space يكون completion لل X
+
+88
+00:06:50,520 --> 00:06:56,120
+الان عندى .. بقولكم أكيد هلاقي space اسمه X hat وD
+
+89
+00:06:56,120 --> 00:07:02,400
+hat هذا ال space يتمتع بالآتى اللى فيه W فيه ال
+
+90
+00:07:02,400 --> 00:07:07,250
+closure إيه هي أشبت ثانية؟ X hatو الـ W هذه و
+
+91
+00:07:07,250 --> 00:07:12,870
+كأنها هي X لإنها الـ W إيش مانها؟ Isometric لمين؟
+
+92
+00:07:12,870 --> 00:07:19,290
+للـ X و كأنه صار عندي الـ X hat هي عبارة عن اللي
+
+93
+00:07:19,290 --> 00:07:22,750
+هي الـ X مضافة إلى ال closure اللي خلاها complete
+
+94
+00:07:22,750 --> 00:07:28,700
+مافيه؟ و كأنه صارت X hat complete space اللي هوفي
+
+95
+00:07:28,700 --> 00:07:32,160
+subspace منه isometric للـ X اللي هو هذا اللي
+
+96
+00:07:32,160 --> 00:07:38,620
+هنسمي انه completion لمين للـ X أي سؤال يعني مش
+
+97
+00:07:38,620 --> 00:07:41,580
+شرط انه احنا يجينا و الله نحطنا limit points هنا و
+
+98
+00:07:41,580 --> 00:07:45,520
+هنا نحطناها لأ احنا بنجيب space complete كامل و
+
+99
+00:07:45,520 --> 00:07:51,530
+نclosure ل W هي عبارة عن ال X hat و ال W هي ال Xأو
+
+100
+00:07:51,530 --> 00:07:57,390
+بمعنى مش هي هي w isometric لمين لل X واضح طيب هذا
+
+101
+00:07:57,390 --> 00:08:01,350
+اللي هو خلينا نقول نص نظريه ومش هيك كمان وبيقولك
+
+102
+00:08:01,350 --> 00:08:05,870
+this space X hat راقزوا معايا this space X hat is
+
+103
+00:08:05,870 --> 00:08:09,730
+unique except for isometers يعني هذا ال space X
+
+104
+00:08:09,730 --> 00:08:14,120
+hat إيش ماله وحيدexcept isometrics يعني لو بتدلج
+
+105
+00:08:14,120 --> 00:08:19,420
+space تاني مشابه إله هكون isometric إله يعني لو
+
+106
+00:08:19,420 --> 00:08:24,700
+كان في عند X تلدة ال complete isometric space و
+
+107
+00:08:24,700 --> 00:08:29,160
+half نفس الخواص تبع X hat يعني having dense
+
+108
+00:08:29,160 --> 00:08:34,210
+subspace W تلدة و W تلدة isometric لل Xلازم الـ x
+
+109
+00:08:34,210 --> 00:08:37,630
+تلدة و الـ x هات أشمالين يكون isometric يعني لو
+
+110
+00:08:37,630 --> 00:08:42,050
+بدنا نلاقي كمان واحد اسمه x تلدة أو d تلدة و هذا
+
+111
+00:08:42,050 --> 00:08:47,390
+اللي هو ال space في w تلدة sub space منه و الـ w
+
+112
+00:08:47,390 --> 00:08:50,450
+تلدة اللي هي dense فيه و في نفس الودة isometric
+
+113
+00:08:50,450 --> 00:08:54,210
+للـ x هيطلع اللي هو ال x تلدة و ال x هات are
+
+114
+00:08:54,210 --> 00:09:00,550
+isometricواضح اذا نرخص النظرية there exist a
+
+115
+00:09:00,550 --> 00:09:05,270
+complete metric space او
+
+116
+00:09:05,270 --> 00:09:08,250
+a completion metric space لهذا ال space بالمفهوم
+
+117
+00:09:08,250 --> 00:09:14,510
+اللي حكيناه وهذا ال metric واحد except for
+
+118
+00:09:14,510 --> 00:09:15,530
+isometric
+
+119
+00:09:19,020 --> 00:09:23,740
+طيب نيجي البرهان البرهان يا جماعة هيتكون من أربع
+
+120
+00:09:23,740 --> 00:09:28,940
+اللي هو اللي هي أجزاء بتطولوا روحكم عليها الجزء
+
+121
+00:09:28,940 --> 00:09:32,240
+الأول اللي هو constructing X hat وD hat يعني بدي
+
+122
+00:09:32,240 --> 00:09:37,140
+أعملكم construction بدي أركّنكم ل space اللي احنا
+
+123
+00:09:37,140 --> 00:09:40,900
+بدناه اللي هو اللي متوقعين ان يكون completion
+
+124
+00:09:40,900 --> 00:09:46,210
+لنهينا ال Xوبعد ذلك سأعمل لكم Constructing an
+
+125
+00:09:46,210 --> 00:09:51,310
+Isometry T of X onto W الأن سأعمل لكم ما هو
+
+126
+00:09:51,310 --> 00:09:55,350
+Isometry بين X و بين W اللي يبقى خشوط اللي قبل
+
+127
+00:09:55,350 --> 00:09:59,590
+شوية الـ W سيكون من مين جزء من الـ X هذا و الـ
+
+128
+00:09:59,590 --> 00:10:03,470
+Closure اللي سيكون من مين هو الـ X هذا سيخلصنا
+
+129
+00:10:03,470 --> 00:10:07,310
+اللي هو الجزء هذا بعد ذلك سأثبت لكم أن الـ X نحن
+
+130
+00:10:07,310 --> 00:10:11,900
+نبحث عنه أشيكون Completeبدأ أثبت لكم أن الـ space
+
+131
+00:10:11,900 --> 00:10:17,040
+X hat is complete بعد هيك الخطوة الأخيرة بتدابلكم
+
+132
+00:10:17,040 --> 00:10:20,080
+proving the uniqueness of X hat except for
+
+133
+00:10:20,080 --> 00:10:22,820
+isometries يعني بتدفر الـ XL ده واحد تاني بنفسه
+
+134
+00:10:22,820 --> 00:10:26,640
+كده كده الاخر شروط ويطلع XL ده يشمله isometric
+
+135
+00:10:26,640 --> 00:10:31,690
+لمين للـ X hatتابعوا معايا بالتفصيل الآن اطلعوا
+
+136
+00:10:31,690 --> 00:10:35,190
+لفوق خلّينا نفصل اللي حكيناها قبل بشوية اول حاجة
+
+137
+00:10:35,190 --> 00:10:39,490
+اللي هو مين انها Constructing X هات وD هات بدي اش
+
+138
+00:10:39,490 --> 00:10:47,860
+اسوي بدي اركب ال X هات و احطه بين اديكمخلّينا ناخد
+
+139
+00:10:47,860 --> 00:10:52,860
+Xn و Zn أني كوشي سيكوانسيز in main in X لإن كوشي
+
+140
+00:10:52,860 --> 00:10:56,220
+سيكوانسيز ما احنا احنا اصلا من الأول احنا متوقعين
+
+141
+00:10:56,220 --> 00:11:01,280
+اصلا انه ال X خاسس مين خاسس انه انه تروح ال limits
+
+142
+00:11:01,280 --> 00:11:03,900
+فيه يعني الكوشي سيكوانسيز دي عبالها تعمل
+
+143
+00:11:03,900 --> 00:11:07,280
+convergence لكن ال space مافيش فيه لأن ال limit
+
+144
+00:11:07,280 --> 00:11:10,740
+اللي هو تروح له فعشان ذلك احنا بدّينا بالكوشي
+
+145
+00:11:10,740 --> 00:11:15,360
+سيكوانسيز let Xn and Zn بيكون كوشي سيكوانسيز in X
+
+146
+00:11:16,200 --> 00:11:20,880
+الان بدنا نعرف xₙ related to zₙ يعني مجرد ايش ما
+
+147
+00:11:20,880 --> 00:11:26,020
+لها relation ال relation هذه كيف بدى اعرفها ان ال
+
+148
+00:11:26,020 --> 00:11:29,940
+limit لل distance بين xₙ و zₙ ايش ساية سفر اذا ال
+
+149
+00:11:29,940 --> 00:11:33,210
+relation العامة اللي بعرفهاأخدت اي two sequences
+
+150
+00:11:33,210 --> 00:11:37,250
+كوشي sequences Xn و Zn بقول ان الكوشي sequences
+
+151
+00:11:37,250 --> 00:11:40,890
+هدولة are related إذا كانت ال limit للمسافات اللي
+
+152
+00:11:40,890 --> 00:11:48,410
+بين X1 و X2 و X3 X2 و Z2
+
+153
+00:11:48,410 --> 00:11:53,870
+Xn و Zn المسافة is n cos infinity ايش تساوي؟ ساوي
+
+154
+00:11:53,870 --> 00:11:57,560
+صفر هذه is an equivalence relationوكوف الانسان
+
+155
+00:11:57,560 --> 00:12:03,220
+عشان نسيوله عندى اول حاجة ال Xn related لل Xn ليه؟
+
+156
+00:12:03,220 --> 00:12:08,120
+لأن المسافة بين Xn و Xn دايما مش متساوية ف limit
+
+157
+00:12:08,120 --> 00:12:12,380
+ها اكيد مش متساوية اذا اللي هو اللي ازال سواها
+
+158
+00:12:12,380 --> 00:12:17,200
+اولاشه reflexive اتنين الان symmetric اكيد اللي هو
+
+159
+00:12:17,200 --> 00:12:27,960
+Xn related to Yn معناتها limit Xn Yn بساوية0 و هذي
+
+160
+00:12:27,960 --> 00:12:36,020
+اكيد limit dyn و xn هيساوي سفر لأن هذي يعني هذي و
+
+161
+00:12:36,020 --> 00:12:42,440
+هذا هيعطيني انه اللي هو yn related to xn إذا كانت
+
+162
+00:12:42,440 --> 00:12:47,360
+اللي هو هذي هتكون symmetric برضه الان تلاتة اللي
+
+163
+00:12:47,360 --> 00:12:51,940
+هي النقطة الأخيرة برضه لو فرضنا ان xn related to
+
+164
+00:12:51,940 --> 00:13:02,830
+yn و ynمع Zn مايعطينا هنا limit distance Xn و Yn
+
+165
+00:13:02,830 --> 00:13:10,410
+بساوي0 والـ Limit للـ Distance بين YN و ZN بساوية
+
+166
+00:13:10,410 --> 00:13:16,310
+0 إذا أنا بدي XN و مين و ZN خدوا Limit الـ
+
+167
+00:13:16,310 --> 00:13:20,330
+Distance بين XN و ZN طبيعي بالطريقة نقول الـ
+
+168
+00:13:20,330 --> 00:13:24,730
+Equality XN و ZN أصغر أو شاوي الـ Distance بين XN
+
+169
+00:13:24,730 --> 00:13:30,470
+و YN زائد الـ Distance بين YN و ZNخُدوا الـ limit
+
+170
+00:13:30,470 --> 00:13:35,170
+للجهتين اللي غالب بيصير limit limit as n goes to
+
+171
+00:13:35,170 --> 00:13:37,630
+infinity هذي as n goes to infinity من اللي فوق هذي
+
+172
+00:13:37,630 --> 00:13:41,730
+سفر إذا تطلع وهذا أكبر ساو سفر إذا هذي هتطلع
+
+173
+00:13:41,730 --> 00:13:48,010
+بتساوي سفر إذا أشملها إذا صارت Zn أو Xn related Zn
+
+174
+00:13:48,010 --> 00:13:51,770
+يعني بمعنى أخر transitive إذا صارت عندي is an
+
+175
+00:13:51,770 --> 00:13:54,770
+equivalence relation إيش بدك في ال equivalence
+
+176
+00:13:54,770 --> 00:13:57,050
+relation؟ بد ال equivalence relation عارفين ليش؟
+
+177
+00:13:58,220 --> 00:14:04,660
+عشان أنا الآن بدي أركّب الـ X hat الـ X hat
+
+178
+00:14:04,660 --> 00:14:08,640
+هركّبها من ال equivalence classes لل relation اللي
+
+179
+00:14:08,640 --> 00:14:14,180
+عندي اه يعني الآن ال equivalence classes ايش هي
+
+180
+00:14:14,180 --> 00:14:22,100
+مثلا لو عندي X n عشان X n قوشي sequence ماشي في
+
+181
+00:14:22,100 --> 00:14:24,940
+الاسم السابع اللي هو main قوشي sequence in main in
+
+182
+00:14:24,940 --> 00:14:31,000
+X عناصره من وين جاي من Xكل الـ sequences الـ
+
+183
+00:14:31,000 --> 00:14:36,520
+Cauchy اللي related لها يعني IZN related to XN
+
+184
+00:14:36,520 --> 00:14:40,860
+هيكونوا إيش مانوا كلهم في نفس ال equivalence class
+
+185
+00:14:40,860 --> 00:14:47,200
+يعني ال equivalence class لل XN هذه اللي هي فيها
+
+186
+00:14:47,200 --> 00:14:53,160
+IZN و ال YN و كل الناس اللي او ال sequences اللي
+
+187
+00:14:53,160 --> 00:14:56,060
+Cauchy sequences و related لهذه عبر ال relation
+
+188
+00:14:56,060 --> 00:15:02,000
+اللي عنديالان انا بدي اسمي ال X hat بي the set of
+
+189
+00:15:02,000 --> 00:15:05,940
+all equivalence classes اللي بدي اسميها يعني هذه
+
+190
+00:15:05,940 --> 00:15:08,780
+بدل ما اسميها زي هيك اسهل اللي بدي اسميها X hat
+
+191
+00:15:08,780 --> 00:15:13,480
+ماشي و هكذا واضحيش هذه ال X hat ايش هي عبارة عن
+
+192
+00:15:13,480 --> 00:15:16,500
+the equivalence class of all اللي هي كوشي
+
+193
+00:15:16,500 --> 00:15:20,280
+sequences related to بعض ماشي طيب الان
+
+194
+00:15:22,770 --> 00:15:25,550
+لت X hat be the set of all equivalency classes X
+
+195
+00:15:25,550 --> 00:15:29,790
+hat و Y hat و Z hat الاخره of Cauchy sequences
+
+196
+00:15:29,790 --> 00:15:33,790
+اللي هو rough obtained above اللي هو عن طريق ال
+
+197
+00:15:33,790 --> 00:15:38,250
+limit distance بين X and Y and ساوة سفرالان بتدعرف
+
+198
+00:15:38,250 --> 00:15:43,130
+ال d hat ايش ال d hat بتدعرف ال d hat of x hat و y
+
+199
+00:15:43,130 --> 00:15:47,910
+hat بساوى ال limit لل distance xn yn as n goes to
+
+200
+00:15:47,910 --> 00:15:51,610
+infinity ال xn مالها كوش ال sequences فيها دي و ال
+
+201
+00:15:51,610 --> 00:15:56,160
+yn كوش ال sequences في مين؟ في التانيةفالان هذا
+
+202
+00:15:56,160 --> 00:15:59,560
+التعريف اللي هو اللي أمامي بدي أثبت انه well
+
+203
+00:15:59,560 --> 00:16:04,040
+defined where xn element of x hat and yn element
+
+204
+00:16:04,040 --> 00:16:07,060
+of y hat و ال x hat و ال y hat ايش ما اللي موجودات
+
+205
+00:16:07,060 --> 00:16:10,880
+في ال x hat ليش اثبتوا well defined؟ لحسن مش احنا
+
+206
+00:16:10,880 --> 00:16:13,280
+بنتعامل معاكوا equivalency class انتوا تروحوا
+
+207
+00:16:13,280 --> 00:16:19,020
+تاخدوا ناخد xn و تاخدوا zالواحد ياخد دي يبدو YN و
+
+208
+00:16:19,020 --> 00:16:22,180
+KN و YN و KN أشمالين related لبعض في نفس ال
+
+209
+00:16:22,180 --> 00:16:25,500
+equivalency class خايفين يطلع جواب يعني لما ناخد
+
+210
+00:16:25,500 --> 00:16:28,300
+ال limit لل distance بين XN و YN و جوابكم يبدأ ال
+
+211
+00:16:28,300 --> 00:16:33,040
+limit لل distance بين ZN و KN يطلع مش زي بعض فلأ
+
+212
+00:16:33,040 --> 00:16:36,880
+بدنا نثبت لكم أنه بطلع زي بعض دعونا نشوف كيف ..
+
+213
+00:16:36,880 --> 00:16:42,340
+اطلع على فوقto prove that this limit exists we do
+
+214
+00:16:42,340 --> 00:16:45,620
+as follow بدنا نعمل كمان يعني ب triangling quality
+
+215
+00:16:45,620 --> 00:16:49,220
+سهلة اللي هو distance بين Xm و Ym ب triangling
+
+216
+00:16:49,220 --> 00:16:54,240
+quality أثر سواء distance بين Xm و Xm ماشي زاد
+
+217
+00:16:54,240 --> 00:16:58,320
+distance بين Xm و Ym زاد ال distance بين Ym و Ym
+
+218
+00:16:58,320 --> 00:17:04,260
+انه un-arbitrary ماشي then جيبولي هذه hand اللي هي
+
+219
+00:17:04,260 --> 00:17:08,000
+ال Ym و Xm على الجهة دي بيصير عندى distance بين Xm
+
+220
+00:17:08,000 --> 00:17:13,730
+و Ymنقص هذه جيبتها هنا ال distance بين YM و XM و
+
+221
+00:17:13,730 --> 00:17:18,390
+YM أصغر و أصغر اللي بيظل اللي هو هذه و هذه اللي هي
+
+222
+00:17:18,390 --> 00:17:22,430
+ال distance بين XN و XM و ال distance بين YM و YN
+
+223
+00:17:22,430 --> 00:17:26,070
+اللي حصلت على هذه similarly بنفس الطريقة بدل ما
+
+224
+00:17:26,070 --> 00:17:29,770
+بدأ بدأ بال distance XN و YN ببدأ بال distance XM
+
+225
+00:17:29,770 --> 00:17:34,230
+و YMو بعمل نفس ال triangle inequality بطلع عندى ..
+
+226
+00:17:34,230 --> 00:17:36,630
+و بجيب هذه اللي .. اللي .. اللي هي في هذه الحالة
+
+227
+00:17:36,630 --> 00:17:41,270
+بتطلع بدل Xm Ym على الجهة هذه بتطلع Xn Yn بجيبها
+
+228
+00:17:41,270 --> 00:17:45,350
+هنا على الجهة هذه بصير المسافة بين Xm Ym ناقص Xn
+
+229
+00:17:45,350 --> 00:17:49,830
+Yn أصغر أو يساوي نفس الكمية اللي طلعت قبل بشوية و
+
+230
+00:17:49,830 --> 00:17:52,910
+ضربها في سالبحط و .. و .. و .. و .. و .. و .. و ..
+
+231
+00:17:52,910 --> 00:17:53,070
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+232
+00:17:53,070 --> 00:17:54,310
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+233
+00:17:54,310 --> 00:17:55,610
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+234
+00:17:55,610 --> 00:17:56,290
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+235
+00:17:56,290 --> 00:18:01,030
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+236
+00:18:01,030 --> 00:18:01,030
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+237
+00:18:01,030 --> 00:18:02,490
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+238
+00:18:02,490 --> 00:18:04,030
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+239
+00:18:04,030 --> 00:18:08,590
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+240
+00:18:08,590 --> 00:18:08,690
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+241
+00:18:08,690 --> 00:18:16,610
+و .. و .. و .. و
+
+242
+00:18:16,610 --> 00:18:19,840
+..بالرغم من أن Xn وYn هما عاملين عاملين عاملين
+
+243
+00:18:19,840 --> 00:18:20,480
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+244
+00:18:20,480 --> 00:18:21,760
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+245
+00:18:21,760 --> 00:18:29,480
+عاملين عاملين عاملين عاملين عاملين
+
+246
+00:18:29,480 --> 00:18:31,360
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+247
+00:18:31,360 --> 00:18:31,360
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+248
+00:18:31,360 --> 00:18:31,440
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+249
+00:18:31,440 --> 00:18:32,260
+عاملين عاملين عاملين عاملين عاملين عاملين عاملين
+
+250
+00:18:32,260 --> 00:18:37,840
+عاملين عاملين
+
+251
+00:18:37,840 --> 00:18:47,260
+عام
+
+252
+00:18:47,280 --> 00:18:52,460
+أصغر من إبسلون لحدها واضح إيش معناته صار عندي اللي
+
+253
+00:18:52,460 --> 00:18:57,980
+هو هذا هذا رقم عدد عدد يعني وكأنه عبارة عن
+
+254
+00:18:57,980 --> 00:19:01,260
+sequence of أعداد وهذا عبارة عن أعداد إذا صارت
+
+255
+00:19:01,260 --> 00:19:06,750
+الـDX and Y and هذهاللي هي عبارة عن sequences of
+
+256
+00:19:06,750 --> 00:19:10,190
+mean of real numbers واحنا بنعرف الـ real number
+
+257
+00:19:10,190 --> 00:19:15,090
+إيش ماله، complete إذا then it converges، thus ال
+
+258
+00:19:15,090 --> 00:19:19,310
+limit لل distance xₙ و yₙ إيش ماله exist، exist
+
+259
+00:19:19,310 --> 00:19:25,230
+وكمان وحيد، طيب، طيب، الآن now we show that this
+
+260
+00:19:25,230 --> 00:19:28,710
+limit is إيش، is independent، إذا الأول إشي أثبتنا
+
+261
+00:19:28,710 --> 00:19:32,730
+إنه ال limit موجودة، بمعنى آخر الديهات اللي عرفته
+
+262
+00:19:33,450 --> 00:19:38,350
+بين x hat و y hat اللي هو بيساوي ال limit لل
+
+263
+00:19:38,350 --> 00:19:42,570
+distance بين x n و y n as n goes to infinity
+
+264
+00:19:42,570 --> 00:19:43,950
+exists
+
+265
+00:19:46,230 --> 00:19:49,910
+هذه واحدة الان بدأ اثبت لكم انه independent of the
+
+266
+00:19:49,910 --> 00:19:55,250
+choice of xn من ال x hat و ال y hat من ال y hat
+
+267
+00:19:55,250 --> 00:19:58,670
+يعني انت لو اخترت xn في ال y hat في ال x hat و
+
+268
+00:19:58,670 --> 00:20:04,710
+اخترت zn في ال y hat و واحد اختار zkn مثلا في ال y
+
+269
+00:20:04,710 --> 00:20:08,330
+hat هيطلع ال limit بناء على هذا و ال limit بناء
+
+270
+00:20:08,330 --> 00:20:12,750
+على ال distance بين zn و kn اللي هو R equivalent
+
+271
+00:20:12,750 --> 00:20:19,140
+تنشوفالان نظرح ان هذا الانتقال مستقل من الاختيار
+
+272
+00:20:19,140 --> 00:20:23,420
+اذا انا الآن اذكركم ركبت ال X hat من اين؟ من ال
+
+273
+00:20:23,420 --> 00:20:27,220
+equivalency classes عرفت ال D hat اللي هو metric
+
+274
+00:20:27,220 --> 00:20:33,020
+عليها اسمه D hat حسب اللي حكيته فوق، ضال عندي ايش
+
+275
+00:20:33,020 --> 00:20:38,580
+اسوي؟ ان اثبتلكم ان هذا الانتقال مستقل من الاختيار
+
+276
+00:20:38,580 --> 00:20:42,820
+من الاختيارات الخاصة من الاختيارات الخاصة اللي
+
+277
+00:20:42,820 --> 00:20:43,520
+بنحكي عنها
+
+278
+00:20:46,370 --> 00:20:53,830
+لأ سنة خلّيني أنزل بقول لك we show that this limit
+
+279
+00:20:53,830 --> 00:20:56,590
+is independent of the choice of xₙ elemental x hat
+
+280
+00:20:56,590 --> 00:21:00,610
+and yₙ elemental y hat in other words خلّيني نفترض
+
+281
+00:21:00,610 --> 00:21:03,690
+أن xₙ و zₙ من نفس ال equivalency class تطلع على
+
+282
+00:21:03,690 --> 00:21:07,710
+فوق و نفترض أن ال yₙ و ال wₙ من نفس ال equivalency
+
+283
+00:21:07,710 --> 00:21:11,440
+class تبعتي اللي هي mean y hatthen by one اللي هي
+
+284
+00:21:11,440 --> 00:21:14,660
+قبل شوية اللي عملناها المسافة بين Xn وYn والمسافة
+
+285
+00:21:14,660 --> 00:21:20,980
+بين Zn وWn أصغر أو يساوي Xn وZn زائد Yn وMain وWn
+
+286
+00:21:20,980 --> 00:21:25,760
+هذي عملناها قبل هيك الان as n goes to infinityاللي
+
+287
+00:21:25,760 --> 00:21:29,240
+هي هذا هتروح للصفر وهذا هتروح للصفر ليش؟ لأن Xn
+
+288
+00:21:29,240 --> 00:21:33,240
+وZn مالهن من نفس ال .. related مدام related على
+
+289
+00:21:33,240 --> 00:21:36,060
+حسب اللي هي Xn related to Zn هيكون ال limit بيساوي
+
+290
+00:21:36,060 --> 00:21:39,220
+صفر وهذا ال limit أيش بيساوي صفر إذا as n goes to
+
+291
+00:21:39,220 --> 00:21:41,780
+infinity هذا هيروح للصفر إذا as n goes to infinity
+
+292
+00:21:41,780 --> 00:21:45,560
+هذا المقطار هيساوي صفر يعني بمعنى آخر limit هذه
+
+293
+00:21:45,560 --> 00:21:49,100
+بيساوي limit التانية إذا limit هذه بيساوي limit
+
+294
+00:21:49,100 --> 00:21:53,660
+هذا إذايوابي وجوابكم هو نفس الشيء إذا الـD hat
+
+295
+00:21:53,660 --> 00:21:57,660
+الـL على أي كوشي sequence تاخدها من جوا ال
+
+296
+00:21:57,660 --> 00:22:00,800
+equivalency class أي إن كانت اللي إلي و اللي إلك و
+
+297
+00:22:00,800 --> 00:22:04,300
+اللي إلي و اللي إلك و اللي هتطلع نفس الجواب إذا
+
+298
+00:22:04,300 --> 00:22:08,760
+أمورنا تمامة تمام و we prove that الـD hat into is
+
+299
+00:22:08,760 --> 00:22:12,920
+a metric on X hat إذا أثبتنا الخطوة التانية بعد ما
+
+300
+00:22:12,920 --> 00:22:16,200
+أثبتنا إن exist أثبتنا إنه well defined يعني اللي
+
+301
+00:22:16,200 --> 00:22:20,130
+هو لا يعتمد على ال choice تبع ال Xالـ Xn اللي في
+
+302
+00:22:20,130 --> 00:22:24,630
+الـ X hat طيب هبنا نثبت .. و من ال trick اطلع لفوق
+
+303
+00:22:24,630 --> 00:22:29,610
+طولوا روحكم عليها الان بدنا نثبت انه هو prove that
+
+304
+00:22:29,610 --> 00:22:33,770
+D hat in two is a metric on X اول اشي it is clear
+
+305
+00:22:33,770 --> 00:22:38,650
+that D hat satisfy M واحد عند M تلاتة ليش؟ لقيتها
+
+306
+00:22:38,650 --> 00:22:44,120
+هذه أكبر أو سوء سفر أكيد صح؟مظبوط ولا لأ؟ الان و
+
+307
+00:22:44,120 --> 00:22:49,440
+لو بدنا ناخد dy hat و x hat على طول بيصير ال limit
+
+308
+00:22:49,440 --> 00:22:54,680
+بتنقلب فبتطلع نفس الاشي واضح؟ اذا برضه dy hat hat
+
+309
+00:22:54,680 --> 00:23:00,400
+و x hat بيساوي dx hat y hat، مظبوط؟ اذا الشروط هذه
+
+310
+00:23:00,400 --> 00:23:09,150
+سهلة، اللي هي و نيجي اللي هو خلاص انتوا بتكملهالان
+
+311
+00:23:09,150 --> 00:23:11,050
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+312
+00:23:11,050 --> 00:23:11,150
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+313
+00:23:11,150 --> 00:23:11,330
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+314
+00:23:11,330 --> 00:23:12,070
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+315
+00:23:12,070 --> 00:23:12,190
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+316
+00:23:12,190 --> 00:23:14,990
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+317
+00:23:14,990 --> 00:23:14,990
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+318
+00:23:14,990 --> 00:23:19,730
+M M M M M M
+
+319
+00:23:19,730 --> 00:23:20,030
+M M M M M M M M M M M M M M M M M M M M M M M M M
+
+320
+00:23:20,030 --> 00:23:22,450
+M M M M M M M M M M M M M M M Mأه then ال limit دي
+
+321
+00:23:22,450 --> 00:23:26,730
+xn و yn بساوة سفر وهذه ايش معناه بساوة سفر ان xn
+
+322
+00:23:26,730 --> 00:23:30,850
+equivalent ل yn hence the equivalence classes x
+
+323
+00:23:30,850 --> 00:23:34,770
+hat and y hat are either equal لأن احنا عارفين ان
+
+324
+00:23:34,770 --> 00:23:37,890
+ال equivalence class اللي .. اللي كان فيه عندى
+
+325
+00:23:37,890 --> 00:23:41,050
+اللي هو ال equivalence classes عارفين يا this
+
+326
+00:23:41,050 --> 00:23:41,810
+joint
+
+327
+00:23:45,020 --> 00:23:48,800
+يا متسوية يا متسوية مادام في عنصر مشترك بينهم
+
+328
+00:23:48,800 --> 00:23:55,440
+مادام Xn و Yn related وال Xn في ال X hat وال Yn في
+
+329
+00:23:55,440 --> 00:23:59,260
+ال Y hat إذا اللي هو إيش مالهن إذا صار في عنصر
+
+330
+00:23:59,260 --> 00:24:01,180
+مشترك إذا التنتين لازم يكون إيه إيه إيه إيه إيه
+
+331
+00:24:01,180 --> 00:24:03,540
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+332
+00:24:03,540 --> 00:24:03,560
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+333
+00:24:03,560 --> 00:24:03,560
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+334
+00:24:03,560 --> 00:24:06,850
+إيه إيه إيه إيه إيه إيه إيه إيطيب إذا صار عندى لان
+
+335
+00:24:06,850 --> 00:24:11,290
+hence x and x hat the equivalence class x hat and
+
+336
+00:24:11,290 --> 00:24:15,970
+y hat ايش بالي متساويتين وهذا بدأنا x d hat لل x
+
+337
+00:24:15,970 --> 00:24:18,890
+hat و y hat بصفر وصلنا ل x hat و y hat ايش بيساوي
+
+338
+00:24:18,890 --> 00:24:26,440
+بساوى صفر ماهي سؤالالان conversely اللي هو المسافة
+
+339
+00:24:26,440 --> 00:24:30,060
+بين X hat و Y hat ايش هيساوي صفر لذا خلاص الخاصية
+
+340
+00:24:30,060 --> 00:24:35,520
+التانية متحققة تماما to prove M4 اللي عن اتنين هين
+
+341
+00:24:35,520 --> 00:24:40,440
+عملتها اه ال M تلاتة هذي و هذي اللي هي أكبر يساوي
+
+342
+00:24:40,440 --> 00:24:45,420
+صفر M واحد خلصتها ضال مين اللي هي M4 مستوعبين اه
+
+343
+00:24:47,110 --> 00:24:50,810
+أما اربعة اطلع فوق اما اربعة نركز عليها to prove
+
+344
+00:24:50,810 --> 00:24:55,620
+اما اربعة نركز عليها بس في الهدف هي سهلة برضهNote
+
+345
+00:24:55,620 --> 00:25:01,520
+that for all xₙ in X hat وYₙ in Y hat وZₙ في Z hat
+
+346
+00:25:01,520 --> 00:25:06,580
+والـ X hat وYₙ وZₙ إيش موجودة؟ اللي هي X hat، بتدا
+
+347
+00:25:06,580 --> 00:25:10,560
+وجد ال triangle inequality We have المسافة بين Xₙ
+
+348
+00:25:10,560 --> 00:25:15,920
+وYₙ أصغر بسهول مسافة بين Xₙ وZₙ وZₙ ومين وYₙ بال
+
+349
+00:25:15,920 --> 00:25:19,640
+triangle inequality لإن الـ D is a metric أنا
+
+350
+00:25:19,640 --> 00:25:24,620
+بتذكر بتمين الآن ال metric الـ D hatالان d hat لـ
+
+351
+00:25:24,620 --> 00:25:28,700
+x hat و y hat ايش بيساوي ال limit هذا طب ما هو ال
+
+352
+00:25:28,700 --> 00:25:30,820
+limit هذا هيكون أصغر بيساوي ال limit هذا زاد ال
+
+353
+00:25:30,820 --> 00:25:33,840
+limit هذا صح ولا لأ اذا أصغر بيساوي ال limit هذا
+
+354
+00:25:33,840 --> 00:25:36,820
+زاد ال limit هذا طب ما هو ال limit هذا هو فعلا
+
+355
+00:25:36,820 --> 00:25:40,320
+التعريف التعريف اللي هو ال distance بين x hat و
+
+356
+00:25:40,320 --> 00:25:46,820
+main و z hat وهذا اللي بعده تعريف ال limitهذا
+
+357
+00:25:46,820 --> 00:25:50,460
+تعريف لـ D hat بين XZ hat وY hat
+
+358
+00:26:16,830 --> 00:26:23,270
+بنعمل construction لإيزومتري T من X لعين و لعين W
+
+359
+00:26:23,270 --> 00:26:27,250
+W
+
+360
+00:26:27,250 --> 00:26:34,210
+مين يا جماعة W هتكون لازم تكون W جزء من مين؟ من ال
+
+361
+00:26:34,210 --> 00:26:39,510
+X hat و لازم تكون W closure بسوء ال X hat و لازم
+
+362
+00:26:39,510 --> 00:26:44,810
+يكون عنده يقولوا معايا اللي هو W إيزومتري لمين؟ لل
+
+363
+00:26:44,810 --> 00:26:49,720
+Xطيب شوفوا صلّوا على النبي عليه الصلاة والسلام
+
+364
+00:26:49,720 --> 00:26:55,380
+Constructing an isometry T of X onto Y, we have W
+
+365
+00:26:55,380 --> 00:27:00,680
+closure أش بساوي X hat، هي ما بنعمله، الآن define
+
+366
+00:27:00,680 --> 00:27:07,660
+T من X لعن W subset من X hatأذا بدي أرمي عنصر ال X
+
+367
+00:27:07,660 --> 00:27:13,160
+في وين في ال W ويكون ال W جزء من من X وكأنني بدي
+
+368
+00:27:13,160 --> 00:27:17,640
+أرميه في equivalency classes طيب، الان كيف بدي
+
+369
+00:27:17,640 --> 00:27:22,140
+أعرفه طريقة بصراحة يعني رائعة معرفته إياها معرف لك
+
+370
+00:27:22,140 --> 00:27:27,940
+T of any element هنا بساوي ال B hat طب كده الآن
+
+371
+00:27:27,940 --> 00:27:33,810
+أخد لك اللي هو انت بوهان عندىمن X لعين W و جالك
+
+372
+00:27:33,810 --> 00:27:38,410
+هذه W بتاخدها جزء من X هذه هتشوف كم جزء بدي أعرف
+
+373
+00:27:38,410 --> 00:27:45,470
+لك T of B B المتنوين من X بساوي الـ B hat طب كيف
+
+374
+00:27:45,470 --> 00:27:49,350
+هذه الـ B hat عبارة عن equivalence classes صح ولا
+
+375
+00:27:49,350 --> 00:27:55,500
+لأ؟الان ايش قال لك انا بدي اخد اللي هو الـ B hat
+
+376
+00:27:55,500 --> 00:28:02,360
+اللي بدو حدد هويتها هي ال sequence B وB وB وB وB
+
+377
+00:28:02,360 --> 00:28:02,840
+وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB
+
+378
+00:28:02,840 --> 00:28:03,960
+وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB
+
+379
+00:28:03,960 --> 00:28:04,180
+وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB
+
+380
+00:28:04,180 --> 00:28:04,180
+وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB
+
+381
+00:28:04,180 --> 00:28:07,540
+وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB وB
+
+382
+00:28:07,540 --> 00:28:09,560
+وB وB وB وB وBالأن هذه الـ Cauchy Sequence الـ
+
+383
+00:28:09,560 --> 00:28:13,660
+equivalence class لها هي اللي بيسميها إيش مالها؟ B
+
+384
+00:28:13,660 --> 00:28:19,000
+hat وكل الـ sequences اللي related لها هيكون
+
+385
+00:28:19,000 --> 00:28:22,460
+موجودات في الـ B hat فراحظوا إن كل عوصر من هان
+
+386
+00:28:22,460 --> 00:28:27,600
+وديته لعوصر اسم بيهتها، ماشي الحال، هذه اللي هي W
+
+387
+00:28:27,600 --> 00:28:33,050
+اللي بتديها جزء من X hat ولا لأ؟ أكيد جزء منهاو W
+
+388
+00:28:33,050 --> 00:28:38,790
+في الواقع أنا ماخدها W هاخدها انا هي عبارة عن T ل
+
+389
+00:28:38,790 --> 00:28:44,030
+X انا هاخدها هيك يعني هاخد ال W ايش بتعملها بتقول
+
+390
+00:28:44,030 --> 00:28:49,610
+T of X هي مين هي ال W هال جيت مش عارفت هال جيت T
+
+391
+00:28:49,610 --> 00:28:54,130
+من X ل عنده لأ هال جيت عرفت هيك صح؟عرفتها زهير لإن
+
+392
+00:28:54,130 --> 00:28:58,030
+هدولة موجودة وين في الـVها الآن مين اللي بديها
+
+393
+00:28:58,030 --> 00:29:03,610
+يسميها W؟ بدي أسميها W هي صور مين الـX إذا إذا
+
+394
+00:29:03,610 --> 00:29:09,210
+الـW عرفتها أنا هي عبارة عن TX إذا صار الـT عدى
+
+395
+00:29:09,210 --> 00:29:16,260
+automatic أنا وأنتواأثبت انه ايزومتري و اثبت انه
+
+396
+00:29:16,260 --> 00:29:20,500
+ايزومتري خلص لان ايزومتري يكون one to one فبصير
+
+397
+00:29:20,500 --> 00:29:26,740
+عندى الان T من X لعين W one to one on to function
+
+398
+00:29:26,740 --> 00:29:31,020
+which is ايزومتري اذا دل بس شغل اخرى ان اثبت W
+
+399
+00:29:31,020 --> 00:29:38,670
+closure بساوة X hat طيب نشوف مع بعضالان where T
+
+400
+00:29:38,670 --> 00:29:41,790
+بيساوي W بيساوي TX and for B element in X we
+
+401
+00:29:41,790 --> 00:29:45,030
+associate the class B hat element in X which
+
+402
+00:29:45,030 --> 00:29:48,910
+contains the constant Cauchy sequence BBB زي ما
+
+403
+00:29:48,910 --> 00:29:53,070
+حكيته لكم الان for any A و B element in X hat
+
+404
+00:29:53,070 --> 00:29:57,910
+لاحظوا أن المسافة سهلة هذه بتنهي زيومتري D hat بين
+
+405
+00:29:57,910 --> 00:30:03,270
+TA و TB بيساوي ال D hat بين A hat و B hat لأن TA
+
+406
+00:30:03,270 --> 00:30:08,350
+انا هي أسميتها A hat وTBاش بيساوي B hatلكن هذه ايش
+
+407
+00:30:08,350 --> 00:30:12,430
+بتساوي؟ limit للـ distance بين اللي هي الـ Cauchy
+
+408
+00:30:12,430 --> 00:30:15,470
+Sequences اللي فيها من الـ Cauchy Sequences اللي
+
+409
+00:30:15,470 --> 00:30:18,090
+فيها اللي انا اصلا ركبت هنا عليها اللي هي الـ
+
+410
+00:30:18,090 --> 00:30:21,230
+constant sequence الـ a, a, a إذا الـ limit للـ d,
+
+411
+00:30:21,310 --> 00:30:24,690
+a ونفس الاشي هدمين اللي هو الـ sequence b, b, b
+
+412
+00:30:24,690 --> 00:30:27,990
+اللي هي d ال distance بين a و b و ال limit اللي
+
+413
+00:30:27,990 --> 00:30:30,950
+هنا as n goes to infinity أصلا ثبتت هنا بساوي d, a
+
+414
+00:30:30,950 --> 00:30:31,290
+و b
+
+415
+00:30:35,330 --> 00:30:40,770
+إذا صار عندى isometry و on to function دل علي بس
+
+416
+00:30:40,770 --> 00:30:46,730
+أثبت ان الـ W closure بساوة مين ال X هت however
+
+417
+00:30:46,730 --> 00:30:51,010
+any isometry is one to one then X and W are
+
+418
+00:30:51,010 --> 00:30:56,570
+isometric we show that W closure بساوة مين X هت
+
+419
+00:31:01,130 --> 00:31:06,170
+الان الـ W و الـ W closure أي إن كان ال subset من
+
+420
+00:31:06,170 --> 00:31:09,370
+مين من ال X hat إذا بدي أثبت ال X hat subset من
+
+421
+00:31:09,370 --> 00:31:14,450
+مين من ال W closure يعني بدي أاخد X hat element in
+
+422
+00:31:14,450 --> 00:31:19,570
+X hat capital و أثبتلك إن ال X hat وين موجودة في
+
+423
+00:31:19,570 --> 00:31:26,630
+ال W closure ماشي الحال؟ طيب الآن عندي
+
+424
+00:31:33,000 --> 00:31:39,360
+متى الـ except في الـ W closure ان لو أخدت اي open
+
+425
+00:31:39,360 --> 00:31:45,930
+ballحوالين ال X hat أي open ball حوالين ال X hat
+
+426
+00:31:45,930 --> 00:31:51,210
+لازم تتقاطع مع مبتع الأقل من مين؟ من W يعني بمعنى
+
+427
+00:31:51,210 --> 00:31:56,030
+أخر أخد أي ball اللي هو centerها اللي هو X hat ولا
+
+428
+00:31:56,030 --> 00:32:00,830
+أي Y في الدنيا تقطحها مع ال W أيش مهله؟ له يساوي
+
+429
+00:32:00,830 --> 00:32:04,490
+Phi هي اللي بدثبته، بكون خلصت، شوفوا مع بعض، شوفوا
+
+430
+00:32:04,490 --> 00:32:11,790
+الانWe show that W closure is equal to X hat Let X
+
+431
+00:32:11,790 --> 00:32:14,550
+hat element in X hat capital and Xn element in
+
+432
+00:32:14,550 --> 00:32:20,750
+mean in X hat ماشي الحال ملام Xn element in X hat
+
+433
+00:32:20,750 --> 00:32:24,550
+إذا Xn كوشي سيكوينس أكيد كوشي سيكوينس إذا for
+
+434
+00:32:24,550 --> 00:32:28,490
+every Y أكبر من 0 there exists K element in N such
+
+435
+00:32:28,490 --> 00:32:34,870
+that المسافة بين Xn وXk أشمالها أصغر من Y على 2الـ
+
+436
+00:32:34,870 --> 00:32:41,310
+N for all N أكبر من K هذا صحيح الـ N أكبر أو يساوي
+
+437
+00:32:41,310 --> 00:32:46,500
+حتى عشان بتستخدمها أكبر أو يساوي من Kالآن خُدلي
+
+438
+00:32:46,500 --> 00:32:52,880
+الـ sequence xk xk xk الاخره أكيد موجودة خارج
+
+439
+00:32:52,880 --> 00:32:56,880
+معناه أدنال أكيد موجودة في مين في الـ xk إيش hat
+
+440
+00:32:56,880 --> 00:32:59,700
+لإن هذه عبارة عن كوشي sequence هذا أخدت الـ xk
+
+441
+00:32:59,700 --> 00:33:03,720
+council يعني اسمه council xk xk xk هذه الكوشي
+
+442
+00:33:03,720 --> 00:33:05,960
+sequence هذه الكوشي sequence موجودة في ال
+
+443
+00:33:05,960 --> 00:33:10,870
+equivalency class سبعتها لـ xk hatإذا XK هتأكيد
+
+444
+00:33:10,870 --> 00:33:14,790
+وين موجودة؟ في الـW لأن الـW هيك اتركبت علي هيك
+
+445
+00:33:14,790 --> 00:33:18,990
+تربط تركبت هذه الـN هذه الـN هي اللي هيلاجيها
+
+446
+00:33:18,990 --> 00:33:24,450
+مشتركة بين الجهتين السر هنا أن المسافة بين XN و XK
+
+447
+00:33:24,450 --> 00:33:27,450
+أزهر من 1 على 2 و يشاوز 1 على 2 لكل N أكبر سواء
+
+448
+00:33:27,450 --> 00:33:33,650
+مين؟ K هذه الـXK هي اللي لاجيتها هنا دير بالكم طيب
+
+449
+00:33:33,650 --> 00:33:38,530
+شوفوا الآنبعيد 2 من اللي قبل بشوية المسافة بين x
+
+450
+00:33:38,530 --> 00:33:42,230
+hat و xk hat ايش بالساوية ال limit لل sequence
+
+451
+00:33:42,230 --> 00:33:45,850
+اللي موجودة هنا اسمها xn صح؟ ولل sequence اللي
+
+452
+00:33:45,850 --> 00:33:50,790
+موجودة هنا اللي هي xk xk xk xk xk as n goes to
+
+453
+00:33:50,790 --> 00:33:55,160
+infinityهذه أصلاً أصغر من مين من يبسلون على اتنين
+
+454
+00:33:55,160 --> 00:34:00,200
+صح لكل اذا اذا انا بصي infinity هذه هتبقى المسافة
+
+455
+00:34:00,200 --> 00:34:03,660
+بين هذه اللي قلتلها أصغر أو يساوي هياش بيصير أصغر
+
+456
+00:34:03,660 --> 00:34:06,560
+أو يساوي مين اتنين اللي هي أصغر من مين من يبسلون
+
+457
+00:34:06,560 --> 00:34:11,360
+إذا صارت هذه وهذه أصغر من مين من يبسلون يعني بمعنى
+
+458
+00:34:11,360 --> 00:34:16,380
+أخر في أي يبسلون في الدنيا طلعت ال XK hat موجودة
+
+459
+00:34:16,380 --> 00:34:21,250
+في ال ballاللي بين .. اللي هي مركزها X hat ونصف
+
+460
+00:34:21,250 --> 00:34:25,570
+قطرها Y وهي في الأصل الـ X K hat اللي موجودة في
+
+461
+00:34:25,570 --> 00:34:29,750
+الـ W إذا صارت عند الـ ball X hat وY تقاطع و W ليه
+
+462
+00:34:29,750 --> 00:34:34,830
+سوى 5 4 O وY أكبر من 0 إذا صار عندي اللي هو لجينا
+
+463
+00:34:34,830 --> 00:34:39,550
+ال X hat لازم تكون في الـ W closure والآن صارت عند
+
+464
+00:34:39,550 --> 00:34:43,710
+ال X hat جزء من الـ W closure وW closure طبيعي جزء
+
+465
+00:34:43,710 --> 00:34:46,850
+منها إذا صار الحدث تتمين المساواة وهو المطلوب
+
+466
+00:34:49,140 --> 00:34:54,060
+النظرية غزيرة بالمعلومات عشان هيك انا معنى ان
+
+467
+00:34:54,060 --> 00:34:59,700
+ابرهنها طيب اللي بعدها proving the completeness of
+
+468
+00:34:59,700 --> 00:35:04,520
+X hat الان بدي اركز فيها دي عشان شوية رموز بتلخمكم
+
+469
+00:35:04,520 --> 00:35:08,760
+شوية بضح ان شاء الله بدي اثبت انه اللي هو ال X hat
+
+470
+00:35:08,760 --> 00:35:11,560
+ايش معله complete كيف اثبت انه complete باخد كوشي
+
+471
+00:35:11,560 --> 00:35:18,220
+سيكوانس فيها بدي اسميها X unhatكوشي سيكوانس وين ال
+
+472
+00:35:18,220 --> 00:35:23,920
+X hat وبدأ اثبت لكم ان X un hat هذه لازم تكون
+
+473
+00:35:23,920 --> 00:35:29,630
+convention صميم X برضه موجودة في ال X hatتنسوش ان
+
+474
+00:35:29,630 --> 00:35:34,430
+X1 هات و X2 هات و X3 هات و X4 هات كلهين اصلا
+
+475
+00:35:34,430 --> 00:35:37,190
+equivalency classes يعني كل واحدة فيه في داخلها
+
+476
+00:35:37,190 --> 00:35:42,450
+مين عبارة عن sequences ماشي طيب بدنا نثبت ان
+
+477
+00:35:42,450 --> 00:35:46,750
+الكوشي سيكوانس هذا converse جوا في ال X هات let X
+
+478
+00:35:46,750 --> 00:35:51,520
+انهات بيان الكوشي سيكوانس ال X هاتSince W closure
+
+479
+00:35:51,520 --> 00:35:55,940
+بيساوي X hat لقبل بشوية W closure أش بيساوي X hat
+
+480
+00:35:55,940 --> 00:35:59,560
+W متوال اللي بنحكي عنها اللي عناصرها بيهات بيهات و
+
+481
+00:35:59,560 --> 00:36:04,300
+إيهات و كده بحيث ان بيهات تحدد من بي بي بي بي as a
+
+482
+00:36:04,300 --> 00:36:09,460
+sequence then for all X unhat element in X hat
+
+483
+00:36:10,850 --> 00:36:16,230
+There is الوزج N hat element of W such that
+
+484
+00:36:16,230 --> 00:36:20,230
+المسافة بين X N hat و Z N hat اشمالها أصغر من مين
+
+485
+00:36:20,230 --> 00:36:25,810
+من واحد على N لأنه اشمالها لأن الـ W dense في مين؟
+
+486
+00:36:25,810 --> 00:36:29,290
+في الـ X hat فأي element في الـ X hat بلا جيله
+
+487
+00:36:29,290 --> 00:36:33,280
+element هنااللي هو المسافة بينه وبين هذا أصغر من
+
+488
+00:36:33,280 --> 00:36:37,740
+مين من واحد على أن أي ball بالنصف خطر واحد على أن
+
+489
+00:36:37,740 --> 00:36:42,780
+حلاجي اللي هو الموجود
+
+490
+00:36:42,780 --> 00:36:48,340
+فيه عنصر اللي هو في الـZn مشترك في الـW في الـW
+
+491
+00:36:48,340 --> 00:36:53,260
+أسف مشترك بين الـW وبين هذه ال ball يعني بمعنى أخر
+
+492
+00:36:53,260 --> 00:36:57,700
+المسافة بينه بين Xn وZn أصغر من مين من واحد على أن
+
+493
+00:36:57,700 --> 00:37:06,500
+واضحطيب إذا الان خدلي المسافة بين ZM hat و ZN hat
+
+494
+00:37:06,500 --> 00:37:12,980
+لأي M و N اللي هو أصغر أو يساوي اللي هو D hat ZM
+
+495
+00:37:12,980 --> 00:37:19,780
+hat و XM hat زائد D hat XM hat و XN hat تبين ال
+
+496
+00:37:19,780 --> 00:37:24,460
+equality زائد D hat XM hat و ZM hat و ZN hat الآن
+
+497
+00:37:24,460 --> 00:37:31,420
+في اللي فوق لأي XM hat و XM hat ملاجئ ZM hatلـ X M
+
+498
+00:37:31,420 --> 00:37:36,320
+HAT في الـ X HAT نلاقي الـ Z M HAT واضح؟ وهي كذا
+
+499
+00:37:36,320 --> 00:37:39,920
+اللي هو بحيث أنه المسافة أصغر من واحدة لـ M أو
+
+500
+00:37:39,920 --> 00:37:43,480
+المسافة أصغر واحدة لـ M حسب ما سميها أنا متفجين؟
+
+501
+00:37:43,480 --> 00:37:48,090
+هذا الكلام لـ ANطيب او لأي element x and hat بلاقي
+
+502
+00:37:48,090 --> 00:37:51,610
+اللي هو element z and hat اسمه x and hat او x and
+
+503
+00:37:51,610 --> 00:37:56,070
+hat او اللي بدكميه صار عندى الان المسافة بين z and
+
+504
+00:37:56,070 --> 00:38:00,750
+hat و z and hat اصغر و اصغر وهذه زائد هذه زائد هذه
+
+505
+00:38:00,750 --> 00:38:04,550
+هذه حسب الحديث اللى فوق حسب الحديث اللى فوق هذه
+
+506
+00:38:04,550 --> 00:38:09,450
+اشمالها اصغر من واحدة لان وهذه بنزلها زي ما هي x
+
+507
+00:38:09,450 --> 00:38:13,330
+and hat وx and hat وهذه اصغر من نيل من واحدة لان
+
+508
+00:38:13,870 --> 00:38:20,270
+لكن أنا ناخد الـ Xm هادهات مادان كوشي سيكوانس
+
+509
+00:38:20,270 --> 00:38:22,450
+مادان كوشي سيكوانس مادان كوشي سيكوانس مادان كوشي
+
+510
+00:38:22,450 --> 00:38:23,610
+سيكوانس مادان كوشي سيكوانس مادان كوشي سيكوانس
+
+511
+00:38:23,610 --> 00:38:24,590
+مادان كوشي سيكوانس مادان كوشي سيكوانس مادان كوشي
+
+512
+00:38:24,590 --> 00:38:25,370
+سيكوانس مادان كوشي سيكوانس مادان كوشي سيكوانس
+
+513
+00:38:25,370 --> 00:38:28,850
+مادان كوشي سيكوانس مادان كوشي سيكوانس مادان كوشي
+
+514
+00:38:28,850 --> 00:38:34,370
+سيكوانس مادان كوشي سيكوانس مادان كوشي سيكوانس ماد
+
+515
+00:38:34,390 --> 00:38:38,050
+However, Xn hat is a Cauchy sequence، إذاً for
+
+516
+00:38:38,050 --> 00:38:42,230
+every Y أكبر من 0، there exists K such that 1 على
+
+517
+00:38:42,230 --> 00:38:48,490
+M زائد هذا المسافة زائد 1 على M أصغر من إبسلون هذا
+
+518
+00:38:48,490 --> 00:38:53,630
+إيش معناته؟ معناته صارت هذه الآن أصغر من أي إبسلون
+
+519
+00:38:53,630 --> 00:38:59,190
+في الدنيالكل Y أكبر من 0 للي جيت K بحيث لكل N و M
+
+520
+00:38:59,190 --> 00:39:03,850
+أكبر من K البسافة أصغر من مين من Y يعني بمعنى أخر
+
+521
+00:39:03,850 --> 00:39:07,570
+هذه اللي اللي جيتها اللي كل مرة بلاقي اللي هو
+
+522
+00:39:07,570 --> 00:39:13,610
+إليها ZN hat للي هي X1 hat بلاقي Z1 hat ل X2 hat
+
+523
+00:39:13,610 --> 00:39:17,110
+بلاقي Z2 hat ال sequence هذه اللي اللي جيتها اللي
+
+524
+00:39:17,110 --> 00:39:22,410
+هي ZN ZN hat هذه ال sequence اتمتعت بخاصية نقاش
+
+525
+00:39:22,410 --> 00:39:28,040
+Sequencetherefore z unhat is a Cauchy sequence أي
+
+526
+00:39:28,040 --> 00:39:32,720
+سؤال طيب الان اطلع على فوق خليها في الذاكرة اذا
+
+527
+00:39:32,720 --> 00:39:40,480
+هذه الان انا حصلت على ال z unhat ال z unhat حصلت
+
+528
+00:39:40,480 --> 00:39:47,180
+عليها ال z unhat Cauchy sequence خليها في الذاكرة
+
+529
+00:39:47,180 --> 00:39:51,620
+انا هساخدمها طيب
+
+530
+00:39:53,440 --> 00:39:58,960
+الآن since T من X لعن W إذا كان I جيومتريمظبوط و
+
+531
+00:39:58,960 --> 00:40:04,920
+الـ Z M hat element من الـ W ليش Z M hat element
+
+532
+00:40:04,920 --> 00:40:10,040
+من الـ W لأن فيها اللي هي عندي اللي هي اللي أنا
+
+533
+00:40:10,040 --> 00:40:14,120
+جاتهم ال sequence دي اللي ركّبتها مالها من ال W
+
+534
+00:40:14,120 --> 00:40:18,280
+أصلا ماشي طيب شوفوا صلى على النبي عليه الصلاة
+
+535
+00:40:18,280 --> 00:40:23,360
+والسلام الآن ال sequence Z M hat element من ال W
+
+536
+00:40:23,360 --> 00:40:28,220
+كل واحدة فيه element من ال W إذا ال sequence Z MZM
+
+537
+00:40:28,220 --> 00:40:32,940
+اللي هي موجودة في الـ ZM هات لإن الـ WH مكوّنة
+
+538
+00:40:32,940 --> 00:40:37,440
+مكوّنة اللي هو من اللي هي اللي هي ال equivalency
+
+539
+00:40:37,440 --> 00:40:44,480
+classes اللي هويتها A,A,A,A,A أو B,B,B أو ZM اللي
+
+540
+00:40:44,480 --> 00:40:52,740
+هي ZM,ZM,ZM ماشي الحال الآن بتاخد واحد منهم وعمل
+
+541
+00:40:52,740 --> 00:40:57,660
+منه sequence H مالهازد ام ماشي الحال الان زد ام
+
+542
+00:40:57,660 --> 00:40:59,960
+يعني زد واحد ده اخدوا زد اتنين زد تلتة زد اربعة
+
+543
+00:40:59,960 --> 00:41:04,380
+الى اخرين الان where زد ام ايش بساوي اللي كيف اللي
+
+544
+00:41:04,380 --> 00:41:10,660
+بدي أركبه بادي انا عندي انا T من X لعند Y اتفجنا
+
+545
+00:41:10,660 --> 00:41:17,850
+انه T من X لعند W عيزومتريعندى one to one لونتو او
+
+546
+00:41:17,850 --> 00:41:19,030
+او او او او او او او او او او او او او او او او او
+
+547
+00:41:19,030 --> 00:41:19,030
+او او او او او او او او او او او او او او او او او
+
+548
+00:41:19,030 --> 00:41:19,530
+او او او او او او او او او او او او او او او او او
+
+549
+00:41:19,530 --> 00:41:19,530
+او او او او او او او او او او او او او او او او او
+
+550
+00:41:19,530 --> 00:41:21,790
+او او او او او او او او او او او او او او او او او
+
+551
+00:41:21,790 --> 00:41:29,190
+او او او او او او او او او او او او او او او او او
+
+552
+00:41:29,190 --> 00:41:32,610
+او او او اوالـ T inverse اللي هو موجودة لان وانتوا
+
+553
+00:41:32,610 --> 00:41:38,670
+هم نونتو فانكشن الـ T inverse لـ ZM hat هو الوين
+
+554
+00:41:38,670 --> 00:41:44,970
+وين هيكون flex سمونيها ZM إذا صارت الـ ZM هذه
+
+555
+00:41:44,970 --> 00:41:49,530
+عبارة عن sequence وين موجودة؟ هنا و هذه كوشي إذا
+
+556
+00:41:49,530 --> 00:41:51,990
+اللي هي و preserve distances إذا هتكون هذه برضه
+
+557
+00:41:51,990 --> 00:41:56,580
+أشمالها برضه كوشيمعايا الـ isometric من جل الكوشي
+
+558
+00:41:56,580 --> 00:42:00,020
+لكوشي وبرجع بالكوشي لكوشي ماشي الحال و أثمانه مش
+
+559
+00:42:00,020 --> 00:42:03,240
+صعب لأنه preserve distances هذا اللي بيبقى لها لكم
+
+560
+00:42:03,240 --> 00:42:08,020
+أنه لو كانت اللي هي اللي هنا كوشي sequence هترجع
+
+561
+00:42:08,020 --> 00:42:12,560
+لكوشي و لو كانت كوشي بتروح لكوشي مادام الـ T is
+
+562
+00:42:12,560 --> 00:42:18,920
+isometricو onto طيب صلى على النبي عليه الصلاة
+
+563
+00:42:18,920 --> 00:42:22,440
+والسلام إذا صارت ZM بتساوي T inverse ZM hat is a
+
+564
+00:42:22,440 --> 00:42:28,540
+Cauchy sequence inين؟ in X الان شوف كيف بده يركب
+
+565
+00:42:28,540 --> 00:42:34,240
+ال X hat احنا ليش غربنا احنا غربنا انه ناخد اللي
+
+566
+00:42:34,240 --> 00:42:42,620
+هو X M hat هيك عملنا Cauchy sequenceونوصل ال X hat
+
+567
+00:42:42,620 --> 00:42:47,520
+ونوصل إنه في X hat اسمه ال element ال X hat
+
+568
+00:42:47,520 --> 00:42:52,640
+capital such that X unhat converts نمين لل X hat
+
+569
+00:42:52,640 --> 00:42:56,560
+شوفوا الآن كيف يتركب لكم ال X hat اللي هخل ال X
+
+570
+00:42:56,560 --> 00:43:01,080
+unhat الأصلي تروح نمين لل X hat هذه ماشي؟ طيب شوف
+
+571
+00:43:01,080 --> 00:43:07,760
+let X hat element X كيف يتركبها؟الان let X hat
+
+572
+00:43:07,760 --> 00:43:14,420
+element in X and Z M hat element in X hat صح؟
+
+573
+00:43:14,420 --> 00:43:20,120
+صح؟ ليش Z M element in X hat؟ لأنه الآن الـ Z الـ
+
+574
+00:43:20,120 --> 00:43:25,400
+Z و الـ Z الـ Z M في الأصل من وين جاية؟الاصل ZM من
+
+575
+00:43:25,400 --> 00:43:28,420
+وين جاية؟ ZM hat من وين جاية؟ ZM hat من وين جاية؟
+
+576
+00:43:28,420 --> 00:43:29,560
+ZM hat من وين جاية؟ ZM hat من وين جاية؟ ZM hat من
+
+577
+00:43:29,560 --> 00:43:30,060
+وين جاية؟ ZM hat من وين جاية؟ ZM hat من وين جاية؟
+
+578
+00:43:30,060 --> 00:43:30,200
+ZM hat من وين جاية؟ ZM hat من وين جاية؟ ZM hat من
+
+579
+00:43:30,200 --> 00:43:32,580
+وين جاية؟ ZM hat من وين جاية؟ ZM hat من وين جاية؟
+
+580
+00:43:32,580 --> 00:43:36,040
+ZM
+
+581
+00:43:36,040 --> 00:43:40,000
+hat من وين جاية؟ ZM hat من وين جاية؟ ZM hat من وين
+
+582
+00:43:40,000 --> 00:43:45,380
+جاية؟ ZM
+
+583
+00:43:45,380 --> 00:43:49,520
+hat من وين جاية؟من الـ W واضح كيف اتكونت الآن الـ
+
+584
+00:43:49,520 --> 00:43:53,560
+ZM الـ X hat الـ X hat تكونت من الـ Cauchy
+
+585
+00:43:53,560 --> 00:43:56,320
+sequence يعني عبارة عن ال equivalence class لهذه
+
+586
+00:43:56,320 --> 00:43:59,320
+الـ Cauchy sequence الـ Cauchy sequence هذه اتكونت
+
+587
+00:43:59,320 --> 00:44:02,880
+من الاصل لـ T inverse الـ ZM hat اللي ZM hat من
+
+588
+00:44:02,880 --> 00:44:08,860
+مين كانت من الـ W خلوها في الذاكرة طيب إذا ال
+
+589
+00:44:08,860 --> 00:44:13,300
+distance بين الـ X un hat و الـ X hat أبدا يتفرج
+
+590
+00:44:13,300 --> 00:44:17,440
+على الـ Y و بيكون خلصةانت فاقتت ان الـ Limit لهذه
+
+591
+00:44:17,440 --> 00:44:21,700
+اللي هو الـ Distance بينها أصغر من Y ممكن خلصت اه
+
+592
+00:44:21,700 --> 00:44:27,020
+الآن أصغر أوي سوى X أنهات و Z أنهات زاد Z أنهات و
+
+593
+00:44:27,020 --> 00:44:30,980
+مين و X هات X أنهات و Z أنهات تتقبل بشوية عشان
+
+594
+00:44:30,980 --> 00:44:34,820
+عاملنا أنهات ولا أصغر من مين من واحدة لأن وهذه Z
+
+595
+00:44:34,820 --> 00:44:40,640
+أنهات و X هات أيش معنى؟ زي ما هي الآن عندي الـ Z
+
+596
+00:44:40,640 --> 00:44:46,630
+أموال موجودة في ال X هات مظبوط ولا لأ؟و الـ ZN hat
+
+597
+00:44:46,630 --> 00:44:51,450
+هو الموجودة في الـ W إذا أكيد الـ ZN و الـ ZN و
+
+598
+00:44:51,450 --> 00:44:57,060
+الـ ZN و الـ ZN هو الموجودة في الـ ZN main hatالان
+
+599
+00:44:57,060 --> 00:45:00,780
+تلاتة بتسير اللي عندى تلاتة هدى بتسير ال distance
+
+600
+00:45:00,780 --> 00:45:04,640
+بين ال X and هت وال X هت أصغر من واحد على N زائد
+
+601
+00:45:04,640 --> 00:45:09,860
+هدى اللي هي limit limit ل sequence من هنا و
+
+602
+00:45:09,860 --> 00:45:13,620
+sequence من هنا ال sequence من هنا اللي هي ZN ماشي
+
+603
+00:45:13,620 --> 00:45:21,280
+الحال اللي هي عندى ZN ZN ZN ZNأو الـ X hat اللي هي
+
+604
+00:45:21,280 --> 00:45:25,020
+من وين جاية من الـ sequence ZM اللي هي distance
+
+605
+00:45:25,020 --> 00:45:30,000
+بين XN ومين وZM و as N goes to infinity اللي عندي
+
+606
+00:45:30,000 --> 00:45:34,600
+طبعا ZM كوش ال sequence كلها كوش ال sequence فال
+
+607
+00:45:34,600 --> 00:45:38,700
+limit لهذه as N goes to infinity طبعا for M أكبر
+
+608
+00:45:38,700 --> 00:45:42,600
+من N بتصير عندي اللي هي هذه بقيت أه زغيرها أه
+
+609
+00:45:42,600 --> 00:45:45,510
+أصغرها Y في الدنياوهذه أزن قصون فيها أصغر من
+
+610
+00:45:45,510 --> 00:45:48,950
+إبسلون في الدنيا إذا دي x أن هات وx هات اللي هي
+
+611
+00:45:48,950 --> 00:45:54,490
+أصغر من إبسلون إذا صارت ال x أن هات then for
+
+612
+00:45:54,490 --> 00:45:56,730
+sufficiently for every إبسلون there exists k
+
+613
+00:45:56,730 --> 00:45:59,070
+sufficiently large such that for all أكبر من k ده
+
+614
+00:45:59,070 --> 00:46:01,790
+اللي حكيته المسافة بين هذه و هذه بتكون أصغر من
+
+615
+00:46:01,790 --> 00:46:04,370
+إبسلون إذا صارت ال x أن هات converged to x hat in
+
+616
+00:46:04,370 --> 00:46:10,990
+x therefore x hat is a complete metric space
+
+617
+00:46:19,200 --> 00:46:27,320
+طيب نسرعه الجزء الأخير الجزء الأخير proving the
+
+618
+00:46:27,320 --> 00:46:30,620
+uniqueness of X hat except for isometries خلّيني
+
+619
+00:46:30,620 --> 00:46:36,520
+أركز طويل شوية هذا بس مش صعببدنا نثبت اللي هو الـ
+
+620
+00:46:36,520 --> 00:46:40,240
+uniqueness يعني بمعنى اخر نفترض X ده و D ده ده
+
+621
+00:46:40,240 --> 00:46:45,960
+بنفس مواصفات X hat و D hat
+
+622
+00:46:45,960 --> 00:46:51,100
+و نثبت إن هدول التنين are isometric اللي هو فيه
+
+623
+00:46:51,100 --> 00:46:55,720
+one to one, one to one function بينهم شوفوا
+
+624
+00:46:55,720 --> 00:46:58,680
+Proving the uniqueness of X hat except for
+
+625
+00:46:58,680 --> 00:47:02,220
+isometries يعني اللي بده يعمل زي هيك يكون
+
+626
+00:47:02,220 --> 00:47:08,460
+isometric لهلت X hat و D hat ب another complete
+
+627
+00:47:08,460 --> 00:47:13,000
+metric space واحد تاني completion تاني with a
+
+628
+00:47:13,000 --> 00:47:17,060
+subspace W بنفس المواصفات W تلدة دي نصف مين في ال
+
+629
+00:47:17,060 --> 00:47:23,040
+X hat يعني ان انا جيبنا X تلدة وD تلدة قولنا هذا
+
+630
+00:47:23,040 --> 00:47:28,360
+complete metric space وفي داخله W تلدة subset من X
+
+631
+00:47:28,360 --> 00:47:49,840
+تلدة حيثحيث و closure بسوء مين اللي هو x تلده عشان
+
+632
+00:47:49,840 --> 00:47:56,960
+نفس المواصفات و تلد ايش ما لهااللي هو فيه عيزومتري
+
+633
+00:47:56,960 --> 00:48:03,800
+بينها عيزومتريك خلّيني أقول معين مع ال X فرضنا هذه
+
+634
+00:48:03,800 --> 00:48:08,260
+كلها وعندنا في الأصل اللي هو طبعنا هذا اللي عملناه
+
+635
+00:48:08,260 --> 00:48:13,460
+ال construction قبل شوية اللي هو W تبعته subset من
+
+636
+00:48:13,460 --> 00:48:19,180
+X hat و W closure بسوء X hat و اللي هي W اللي هي
+
+637
+00:48:19,180 --> 00:48:25,400
+عيزومتريكلمن؟ لـ X بدأ أثبت لك الآن أن الجديد هذا
+
+638
+00:48:25,400 --> 00:48:29,460
+لازم يكون بين هذا وبين هذا أيش فيه؟ عيزومتري بيكون
+
+639
+00:48:29,460 --> 00:48:34,560
+اللي هو يعني بمعنى أخر نفسه اللي هو بس اختلفت
+
+640
+00:48:34,560 --> 00:48:39,240
+الأسماء let X تلده وB تلده وD تلده be another
+
+641
+00:48:39,240 --> 00:48:42,020
+complete metric space with a subspace كده and
+
+642
+00:48:42,020 --> 00:48:44,980
+عيزومتر كده then for any X تلده وY تلده element in
+
+643
+00:48:44,980 --> 00:48:45,760
+X تلده
+
+644
+00:48:48,890 --> 00:48:54,430
+Xn تلدة سيكوانس وهو احنا بنعرف Y وW تلدة ايش ماله
+
+645
+00:48:54,430 --> 00:49:01,030
+اللي هو dense المين X تلدة مادام dense وهذه X تلدة
+
+646
+00:49:01,030 --> 00:49:04,770
+وY تلدة موجودة هنا اذا اكيد في sequence of points
+
+647
+00:49:04,770 --> 00:49:08,950
+converge لهذه وsequence of points converge لهذه من
+
+648
+00:49:08,950 --> 00:49:14,670
+تعريف مين اللي هو ال closure عندى اللي هو هذه ال
+
+649
+00:49:14,670 --> 00:49:19,680
+dense من تعريف انه dense هذه denseانتبهوا هذه
+
+650
+00:49:19,680 --> 00:49:25,160
+dense ان هذه إذا لأي element هنا بقدر ألاقي
+
+651
+00:49:25,160 --> 00:49:29,460
+sequence من هنا converge zero لما يكون يا جماعة
+
+652
+00:49:29,460 --> 00:49:35,400
+الآن أي حاجة في الدنيا y closure اللي هو بيساوي x
+
+653
+00:49:35,400 --> 00:49:41,530
+مثلاو جيت أخدت أي مُخطأ x في الـ x الهادى بقدر
+
+654
+00:49:41,530 --> 00:49:48,090
+ألاقي sequence xn in y such that xn converge لمين
+
+655
+00:49:48,090 --> 00:49:52,390
+للx اللي هو في كل .. لكل واحد .. لكل n بقدر ألاقي
+
+656
+00:49:52,390 --> 00:49:55,950
+ball .. ball المسافة بينهم أصغر من واحد، أصغر من
+
+657
+00:49:55,950 --> 00:49:58,770
+نص، أصغر من تلت، أصغر من كده، بلاقي x واحد أصغر من
+
+658
+00:49:58,770 --> 00:50:04,050
+واحد، x اتنين .. يعني ال .. فاهمين علشه بحكيه؟هذا
+
+659
+00:50:04,050 --> 00:50:09,250
+الكلام معروف إذا لـ gate sequences XN تلدة و YN
+
+660
+00:50:09,250 --> 00:50:12,670
+تلدة موجودة في الـ W تلدة كل واحدة منهم بتروح
+
+661
+00:50:12,670 --> 00:50:19,050
+واحدة لل X واحدة بتروح لمين لل Y تلدةSuch that X
+
+662
+00:50:19,050 --> 00:50:22,590
+and تلدة تقوم بالإعادة للـ X تلدة و Y تلدة تقوم
+
+663
+00:50:22,590 --> 00:50:29,770
+بالإعادة للـ Y As in A فوق و
+
+664
+00:50:29,770 --> 00:50:34,890
+نشهد أن الـ absolute value للمسافة بين X تلدة و Y
+
+665
+00:50:34,890 --> 00:50:38,370
+تلدة نقص المسافة تلدة بين X and تلدة و Y and تلدة
+
+666
+00:50:38,370 --> 00:50:41,550
+أصغر أو سوى اللي هي بالتباين green quality زي ما
+
+667
+00:50:41,550 --> 00:50:46,610
+عملنا قبل شوية X تلدة و X and تلدة زائد Y تلدة و Y
+
+668
+00:50:46,610 --> 00:50:50,620
+and تلدةالآن هذه converts صح ولا لأ هذه converts
+
+669
+00:50:50,620 --> 00:50:54,260
+لهذه إذا هذه بتروح للصفر وهذه converts لهذه إذا
+
+670
+00:50:54,260 --> 00:50:58,540
+هذه بتروح للصفر إذا كل هذا هيروح لمين للصفر إذا
+
+671
+00:50:58,540 --> 00:51:03,680
+المقدار هذا هيروح للصفر إذا وكأنه limit هذا هو هذا
+
+672
+00:51:03,680 --> 00:51:09,420
+فبصير D تلدة لان X تلدة وY تلدة بساوة limit D تلدة
+
+673
+00:51:09,420 --> 00:51:14,940
+Xn تلدة وYn تلدة إذا صار عندي اللي هو ال limit هذا
+
+674
+00:51:14,940 --> 00:51:20,720
+بساوة هذاماشي الحال خلّيها ده برضه عندك الان صار
+
+675
+00:51:20,720 --> 00:51:27,140
+عيدي المسافة المسافة بين نقطتين ان تستمتعي مش اللي
+
+676
+00:51:27,140 --> 00:51:33,060
+صار المسافة بين أي نقطين Y تلدهأو X تلد و Y تلد هو
+
+677
+00:51:33,060 --> 00:51:36,360
+الموجودة في الـ X تلد أخدتها النقطتين أبتكرانها
+
+678
+00:51:36,360 --> 00:51:41,580
+لجيه من المسافة بينهم بقدر أقول بتساوي ال limit لل
+
+679
+00:51:41,580 --> 00:51:49,480
+D تلد لل X N تلد و Y N تلد as N goes to mean to
+
+680
+00:51:49,480 --> 00:51:55,140
+infinity حيث ال X N تلد و Y N تلد جايات من وين من
+
+681
+00:51:55,140 --> 00:51:57,900
+ال W طيب
+
+682
+00:52:00,450 --> 00:52:07,810
+ماشي حالي الان لل T الان من W تلقاه W اللي هي W
+
+683
+00:52:07,810 --> 00:52:12,570
+subset من ال Xات اللي أصلي اللي ركبناهابـ
+
+684
+00:52:12,570 --> 00:52:15,630
+Abjection Isometry بقدر أقول هيك أه ما أحنا إيش
+
+685
+00:52:15,630 --> 00:52:20,690
+مفترضين ما أحنا مفترضين و تلدة dense في ال X
+
+686
+00:52:20,690 --> 00:52:25,570
+عيزومتريك لل X و مفترضين إن و عيزومتريك لل X إذا و
+
+687
+00:52:25,570 --> 00:52:30,530
+تلدة و و أشمالين are isometric طيب إذا صارت عندي
+
+688
+00:52:30,530 --> 00:52:36,290
+اللي هو بقدر أقول نفترض إن T من و تلدة لW سبس من X
+
+689
+00:52:36,290 --> 00:52:41,930
+hat is Abjection Isometryالان بما ان X until ده و
+
+690
+00:52:41,930 --> 00:52:45,750
+Y until ده كوشي سيكوانسيز converge اصلا هنا لكن
+
+691
+00:52:45,750 --> 00:52:50,370
+هنا كوشي سيكوانسيز وين في الـ W هي converge وين؟
+
+692
+00:52:50,370 --> 00:52:54,410
+في الـ X تلده converge في ال X تلده لأن ال limit
+
+693
+00:52:54,410 --> 00:52:58,930
+هنا وين موجودة؟ في ال X تلده لكن هنا هما نفس
+
+694
+00:52:58,930 --> 00:53:03,270
+الموجودات في الـ W تلده فهنا في الواقع بقدر اكد ان
+
+695
+00:53:03,270 --> 00:53:07,230
+هنا كوشي سيكوانسيز بس في الـ W تلده اذا صار عندى
+
+696
+00:53:07,230 --> 00:53:15,050
+الانكوشي سيكوانسي و W تلدة تتعامل مع X تلدة و Y
+
+697
+00:53:15,050 --> 00:53:20,130
+تلدة في X تلدة وY تلدة في X تلدة وY تلدة في X تلدة
+
+698
+00:53:20,130 --> 00:53:20,770
+وY تلدة في X تلدة وY تلدة في X تلدة وY تلدة في X
+
+699
+00:53:20,770 --> 00:53:21,250
+تلدة وY تلدة في X تلدة وY تلدة في X تلدة وY تلدة
+
+700
+00:53:21,250 --> 00:53:22,790
+في X تلدة وY تلدة في X تلدة وY تلدة في X تلدة وY
+
+701
+00:53:22,790 --> 00:53:27,190
+تلدة في X تلدة وY تلدة في X تلدة وY تلدة في X تلدة
+
+702
+00:53:27,190 --> 00:53:34,250
+وY تلدة في X تلدة وY تلدة في X
+
+703
+00:53:34,250 --> 00:53:41,510
+تلدة وY تلin x hat then they converts in mean in x
+
+704
+00:53:41,510 --> 00:53:46,570
+hat اذا صار عندى لان limit لتى xn تلدى موجود فى ال
+
+705
+00:53:46,570 --> 00:53:51,350
+x hat سميه ايش بساوي اذا انا ايش جيت قولت limit
+
+706
+00:53:51,350 --> 00:54:01,020
+لتى xn تلدى صح limit لتى xn تلدى بساوي x hatas n
+
+707
+00:54:01,020 --> 00:54:06,940
+goes to infinity و limit لتي y n تلده بساوي y hat
+
+708
+00:54:06,940 --> 00:54:11,480
+لاحظوا انا ايش اللي بسويه انا بمعنى اخر انتبهوا
+
+709
+00:54:11,480 --> 00:54:19,320
+بالله يا جماعة انتبهوا انا اجيت اخدتلكم ال x تلده
+
+710
+00:54:19,320 --> 00:54:23,360
+و ال y تلده ال arbitrary points اللي موجودات في ال
+
+711
+00:54:23,360 --> 00:54:28,560
+x تلدهو جيت للجسر اللي .. اللي .. اللي .. اللي من
+
+712
+00:54:28,560 --> 00:54:32,820
+خلاله بالدسال ان ال limit D تلده XN تلده YN تلده
+
+713
+00:54:32,820 --> 00:54:38,060
+هو هذا ال distance هذوله من وين جيات؟ من ال W تلده
+
+714
+00:54:38,060 --> 00:54:45,010
+و انا بكتب W تلده isometric لمين؟ لل Wفجيت صورة
+
+715
+00:54:45,010 --> 00:54:49,690
+هذه اسمها TX انتل ده وصورة هذه اسمها TY انتل ده
+
+716
+00:54:49,690 --> 00:54:52,670
+طلع مكونش Sequences اذا Converse مازال Converse
+
+717
+00:54:52,670 --> 00:54:58,130
+اذا مابدي نروح لمين لأ عناصر هدولة موجودات في ال X
+
+718
+00:54:58,130 --> 00:55:02,250
+هذا اذا انا الجسرين اللي صلت مني انا بتسأل انا من
+
+719
+00:55:02,250 --> 00:55:09,240
+وين لوين انا بتسأل ان Xهات والـ x تل ده بدأ أصل M
+
+720
+00:55:09,240 --> 00:55:14,920
+and R isometric بدأت في two elements هنا وهين وصلت
+
+721
+00:55:14,920 --> 00:55:18,920
+ل two elements هنا عبر الجسر هذا اللي بدأويا من
+
+722
+00:55:18,920 --> 00:55:23,200
+خلاله أصل إذا صار عندي الآن ال limit T x M تل ده
+
+723
+00:55:23,200 --> 00:55:27,920
+بسوء x hat وT y M تل ده بسوء y hat وبدأت هنا في ال
+
+724
+00:55:27,920 --> 00:55:32,060
+x hat إذا كل هذا اللي حكي عشان أصل أوصل بين x تل
+
+725
+00:55:32,060 --> 00:55:38,660
+ده وx hatالان وصلنا
+
+726
+00:55:38,660 --> 00:55:43,160
+لعند الحال ماشي الحال الان let S be the extension
+
+727
+00:55:43,160 --> 00:55:50,520
+of T to X tilde S الان S الان عند T تبقى يا جماعة
+
+728
+00:55:50,520 --> 00:56:01,220
+T من وإن وإين من X من Wو تل ده لعين و صح ولا لأ ال
+
+729
+00:56:01,220 --> 00:56:08,920
+بتوسع S S بتخليها تشتغل من X till ده لعين 2 ل X
+
+730
+00:56:08,920 --> 00:56:12,690
+hatهذه dense في هذه طبعا وهذه dense في هذه و
+
+731
+00:56:12,690 --> 00:56:17,310
+الأمور بدأت اللي هي أياش اللي هي تتمهد أمامها let
+
+732
+00:56:17,310 --> 00:56:21,270
+us be the extension of T to X تلدة extension
+
+733
+00:56:21,270 --> 00:56:24,170
+معناته التعريف الأولان اللي تبعته هيكون زي ما هو
+
+734
+00:56:24,170 --> 00:56:28,250
+بس بده دل التعريف لإنزيد التعريف لمين لباقى النقاط
+
+735
+00:56:28,250 --> 00:56:35,440
+اللي اللي اللي هي X تلدة ناقص W تلدةطيب let S be
+
+736
+00:56:35,440 --> 00:56:39,720
+the extension of T to X تلدى and S من X تلدى لعند
+
+737
+00:56:39,720 --> 00:56:46,060
+X hat اللي هو defined by S X تلدى بساومين X hat
+
+738
+00:56:46,060 --> 00:56:50,480
+اللي عملناها هو كل الجثة اللي عملناها صارت الآن S
+
+739
+00:56:50,480 --> 00:56:58,000
+X تلدى اللي بدأنا فيها هتكون يشمين هي X hat اللي
+
+740
+00:56:58,000 --> 00:57:04,080
+هي اللي سيرنا فيها طول الطريق اللي هي الماضيةطيب
+
+741
+00:57:04,080 --> 00:57:10,180
+where .. أقولكم أوضح where T X N تلده بسوء X hat
+
+742
+00:57:10,180 --> 00:57:14,480
+يعني X hat مركبة من مين؟ من ال T X N تلده اللي
+
+743
+00:57:14,480 --> 00:57:19,680
+لاجيناها هاد و اللي هي and limit X N تلده هو مين
+
+744
+00:57:19,680 --> 00:57:23,440
+اللي هي ال X تلده الأصلية اللي هي هذا هتكون في ال
+
+745
+00:57:23,440 --> 00:57:28,860
+W تلده و هذا هتكون اللي هي في ال W نفسها by using
+
+746
+00:57:28,860 --> 00:57:34,470
+the isometry of T we haveD تلدة of X تلدة و Y تلدة
+
+747
+00:57:34,470 --> 00:57:39,590
+اتعرفنا الـ Extension D تلدة X تلدة و Y تلدة ايش
+
+748
+00:57:39,590 --> 00:57:45,710
+بيساوي limit D تلدة X انتلدة و Y انتلدة أكيد هو
+
+749
+00:57:45,710 --> 00:57:48,710
+هيك التعريف مش هيك التعريف الـ D تلدة مش عرفناه
+
+750
+00:57:48,710 --> 00:57:55,860
+بشكل هذا أثبتناه في الأول Y ساوي هذا عبارة عنقلنا
+
+751
+00:57:55,860 --> 00:58:01,440
+بـ reserve mean T من الـ W لـ W من W تلدة ل W من W
+
+752
+00:58:01,440 --> 00:58:06,200
+تلدة ل W بـ reserve ده distance و الـ W .. هدول
+
+753
+00:58:06,200 --> 00:58:10,560
+عناصر في الـ W تلدة و هدول عناصر في مين؟ في الـ W
+
+754
+00:58:10,560 --> 00:58:13,740
+فال limit .. فال distance بين هدولة هي نفس ال
+
+755
+00:58:13,740 --> 00:58:17,540
+distance بين هدولة الأولى تلدة و التاني مين؟ hat
+
+756
+00:58:17,540 --> 00:58:23,360
+هد في الـ W و هد في الـ W تلدة طيب مايساوي هد الآن
+
+757
+00:58:24,120 --> 00:58:28,900
+الـ distance هات بين TXN تلده و YN تلده الان
+
+758
+00:58:28,900 --> 00:58:34,180
+limitها limitها limit ال TXN تلده هي X hat و
+
+759
+00:58:34,180 --> 00:58:37,880
+limitها دي كإيش بيساوي YN hat إذا ال limit لهذه D
+
+760
+00:58:37,880 --> 00:58:42,860
+hat هو عبارة عن تدخل جوا اللي هي D hat X hat و Y
+
+761
+00:58:42,860 --> 00:58:48,590
+hatماشي الحال اللي هي ال D hat من X hat ايش هي
+
+762
+00:58:48,590 --> 00:58:55,790
+اللي عرفناها S X تلده وهذا S Y تلده إذا اللي بدأنا
+
+763
+00:58:55,790 --> 00:59:00,750
+فيه D تلده ل X تلده وY تلده بساوي ال D hat لل S X
+
+764
+00:59:00,750 --> 00:59:04,550
+تلده وS Y تلده يعني بمعنى آخر اللي هي ال S ب
+
+765
+00:59:04,550 --> 00:59:06,510
+reserve the distance
+
+766
+00:59:14,080 --> 00:59:18,600
+هذا اذا انتوا بدي اثبت انه اللي عندى اذا انتوا بدي
+
+767
+00:59:18,600 --> 00:59:21,780
+اخد element هنا و ارجع جوه على جيله صورة هنا بحيث
+
+768
+00:59:21,780 --> 00:59:24,200
+اصل هنا بحيث ان صورته هو اللي بدأت فيه
+
+769
+00:59:32,930 --> 00:59:36,850
+النظرية .. النظرية .. النظرية يا جماعة فيها كثير
+
+770
+00:59:36,850 --> 00:59:41,370
+من المعلومات صح هي تركبتها كبيرة لكن معلوماتها
+
+771
+00:59:41,370 --> 00:59:43,310
+كثيرة ومفيدة
+
+772
+00:59:46,890 --> 00:59:51,010
+طبعا هي أطول نظرية في الكتاب مافيش عديق مافيش اشي
+
+773
+00:59:51,010 --> 00:59:59,150
+زي هي طيب therefore therefore S is an isometry and
+
+774
+00:59:59,150 --> 01:00:02,250
+so ايش مالها is one to another يعني مروع شعوركم
+
+775
+01:00:02,250 --> 01:00:07,070
+لكن العلم بدهيك يعنيlet x hat element in x hat
+
+776
+01:00:07,070 --> 01:00:12,130
+capital هذا ما بدأت بتونته بدي أخد element في ال
+
+777
+01:00:12,130 --> 01:00:18,030
+code domain هنا و أقول فيه اللي هو element في ال
+
+778
+01:00:18,030 --> 01:00:20,950
+domain بحيث ان صورة هذا element هو اللي بدأت فيه
+
+779
+01:00:20,950 --> 01:00:26,840
+طيب صلى على النبي عليه الصلاة والسلامما دام x hat
+
+780
+01:00:26,840 --> 01:00:30,420
+في الـ x hat أنا بدي أروح للجسر، للجسر، الجسر مين؟
+
+781
+01:00:30,420 --> 01:00:34,960
+الجسر w و w تلدة اني اللي بوصلني لمين؟ لأصل من x
+
+782
+01:00:34,960 --> 01:00:38,800
+hat ل x تلدة و من x تلدة ل x hat let x hat element
+
+783
+01:00:38,800 --> 01:00:42,400
+in x تلدة then there is a sequence x unhat of
+
+784
+01:00:42,400 --> 01:00:46,460
+elements in w لأنها w dense فيها such that limit x
+
+785
+01:00:46,460 --> 01:00:50,680
+unhat إيش بيساوي ال x hat اللي عندي لأن since T is
+
+786
+01:00:50,680 --> 01:00:55,800
+onto T نفسها is ontoما هي تي ازومتريك ازومتريك و
+
+787
+01:00:55,800 --> 01:01:00,140
+bijection اللي بدأنا فيها مدام تي on two إذا هذه
+
+788
+01:01:00,140 --> 01:01:04,120
+اللي لجيهت هناك الواحدة فيه اللي هي إيش أصل then
+
+789
+01:01:04,120 --> 01:01:07,960
+since T is on two then there is a sequence xn تلدة
+
+790
+01:01:07,960 --> 01:01:11,800
+of elements in y تلدة such that T xn تلدة هذه
+
+791
+01:01:11,800 --> 01:01:17,200
+بتساومين ال xn head لإن تي الأصلية on two for all
+
+792
+01:01:17,200 --> 01:01:23,280
+nthen limit هذا بيساوي limit هذا limit TXN تلده
+
+793
+01:01:23,280 --> 01:01:28,360
+بيساوي من ال X هذا بظبط؟ بطبيعي بيساوي limit XN
+
+794
+01:01:28,360 --> 01:01:32,960
+هذه و XN limitها من من هو ال X هذا الآن إذا صارت
+
+795
+01:01:32,960 --> 01:01:38,360
+ال TXN تلده نفسها كوشي sequence in من W ماعش الحال
+
+796
+01:01:38,360 --> 01:01:45,040
+من تعريف الأصل بين W ومن من من ال .. ال .. ال ..
+
+797
+01:01:45,040 --> 01:01:46,840
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+798
+01:01:46,840 --> 01:01:49,120
+.. ال .. ال .. ال .. ال .. ال ..However, T is an
+
+799
+01:01:49,120 --> 01:01:51,020
+isometry مدينة T هي عبارة عن عبارة عن عبارة عن
+
+800
+01:01:51,020 --> 01:01:53,660
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+801
+01:01:53,660 --> 01:01:56,040
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+802
+01:01:56,040 --> 01:01:56,480
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+803
+01:01:56,480 --> 01:01:57,700
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+804
+01:01:57,700 --> 01:02:04,280
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+805
+01:02:04,280 --> 01:02:06,060
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+806
+01:02:06,060 --> 01:02:14,140
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+807
+01:02:14,140 --> 01:02:21,990
+عنإذا الان x تلده is complete إذا أكيد في x تلده
+
+808
+01:02:21,990 --> 01:02:25,690
+في ال x تلده such that x until ده هذي بتروح لمين
+
+809
+01:02:25,690 --> 01:02:30,840
+لل x ماشيإذا نخلص اللي جينا في الآخر مين X تلده
+
+810
+01:02:30,840 --> 01:02:34,560
+بدينا ب X hat في ال X hat و اللي جينا X تلده
+
+811
+01:02:34,560 --> 01:02:38,760
+موجودة في ال X تلده capital ابحث by the definition
+
+812
+01:02:38,760 --> 01:02:44,200
+of S S X تلده هي مين ال X hat إذا صارت ال S is
+
+813
+01:02:44,200 --> 01:02:49,400
+onto therefore X تلده and X hat are isometric this
+
+814
+01:02:49,400 --> 01:02:56,680
+completes the proofوهي الأسئلة وnote that the
+
+815
+01:02:56,680 --> 01:03:01,120
+space x hat occurring in the above theorem is
+
+816
+01:03:01,120 --> 01:03:05,920
+called the completion of the given space x و الله
+
+817
+01:03:05,920 --> 01:03:09,140
+يعطيكم العافية والسلام عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/v06nynwDfxc_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/v06nynwDfxc_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..22d02c9867ad0a1bdda33e16908c9a3b8c6878ee
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/v06nynwDfxc_raw.json
@@ -0,0 +1 @@
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{"id": 22, "seek": 48984, "start": 469.8, "end": 489.84, "text": "then خد هنا ال absolute value of f of x اللي هو ايش حسب التعريف بساوي g of t of x هيها لسه محتاج تي كروس g of x بساوي f of x اللي هي g of t of x بساوي t cross g of x اللي عنده اللي هي بيصير عنده اللي هو ال f of x بساوي g of t of x", "tokens": [19096, 16490, 3215, 34105, 2423, 8236, 2158, 295, 283, 295, 2031, 13672, 1829, 31439, 1975, 1829, 8592, 11331, 35457, 16712, 3615, 16572, 5172, 4724, 3794, 995, 45865, 290, 295, 256, 295, 2031, 39896, 11296, 5296, 3794, 3224, 3714, 33753, 26108, 6055, 1829, 9122, 32887, 3794, 290, 295, 2031, 4724, 3794, 995, 45865, 283, 295, 2031, 13672, 1829, 39896, 290, 295, 256, 295, 2031, 4724, 3794, 995, 45865, 256, 3278, 290, 295, 2031, 13672, 1829, 43242, 3224, 13672, 1829, 39896, 4724, 1829, 9381, 13546, 43242, 3224, 13672, 1829, 31439, 2423, 283, 295, 2031, 4724, 3794, 995, 45865, 290, 295, 256, 295, 2031], "avg_logprob": -0.24800858106098922, "compression_ratio": 1.9022988505747127, 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"text": "للـ X0 لها تساوي صفر في X هناك مصطلح جي نوت يسميه Y1 لذلك نورم الجي نوت يساوي واحد and G note of T X0 لأن X0 في X صحيح", "tokens": [1211, 1211, 39184, 1783, 15, 5296, 11296, 6055, 3794, 995, 45865, 20328, 5172, 2288, 8978, 1783, 34105, 4117, 3714, 9381, 9566, 1211, 5016, 10874, 1829, 8717, 35473, 7251, 38251, 1829, 3224, 398, 16, 5296, 8848, 23275, 8717, 13063, 2304, 25724, 1829, 8717, 35473, 7251, 3794, 995, 45865, 36764, 24401, 293, 460, 3637, 295, 314, 1783, 15, 5296, 33456, 1783, 15, 8978, 1783, 20328, 5016, 1829, 5016], "avg_logprob": -0.6259328553925699, "compression_ratio": 1.3576642335766422, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 699.55, "end": 699.93, "word": "للـ", "probability": 0.4670817057291667}, {"start": 699.93, "end": 700.57, "word": " X0", "probability": 0.5308837890625}, {"start": 700.57, "end": 700.83, "word": " لها", "probability": 0.3109130859375}, {"start": 700.83, "end": 701.23, "word": " تساوي", "probability": 0.835693359375}, 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" الأن", "probability": 0.717529296875}, {"start": 759.29, "end": 759.49, "word": " X", "probability": 0.982421875}, {"start": 759.49, "end": 759.73, "word": " note", "probability": 0.94189453125}, {"start": 759.73, "end": 759.89, "word": " في", "probability": 0.982421875}, {"start": 759.89, "end": 760.31, "word": " الـX", "probability": 0.91064453125}, {"start": 760.31, "end": 761.69, "word": " أخدت", "probability": 0.943359375}, {"start": 761.69, "end": 761.89, "word": " X", "probability": 0.990234375}, {"start": 761.89, "end": 762.31, "word": " note", "probability": 0.93603515625}, {"start": 762.31, "end": 762.81, "word": " في", "probability": 0.990234375}, {"start": 762.81, "end": 763.17, "word": " الـX", "probability": 0.9568684895833334}, {"start": 763.17, "end": 763.89, "word": " هذا", "probability": 0.89013671875}, {"start": 763.89, "end": 764.35, "word": " أعطانا", "probability": 0.864501953125}, {"start": 764.35, "end": 764.85, "word": " الـTX", "probability": 0.86279296875}, 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0.6318359375}, {"start": 1298.87, "end": 1299.55, "word": " by", "probability": 0.5732421875}, {"start": 1299.55, "end": 1300.15, "word": " اطلع", "probability": 0.8941650390625}, {"start": 1300.15, "end": 1300.47, "word": " الآن", "probability": 0.784423828125}, {"start": 1300.47, "end": 1301.25, "word": " by", "probability": 0.81396484375}, {"start": 1301.25, "end": 1301.63, "word": " theorem", "probability": 0.84716796875}, {"start": 1301.63, "end": 1302.01, "word": " تلاتة", "probability": 0.7880859375}, {"start": 1302.01, "end": 1302.33, "word": " تمانية", "probability": 0.9645182291666666}, {"start": 1302.33, "end": 1302.63, "word": " واحد", "probability": 0.98291015625}, {"start": 1302.63, "end": 1302.77, "word": " اللي", "probability": 0.97705078125}, {"start": 1302.77, "end": 1302.89, "word": " هي", "probability": 0.63525390625}, {"start": 1302.89, "end": 1303.31, "word": " بتعملي", "probability": 0.8223470052083334}, {"start": 1303.31, "end": 1304.31, "word": " representation", "probability": 0.83154296875}, {"start": 1304.31, "end": 1305.39, "word": " لل", "probability": 0.76513671875}, {"start": 1305.39, "end": 1305.91, "word": " element", "probability": 0.75}, {"start": 1305.91, "end": 1306.63, "word": " بواسطتين", "probability": 0.7545979817708334}, {"start": 1306.63, "end": 1307.01, "word": " product", "probability": 0.30078125}], "temperature": 1.0}, {"id": 59, "seek": 133537, "start": 1308.75, "end": 1335.37, "text": "then by theorem 3.3.1 there exists a unique X note element in H1 بدي أطبّق على الـH1 وعلى مين؟ على H2 الـH1 فيه الهينيروبرودكت والـH2 الهينيروبرودكت كل واحدة خاص بها a unique X note و a unique Y note such that F of X can be .. مدام F bounded linear functional on H1 then it can be written as an inner product", "tokens": [19096, 538, 20904, 805, 13, 18, 13, 16, 456, 8198, 257, 3845, 1783, 3637, 4478, 294, 389, 16, 4724, 16254, 5551, 9566, 3555, 11703, 4587, 15844, 2423, 39184, 39, 16, 4032, 3615, 23942, 3714, 9957, 22807, 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"probability": 0.958984375}, {"start": 2248.13, "end": 2249.13, "word": " دائما", "probability": 0.927734375}, {"start": 2249.13, "end": 2250.31, "word": " لكل", "probability": 0.9072265625}, {"start": 2250.31, "end": 2251.23, "word": " مين", "probability": 0.928466796875}, {"start": 2251.23, "end": 2252.19, "word": " لكل", "probability": 0.919677734375}, {"start": 2252.19, "end": 2252.55, "word": " X", "probability": 0.78271484375}, {"start": 2252.55, "end": 2252.73, "word": " في", "probability": 0.95849609375}, {"start": 2252.73, "end": 2253.41, "word": " الدنيا", "probability": 0.9925130208333334}, {"start": 2253.41, "end": 2254.55, "word": " لكل", "probability": 0.938232421875}, {"start": 2254.55, "end": 2254.79, "word": " X", "probability": 0.98095703125}, {"start": 2254.79, "end": 2254.91, "word": " في", "probability": 0.98388671875}, {"start": 2254.91, "end": 2255.13, "word": " الدنيا", "probability": 0.9923502604166666}, {"start": 2255.13, "end": 2255.31, "word": " هذا", "probability": 0.875}, {"start": 2255.31, "end": 2255.83, "word": " صحيح", "probability": 0.9970703125}, {"start": 2255.83, "end": 2256.35, "word": " إذا", "probability": 0.937255859375}, {"start": 2256.35, "end": 2256.89, "word": " لازم", "probability": 0.9890950520833334}, {"start": 2256.89, "end": 2257.35, "word": " هذا", "probability": 0.97119140625}, {"start": 2257.35, "end": 2258.11, "word": " يساوي", "probability": 0.9788818359375}, {"start": 2258.11, "end": 2258.27, "word": " هذا", "probability": 0.869140625}, {"start": 2258.27, "end": 2258.51, "word": " كله", "probability": 0.4466552734375}, {"start": 2258.51, "end": 2258.83, "word": " لريه", "probability": 0.4087727864583333}, {"start": 2258.83, "end": 2259.29, "word": " أخدناها", "probability": 0.90029296875}, {"start": 2259.29, "end": 2259.53, "word": " قبل", "probability": 0.874267578125}, {"start": 2259.53, "end": 2259.71, "word": " هيك", "probability": 0.679931640625}, {"start": 2259.71, "end": 2260.23, "word": " لمّا", "probability": 0.7854817708333334}, {"start": 2260.23, "end": 2260.89, "word": " إذا", "probability": 0.89990234375}, {"start": 2260.89, "end": 2261.25, "word": " صار", "probability": 0.9755859375}, {"start": 2261.25, "end": 2261.69, "word": " عندي", "probability": 0.807861328125}, {"start": 2261.69, "end": 2261.93, "word": " اللي", "probability": 0.892333984375}, {"start": 2261.93, "end": 2262.11, "word": " هو", "probability": 0.97705078125}, {"start": 2262.11, "end": 2262.37, "word": " T", "probability": 0.904296875}, {"start": 2262.37, "end": 2263.01, "word": " star", "probability": 0.76953125}], "temperature": 1.0}, {"id": 100, "seek": 228923, "start": 2263.69, "end": 2289.23, "text": "Y0 بساول A1 T X A2 Inverse Y0 والـ Y0 كانت أشمالها arbitrary هنا for any لحدية for any ومين وY0 element انهيش الـ H2والدلتين هدولة قيمتهم عند أي قيمة في الـ Y0 في الدمين متساوية إذا أكيد الدلتين T star", "tokens": [56, 15, 4724, 3794, 995, 12610, 316, 16, 314, 1783, 316, 17, 682, 4308, 398, 15, 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"probability": 0.2178955078125}, {"start": 2267.53, "end": 2268.83, "word": " A2", "probability": 0.940185546875}, {"start": 2268.83, "end": 2269.41, "word": " Inverse", "probability": 0.7236328125}, {"start": 2269.41, "end": 2270.05, "word": " Y0", "probability": 0.9296875}, {"start": 2270.05, "end": 2270.75, "word": " والـ", "probability": 0.6580810546875}, {"start": 2270.75, "end": 2271.11, "word": " Y0", "probability": 0.780029296875}, {"start": 2271.11, "end": 2271.55, "word": " كانت", "probability": 0.951416015625}, {"start": 2271.55, "end": 2272.21, "word": " أشمالها", "probability": 0.81787109375}, {"start": 2272.21, "end": 2272.81, "word": " arbitrary", "probability": 0.59326171875}, {"start": 2272.81, "end": 2273.21, "word": " هنا", "probability": 0.214111328125}, {"start": 2273.21, "end": 2273.49, "word": " for", "probability": 0.73193359375}, {"start": 2273.49, "end": 2273.99, "word": " any", "probability": 0.86181640625}, {"start": 2273.99, "end": 2275.11, "word": " لحدية", "probability": 0.54827880859375}, {"start": 2275.11, "end": 2275.37, "word": " for", "probability": 0.92724609375}, {"start": 2275.37, "end": 2275.67, "word": " any", "probability": 0.87548828125}, {"start": 2275.67, "end": 2276.27, "word": " ومين", "probability": 0.9033203125}, {"start": 2276.27, "end": 2276.91, "word": " وY0", "probability": 0.60302734375}, {"start": 2276.91, "end": 2277.27, "word": " element", "probability": 0.6025390625}, {"start": 2277.27, "end": 2277.83, "word": " انهيش", "probability": 0.420989990234375}, {"start": 2277.83, "end": 2278.21, "word": " الـ", "probability": 0.5689697265625}, {"start": 2278.21, "end": 2280.09, "word": " H2والدلتين", "probability": 0.64483642578125}, {"start": 2280.09, "end": 2281.23, "word": " هدولة", "probability": 0.7523193359375}, {"start": 2281.23, "end": 2281.97, "word": " قيمتهم", "probability": 0.968994140625}, {"start": 2281.97, "end": 2282.35, "word": " عند", "probability": 0.98046875}, {"start": 2282.35, "end": 2282.59, "word": " أي", "probability": 0.86474609375}, {"start": 2282.59, "end": 2283.09, "word": " قيمة", "probability": 0.990234375}, {"start": 2283.09, "end": 2283.19, "word": " في", "probability": 0.83349609375}, {"start": 2283.19, "end": 2283.67, "word": " الـ", "probability": 0.950439453125}, {"start": 2283.67, "end": 2284.01, "word": " Y0", "probability": 0.851318359375}, {"start": 2284.01, "end": 2284.15, "word": " في", "probability": 0.93359375}, {"start": 2284.15, "end": 2284.69, "word": " الدمين", "probability": 0.7106119791666666}, {"start": 2284.69, "end": 2285.91, "word": " متساوية", "probability": 0.9748046875}, {"start": 2285.91, "end": 2286.29, "word": " إذا", "probability": 0.62451171875}, {"start": 2286.29, "end": 2286.77, "word": " أكيد", "probability": 0.9156901041666666}, {"start": 2286.77, "end": 2287.71, "word": " الدلتين", "probability": 0.9853515625}, {"start": 2287.71, "end": 2288.49, "word": " T", "probability": 0.85986328125}, {"start": 2288.49, "end": 2289.23, "word": " star", "probability": 0.02349853515625}], "temperature": 1.0}, {"id": 101, "seek": 230329, "start": 2290.99, "end": 2303.29, "text": "بساوي a1t cross a2 inverse و هو المطلوب و إلى لقاء آخر السلام عليكم و رحمة الله الله يعطيكم العافية", "tokens": [3555, 3794, 995, 45865, 257, 16, 83, 3278, 257, 17, 17340, 4032, 31439, 9673, 9566, 1211, 37746, 4032, 30731, 5296, 4587, 16606, 19753, 34740, 21136, 37440, 25894, 24793, 4032, 12602, 35571, 3660, 21984, 21984, 37495, 9566, 1829, 24793, 18863, 31845, 10632], "avg_logprob": -0.2931547732580276, "compression_ratio": 1.265625, "no_speech_prob": 3.039836883544922e-06, "words": [{"start": 2290.99, "end": 2291.99, "word": "بساوي", "probability": 0.580169677734375}, {"start": 2291.99, "end": 2292.99, "word": " a1t", "probability": 0.3062540690104167}, {"start": 2292.99, "end": 2293.71, "word": " cross", "probability": 0.54345703125}, {"start": 2293.71, "end": 2295.63, "word": " a2", "probability": 0.923583984375}, {"start": 2295.63, "end": 2296.41, "word": " inverse", "probability": 0.9072265625}, {"start": 2296.41, "end": 2297.23, "word": " و", "probability": 0.306884765625}, {"start": 2297.23, "end": 2297.65, "word": " هو", "probability": 0.8017578125}, {"start": 2297.65, "end": 2298.77, "word": " المطلوب", "probability": 0.9842529296875}, {"start": 2298.77, "end": 2299.35, "word": " و", "probability": 0.88720703125}, {"start": 2299.35, "end": 2299.67, "word": " إلى", "probability": 0.91943359375}, {"start": 2299.67, "end": 2300.35, "word": " لقاء", "probability": 0.96240234375}, {"start": 2300.35, "end": 2300.85, "word": " آخر", "probability": 0.86865234375}, {"start": 2300.85, "end": 2301.27, "word": " السلام", "probability": 0.846435546875}, {"start": 2301.27, "end": 2301.57, "word": " عليكم", "probability": 0.9091796875}, {"start": 2301.57, "end": 2301.77, "word": " و", "probability": 0.88916015625}, {"start": 2301.77, "end": 2301.77, "word": " رحمة", "probability": 0.8155924479166666}, {"start": 2301.77, "end": 2302.23, "word": " الله", "probability": 0.9609375}, {"start": 2302.23, "end": 2302.65, "word": " الله", "probability": 0.56787109375}, {"start": 2302.65, "end": 2302.93, "word": " يعطيكم", "probability": 0.7763671875}, {"start": 2302.93, "end": 2303.29, "word": " العافية", "probability": 0.9031575520833334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2303.86075, "duration_after_vad": 2257.328749999994}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/vjF46QrstMA_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/vjF46QrstMA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..be7160ce7d92c8b3dd3f99d4d47983334c87b081
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/vjF46QrstMA_postprocess.srt
@@ -0,0 +1,3900 @@
+1
+00:00:04,960 --> 00:00:07,640
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,640 --> 00:00:11,200
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:11,200 --> 00:00:17,500
+أهله وصحبه أجمعين هذه هي المحاضرة رقم 16 تحليل
+
+4
+00:00:17,500 --> 00:00:20,980
+اقتراني او تحليل دالي طلاب طالبات الجامعة
+
+5
+00:00:20,980 --> 00:00:27,200
+الإسلاميةوصلنا احنا لعند ال section الأخير في اللي
+
+6
+00:00:27,200 --> 00:00:32,760
+هو chapter 2 وهو يمكن يعني من أحد ثمرات ال .. ال
+
+7
+00:00:32,760 --> 00:00:38,640
+.. ال chapter و .. و مليء بالمعلومات اللي هو 2
+
+8
+00:00:38,640 --> 00:00:43,380
+عشرة اللي هو تحت عنوان normed spaces of operators
+
+9
+00:00:43,380 --> 00:00:47,940
+أو اللي بنسمي ال dual space المرة الماضية احنا
+
+10
+00:00:47,940 --> 00:00:52,270
+حكينا عن ال algebraic dual spaceاللي هو the space
+
+11
+00:00:52,270 --> 00:00:58,470
+of all linear functionals الان بدنا نحكي عن اللي
+
+12
+00:00:58,470 --> 00:01:05,490
+هو ال dual space اللي بنسميه ال space of all
+
+13
+00:01:06,190 --> 00:01:09,910
+bounded linear functional هو اللي خلّيني أقول محل
+
+14
+00:01:09,910 --> 00:01:13,570
+اهتمامنا لأنه احنا بنشتغل على اشي فيه norm فهي
+
+15
+00:01:13,570 --> 00:01:17,030
+عندنا اللي هو بدنا نبدأ نشتغل على هذا ال space
+
+16
+00:01:17,030 --> 00:01:21,110
+اللي هنعمل فيه norm و هنشوف و كيف بدنا اللي هو
+
+17
+00:01:21,110 --> 00:01:22,710
+نحصل على هذا ال space
+
+18
+00:01:26,910 --> 00:01:34,690
+الان نذكركم بالرمارك التالية بيكس واي اللي هو رموز
+
+19
+00:01:34,690 --> 00:01:38,450
+الها بالرمز denotes as of the set of all bounded
+
+20
+00:01:38,450 --> 00:01:45,990
+linear operatorsلت بيكس واي او لأ dual space ال X
+
+21
+00:01:45,990 --> 00:01:49,330
+prime اللي هي bounded linear functions اما احنا ال
+
+22
+00:01:49,330 --> 00:01:52,630
+بيكس واي ايش هنرمزلها denote the set of all
+
+23
+00:01:52,630 --> 00:01:58,110
+bounded linear operators من X لعند مين لعند Y نتفق
+
+24
+00:01:58,110 --> 00:02:02,780
+عليا هذا اللي هو الرمزمن normed space ل normed
+
+25
+00:02:02,780 --> 00:02:07,620
+space هذا اللي هو الرمز برمز اللي حكيناه الآن بدنا
+
+26
+00:02:07,620 --> 00:02:11,680
+نعرف على اللي هي الدوالي اللي موجودة هنا عمليتين
+
+27
+00:02:11,680 --> 00:02:14,980
+عملية الأولى اللي هي عملية اللي هي ال vector
+
+28
+00:02:14,980 --> 00:02:18,560
+addition او ال addition لأي two elements في ال Bxy
+
+29
+00:02:18,560 --> 00:02:24,230
+بدنا نعرف اللي هو T زائد Sكالتالي إن هو مجموعة في
+
+30
+00:02:24,230 --> 00:02:27,290
+الدائلتين عادي T زي دقاسة of X بيساوي T of X زي
+
+31
+00:02:27,290 --> 00:02:30,830
+دقاسة of X لكل X وين معله في ال domain اللي هي
+
+32
+00:02:30,830 --> 00:02:34,230
+اللي هي ال X اللي عندي X هنا و ال scalar
+
+33
+00:02:34,230 --> 00:02:39,490
+multiplication Alpha T of X بتعني Alpha في T of X
+
+34
+00:02:39,490 --> 00:02:42,780
+اللي هي point twiceبنفس الشيء for all x element in
+
+35
+00:02:42,780 --> 00:02:48,900
+x الان تحت هذه العمليتين هيطلع عند bxy is a vector
+
+36
+00:02:48,900 --> 00:02:52,180
+space تجربوها هتلاقوها انها تطلع عند vector space
+
+37
+00:02:52,180 --> 00:02:56,500
+و اصلا في اي كتاب جاب الخطة هتلاقوا اللي هو ال set
+
+38
+00:02:56,500 --> 00:02:58,940
+هذي تحت هذول العمليتين بتطلع ان vector space
+
+39
+00:02:58,940 --> 00:03:06,140
+وسهلات و ال zero vector هو ال zero function و كل
+
+40
+00:03:06,140 --> 00:03:10,360
+أمور سهل ان شاء الله نجي لان لنظرية 2 عشر واحد
+
+41
+00:03:10,800 --> 00:03:14,420
+أتنين عشرة واحد صار عندنا vector space بس انتوا
+
+42
+00:03:14,420 --> 00:03:17,380
+عارفين ان احنا شغلنا هنا احنا يعني بتجيب ال vector
+
+43
+00:03:17,380 --> 00:03:20,760
+ال vector space عشان نعمل ال norm عشان نحصل على
+
+44
+00:03:20,760 --> 00:03:25,020
+normed space اللي عندنا vector space Pxy اللي
+
+45
+00:03:25,020 --> 00:03:28,240
+حكينا عنه فوق of all bounded linear operators from
+
+46
+00:03:28,240 --> 00:03:33,280
+a normed space X into a normed space Yماله is
+
+47
+00:03:33,280 --> 00:03:38,960
+itself a normed space ونرمه مين هو النرم with norm
+
+48
+00:03:38,960 --> 00:03:42,920
+defined by نرمه نرم الـ T هو عبارة عن الـ Supremum
+
+49
+00:03:42,920 --> 00:03:46,200
+عرفناه قبل هيك Supremum لنرم الـ T X على نرم الـ X
+
+50
+00:03:46,200 --> 00:03:49,600
+X element in domain of T و X ده تسوى سفر أو زي ما
+
+51
+00:03:49,600 --> 00:03:53,020
+قلنا سابقا هو Supremum لنرم T X X element in
+
+52
+00:03:53,020 --> 00:03:57,720
+domain of T ونرمات لنرمات الـ X أشماله سوى نرمها
+
+53
+00:03:57,720 --> 00:04:03,050
+سوى واحدهذا الآن عبارة عن هيعملني normed SBS وهذا
+
+54
+00:04:03,050 --> 00:04:06,930
+ال remark طبعا من اللي هي النظرية من ال remark
+
+55
+00:04:06,930 --> 00:04:10,050
+اللي فوق ومن اللي لمّة اتنين سبعة واحد اللي
+
+56
+00:04:10,050 --> 00:04:13,690
+جالتلنا ان هذا عبارة عن عشان norm فبطلع كله على
+
+57
+00:04:13,690 --> 00:04:21,020
+بعض اشمله normed SBS إذا ال BXYالآن الـ B X Y the
+
+58
+00:04:21,020 --> 00:04:25,360
+space of all bounded linear operators مع ال norm
+
+59
+00:04:25,360 --> 00:04:29,660
+لـ T هذا بيعملي أو ال norm اللي عرفناها لـ T قبل
+
+60
+00:04:29,660 --> 00:04:35,600
+شوية اللي هو بيعملي norm of this space نيجي الآن
+
+61
+00:04:35,600 --> 00:04:43,940
+نفحص اللي هوالنظرية التالية اللي يبدأ تجيبنا على
+
+62
+00:04:43,940 --> 00:04:50,140
+سؤال متى احنا بنضمن عندي ال Bxy يكون عبارة عن بنخ
+
+63
+00:04:50,140 --> 00:04:54,660
+space عبارة عن بنخ space النظرية بتقول التالي اطلع
+
+64
+00:04:54,660 --> 00:05:00,840
+لفوق بال .. ادنان if y is a بنخ spaceيعني بترمي في
+
+65
+00:05:00,840 --> 00:05:06,360
+بنخ space if Y is a بنخ space then ال Bxy أشماله
+
+66
+00:05:06,360 --> 00:05:11,020
+is a بنخ space for any normed space من X إذا اللي
+
+67
+00:05:11,020 --> 00:05:14,780
+بهمني أنا إذا كان اللي هو ال Y norm بنخ space
+
+68
+00:05:14,780 --> 00:05:20,360
+بضمنكم أن ال Bxy تكون أشمالها is a بنخ spaceعشان
+
+69
+00:05:20,360 --> 00:05:24,920
+نثبت بنخ space كالعادة بناخد قوشي sequence في هذا
+
+70
+00:05:24,920 --> 00:05:28,820
+ال space و بنثبت أنها converts إذا أثبتنا أنها
+
+71
+00:05:28,820 --> 00:05:32,340
+converts بتكون أشمالها اللي هي صار عندي complete
+
+72
+00:05:32,340 --> 00:05:35,860
+إذا في البداية أكيد هقول let TN be any Cauchy
+
+73
+00:05:35,860 --> 00:05:40,760
+sequence in B XY فكرة البرهان أنه بدي أغير الحديد
+
+74
+00:05:41,230 --> 00:05:44,670
+من اللي هو الـ Cauchy Sequence «CN» في الـ «A» في
+
+75
+00:05:44,670 --> 00:05:50,310
+الـ «BXY» إلى الحديث إن هنحصل منها Cauchy Sequence
+
+76
+00:05:50,310 --> 00:05:53,310
+«N» في الـ «Y» والـ «Y» Complete إذن Converted من
+
+77
+00:05:53,310 --> 00:05:56,790
+الأصلية اللي نجيها بعرفناها اللي هو فانكشف معينة
+
+78
+00:05:56,790 --> 00:05:59,450
+تكون هي إيش ما اللي هي Converted لها، هذه قصتنا في
+
+79
+00:05:59,450 --> 00:06:04,000
+كل البرهن، هذه برهنها، خلّينا نجي للتفاصيلزي ما
+
+80
+00:06:04,000 --> 00:06:08,560
+قلنا ناخد TN أنه كوشي سيكوينس في الـ Bxy إذا من
+
+81
+00:06:08,560 --> 00:06:11,260
+تعريف الكوشي سيكوينس لاقي يأبسلون أكبر من صفر
+
+82
+00:06:11,260 --> 00:06:15,200
+there exist K element in such that نورم الـ TN
+
+83
+00:06:15,200 --> 00:06:19,960
+ناقص TM أصغر من 100 من إبسلون لكل أنه M أكبر من K
+
+84
+00:06:19,960 --> 00:06:26,020
+وهذا تعريف الكوشي سيكوينسطيب إن أنا then for all x
+
+85
+00:06:26,020 --> 00:06:29,800
+element in X خد لأي x element in X مدام ال norm
+
+86
+00:06:29,800 --> 00:06:34,160
+هذا أصغر من يبسلون بدي أحصل على ما يلي أنه لكل n و
+
+87
+00:06:34,160 --> 00:06:38,740
+m أكبر من k اللي هذا صحيح إليها احسب ل norm Tn x
+
+88
+00:06:38,740 --> 00:06:44,000
+ناقص Tm x بساوي اللي هو Tn ناقص Tm of x من تعريف
+
+89
+00:06:44,000 --> 00:06:48,750
+اللي هو main functions أو اللي هي ال operatorبهي
+
+90
+00:06:48,750 --> 00:06:51,630
+هذه طبعاً اللي هي bounded وهذه bounded إذا أنت
+
+91
+00:06:51,630 --> 00:06:54,910
+تنتهي مع بعض bounded إذا أكيد أصغر أو أسوأ نورم
+
+92
+00:06:54,910 --> 00:06:58,030
+الأولى في نورم التانية نورم TN نقص TM في نورم مين
+
+93
+00:06:58,030 --> 00:07:02,290
+ال X ده إنه TN نقص TM is a bounded linear operator
+
+94
+00:07:02,290 --> 00:07:09,080
+طيب الآن هذه من فوق أصغر من مين من Y في X الآنثبت
+
+95
+00:07:09,080 --> 00:07:13,180
+لي X عندك for any fixed X element in X و given أني
+
+96
+00:07:13,180 --> 00:07:18,400
+الـY الـPrime بدي أثبتلك الآن الـTNX ناقص الـTNX
+
+97
+00:07:18,400 --> 00:07:24,040
+أصغر من مين من Y ده نخد الآن for every Y الـPrime
+
+98
+00:07:24,040 --> 00:07:28,630
+أكبر من 0طبعا احنا مثلا بنحكي عن مين for fixed مين
+
+99
+00:07:28,630 --> 00:07:34,730
+for fixed x اه الان بدى اثبتلك ان ال norm ل Tm x
+
+100
+00:07:34,730 --> 00:07:39,950
+ناقص Tm x اصغر من مين من يبسلون براى اذا اثبتت
+
+101
+00:07:39,950 --> 00:07:43,470
+صارت ال Tm x هذه نفسها ايش مالها كوشي sequence
+
+102
+00:07:43,470 --> 00:07:48,190
+لمين لل x هذه ماشي الحال بحكي عن x arbitrary لكن
+
+103
+00:07:48,190 --> 00:07:53,680
+بحكي عن اشي محدد معايا ماشي الحالطيب انا لان عندى
+
+104
+00:07:53,680 --> 00:08:00,900
+انا نور الـ TN ناقص الـ TN ماله اصغر من إبشلونماشي
+
+105
+00:08:00,900 --> 00:08:04,580
+الحال أصغر من يبسلون الان اليبسلون هذا الكلام صحيح
+
+106
+00:08:04,580 --> 00:08:07,940
+لأي يبسلون في الدنيا بقدر أحصل على هذا ماشي الحال
+
+107
+00:08:07,940 --> 00:08:11,680
+الان اليبسلون ال prime مالها بيبقى إيديا إذا أنا
+
+108
+00:08:11,680 --> 00:08:15,940
+اليبسلون هذه بقدر أزيّرها جد ما بدي هذا أصغر من
+
+109
+00:08:15,940 --> 00:08:21,120
+مين عندي أصغر من يبسلون من يبسلون طلع عندي TNX
+
+110
+00:08:21,120 --> 00:08:28,180
+ناقص TMX من هذه طلع عندي norm TNX ناقص TMXماله
+
+111
+00:08:28,180 --> 00:08:33,740
+أصغر من مين من إبسلون في نورم الـX هذا اللي حصلناه
+
+112
+00:08:33,740 --> 00:08:37,160
+وعليه أصلا البداية التامة اللي هو واحد الآن زي ما
+
+113
+00:08:37,160 --> 00:08:40,480
+قلنا إبسلون برايم أنت عطيتني أي إبسلون برايم بدك
+
+114
+00:08:40,480 --> 00:08:45,920
+تعجزني مش الحال الآن أنا هذه صحيحة لأي إبسلون
+
+115
+00:08:45,920 --> 00:08:50,820
+مالها في الدنيا إذا أنا بقدر أزغرها جد ما بدي جد
+
+116
+00:08:50,820 --> 00:08:54,640
+ما بدي سرعة نحكي عن نورم الـX أشماله محددبحيث أنه
+
+117
+00:08:54,640 --> 00:08:58,280
+مو أن الـ Epsilon في الـ Normal X بقدر أذاكر هذه
+
+118
+00:08:58,280 --> 00:09:01,860
+جدّا بدي بحيث أنه يكون أصغر من مين من Epsilon
+
+119
+00:09:01,860 --> 00:09:05,720
+برايم عطيتني Epsilon برايم ماشي الحال بقولك اللي
+
+120
+00:09:05,720 --> 00:09:09,300
+هو الآن اختار الـ Epsilon هذه تكون أضرر أصغر من
+
+121
+00:09:09,300 --> 00:09:12,140
+Epsilon برايم من Normal X بقدر لأن هذا صحيح لكل
+
+122
+00:09:12,140 --> 00:09:16,560
+مين لكل Epsilon من هذه الحالة صار عندى الـ TN ناقص
+
+123
+00:09:16,560 --> 00:09:19,940
+الـ TN X ناقص TN X أصغر من مين Epsilon برايم و
+
+124
+00:09:19,940 --> 00:09:24,350
+Epsilon برايم أصغر بترى إذا صارت عندى TN Xأيش
+
+125
+00:09:24,350 --> 00:09:28,230
+مالها عبارة عن كوشي sequence وهذا الكلام بوضوح
+
+126
+00:09:28,230 --> 00:09:32,110
+هايه عندنا هان for any fixed x and any given x او
+
+127
+00:09:32,110 --> 00:09:35,150
+epsilon prime given epsilon prime we can choose
+
+128
+00:09:35,150 --> 00:09:39,190
+epsilon بتساوي epsilon x such that epsilon x في
+
+129
+00:09:39,190 --> 00:09:42,710
+المهم ال x أصغر من مين من epsilon ابراهيم بقدر
+
+130
+00:09:42,710 --> 00:09:47,130
+اختار مين epsilon اللي هي ال arbiter الأولىأه اللي
+
+131
+00:09:47,130 --> 00:09:49,290
+بتساوي مين ابسلون اكت اكت اكت اكت اكت اكت اكت اكت
+
+132
+00:09:49,290 --> 00:09:49,910
+اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت
+
+133
+00:09:49,910 --> 00:09:51,250
+اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت
+
+134
+00:09:51,250 --> 00:09:53,970
+اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت
+
+135
+00:09:53,970 --> 00:09:59,530
+اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت
+
+136
+00:09:59,530 --> 00:10:01,490
+اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت
+
+137
+00:10:01,490 --> 00:10:07,060
+اكت اكالان هذه احنا هذا الكلام صحيح لمين؟ لأي X
+
+138
+00:10:07,060 --> 00:10:12,800
+سميت اللي هي الـY اللي بتناسب الـX اللي حتى الزمن
+
+139
+00:10:12,800 --> 00:10:17,460
+سميتها Y X ماسمتهاش خلوها Y بس عشان تتعرف ان الـY
+
+140
+00:10:17,460 --> 00:10:22,140
+اللي اخترتها تعتمد على مين؟ على الـX اللي انت عشان
+
+141
+00:10:22,140 --> 00:10:27,420
+تضمن انه Y X هذه في norm الـX يكون أصغر من مين؟من
+
+142
+00:10:27,420 --> 00:10:30,300
+epsilon إبراهيم وبقدر أعمل هيك أه بقدر لإن فعلا ال
+
+143
+00:10:30,300 --> 00:10:32,440
+epsilon إيه شمالها arbitrary وبختار زي ما بدي
+
+144
+00:10:32,440 --> 00:10:38,580
+بزغيرها بحيث أننا نحصل على اللي هي ال norm ل TNX
+
+145
+00:10:38,580 --> 00:10:42,500
+نقص TNX أزرع من epsilon إبراهيم hence TNX is a
+
+146
+00:10:42,500 --> 00:10:46,280
+Cauchy sequence in Yإذا حصلنا TN X الشمال هيكلش
+
+147
+00:10:46,280 --> 00:10:48,820
+الـ sequence للـ Y هذا الـ X أخدناها arbitrarily
+
+148
+00:10:48,820 --> 00:10:54,060
+لكن fixed من هذه بدي أعرف الآن however Y is
+
+149
+00:10:54,060 --> 00:10:58,980
+complete إذا TN X هذه صارت converged to converged
+
+150
+00:10:58,980 --> 00:11:03,680
+إذا خلّيني أقول إن TN X هذه converged من Y ماشي
+
+151
+00:11:03,680 --> 00:11:11,120
+بدي أعرف الآن أنا إيش غرضي بدي ألاقي TNو تروح لصم
+
+152
+00:11:11,120 --> 00:11:15,700
+T و تكون الـ T موجودة في الـ P X و Y شوفوا كيف بدي
+
+153
+00:11:15,700 --> 00:11:20,060
+أعرفها بدي أعرف الـ T هي عبارة عن الأداة اللي
+
+154
+00:11:20,060 --> 00:11:26,400
+جبتها عند T of X تساوي مين Y اللي هي مين Y limited
+
+155
+00:11:26,400 --> 00:11:32,380
+T and X و كإني بدي أقول define T من X لعين Y by T
+
+156
+00:11:32,380 --> 00:11:36,900
+Xحكي عن الـ X الـ Fix اللي أخدتها arbitrary بثاوة
+
+157
+00:11:36,900 --> 00:11:42,260
+من الـ Y اللي هي في الواقع limit من T N X وهذه ال
+
+158
+00:11:42,260 --> 00:11:48,600
+limit موجودة وقلنا تنتقل بثاوة YوY موجودة في الـ I
+
+159
+00:11:48,600 --> 00:11:52,740
+كابيتال والـ X من أين جاء من الـ X التي هي كابيتال
+
+160
+00:11:52,740 --> 00:11:57,180
+إذاً الـ T تبعته اللي صارت تشتغل من X لعند مين
+
+161
+00:11:57,180 --> 00:12:00,640
+لعند Y بمنافقة لكم إن هذا الـ T عبارة عن bounded
+
+162
+00:12:00,640 --> 00:12:05,240
+وlinear بيكون وين ما لها قعدت هان معناته صار عنده
+
+163
+00:12:05,240 --> 00:12:07,780
+الـ Cauchy sequence converged to some T element
+
+164
+00:12:07,780 --> 00:12:11,460
+بيكسوا Y صار بيكسوا Y is complete خلّيني أشوف
+
+165
+00:12:15,020 --> 00:12:18,620
+عرفنا الـ T زي ما قلنا الان لك كل .. بتثبتلكم انها
+
+166
+00:12:18,620 --> 00:12:23,640
+Linear T Linear for any X و Z element in X and any
+
+167
+00:12:23,640 --> 00:12:27,700
+scalar Alpha خد للـ T و Alpha X زائد Z كيف عرفته
+
+168
+00:12:27,700 --> 00:12:31,180
+هذا؟ كيف بعرف T Alpha X زائد Z؟ هو عبارة عن Limit
+
+169
+00:12:31,180 --> 00:12:36,300
+TL اللي بتاخد هذه اللي هي Alpha X زائد Main زائد Z
+
+170
+00:12:36,300 --> 00:12:39,100
+من تعريف اللي قبل بشوية، كنا X أكرا Fixed لكن
+
+171
+00:12:39,100 --> 00:12:43,880
+Arbitraryإذن ويساوي الآن هذه الـ TN كلها الـ T1
+
+172
+00:12:43,880 --> 00:12:48,320
+وT2 وT3 وT4 هي عبارة عن limits وين في الـ Bxy
+
+173
+00:12:48,320 --> 00:12:52,260
+وكلها نشمالين linear و bounded إذن الـ Alpha بتقدر
+
+174
+00:12:52,260 --> 00:13:00,360
+تطلع مباشرة من عند اللي هو عند اللي هي Alpha بتطلع
+
+175
+00:13:00,360 --> 00:13:05,230
+من هنافاهمين؟ وبتطلع برا مباشرة Alpha في TNX زائد
+
+176
+00:13:05,230 --> 00:13:08,590
+limit TNZ لأن ال limit ما لها بتتوزع زي ما انتوا
+
+177
+00:13:08,590 --> 00:13:13,070
+عارفين وهي ساوي هذه مين هي عبارة عن TX وهذه مين هي
+
+178
+00:13:13,070 --> 00:13:16,730
+TZ إذا صارت اللي هي Alpha TX زائد TZ يعني معناته
+
+179
+00:13:16,730 --> 00:13:21,640
+صارت T إيش ما لها is linear كلام سهل هذالان نيجي
+
+180
+00:13:21,640 --> 00:13:27,200
+نثبت الـ boundedness لـ T إنها T is bounded قبل ما
+
+181
+00:13:27,200 --> 00:13:31,680
+أثبت T is bounded بدي أستعين باللي فوق و أثبتلك إن
+
+182
+00:13:31,680 --> 00:13:35,880
+T N ناقص T هي ال bounded و عند T N bounded إذا
+
+183
+00:13:35,880 --> 00:13:40,660
+صارت حاصل طرحين اللي هو T تطلع bounded شوف كامالان
+
+184
+00:13:40,660 --> 00:13:46,960
+norm Tn نقص Tx من وين بده احصله شوف الواحد خد لها
+
+185
+00:13:46,960 --> 00:13:50,280
+ال limit صار ال limit موجودة احنا خد ال limit as M
+
+186
+00:13:50,280 --> 00:13:53,460
+goes to infinity هذا صحيح على كل M .. M .. M و M
+
+187
+00:13:53,460 --> 00:13:56,960
+أكبر من K من ضمنه M لما تكون أكبر من N و أكبر من K
+
+188
+00:13:56,960 --> 00:14:02,100
+و بود ال M إلى نهاية بيصير عندي الان هذه limit as
+
+189
+00:14:02,100 --> 00:14:05,460
+M goes to infinity بيصير هذه T of X لأن عارفين
+
+190
+00:14:05,460 --> 00:14:08,160
+احنا ال norm is continuous بتدخل ال limit جوا ال
+
+191
+00:14:08,160 --> 00:14:12,750
+normوبتطلع طبيعي وبتدخل ل .. اللي هي عندي limit
+
+192
+00:14:12,750 --> 00:14:17,350
+TMX اللي هي بيصير T of X فاهمي اللي بحكيه صار عندي
+
+193
+00:14:17,350 --> 00:14:23,530
+لأن TN of X نقص T of X اللي هي أصغر من مين من
+
+194
+00:14:23,530 --> 00:14:27,550
+إبسلون في نورملة X أعملكوا بيها على اللوح لكي
+
+195
+00:14:27,550 --> 00:14:30,770
+تكونوا مش مستوعبين أشي اللي بقوله اللي بحكيه أنا
+
+196
+00:14:30,770 --> 00:14:35,950
+حصلت حصلت
+
+197
+00:14:39,410 --> 00:14:45,610
+نورم الـ TNX لاقص TX أصغر أو يساوي Y في نورم لمن؟
+
+198
+00:14:45,610 --> 00:14:50,050
+للـ X، TN اللي أنا بتدخلي اللي أنا بتروح إلى مين؟
+
+199
+00:14:50,050 --> 00:14:53,050
+إلينا للهيئة as N goes to infinity بصير هذا ال
+
+200
+00:14:53,050 --> 00:14:59,380
+limitن أخد م أكبر من ان و هي أكبر أو يساوي مين كما
+
+201
+00:14:59,380 --> 00:15:03,060
+صحيح لكل أمها من ضمنها دولة الان ود ام لنهاية
+
+202
+00:15:03,060 --> 00:15:05,820
+مالهاش علاقة ان ضالتها زي ما هي مالهاش علاقة فيها
+
+203
+00:15:05,820 --> 00:15:09,120
+مين اللي بده يوديها لما لنهاية ام اذا بيصير ت ان
+
+204
+00:15:09,120 --> 00:15:13,440
+اكس ناقص لما ال limit تخش هنا as m goes to
+
+205
+00:15:13,440 --> 00:15:17,360
+infinity بتصير ايش بتساوي ت اكس انه أثبتنا limit ت
+
+206
+00:15:17,360 --> 00:15:21,920
+ام اكس as m goes to infinity بساوي اللي هو ت اكس
+
+207
+00:15:21,920 --> 00:15:26,810
+اللي سمناها قبل شويه ايش اسمهاهذا بيصير اصغر او
+
+208
+00:15:26,810 --> 00:15:28,190
+يساوي او يساوي او يساوي او يساوي او يساوي او يساوي
+
+209
+00:15:28,190 --> 00:15:30,750
+او يساوي او يساوي او يساوي او يساوي او يساوي او
+
+210
+00:15:30,750 --> 00:15:31,590
+يساوي او يساوي او يساوي او يساوي او يساوي او يساوي
+
+211
+00:15:31,590 --> 00:15:32,650
+او يساوي او يساوي او يساوي او يساوي او يساوي او
+
+212
+00:15:32,650 --> 00:15:35,550
+يساوي او يساوي او يساوي او يساوي او يساوي او يساوي
+
+213
+00:15:35,550 --> 00:15:35,990
+او يساوي او يساوي او يساوي او يساوي او يساوي او
+
+214
+00:15:35,990 --> 00:15:43,180
+يساوي او يساوي او يسبناء عليه norm of Tn-T of X
+
+215
+00:15:43,180 --> 00:15:47,660
+ايش بتساوي؟ Tn X نقص CX، حسبتها دي هذي اللي
+
+216
+00:15:47,660 --> 00:15:50,540
+اثبتناها ايش مالها أضغط من Y في مين؟ في الـnormal
+
+217
+00:15:50,540 --> 00:15:55,420
+X هذا معناته، هذه مع هذه معناته ان Tn-Tn بيشملها
+
+218
+00:15:55,420 --> 00:16:01,050
+bounded operatorإذا صار عندى الان TN ناقص T is a
+
+219
+00:16:01,050 --> 00:16:05,230
+bounded operator هذا لكل مين لكل N أكبر من مين من
+
+220
+00:16:05,230 --> 00:16:08,630
+K لكن أنا بعرف إن ال TN كل واحدة فيها is bounded
+
+221
+00:16:08,630 --> 00:16:13,490
+إذا ال T بيساوي TN ناقص TN ناقص TN برضه مش هتكون
+
+222
+00:16:13,490 --> 00:16:17,970
+bounded ومن ثم ال T صارت عبارة عن Linear فوق و
+
+223
+00:16:17,970 --> 00:16:22,730
+bounded then T element in B XY من اتنين من اتنين
+
+224
+00:16:22,730 --> 00:16:30,590
+اللي احنا وصلنا إلى هنااللي هو for all n أكبر من K
+
+225
+00:16:30,590 --> 00:16:35,950
+نورم الـ T أن ناقص الـ T إيش بيساوي؟ يعني أخدوا
+
+226
+00:16:35,950 --> 00:16:39,250
+الـ Supremum بيساوي الـ Supremum للنورم هذا اللي
+
+227
+00:16:39,250 --> 00:16:41,830
+هو أصغر أيه بيساوي مين؟ الـ Supremum على مين؟ على
+
+228
+00:16:41,830 --> 00:16:44,470
+النورمات اللي بيساوي واحد فلمّا أخدوا الـ Supremum
+
+229
+00:16:44,470 --> 00:16:49,480
+بين هذه و بين هذهوالـ Norm للـ XH بساوي 1 فبصير
+
+230
+00:16:49,480 --> 00:16:51,960
+الـ Supremum لهذه أصغر أو ساوي اللي هو الـ
+
+231
+00:16:51,960 --> 00:16:56,380
+Epsilon، مظبوط؟ الـ Supremum هو تعريف الـ Norm
+
+232
+00:16:56,380 --> 00:17:01,840
+اللي هو TN ناقصي صار Norm TN ناقصي بساوي اللي هو
+
+233
+00:17:01,840 --> 00:17:06,280
+هذا المقدار أصغر أو ساوي Epsilon وهذا معناته أنه
+
+234
+00:17:06,280 --> 00:17:10,060
+جينا أخدنا أي Epsilon في الدنيا لجينا K بحيث لأ كل
+
+235
+00:17:10,060 --> 00:17:15,610
+N أكبر من KTn نقص T normalها أصغر من إبسلون وهذا
+
+236
+00:17:15,610 --> 00:17:19,650
+تعريف أن Tn converges لT Therefore صار عندي الـ
+
+237
+00:17:19,650 --> 00:17:22,070
+Cauchy sequence الـ arbitrary اللي أخدتها في Bxy
+
+238
+00:17:22,070 --> 00:17:28,130
+راحت لـT في Bxy ومعناته أنه صار Bxy is a complete
+
+239
+00:17:28,130 --> 00:17:38,480
+non space اللي بعدهالان بدنا نرجع نرجع زي الراجعة
+
+240
+00:17:38,480 --> 00:17:41,600
+اللى فعلناها المرة اللى فاتت بدل ما نحكي عن ال
+
+241
+00:17:41,600 --> 00:17:44,880
+algebraic dual space اللى هو the space of all
+
+242
+00:17:44,880 --> 00:17:50,780
+bounded linear functionials بدنا ناخد الآن the
+
+243
+00:17:50,780 --> 00:17:54,480
+space of all bounded linear functionials وهذا اللى
+
+244
+00:17:54,480 --> 00:18:00,340
+بنسميه ال dual space وبدنا نرمزله بعد اذنكم بالرمز
+
+245
+00:18:00,340 --> 00:18:07,350
+X'الدفينيشن التالي let X be a normed space then
+
+246
+00:18:07,350 --> 00:18:10,610
+the set of all bounded linear functionals on X
+
+247
+00:18:10,610 --> 00:18:16,530
+constitutes a normed spaceأكيد لأنه حالة خاصة من
+
+248
+00:18:16,530 --> 00:18:19,330
+اللي فوق اللي عندنا ال .. ال .. ال .. هذا بيصير ال
+
+249
+00:18:19,330 --> 00:18:21,630
+.. ال .. ال .. ال space of all bounded functional
+
+250
+00:18:21,630 --> 00:18:25,770
+دي عارفين هو .. مين هو؟ هذا ال space اللي عناصره
+
+251
+00:18:25,770 --> 00:18:31,050
+اللي هو P of X و ال scalar field يعني بمعنى آخر و
+
+252
+00:18:31,050 --> 00:18:33,750
+ال scalar field سواء ال R أو ال C is a complete ..
+
+253
+00:18:33,750 --> 00:18:38,050
+complete non space إذن أكيد كله على بعض أشماله
+
+254
+00:18:38,050 --> 00:18:44,500
+هيطلع بنخ spaceوهنرمزه بالرمز X' إذا ان X' هو the
+
+255
+00:18:44,500 --> 00:18:47,820
+dual space of X which is the set of all bounded
+
+256
+00:18:47,820 --> 00:18:52,300
+linear functionals on X which is a بنخ space
+
+257
+00:18:53,840 --> 00:18:56,400
+Constitute a normed space with norm defined by
+
+258
+00:18:56,400 --> 00:18:59,720
+norm الـ F هو نفسه norm الـ absolute value عن norm
+
+259
+00:18:59,720 --> 00:19:02,460
+الـ X لما الـ X تسوى سفر هو اللي هو نفسه the
+
+260
+00:19:02,460 --> 00:19:04,580
+supremum of the absolute value of F of X أو المدلس
+
+261
+00:19:04,580 --> 00:19:07,820
+X المدلس من X و norm الـ X تسوى واحد which is
+
+262
+00:19:07,820 --> 00:19:12,120
+called the dual space of X and is denoted by مين؟
+
+263
+00:19:12,120 --> 00:19:16,280
+X' وهي النظرية the dual space X' of a normed space
+
+264
+00:19:16,280 --> 00:19:20,200
+X إذا بنخ space هذا من automatic من مين؟ من اللي
+
+265
+00:19:20,200 --> 00:19:24,590
+حكيته اللي هي النظرية اللي جاب بشويةاطلع لفوق نيجي
+
+266
+00:19:24,590 --> 00:19:32,970
+لان لكيفية اثبات اللي هو كده is a dual space او
+
+267
+00:19:32,970 --> 00:19:38,970
+كده يعني بدنا نشوف كيف نثبت ال dual space لأمثلة
+
+268
+00:19:38,970 --> 00:19:44,170
+اول واحد بدنا ناخده مين ال RN بدنا نثبتلكم ان ال
+
+269
+00:19:44,170 --> 00:19:50,990
+dual space of RN is RN شو معناته عشان ندخل للأمر
+
+270
+00:19:50,990 --> 00:20:00,390
+بدنابدأ أثبتلكم ثلاث شغلات أو ثلاث أنثلة اللي هو
+
+271
+00:20:00,390 --> 00:20:14,790
+نقول واحد the dual space of Rn is Rn هاي واحد نين
+
+272
+00:20:14,790 --> 00:20:23,780
+the dual space of L1 is L infinityهذه اتنين تلاتة
+
+273
+00:20:23,780 --> 00:20:31,800
+the dual space of LB is LQ حيث واحد على B واحد على
+
+274
+00:20:31,800 --> 00:20:37,270
+Q بسوء ايش؟ بسوء واحدالعنوان شو معناته اللي هو
+
+275
+00:20:37,270 --> 00:20:42,490
+dual space of Rn اللي هو عبارة عن Rn إيش ماله؟
+
+276
+00:20:42,490 --> 00:20:46,330
+البراهي اللي هو the space of all bounded linear
+
+277
+00:20:46,330 --> 00:20:51,010
+functionals from Rn to the scalar field بتاعها،
+
+278
+00:20:51,010 --> 00:20:56,140
+ماشي الحالالان بتثبتوا لكم ان RN' هو مين هو RN هو
+
+279
+00:20:56,140 --> 00:21:03,960
+في الواقع بتثبت انه في isomorphism F من عند RN'
+
+280
+00:21:04,440 --> 00:21:08,980
+لعند مين لعند RN ايش ال isomorphism هذا ال
+
+281
+00:21:08,980 --> 00:21:13,560
+isomorphism one to oneon to function هذي اللي
+
+282
+00:21:13,560 --> 00:21:17,600
+بتحافظ زي ما قلنا عن cardinality هاي واحد اتنين
+
+283
+00:21:17,600 --> 00:21:23,040
+اللي هو preserve the norm يعني F of اللي هو الاشي
+
+284
+00:21:23,040 --> 00:21:27,940
+اللي هنا F أو نسميه C هو T مش مشكلة T of أي
+
+285
+00:21:27,940 --> 00:21:32,380
+element هنا ال element اللي هنا دوال T of F مثلا
+
+286
+00:21:32,380 --> 00:21:38,510
+normة بساوي norm ال F ماشياللي هي الـ Isometry
+
+287
+00:21:38,510 --> 00:21:40,490
+اللي سمناها اللي هي في الواقع على طول بتطلعيلنا
+
+288
+00:21:40,490 --> 00:21:45,310
+one to one الشغل الثالثة اللي هو preserve the norm
+
+289
+00:21:45,310 --> 00:21:49,510
+و preserve the cardinality و الشغل الثالثة اللي هي
+
+290
+00:21:49,510 --> 00:21:52,930
+عالمنا عالمنا اللي متكون من الـ RN براميل العمليات
+
+291
+00:21:52,930 --> 00:21:56,030
+الحسابية اللي عليها يعني preserve of العمليات
+
+292
+00:21:56,030 --> 00:21:58,410
+الحسابية اللي هي عبارة عن مين ال scalar
+
+293
+00:21:58,410 --> 00:22:01,770
+multiplication و ال vector addition يعني T of
+
+294
+00:22:01,770 --> 00:22:08,690
+Alpha F زائد G اللي هو بتثبتها L TAlpha of T F زي
+
+295
+00:22:08,690 --> 00:22:14,050
+الـ T mean اللي هو إيش الـ G ماشي معايا يا جماعة
+
+296
+00:22:14,050 --> 00:22:18,450
+هاي الآن فلسفة اللي هي أثبات أنه الـ Dual space of
+
+297
+00:22:18,450 --> 00:22:21,790
+RN اللي هو RN يعني بما هو أصلا شو معناته الـ
+
+298
+00:22:21,790 --> 00:22:25,870
+isomorphism أنه بس هذا هو هذا بس اتغيرت الأسامي
+
+299
+00:22:25,870 --> 00:22:29,570
+هذا أساميهم العناصر F وهذا اسم هي إيش اللي هو
+
+300
+00:22:29,570 --> 00:22:34,100
+Untablesماشي الحال، إذاً اللي هي بس ما هي إلا غير
+
+301
+00:22:34,100 --> 00:22:39,400
+تغيير أسماء أما هو التركيبة الجبرية والتركيبة ال
+
+302
+00:22:39,400 --> 00:22:41,480
+.. ال .. ال .. ال .. ال .. ال .. بالنسبة لعدد
+
+303
+00:22:41,480 --> 00:22:44,780
+العناصر أو ال cardinality وبالنسبة للتركيبة
+
+304
+00:22:44,780 --> 00:22:49,540
+التوبوليجية هي نفسها تماماً واضح شو معناته اللي هو
+
+305
+00:22:49,540 --> 00:22:55,080
+ال isomorphism؟ طيبو لو كان عندنا الـ structure مش
+
+306
+00:22:55,080 --> 00:22:57,300
+اللي هو vector space لو الـ structure اللي هو
+
+307
+00:22:57,300 --> 00:23:00,860
+الجبري كان عندنا group او .. او .. او ring او كده
+
+308
+00:23:00,860 --> 00:23:04,840
+بيبدأ تنجل اللي هي عملية ال group إلى العملية اللي
+
+309
+00:23:04,840 --> 00:23:08,020
+عاجبالها و تنجل اللي هو اللي لو كانت ring بيبدأ
+
+310
+00:23:08,020 --> 00:23:12,460
+تنجل لعمليتينلأ، لأ، لأ، عمليتين ولو كانت بنخ
+
+311
+00:23:12,460 --> 00:23:14,920
+الجيبران تنجي الـ vector space مع vector space
+
+312
+00:23:14,920 --> 00:23:18,780
+وبعدين اللي هو عملية الضرب وعملية اللي هو ال .. ال
+
+313
+00:23:18,780 --> 00:23:21,100
+.. ال .. ال vector addition كلها تنجي لها بنفس
+
+314
+00:23:21,100 --> 00:23:23,860
+الاسم وبعدين ال .. التشاكل اللي خلينا نقول ال
+
+315
+00:23:23,860 --> 00:23:28,300
+isomorphism ما هو اللي .. التركيبتين أو ال .. ال
+
+316
+00:23:28,300 --> 00:23:32,400
+.. العالمين هن نفسهم بس اختلفت في الأسماء يلا نيجي
+
+317
+00:23:32,400 --> 00:23:34,920
+اللي موضوعناه الكلام اللي حكيته مهم لإنه على أساس
+
+318
+00:23:35,760 --> 00:23:38,060
+بلخص لك كل الدنيا اللي هي بما يتعلق بالـ
+
+319
+00:23:38,060 --> 00:23:40,780
+isomorphism في الجبرو في الـ topology و في غيره و
+
+320
+00:23:40,780 --> 00:23:44,060
+حتى في ال 6 يوري في كل الأماكن اللي انت بدي كتبت
+
+321
+00:23:44,060 --> 00:23:46,820
+فيها اللي هو اتنين متكافئين
+
+322
+00:23:49,470 --> 00:23:53,130
+Space RN كما قلنا الـ dual space of RN is RN نعرف
+
+323
+00:23:53,130 --> 00:23:57,970
+انها ايش دييتها انه بدنا نجيه لها function T من RN
+
+324
+00:23:57,970 --> 00:24:00,550
+الـ prime لعند RN تكون one to one و one to one to
+
+325
+00:24:00,550 --> 00:24:03,090
+preserve the norm و preserve اللي هو main
+
+326
+00:24:03,090 --> 00:24:05,730
+operations
+
+327
+00:24:07,520 --> 00:24:12,440
+Since Rn is of finite dimensional قلنا الـ finite
+
+328
+00:24:12,440 --> 00:24:15,900
+dimensional Rn finite dimensional في النظرية 2.78
+
+329
+00:24:15,900 --> 00:24:20,340
+المرة الفاتتة قلنا الـ Rn star هتكون هي الـ Rn
+
+330
+00:24:20,340 --> 00:24:24,340
+prime إيش يعني؟ مش قلنا إنه لو كانت Rn اللي هي
+
+331
+00:24:24,340 --> 00:24:27,620
+finite dimensional أي linear operator عليها إيش
+
+332
+00:24:27,620 --> 00:24:33,350
+هيكون؟ boundedBounded Any linear operator on a
+
+333
+00:24:33,350 --> 00:24:36,350
+finite dimensional space is bounded خدناها المرة
+
+334
+00:24:36,350 --> 00:24:41,370
+الفاتة اللي هو إذا كان عند Tمن finite dimensional
+
+335
+00:24:41,370 --> 00:24:45,850
+space اللي هو إلى برمئهان إذا كان هذا finite
+
+336
+00:24:45,850 --> 00:24:48,930
+dimensional space كل سنة متسلمين بتكون الـT إذا
+
+337
+00:24:48,930 --> 00:24:54,190
+لينر على طول أشمالها is bounded بما أن عليه ليس
+
+338
+00:24:54,190 --> 00:25:00,030
+هناك فرق في هذه الحالة بين ال algebraic dual space
+
+339
+00:25:00,450 --> 00:25:04,130
+والـ Dual Space تبعنا، يعني لا فرق بين The space
+
+340
+00:25:04,130 --> 00:25:07,450
+of all bounded linear operators و The space of all
+
+341
+00:25:07,450 --> 00:25:11,430
+linear functional و The space of all linear
+
+342
+00:25:11,430 --> 00:25:14,970
+functional لا فرق بينهما لأن Any linear functional
+
+343
+00:25:14,970 --> 00:25:18,930
+in a finite dimensional space is a bounded linear
+
+344
+00:25:18,930 --> 00:25:23,510
+functionalإذا الحديث هنا أو الحديث هنا سيان So
+
+345
+00:25:23,510 --> 00:25:30,270
+that for any f element in Rn star أو Rn prime اللي
+
+346
+00:25:30,270 --> 00:25:34,210
+هو can be represented as f of x بيساوي summation
+
+347
+00:25:34,210 --> 00:25:40,830
+xi i gamma i j من واحد لعند n for any x بتساوي
+
+348
+00:25:40,830 --> 00:25:45,850
+summation xi j ej j من عند واحد لعند nأي ..أي ..أي
+
+349
+00:25:45,850 --> 00:25:48,910
+..أي ..أي function bounded linear .. أو linear
+
+350
+00:25:48,910 --> 00:25:52,030
+function هتكون bounded ومن ثم ال F of X هتكون
+
+351
+00:25:52,030 --> 00:25:55,590
+الصورة هذه إيش هذا اللي كاتبينه؟ هذا يمكن أنتم
+
+352
+00:25:55,590 --> 00:26:00,250
+مستغربينه والـ Gamma K هذه مين هي؟ F of EK و الـ
+
+353
+00:26:00,250 --> 00:26:04,190
+E1 و الـ E2 الـ EN is the basis for mean RN هذا
+
+354
+00:26:04,190 --> 00:26:12,410
+الكلام .. الكلام سهل إيش هو؟ احنا لو جينا أخدنالو
+
+355
+00:26:12,410 --> 00:26:17,510
+جينا أخدنا أي element في الارئان طبعا ال basis
+
+356
+00:26:17,510 --> 00:26:21,710
+تبعت الارئان عارفينها E1 E2 عند ال E1 وعارفينها E1
+
+357
+00:26:21,710 --> 00:26:25,250
+اللي هي بارعن واحد و الباقي صفار التانية 01 و
+
+358
+00:26:25,250 --> 00:26:31,230
+الباقي صفار ال A الأخيرة 00000 و آخر 111 هذه ال
+
+359
+00:26:31,230 --> 00:26:37,560
+basis تبعهايعني لو أخدنا أي X بتساوي XI واحد و XI
+
+360
+00:26:37,560 --> 00:26:41,720
+اتنين عند XI N هي في الواقع إيش هنعملها؟ بنقدر
+
+361
+00:26:41,720 --> 00:26:47,200
+نقولها بتساوي الصميجين XI I في EI I من عند واحد
+
+362
+00:26:47,200 --> 00:26:51,440
+لعند مين لعندها، مظبوط ولا لأ؟ لأن بيصير XI واحد
+
+363
+00:26:51,440 --> 00:26:55,500
+في هذه بتيجي XI واحد زاد XI اتنين في هذه اللي هي
+
+364
+00:26:55,500 --> 00:26:59,120
+بيصير يجي XI اتنين مجوحا كلهم بيطلع مين اللي هي
+
+365
+00:26:59,120 --> 00:27:04,860
+اللي فوقالان الـ TX اللي هي .. لو أخدنا F في الـ
+
+366
+00:27:04,860 --> 00:27:09,300
+RN برايم أو الـ RN ستار هذه Linear، مدام Linear،
+
+367
+00:27:09,300 --> 00:27:13,180
+إذا نحن نقول تصير F of X بتساوي الـ F هتدخل على
+
+368
+00:27:13,180 --> 00:27:15,980
+summation، هو Linear، ماشي الحالة بتساوي الـ
+
+369
+00:27:15,980 --> 00:27:20,420
+Summation إكساي I Scalar، بتطلع منها برا، وهذا
+
+370
+00:27:20,420 --> 00:27:25,320
+الـEI هو الـ Vector فبصير إكساي I في F of EI، I من
+
+371
+00:27:25,320 --> 00:27:30,870
+عند واحد لعند أنY ساوي summation XII وهذا يسميه
+
+372
+00:27:30,870 --> 00:27:36,570
+كمين أنا Gamma I I من عند واحد لعندنا إذن يا جماعة
+
+373
+00:27:36,570 --> 00:27:42,630
+أي X في داخل الـ RN اللي هو بقدر أكتب ال F of X
+
+374
+00:27:42,630 --> 00:27:46,850
+على الصورة هذه اللي هي في الواقع F of X بيساوي XII
+
+375
+00:27:46,850 --> 00:27:52,710
+في F of EI أو EJ وEJ سميتها مين أنا ال EK ال Gamma
+
+376
+00:27:52,710 --> 00:27:57,230
+K بيساوي F of EK اتفقنا؟ طيب
+
+377
+00:27:59,130 --> 00:28:04,850
+By cautious words and quality بدنا نحصل مالي نشوف
+
+378
+00:28:04,850 --> 00:28:08,410
+ايش اللي يدنيها طبعا انا وين رايح رايح بدي اثبتلكم
+
+379
+00:28:08,410 --> 00:28:12,130
+T انا اجيلكم T انا اجيلكم اقولكم ايش الـT هذي
+
+380
+00:28:12,130 --> 00:28:19,510
+نعرفها من RNبراي أو star لعين مين أرقن وبديها
+
+381
+00:28:19,510 --> 00:28:26,130
+تنجلي T لل F نورمها يساوي نورمين ال F لنشوف كيف
+
+382
+00:28:26,130 --> 00:28:29,330
+نحصل عليها هتلاقوا أسلوب الحل هنا واسلوب الحل في
+
+383
+00:28:29,330 --> 00:28:33,430
+اللي بعده واللي بعده روحه واحد مع تفاصيل كل واحدة
+
+384
+00:28:33,430 --> 00:28:39,090
+بما يناسبهاالان خدوا ال absolute value ل F of X هي
+
+385
+00:28:39,090 --> 00:28:42,250
+ال absolute value لهدي صح ولا لأ أكيد بال triangle
+
+386
+00:28:42,250 --> 00:28:45,550
+inequality أصغر أو ساوي الصممشي ل absolute values
+
+387
+00:28:45,550 --> 00:28:48,430
+مظبوط اللي هي ال absolute value الأولى في ال
+
+388
+00:28:48,430 --> 00:28:51,650
+absolute value الثانية هذه الان بال Schwarz
+
+389
+00:28:51,650 --> 00:28:55,510
+inequality Schwarz inequality أصغر أو ساوي اللي هو
+
+390
+00:28:55,510 --> 00:28:59,390
+الصممشي لهذا تربيع قص نص في الصممشي لهذا تربيع قص
+
+391
+00:28:59,390 --> 00:29:02,230
+إيش احفظوا هذه Schwarz inequality اللي استخدمناها
+
+392
+00:29:02,230 --> 00:29:07,020
+كثير اللي هي هذه في الواقع اللي هي مينهي نورم الـ
+
+393
+00:29:07,020 --> 00:29:11,160
+X الـ XI واحد، XI اتنين، XI N الـ N norm هي إيش
+
+394
+00:29:11,160 --> 00:29:13,940
+ماله؟ جدري التربيع إلى هذا تربيع، زاد هذا تربيع،
+
+395
+00:29:13,940 --> 00:29:17,360
+زاد هذا تربيع، زاد هذا تربيع، زاد هذا تربيع، زاد
+
+396
+00:29:17,360 --> 00:29:17,660
+هذا تربيع، زاد هذا تربيع، زاد هذا تربيع، زاد هذا
+
+397
+00:29:17,660 --> 00:29:18,040
+تربيع، زاد هذا تربيع، زاد هذا تربيع، زاد هذا
+
+398
+00:29:18,040 --> 00:29:21,200
+تربيع، زاد هذا تربيع، زاد هذا تربيع، زاد هذا
+
+399
+00:29:21,200 --> 00:29:24,520
+تربيع، زاد هذا تربيع، زاد هذا ترمدلص لو كتبنا مدلص
+
+400
+00:29:24,520 --> 00:29:28,080
+بيه عشان نحمي ظهرنا انها تكون ايش ما لها لو .. لو
+
+401
+00:29:28,080 --> 00:29:31,520
+.. لو real تنفع على ال real و لو مش real complex
+
+402
+00:29:31,520 --> 00:29:35,380
+عشان تصير ايه لإنه هذا أصغر أو شووي يعني order و
+
+403
+00:29:35,380 --> 00:29:37,960
+ال order مافيش في ال order في ال complex ال order
+
+404
+00:29:37,960 --> 00:29:43,600
+بين مين بين المدوسات تبعات ال complex فاهمينطيب،
+
+405
+00:29:43,600 --> 00:29:48,120
+هذا إيش اسمه؟ Normal X وهذه خلّوها لحالها زي هيك،
+
+406
+00:29:48,120 --> 00:29:54,880
+ماشي لحال إذا الأن لو أخدنا Normal F هو عبارة عن
+
+407
+00:29:54,880 --> 00:29:58,340
+الـ Supremum لـ Absolute Value of X X Element X لم
+
+408
+00:29:58,340 --> 00:30:02,310
+نورمات ليش بساويةواحد ماشي إذا أنا أخدت من هدولة
+
+409
+00:30:02,310 --> 00:30:06,270
+لنرمات اللي X بيساوي واحد صارت absolute value أصغر
+
+410
+00:30:06,270 --> 00:30:09,530
+أو يساوي هذه لحالة ماشي إذا صار الآن ال supremum
+
+411
+00:30:09,530 --> 00:30:14,870
+إلهم أصغر أو يساوي هذه إذا صار norm ال F بساوي
+
+412
+00:30:14,870 --> 00:30:18,310
+اللي هو ال supremum ده ما هو هذا ال F عبارة عن
+
+413
+00:30:18,310 --> 00:30:21,050
+bounded linear function اللي من وين جاية من R
+
+414
+00:30:21,050 --> 00:30:25,720
+النبرانو نورمها معرف عرفناها قبل شوية و خلاص
+
+415
+00:30:25,720 --> 00:30:31,480
+معرفناها سنة الان نشتغلوا كسلوك نورم ال F أصغر أو
+
+416
+00:30:31,480 --> 00:30:36,860
+ساوي اللي هو هذا الان however اطلعي لفوق however
+
+417
+00:30:36,860 --> 00:30:42,360
+الان نورم ال F أصلا اللي هو عبارة عن ال supremum
+
+418
+00:30:42,360 --> 00:30:47,520
+لهم مظبوط ال supremum لكل هذولإذا أكبر أو يساوي
+
+419
+00:30:47,520 --> 00:30:51,840
+واحدة منهم، مين اختارت بس اللي هي الـAlpha I أفه
+
+420
+00:30:51,840 --> 00:30:57,460
+في Alpha I على norm Alpha I معايا اللي هي بساوي
+
+421
+00:30:57,460 --> 00:31:01,320
+هذا ال absolute value إيها عبارة عن summation
+
+422
+00:31:01,320 --> 00:31:05,990
+Alpha I في Alpha I مشكلة تعريفاللي عرفناها قبل
+
+423
+00:31:05,990 --> 00:31:09,890
+شوية اللي هو Alpha A هذي لما كانت X بتساوي Xi 1,
+
+424
+00:31:09,970 --> 00:31:14,170
+Xi 2, Xi N كان ال F of X هو عبارة عن Xi I فهذه لما
+
+425
+00:31:14,170 --> 00:31:17,690
+ال X صارت Gamma 1, Gamma 2, Gamma N اللي هي هذه
+
+426
+00:31:17,690 --> 00:31:22,080
+بالظبط صارت عندي F of X بتساوي Gammaاللي مفهومين
+
+427
+00:31:22,080 --> 00:31:27,160
+في حالها صارت منها Gamma تربيع واضح إذا صار عندي
+
+428
+00:31:27,160 --> 00:31:32,700
+اللي هي ال F لأبسوليو دويله F of Xi F of Gamma I F
+
+429
+00:31:32,700 --> 00:31:36,840
+of Gamma I هذي اللي هي Gamma I هي اللي هي Gamma
+
+430
+00:31:36,840 --> 00:31:40,740
+الـ an interest Gamma 1 Gamma 2 اللي عند Gamma I
+
+431
+00:31:40,740 --> 00:31:43,900
+إيش بتساوي ال summation لGamma K تربيع K من واحد
+
+432
+00:31:43,900 --> 00:31:47,080
+لأن ده زي ما وضحت على norm هذي اللي هي تربيع أسمين
+
+433
+00:31:47,080 --> 00:31:50,660
+أص نصهذه أس واحد وهذه أس نص بيصير إيه شماله؟ له أس
+
+434
+00:31:50,660 --> 00:31:55,080
+نص يعني وكأني بقوله norm للأف مرة أكبر أو ساوي
+
+435
+00:31:55,080 --> 00:31:57,340
+وجاب الأف بتنا أف أصغر أو ساوي أو نور أو أصغر أو
+
+436
+00:31:57,340 --> 00:32:01,260
+ساوي إذا بالظبط ال norm للأف هو هذا وهذا هو أصلا
+
+437
+00:32:01,260 --> 00:32:04,820
+norm مين؟ norm لـGamma K لأن Gamma K اللي هي Gamma
+
+438
+00:32:04,820 --> 00:32:07,540
+1 Gamma 2 اللي عند Gamma E هي إيش N يعني N
+
+439
+00:32:07,540 --> 00:32:10,660
+interest يعني element في الـR إذا صارت norm للأف
+
+440
+00:32:10,660 --> 00:32:16,730
+بساوي النورم هذهلاحظوا أن هذه الـ Gamma 1 Gamma 2
+
+441
+00:32:16,730 --> 00:32:22,610
+Gamma N التي هي Gamma I Gamma 1 Gamma 2 لعند Gamma
+
+442
+00:32:22,610 --> 00:32:26,290
+N هي اللي سمناها .. طبعا جيبنا Gamma 1 احنا سمناها
+
+443
+00:32:26,290 --> 00:32:31,670
+لمين؟ اللي عندنا F of E واحد سمناها Gamma 1 و F of
+
+444
+00:32:31,670 --> 00:32:37,600
+E 2 Gamma 2 لعند F of E N واضحإن هدولة وين
+
+445
+00:32:37,600 --> 00:32:42,580
+موجودات؟ في الـ RN وانا دلوقتي إيش أعمل؟ أجيب
+
+446
+00:32:42,580 --> 00:32:52,170
+function T من RN' لعندمين RN ولاحظوا إنه هذهاللي
+
+447
+00:32:52,170 --> 00:32:56,490
+معتمدة أمين على الـF وكأن أنا جاية بفرش عشان
+
+448
+00:32:56,490 --> 00:33:02,630
+أقولكم خدوا الـT للـF اللي هي Rm' إيش بتساوي F of
+
+449
+00:33:02,630 --> 00:33:09,230
+E1, F of E2 لعند F of Em اللي هي في الواقع عبارة
+
+450
+00:33:09,230 --> 00:33:12,950
+عن Gamma 1, Gamma 2, Gamma N يعني ويساوي Gamma K
+
+451
+00:33:12,950 --> 00:33:16,760
+اللي هنا K من 1 لعند مين لعند أنتوهذا هو ان كله
+
+452
+00:33:16,760 --> 00:33:21,120
+موجود في الـ RN فالان انا رسيت على الأمر ان الـ
+
+453
+00:33:21,120 --> 00:33:26,080
+function المناسبة لتعريفها من RN' لعند RN اللي هي
+
+454
+00:33:26,080 --> 00:33:32,010
+عبارة عن مين TF بتساوياللي هي الـuntables F of EK
+
+455
+00:33:32,010 --> 00:33:36,830
+ويسوي اللي هي Gamma K لاحظوا أنا ضربت كل الصفيف في
+
+456
+00:33:36,830 --> 00:33:41,670
+حجر واحد ان هو من هذا التعريف لاجئت انه norm of TF
+
+457
+00:33:41,670 --> 00:33:45,490
+من اللي حكيته قبل شوية يسوي norm هذه اللي هو ايش
+
+458
+00:33:45,490 --> 00:33:50,350
+بيساوي norm ال Fماشي الحال هي أثبته نورم الـ F
+
+459
+00:33:50,350 --> 00:33:54,010
+بيساوي هذه وانا عرفت T of F بيساوي هذه إذا نورم
+
+460
+00:33:54,010 --> 00:33:58,070
+هذه بيساوي نورم هذه وهذه نورم ما هو مين نورم الـ F
+
+461
+00:33:58,070 --> 00:34:03,870
+من سابقا إذا صارت عندي T it preserve the norm يعني
+
+462
+00:34:03,870 --> 00:34:09,070
+بمعنى أخر الـ T صارت أيضا إيه شمالها is one to one
+
+463
+00:34:09,070 --> 00:34:17,660
+T is one to one الآن نثبت أنه اللي هوالـ T Linear
+
+464
+00:34:17,660 --> 00:34:21,380
+إثبات الـ T Linear سهلة خدوا الآن أي F وG وإن
+
+465
+00:34:21,380 --> 00:34:25,420
+موجودة في الـ R N' والـ Alpha Scalar اللي لعين T
+
+466
+00:34:25,420 --> 00:34:29,560
+of Alpha F زائد G إيش بتساوي؟ بساوي الـ Element
+
+467
+00:34:29,560 --> 00:34:34,660
+هذا عند E1 E2 E3 اللي عند E N بساوي Alpha F of G
+
+468
+00:34:34,660 --> 00:34:40,280
+of EK اللي هو الـ Untables اللي هي عند E1 عند E2
+
+469
+00:34:40,280 --> 00:34:48,130
+لعند E N ويساويالف اف of ek ب .. انترز هدوله ب ..
+
+470
+00:34:48,130 --> 00:34:53,190
+ب .. ب .. افصلها عن بعض زائد g of ek فاهمين اه؟
+
+471
+00:34:53,190 --> 00:34:58,750
+لإنه هذه عبارة عن الف زايد الف اف أعملكم إيه هان؟
+
+472
+00:34:58,750 --> 00:35:03,110
+عساس مايضلش حاجة مش موضحة
+
+473
+00:35:15,800 --> 00:35:23,000
+طيب يا جماعة هل جت T of Alpha F زائد G بساوي اللي
+
+474
+00:35:23,000 --> 00:35:28,660
+هو زي ما قلنا عبارة عن Alpha F زائد G of mean of E
+
+475
+00:35:28,660 --> 00:35:38,090
+K اللي هي عبارة عن Alpha F زائد G of E واحدألف أف
+
+476
+00:35:38,090 --> 00:35:44,850
+زائد G of E2 لعين ماصة الأخر واحدة ألف أف زائد G
+
+477
+00:35:44,850 --> 00:35:49,390
+of E N هاي ال untables تبعتنا اللي أنا دول بقدر
+
+478
+00:35:49,390 --> 00:35:53,590
+أفصلها لأن بعض هدوي بقدر أفصلها بيصير ألف أف of E1
+
+479
+00:35:53,590 --> 00:35:59,970
+دوالها ده عادي زائد G of E1وهذه αF of E2 زائد G of
+
+480
+00:35:59,970 --> 00:36:03,870
+E2 لعند ما أصل للأخيرة في الواقع هتصير هذه عبارة
+
+481
+00:36:03,870 --> 00:36:11,950
+عن αF of E1 زائد هذه G of E1 لعند ما أصل لآخر
+
+482
+00:36:11,950 --> 00:36:17,550
+واحدة αF of EN زائد G of EN هذه الآن الـ vector
+
+483
+00:36:17,550 --> 00:36:25,150
+buffers law تصير عند ألفة في F of E1 لعند F of EN
+
+484
+00:36:26,190 --> 00:36:35,490
+الزائد اللي هي G of E1 لعين G of EN هذا كله اللي
+
+485
+00:36:35,490 --> 00:36:42,630
+هو عبارة عن Alpha of اللي هي عبارة عن T أو Alpha
+
+486
+00:36:42,630 --> 00:36:47,280
+of T of FT of F هدولها دي مين جامعة واحد جامعة
+
+487
+00:36:47,280 --> 00:36:54,620
+اتنين زائد فاهمين زائد TJ او G اذا صار عندي اللي
+
+488
+00:36:54,620 --> 00:37:00,280
+هو T is linear طيب اخر رقم اللي انا صار عندي T
+
+489
+00:37:00,280 --> 00:37:04,540
+linear و one to one و preserve the norm اذا دل
+
+490
+00:37:04,540 --> 00:37:08,840
+عندي مين اللي قلتهالـ N لونته سهل أموره هنا لأنه
+
+491
+00:37:08,840 --> 00:37:12,320
+finite dimensional أنا الـ N ال dimension للـ R N
+
+492
+00:37:12,320 --> 00:37:17,660
+إيش بيساوي ال dimension للـ R N star و إيش بيساوي
+
+493
+00:37:17,660 --> 00:37:22,020
+هذا التنين بيساوي N إذا على طول T و T كانت linear
+
+494
+00:37:22,020 --> 00:37:26,520
+و one to one إذا T is onto إيش اللي بقوله هذا عندى
+
+495
+00:37:34,360 --> 00:37:44,000
+عندى T من RN أبرايم أو star لعند مين RN ماشي الان
+
+496
+00:37:44,000 --> 00:37:48,000
+ال T هذي one to one اللي احنا قولنا ماشي الحال هذي
+
+497
+00:37:48,000 --> 00:37:56,240
+RN أبرايم و هذي RN الان كل واحد منهم أحلى واحدكله،
+
+498
+00:37:56,240 --> 00:38:00,180
+الـ N هنا يمكن فيه زيادة، يمكن، يمكن، احنا مش
+
+499
+00:38:00,180 --> 00:38:03,220
+عارفين فيه زيادة، اهو مش هيكون فيه زيادة هذا لو في
+
+500
+00:38:03,220 --> 00:38:08,100
+one to one لحالها، بيكون ال dimension للـ R N
+
+501
+00:38:08,100 --> 00:38:12,740
+prime أظهر أو يساوي ال dimension لمين؟ للـ R N،
+
+502
+00:38:12,740 --> 00:38:17,400
+ماشي الحال، هذا في الوضع الطبيعي الـ N، و هذا هو
+
+503
+00:38:17,400 --> 00:38:22,880
+نفسه عبارة عن ال dimension لمين؟ لل T of R N prime
+
+504
+00:38:24,350 --> 00:38:28,310
+ولا صورته ولا صورته لكن طبعا ال dimension لهذا و
+
+505
+00:38:28,310 --> 00:38:31,590
+ال dimension لهذا أشماله متساوي إذا ال dimension
+
+506
+00:38:31,590 --> 00:38:35,990
+للـ T of RN برايم هو نفس ال dimension للـ RN وهذا
+
+507
+00:38:35,990 --> 00:38:40,830
+جزء .. وهذا جزء بالمئة من هذا هذا جزء منه و ال
+
+508
+00:38:40,830 --> 00:38:45,730
+dimension له هو .. إذا صار عند ال .. ال T RN برايم
+
+509
+00:38:45,730 --> 00:38:51,680
+هو مين نفسه الـ RN إذا صارت عبارة عن أنتهاللي صار
+
+510
+00:38:51,680 --> 00:38:55,380
+اللي هو الـ Range كله RN إذا صارت عبارة عن Onetwo
+
+511
+00:38:55,380 --> 00:39:02,660
+واضحة أه؟ يالله اللي بعيدها The dual space of L1
+
+512
+00:39:02,660 --> 00:39:06,120
+is mean is L infinity وبده أسرع هال gate عساس إن
+
+513
+00:39:06,120 --> 00:39:09,780
+الفكرة تقريبا اللي هي مكررة مع بعض اللي هي إيش
+
+514
+00:39:09,780 --> 00:39:15,500
+الشغلات اللي خاصة بالspace تبع L1 و L infinityأحنا
+
+515
+00:39:15,500 --> 00:39:19,620
+عارفين عناصر الألوان الألوان هي العناصر اللي هي
+
+516
+00:39:19,620 --> 00:39:26,340
+sequences اللي هو XI I حيث I من واحد لما لنا طبعا
+
+517
+00:39:26,340 --> 00:39:30,260
+حيث summation XI I I من واحد إلى ما لنا نهاية is
+
+518
+00:39:30,260 --> 00:39:36,440
+finite لأنه عندي ال B واحد طيب لأن ال N infinity
+
+519
+00:39:36,440 --> 00:39:42,790
+is bounded ال supreme مابقاش مهلهأه فاهم معايا أه
+
+520
+00:39:42,790 --> 00:39:47,750
+هذا أس واحد أس واحد على واحد هاي norm هه معايا
+
+521
+00:39:47,750 --> 00:39:51,530
+طبعا زمان أه الآن ال norm اللي في حالتي دلوقتي ال
+
+522
+00:39:51,530 --> 00:39:56,830
+infinity norm هذا بساوي ال supremum لل xi I over I
+
+523
+00:39:56,830 --> 00:39:59,530
+اللي هي the space of all bounded اللي هو أيش
+
+524
+00:39:59,530 --> 00:40:03,130
+sequences طيب إذا هاي ال spaces عشان نذكركوا فيهم
+
+525
+00:40:05,280 --> 00:40:09,400
+الان عندى احنا أثبتنا انه الـ EK عبارة عن shoulder
+
+526
+00:40:09,400 --> 00:40:11,960
+bases ده مين للأل واحد و .. و .. و .. و .. و .. و
+
+527
+00:40:11,960 --> 00:40:12,060
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+528
+00:40:12,060 --> 00:40:12,280
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+529
+00:40:12,280 --> 00:40:12,740
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+530
+00:40:12,740 --> 00:40:13,440
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+531
+00:40:13,440 --> 00:40:13,580
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+532
+00:40:13,580 --> 00:40:16,640
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+533
+00:40:16,640 --> 00:40:16,660
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+534
+00:40:16,660 --> 00:40:18,100
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+535
+00:40:18,100 --> 00:40:22,680
+.. و .. و .. و .. و .. و .. و .. و ..
+
+536
+00:40:22,680 --> 00:40:26,600
+و .. و
+
+537
+00:40:34,620 --> 00:40:38,980
+then أي X في الـ L1 فيه إلها unique representation
+
+538
+00:40:38,980 --> 00:40:44,940
+الـ X أيش بيساوي؟ summation Xik Ek ماشي الحال مدام
+
+539
+00:40:44,940 --> 00:40:48,600
+إلها ال unique representation هذه الآن شوفوا كيف
+
+540
+00:40:48,600 --> 00:40:52,240
+بتدركي بإيش مشابه لللي قبل بشوية خدوا أي أفوان
+
+541
+00:40:52,240 --> 00:40:56,240
+موجودة في الـ L1' أنا H بمين رايح؟ لنتبط إن الدول
+
+542
+00:40:56,240 --> 00:41:00,000
+space لL1 هو L infinity يعني بمعنى آخر
+
+543
+00:41:07,320 --> 00:41:14,720
+بالدلاجة T من الـ one prime لعند ال infinity تقول
+
+544
+00:41:14,720 --> 00:41:17,700
+one to one و one to one و الاخر كل القصة بتاخد
+
+545
+00:41:17,700 --> 00:41:23,690
+الان T of Fوأقولكم إيش بتساوي أرميها وين؟ في الـL
+
+546
+00:41:23,690 --> 00:41:26,270
+infinity أشوف element مناسب يوديها في الـL
+
+547
+00:41:26,270 --> 00:41:31,430
+infinity المعهد ده زمسي الأولاني المفتاح الحالي
+
+548
+00:41:31,430 --> 00:41:38,310
+اللي هو مين؟ اللي هي F of E K خدوا
+
+549
+00:41:38,310 --> 00:41:41,650
+F وين موجودة؟ في الـL1' اللي هو في الـdual space
+
+550
+00:41:41,650 --> 00:41:44,470
+يعني bounded linear functional اللي هن consider
+
+551
+00:41:44,470 --> 00:41:49,530
+any F element in L1'فـ Dual space of L1 هذا طيب
+
+552
+00:41:49,530 --> 00:41:54,470
+since F is linear and bounded إذن ال F of X هتساوي
+
+553
+00:41:54,470 --> 00:41:59,870
+اللي هو ال summation Xik Ek اللي هي حيصيرها عبارة
+
+554
+00:41:59,870 --> 00:42:03,770
+عن Xik زي ما هي و هذه F of Ek اللي هي Gamma K زي
+
+555
+00:42:03,770 --> 00:42:06,910
+اللي قبل بشوية بالظبط بس الآن اللي بدمني هذا
+
+556
+00:42:06,910 --> 00:42:11,440
+السلوك يظبط أن F is continuousمش bounded linear
+
+557
+00:42:11,440 --> 00:42:14,920
+functional هي continuous وقلنا ال bounded مع ال
+
+558
+00:42:14,920 --> 00:42:17,160
+linear أكيد إيش مالها بتعطينا ال continuity و
+
+559
+00:42:17,160 --> 00:42:23,640
+العكس صحيح طيب بالنسبة لل boundedness طيب عند x
+
+560
+00:42:23,640 --> 00:42:29,560
+بتساوي summation إيش ماخده xi k ek كامل عند واحد
+
+561
+00:42:29,560 --> 00:42:34,840
+لما لنهاية خدوا n arbitrary ماشي الحال الان خدوا f
+
+562
+00:42:36,070 --> 00:42:38,890
+أو ليش خلاص ماديش أخد الاربطانية ماديش أخد اللي
+
+563
+00:42:38,890 --> 00:42:44,230
+عندك خده الأن f of x بساوي الأن هذا في الواقع هو
+
+564
+00:42:44,230 --> 00:42:49,290
+إيش limit هذا عبارة عن limit limit as n غصه
+
+565
+00:42:49,290 --> 00:42:55,110
+infinity لصماش xik ek k من عند واحد لعند مين لعندك
+
+566
+00:42:55,390 --> 00:43:01,130
+وبما أن الـ F هو continuous فالـ F في الـ limit
+
+567
+00:43:01,130 --> 00:43:05,910
+يساوي limit الـ F فبصير على طول الـ limit تتجاوزها
+
+568
+00:43:05,910 --> 00:43:09,530
+الـ F و تدخل داخلها لأن الـ F أشمالها is
+
+569
+00:43:09,530 --> 00:43:17,430
+continuous بصير Xik F of Ek Xik K من عند 1 لعند N
+
+570
+00:43:17,430 --> 00:43:22,050
+as N goes to infinity ويساوي الـ limit as N goes
+
+571
+00:43:22,050 --> 00:43:27,110
+to infinityالـ Summation هذي F is linear مهيبون؟
+
+572
+00:43:27,110 --> 00:43:29,990
+إذا .. إذا بتقدر ال scalar بتطلع برا هذا vector دي
+
+573
+00:43:29,990 --> 00:43:34,610
+ببالكم ال E K ال scalar بتطلع برا بصير X I K F of
+
+574
+00:43:34,610 --> 00:43:40,170
+E K .. K من عند 1 لعند Nهذا الـ N as N goes to
+
+575
+00:43:40,170 --> 00:43:42,770
+infinity هذا اللي هو sequence of partial sums
+
+576
+00:43:42,770 --> 00:43:45,290
+وكأنها و ال series converges اذا ايش بيساوي ال
+
+577
+00:43:45,290 --> 00:43:50,590
+summation X I K F of E K كمن عند واحد لعند ن إذا
+
+578
+00:43:50,590 --> 00:43:57,330
+فعلا كلامه صحيح أنه بقدر أقول since F is linear
+
+579
+00:43:57,330 --> 00:43:59,930
+and bounded then F of X بيساوي ال summation X I K
+
+580
+00:43:59,930 --> 00:44:06,200
+Gamma K كمن عند واحد إلى مين إلى ما لا نهايةوها دي
+
+581
+00:44:06,200 --> 00:44:11,120
+سموها الـ Gamma K اللي هي main عبارة عن F of E K
+
+582
+00:44:11,120 --> 00:44:14,880
+وها دي اللي هي تلاتة وها دي are uniquely
+
+583
+00:44:14,880 --> 00:44:19,800
+determined by main by F يعني الجامعة واحد من F of
+
+584
+00:44:19,800 --> 00:44:22,340
+E واحد بالظبط بسوء الجامعة واحد و F of E اتنين
+
+585
+00:44:22,340 --> 00:44:26,360
+بسوء E اتنين وهذا اللي هو ال determination واحد
+
+586
+00:44:26,920 --> 00:44:31,900
+الان لو أخدنا نورم ال EK بتعرف أشهر بتساوي واحد
+
+587
+00:44:31,900 --> 00:44:35,160
+عارفين ليش؟ اللي هو عبارة عن ال summation لكل
+
+588
+00:44:35,160 --> 00:44:38,520
+واحدة من واحد إلى مال نهاية وفي شهر واحدة و الباقى
+
+589
+00:44:38,520 --> 00:44:42,340
+أسفل لذا ال norm كل واحدة أشهر بتساوي واحد وكمان
+
+590
+00:44:42,340 --> 00:44:46,280
+قاعد بحضر لل .. حضر .. ده اللي عملت .. عملت قبل
+
+591
+00:44:46,280 --> 00:44:49,940
+شوية ال absolute value لـ Gamma K بساوي ال
+
+592
+00:44:49,940 --> 00:44:54,050
+absolute value لمين؟ لل F of EKوهذه أصغر يشاوى F
+
+593
+00:44:54,050 --> 00:44:57,990
+is linear أو bounded أصغر يشاوى Normal F في Normal
+
+594
+00:44:57,990 --> 00:45:02,450
+E K وهذه الواحد إذا بيصير إشماله Normal F يعني
+
+595
+00:45:02,450 --> 00:45:06,310
+حصلت ال absolute value أو المدلس للجامعة K أكبر
+
+596
+00:45:06,310 --> 00:45:11,440
+أصغر يشاوى Normal F من جهة أخرى Normal Fلسه
+
+597
+00:45:11,440 --> 00:45:13,780
+ماخلصناش من جواهر لما خلّنا بعدين من جواهر لأن
+
+598
+00:45:13,780 --> 00:45:17,780
+norm ل F صار أكبر و ساوي هذه الكلام لكل K إذا أكيد
+
+599
+00:45:17,780 --> 00:45:20,840
+norm ل F أكبر و ساوي ال supermom لها أكيد لأن هذي
+
+600
+00:45:20,840 --> 00:45:25,000
+صارت أشمالها upper bound لها أه هذي صارت هذه ال
+
+601
+00:45:25,000 --> 00:45:27,860
+sequence ألف واحد ألف اتنين جام واحد جام اتنين جام
+
+602
+00:45:27,860 --> 00:45:30,700
+اتلاته صارت bounded sequence bounded by مين؟ by
+
+603
+00:45:30,700 --> 00:45:33,920
+اللي هو norm ل F إذا صار عند ال supermom أصغر و
+
+604
+00:45:33,920 --> 00:45:37,060
+ساوي هذه إذا صار عند ال supermom لهذه أصغر و ساوي
+
+605
+00:45:37,060 --> 00:45:42,480
+هذه لاحظوا أنا مدام صارت هذه boundedSequence إذا
+
+606
+00:45:42,480 --> 00:45:47,920
+صارت وين بدها تقعد ال Infinity فصار منطقي إن أعرف
+
+607
+00:45:47,920 --> 00:45:51,760
+T of F بساو مين F of EK لإنها صارت bounded
+
+608
+00:45:51,760 --> 00:45:54,700
+automatic ناشي إذا هذا أول واحدة أحطوه على الجهة
+
+609
+00:45:56,380 --> 00:45:59,420
+Hence Gamma K وين موجودة في الـ L Infinity وهي
+
+610
+00:45:59,420 --> 00:46:04,240
+نحطناها في أربعة الآن من تلاتة خدوا ال absolute
+
+611
+00:46:04,240 --> 00:46:08,640
+value ل F of X اللي هي بالساوي ال absolute value
+
+612
+00:46:08,640 --> 00:46:11,740
+لهدي أصغر أو ساوي ال triangle inequality هدي كلمة
+
+613
+00:46:11,740 --> 00:46:15,180
+مقرر وهدي بالشوارز .. ال .. ال .. ال .. ال .. ال
+
+614
+00:46:15,180 --> 00:46:19,440
+.. لأ مش بالشوارز هدي الآن ال .. ال .. هدي في هدي
+
+615
+00:46:19,950 --> 00:46:23,570
+أكيد الـ Supremum لهدولة هكون أكبر من كل واحدة من
+
+616
+00:46:23,570 --> 00:46:27,790
+هدول إذا الـ summation في هذه أكبر أصغر أو شوية
+
+617
+00:46:27,790 --> 00:46:30,910
+الـ summation هذا زي ما هو و حطيت مكان هدولة الـ
+
+618
+00:46:30,910 --> 00:46:33,670
+Supremum الكبيرة اللي موجود الـ Supremum اتبتت فوق
+
+619
+00:46:33,670 --> 00:46:36,910
+أنه موجود إذا صار عنده اللي هو الـ summation في
+
+620
+00:46:36,910 --> 00:46:40,330
+مين اللي هو في هذا اللي هو بمعنى آخر هذا هو عبارة
+
+621
+00:46:40,330 --> 00:46:44,470
+صارقيمة عددية بفلحها برا الـ summation اللي هو
+
+622
+00:46:44,470 --> 00:46:48,990
+اسمه norm الـ X في مين؟ في الـ supremum آسف هذا
+
+623
+00:46:48,990 --> 00:46:51,770
+اسمه norm الـ X وهذا اسمه الـ supremum بعد شوية
+
+624
+00:46:51,770 --> 00:46:57,450
+هيصير norm الجامعة Iلأن نورم الـ L infinity هو الـ
+
+625
+00:46:57,450 --> 00:47:02,930
+Supremum إذا صار عندي نورم الـ F بساوي اللي هو
+
+626
+00:47:02,930 --> 00:47:07,330
+نورم هذه من الجهتين لإن هي عندي اللي هو نورم الـ F
+
+627
+00:47:07,330 --> 00:47:10,770
+وين وين وين وين نورم الـ F نورم الـ Absolute value
+
+628
+00:47:10,770 --> 00:47:15,750
+لـ F أظهر أوي بساوي هذه في هذه لما أخد على اللي هو
+
+629
+00:47:15,750 --> 00:47:18,630
+نورم الـ Xات بساوي واحد بيصير نورم الـ F أظهر أوي
+
+630
+00:47:18,630 --> 00:47:22,190
+بساوي مين الـ Supremumمكرر عشان هيك بس لان انا صار
+
+631
+00:47:22,190 --> 00:47:25,170
+عندى هدى على هدى اللى هو ال supermomal هنايه اصغر
+
+632
+00:47:25,170 --> 00:47:28,130
+بشوة هذا العدد الثابت هو يساوي اللى هو مين هذا
+
+633
+00:47:28,130 --> 00:47:32,530
+قولنا عنه normal gamma k i الان هل جئت هدى و اللى
+
+634
+00:47:32,530 --> 00:47:36,930
+خليناها في الذاكرة مع بعض طلع عندى اه هي ال normal
+
+635
+00:47:36,930 --> 00:47:40,990
+F أكبر شوة هدىنورم الـ F أكبر ساوي ونورم الـ F
+
+636
+00:47:40,990 --> 00:47:44,310
+أكبر ساوي إذا هو بيساوي إذا صار عندي وينها نورم
+
+637
+00:47:44,310 --> 00:47:46,190
+الـ F بتساوي الـ Supremum اللي هو بيساوي هذا
+
+638
+00:47:46,190 --> 00:47:51,510
+النورم إذا الدنيا صارت الآن عندي بنيحة بقدر أتجرأ
+
+639
+00:47:51,510 --> 00:47:56,470
+و أقول اطلع لفوق و أقول Now define T من L1 to L'
+
+640
+00:47:56,470 --> 00:48:02,180
+حضرت تماما لعند L infinity by T of Fبترميها في الـ
+
+641
+00:48:02,180 --> 00:48:05,660
+F of E K اللي هي Gamma K وصار عندي الأن من اللي
+
+642
+00:48:05,660 --> 00:48:09,420
+قبل شوية norm T F بسوء norm هذي اللي هو norm F إذا
+
+643
+00:48:09,420 --> 00:48:13,200
+معناته أن T preserve the norm ومن ثم صارت إيه
+
+644
+00:48:13,200 --> 00:48:18,480
+الشمالة T is one to one دل عندي اللي هو Lينيار سهل
+
+645
+00:48:18,480 --> 00:48:21,860
+زي اللينيار الأولاني ودل عندي إيش أثبت إنها أنتوا
+
+646
+00:48:21,860 --> 00:48:25,440
+خلوكوا معانا نثبت أنتوا لأن هلجيت اللي أنتوا هو
+
+647
+00:48:25,440 --> 00:48:30,340
+اللي شوية بده ياخد معنا شوية حكم إن شاء الله بطولش
+
+648
+00:48:32,930 --> 00:48:36,630
+زي ما بنثبت On To عادةً بناخد element هنا
+
+649
+00:48:36,630 --> 00:48:41,470
+arbitrary وبنجيله أصل هنا وبنكون خلصنا الان هنا
+
+650
+00:48:41,470 --> 00:48:45,830
+element اللي هو اللي بناخده هنا بدعرف من خلال ال
+
+651
+00:48:45,830 --> 00:48:51,610
+function هنا بتكون بتروح بنقدر نرسلها إليه تشوف
+
+652
+00:48:51,610 --> 00:48:56,870
+كدهنفس النهج اللي .. عن النهج اللي حكيناه قبل و
+
+653
+00:48:56,870 --> 00:49:01,150
+شوية ولكن بما يناسب الرجول on the other hand for
+
+654
+00:49:01,150 --> 00:49:05,990
+any B بيساو بي ك element in L infinity we can find
+
+655
+00:49:05,990 --> 00:49:09,030
+G element in L one prime by the following بيجب
+
+656
+00:49:09,030 --> 00:49:13,890
+نلاقي G في ال L one prime بحيث انه TG سو مين اللي
+
+657
+00:49:13,890 --> 00:49:20,020
+بتتهب فيها هذه شوفوا كيفDefine D من ال1 لعند الـK
+
+658
+00:49:20,020 --> 00:49:23,220
+عشان boundedly non-functional ايش اللي بدنا نلاقيه
+
+659
+00:49:23,220 --> 00:49:26,860
+هنا بدنا نلاقي boundedly non-functional تناسب انه
+
+660
+00:49:26,860 --> 00:49:32,220
+الـTD الـTD يطلع هذا الكمبليكس أوريا مش فارقة اللي
+
+661
+00:49:32,220 --> 00:49:36,410
+هو الـKباي، أيش بدي أعرفها؟ أكيد هذه اللي بين
+
+662
+00:49:36,410 --> 00:49:42,330
+إيديا، اللي بين إيديا اللي بين إيديا، اللي بين
+
+663
+00:49:42,330 --> 00:49:45,650
+إيديا
+
+664
+00:49:45,650 --> 00:49:46,550
+اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي
+
+665
+00:49:46,550 --> 00:49:46,650
+إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا
+
+666
+00:49:46,650 --> 00:49:46,690
+اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي
+
+667
+00:49:46,690 --> 00:49:47,550
+بين إيديا اللي بين إيديا اللي بين إيديا اللي بين
+
+668
+00:49:47,550 --> 00:49:49,310
+إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا
+
+669
+00:49:49,310 --> 00:49:57,230
+اللي بين إيديا اللي بين إيديا
+
+670
+00:49:57,230 --> 00:50:01,850
+اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي
+
+671
+00:50:01,850 --> 00:50:05,690
+بيناللي هي ال .. ال .. ال .. ال .. دربت كل entry
+
+672
+00:50:05,690 --> 00:50:09,430
+من تبع الـ X اللي بيدوجدلها صورتها مع مين؟ مع الـ
+
+673
+00:50:09,430 --> 00:50:13,850
+BK اللي أعطانيها بين إيديها هذا أنا بقول الـ G of
+
+674
+00:50:13,850 --> 00:50:17,990
+X هي التي ستؤدى الغرض تنشوف كيف ده تؤدى الغرض
+
+675
+00:50:18,720 --> 00:50:21,140
+احسبني الآن أول حاجة بدأت بتنهيبها و بدليها
+
+676
+00:50:21,140 --> 00:50:25,300
+functional عشان تكون هنا فأخد ال absolute value لل
+
+677
+00:50:25,300 --> 00:50:29,320
+GeoFix ايش بتساوي ال absolute value لهذه أصغر أو
+
+678
+00:50:29,320 --> 00:50:31,100
+ساوي ال absolute value في ال absolute value صارت
+
+679
+00:50:31,100 --> 00:50:35,370
+محفوظة هذه بال triangle inequalityهذه نفسها أظهر
+
+680
+00:50:35,370 --> 00:50:37,990
+يساوي، هذه في الـ Supremum تبعتها، برضه محفوظة
+
+681
+00:50:37,990 --> 00:50:42,190
+الآن هذه اللي عبارة عن مين؟ في الـ L1، إذا Normal
+
+682
+00:50:42,190 --> 00:50:47,270
+X هذا، ماشي، في Supremum لـ Bi، هذا is finite،
+
+683
+00:50:47,270 --> 00:50:50,150
+ماشي الحال، Supremum لـ Bj، عارفين ليش finite؟ لأن
+
+684
+00:50:50,150 --> 00:50:54,600
+الـ Bq الموجودة في الـ Infinityإذا صار عند الـ
+
+685
+00:50:54,600 --> 00:50:57,220
+absolute value of g of x أصغر سواء نورم الـ x في
+
+686
+00:50:57,220 --> 00:51:02,520
+سم عدد إذا صارت bounded g طيب خلصنا بأن الـ g تكون
+
+687
+00:51:02,520 --> 00:51:06,020
+أشمالها bounded اللي الآن بدنا ناخد أنها نثبت أنها
+
+688
+00:51:06,020 --> 00:51:10,580
+Linear اللي Linearity سهلة خد أي x بسوء xy k و أي
+
+689
+00:51:10,580 --> 00:51:14,500
+y بسوء λمضا k element in L1 وان scalar Alpha
+
+690
+00:51:14,500 --> 00:51:17,720
+وحسبلي الآن g of Alpha x زائد y بناء على التعريف
+
+691
+00:51:17,720 --> 00:51:21,820
+اللي عرفناه هنااللي هو بيكون اللي هو الـElement أو
+
+692
+00:51:21,820 --> 00:51:25,260
+الـEntry تبع الـElement مضروف في الـPK الـEntry
+
+693
+00:51:25,260 --> 00:51:29,040
+تبعها دولة Alpha Xi K تبعها دي وGamma Lambda K
+
+694
+00:51:29,040 --> 00:51:31,920
+تبعها دي فتكون هذا كله هو تبعها هذه الـEntry
+
+695
+00:51:31,920 --> 00:51:37,220
+تبعها، فاهمين؟ في الـBeta K، هذا بتوزع، بتوزع،
+
+696
+00:51:37,220 --> 00:51:40,900
+أعداد عادية، Complex Velarial اللي هي بيصير، اللي
+
+697
+00:51:40,900 --> 00:51:46,360
+هي .. هذا طبعا فكتور، Gammaوهنا برضه اللي هو
+
+698
+00:51:46,360 --> 00:51:51,600
+أعداده بيقومها Alpha K في هذه زاد هذه في هذه ال
+
+699
+00:51:51,600 --> 00:51:56,800
+Alpha بتطلع برا Scale up لأن بيصير Alpha في ال
+
+700
+00:51:56,800 --> 00:52:00,140
+summation في ال summation هذا ال summation هو ال G
+
+701
+00:52:00,140 --> 00:52:05,080
+تبع من؟ تبع ال X وهذا ال G تبع من؟ ال Y فصار ال G
+
+702
+00:52:05,080 --> 00:52:10,620
+إشمالها is linear إذا ال G و N موجودة في ال L1
+
+703
+00:52:10,620 --> 00:52:16,990
+إبراينHowever ال X can be written as .. من الأصل
+
+704
+00:52:16,990 --> 00:52:22,440
+هو مش ال X في الألوانواللي هذا shoulder bases إذاً
+
+705
+00:52:22,440 --> 00:52:24,820
+الـ X بنقدر نكتبها على صورة summation xik او ek
+
+706
+00:52:24,820 --> 00:52:28,680
+كامل عند واحد لعند مين لعند infinity إذاً الـ G of
+
+707
+00:52:28,680 --> 00:52:32,040
+X مذا مات الـ G linear إذا أكيد الـ G all bounded
+
+708
+00:52:32,040 --> 00:52:34,920
+أثبتنا إنها Linear و Bounded خلاص ألقيت أتجرأنا إن
+
+709
+00:52:34,920 --> 00:52:37,520
+أقول G of X بيساوي G of هذا و أدخل جوه ال limit و
+
+710
+00:52:37,520 --> 00:52:40,640
+أطلع بره ال limit و أوزع لإن الـ G أشمالها سعارات
+
+711
+00:52:40,640 --> 00:52:43,940
+Linear إذا صار عند الـ G of X بيساوي summation xik
+
+712
+00:52:43,940 --> 00:52:47,380
+G of ek إذاً الآن TG
+
+713
+00:52:49,430 --> 00:52:54,950
+أو TG احنا كيف عرفنا الـ TG هو عبارة عن أو TF
+
+714
+00:52:54,950 --> 00:52:59,430
+عبارة عن الـ F عند مين اللي هي ال .. ال .. ال ..
+
+715
+00:52:59,430 --> 00:53:03,730
+ال .. ال sequence اللي عناصرها مكونات من ال F عند
+
+716
+00:53:03,730 --> 00:53:08,490
+ال E1 عند ال E2 عند ال E3 عند ال E4 TG عبارة عن ال
+
+717
+00:53:08,490 --> 00:53:13,340
+G عند ال E1 عند ال E2 عند ال E3T H H عند الواحد H
+
+718
+00:53:13,340 --> 00:53:17,500
+عند E اتنين H عند E تلاتة واضح كيف عرفنا إذا الـ T
+
+719
+00:53:17,500 --> 00:53:21,740
+G حسب اللي عندي هنا هتكون G of E واحد D of E اتنين
+
+720
+00:53:21,740 --> 00:53:26,680
+اللي هي G of E كتر لكن الـ Representation هذا هذا
+
+721
+00:53:26,680 --> 00:53:30,040
+الـ Representation is unique لأن عندي هذه الـ
+
+722
+00:53:30,040 --> 00:53:33,620
+Representation قبل بشوية حصلت عليه الـ G of X من
+
+723
+00:53:33,620 --> 00:53:36,660
+فوق هي الـ G of X اللي هو بساوة summation X I K
+
+724
+00:53:36,660 --> 00:53:41,370
+Beta Kواللي قبل بشوية بسوّك Psi K في G of EK و ال
+
+725
+00:53:41,370 --> 00:53:44,110
+representation واحد إذا لازم تطلع البيئة و لا
+
+726
+00:53:44,110 --> 00:53:48,850
+بيبطّت ال .. بيصير ال Beta .. ال Beta K إيش؟ هي ال
+
+727
+00:53:48,850 --> 00:53:55,620
+G of EK إذا صار عند ال ..انزل صار عندى الـ TG
+
+728
+00:53:55,620 --> 00:54:00,300
+بساوة اللى هو G of AK اللى هى من ال representation
+
+729
+00:54:00,300 --> 00:54:05,000
+تبع الـ G of X بساوة Xi K G of AK ويساوة Xi K في
+
+730
+00:54:05,000 --> 00:54:09,220
+Beta K هو عبارة عن الـ G of AK هي الـ Beta K إذا
+
+731
+00:54:09,220 --> 00:54:13,200
+الـ TG بساوة الـ Beta K اللى بدأت فيه لجيتله G
+
+732
+00:54:13,200 --> 00:54:17,880
+بحيث انه TG بساوة هذا إذا صارت الـ T is onto والآن
+
+733
+00:54:17,880 --> 00:54:22,760
+الخطوة الأخيرةT is linear و الـ Linearity زي اللي
+
+734
+00:54:22,760 --> 00:54:26,880
+قبل بالظبط على السريع Now for any F و G element in
+
+735
+00:54:26,880 --> 00:54:31,220
+L one prime and any scalar Alpha T of Alpha F زائد
+
+736
+00:54:31,220 --> 00:54:34,320
+G ايش بتساوي زي اللي قبل شوية عملتها في الاران
+
+737
+00:54:34,320 --> 00:54:37,920
+Alpha F زائد G عند مين عند ال EK اللي انت ريها ده
+
+738
+00:54:37,920 --> 00:54:41,990
+إلى مالا نهاية طبعا مش زي الأولى ال finiteبنفس
+
+739
+00:54:41,990 --> 00:54:45,030
+الأسلوب بيطلع الـ α F of EK زي الـ G of EK هو
+
+740
+00:54:45,030 --> 00:54:48,270
+يساوي Alpha F Alpha TF زي الـ TG معناته صار الـ T
+
+741
+00:54:48,270 --> 00:54:52,250
+is linear و في الأول bounded و في الأول اللي هو
+
+742
+00:54:52,250 --> 00:54:56,710
+قولنا اللي هو preserve the norm و في الأول كمان
+
+743
+00:54:56,710 --> 00:54:59,370
+اللي هو one to one onto then صار ال T is an
+
+744
+00:54:59,370 --> 00:55:02,250
+isomorphism و معناته أنه صار عند الألوان is the
+
+745
+00:55:02,250 --> 00:55:04,170
+dual space of ال infinity
+
+746
+00:55:08,240 --> 00:55:18,720
+اللي بعده أخر مثال ربنا بعيننا الان
+
+747
+00:55:18,720 --> 00:55:24,900
+space LB the dual space of LB is LQ ال dual space
+
+748
+00:55:24,900 --> 00:55:27,880
+ل LB is LQ where B أكبر من واحد وأصغر من infinity
+
+749
+00:55:27,880 --> 00:55:31,640
+and Q is the conjugate of mean of B إيش ال
+
+750
+00:55:31,640 --> 00:55:35,020
+conjugation هذا الترافق الترافق على أساس واحد على
+
+751
+00:55:35,020 --> 00:55:39,650
+بي زاد واحد على Q بساوي واحدإذا عشان أثبت أن الـ
+
+752
+00:55:39,650 --> 00:55:43,450
+Dual Space لهذا هو هذا بدي ألاجي function من الـ
+
+753
+00:55:43,450 --> 00:55:48,650
+B' لعند الـ LB one to one أنتوا حاجيها اللي هي
+
+754
+00:55:48,650 --> 00:55:53,530
+بنفس الأسلوب هيختلف بس البرهان خلّيني أقول بما
+
+755
+00:55:53,530 --> 00:55:57,030
+يتعلق بس بالعناصر لهان و لهان شوية هنا فيه تكيات
+
+756
+00:55:57,030 --> 00:56:02,210
+بسيطة بالإضافة لإن أنتوا بدوا شوية فكرة هيكة شوية
+
+757
+00:56:02,210 --> 00:56:07,850
+لكن منيحة و بتمشي عشان ذلك بدي أسرعبما أن الـEK هي
+
+758
+00:56:07,850 --> 00:56:11,970
+أساسي لـLB، أين EK بالساوي لـChronicle Delta، ثم X
+
+759
+00:56:11,970 --> 00:56:14,550
+المتنقل بيها as a unique representation X بالساوي
+
+760
+00:56:14,550 --> 00:56:18,690
+كـPsi K E K من واحد لعند مين إلى مالا نهائيا، ماشي
+
+761
+00:56:18,690 --> 00:56:22,670
+الحال؟ لأن consider أي F في مين في الـLB إيش
+
+762
+00:56:22,670 --> 00:56:26,650
+مالها؟ A'، خدوا الـF وين مالها؟ الـB'، لأن عشان
+
+763
+00:56:26,650 --> 00:56:32,430
+أعرف الـTF من الـB'، أعظيها لمين؟ للـLQ، ماشي
+
+764
+00:56:32,430 --> 00:56:37,920
+الحال؟الآن خدوا أي أف في الأل بي برايم since f is
+
+765
+00:56:37,920 --> 00:56:41,740
+linear and bounded then f of x بالساوية ال
+
+766
+00:56:41,740 --> 00:56:44,640
+summation اللي قلت زي ما عملت قبل شوية بالظبط هذه
+
+767
+00:56:44,640 --> 00:56:48,060
+أسمها إيهاش خمسة where the numbers دعوة ما كالي
+
+768
+00:56:48,060 --> 00:56:52,180
+يمين هي f of ek يعني f دخلت على اللي جوا فلعت عندك
+
+769
+00:56:52,180 --> 00:56:54,960
+5k, f of ek, k من واحد لما نهيه لأن f of one دو
+
+770
+00:56:54,960 --> 00:56:57,540
+دولينر دو دخولة على ال summation اللي ما لنهيه نفس
+
+771
+00:56:57,540 --> 00:57:02,880
+الجثة continuous و linear الاخرينالان جهزة هذه
+
+772
+00:57:02,880 --> 00:57:06,320
+خمسة F of X بساوي هذه شوفوا إيش اللي بنسويه عشان
+
+773
+00:57:06,320 --> 00:57:11,220
+من خلاله نقدر نحصل عالي بدنيا let Q خليني أحضر
+
+774
+00:57:11,220 --> 00:57:15,180
+البرمجان و أصبروا عليا شوية اطلع لفوق let Q be the
+
+775
+00:57:15,180 --> 00:57:20,260
+conjugate linear of B and consider X N بتساوي X I
+
+776
+00:57:20,260 --> 00:57:24,900
+K Nأه ايش اكسان يعني ال .. هاد ال sequence نفسها
+
+777
+00:57:24,900 --> 00:57:30,200
+X1 X2 X3 إلى ما لنهاية ال sequence هذه ال Xات اللي
+
+778
+00:57:30,200 --> 00:57:35,360
+فيها X1 و X2 و X3 و X ما لنهاية هذه اللي هي موجودة
+
+779
+00:57:35,360 --> 00:57:38,740
+وين هاخدها موجودة في القلبي أو في ال ال Q sequence
+
+780
+00:57:38,740 --> 00:57:43,020
+.. sequence من عناصر يعني عناصرها اللي هي ال X1
+
+781
+00:57:43,020 --> 00:57:51,530
+عناصره مين هي XI 1 1 XI 2 1 XI 3 1 أه فاهمينXI 4 1
+
+782
+00:57:51,530 --> 00:58:01,370
+إلى ما لنهاية الآن XN نفسها عبارة عن XI 1N XI 2N
+
+783
+00:58:01,370 --> 00:58:05,770
+XI 3N XI 4N كلهم إلى ما لنهاية الآن هذه الـ
+
+784
+00:58:05,770 --> 00:58:09,770
+sequence بتعرفها بطريقة معينة تخدمني بعد شوية إيش
+
+785
+00:58:09,770 --> 00:58:14,610
+الطريقة اللي بتعرفها؟ بتعرفها كالتالي إن XIKN
+
+786
+00:58:14,610 --> 00:58:20,050
+بتساويهذول هاين صانم بينيداية هذول ال F of E K
+
+787
+00:58:20,050 --> 00:58:23,590
+بتساوي ال Epsilon .. بدي أخد إشي معحدد عشان هو
+
+788
+00:58:23,590 --> 00:58:29,250
+اللي هيسخدمني في التعريف الجمال دي شوية بدي أعرف
+
+789
+00:58:29,250 --> 00:58:34,610
+Epsilon K M بساوي Gamma K أُس Q Gamma K هدى على
+
+790
+00:58:34,610 --> 00:58:39,480
+mean Gamma Kإذا كانت K أصغر أوي شويه N والـGamma K
+
+791
+00:58:39,480 --> 00:58:43,840
+أشمالها لها تساوي 0 في حالة الـGamma K بتساوي 0
+
+792
+00:58:43,840 --> 00:58:47,980
+أتوماتيك بدي أعرفها ده إيش بتساوي 0 في حالة اللي
+
+793
+00:58:47,980 --> 00:58:55,300
+هي الـK أكبر من N يعني لو الآن عندي بدي أحكي عن
+
+794
+00:58:55,300 --> 00:58:57,420
+XIK1
+
+795
+00:59:00,460 --> 00:59:04,860
+Xi K طبعاً اللي هي واحد انترين من مين من هدول يعني
+
+796
+00:59:04,860 --> 00:59:10,300
+الـ N على سبيل المثال أعطيكم عشان
+
+797
+00:59:10,300 --> 00:59:16,320
+تكون الصورة واضحة لكم وللي بسمعها الـ N انتفجنا X
+
+798
+00:59:16,320 --> 00:59:22,080
+N بتعرفها عبارة عن Xi K N ماشي الحاجة هذه في حد
+
+799
+00:59:22,080 --> 00:59:27,420
+ذاتها الـ sequence الـ X واحد تبعتها بساوي Xi K
+
+800
+00:59:27,420 --> 00:59:32,870
+واحداللي هو K طبعا ايش بناخدها واحد اتنين واحد
+
+801
+00:59:32,870 --> 00:59:41,290
+ثمين XI واحد ثلاثة XI واحد اربعة إلى ما لا نهاية X
+
+802
+00:59:41,290 --> 00:59:48,370
+اتنين بساوي XI واحد اتنين XI اتنين اتنين XI تلاتة
+
+803
+00:59:48,370 --> 00:59:53,790
+اتنين XI اربعة اتنين إلى ما لا نهاية شوفوا الآن
+
+804
+00:59:53,790 --> 01:00:00,240
+حسب التعريف اللي ماخده انا XIKN بساويةفي حالة الآن
+
+805
+01:00:00,240 --> 01:00:05,120
+خلّينا ناخد على الأولى على مين؟ على X1 بدي أشوف XI
+
+806
+01:00:05,120 --> 01:00:13,560
+11 XI 11 عندي الآن 11 يعني هذه 11 وهذه 1 بتجه في
+
+807
+01:00:13,560 --> 01:00:17,560
+النطاق هذا مظبوط؟ الآن في النطاق هذا بيساوي Gamma
+
+808
+01:00:17,560 --> 01:00:22,840
+1 على Gamma 1يعني بمعنى آخر هذه بتصير عبارة عن الـ
+
+809
+01:00:22,840 --> 01:00:29,440
+absolute value لقمة واحد أس بي أس كيو على قمة واحد
+
+810
+01:00:29,440 --> 01:00:32,280
+هذا provided that اكساية اللي هي القمة واحد مش سفر
+
+811
+01:00:32,280 --> 01:00:37,280
+ماشي خلّينا نقلط السفر الان الباقي كله بيجي من
+
+812
+01:00:37,280 --> 01:00:41,880
+اتنين اللي هي ال K أكبر من مين من الان إذا كل
+
+813
+01:00:41,880 --> 01:00:45,780
+الناس هيكونين Zero Zero Zero Zero إلى مالا نهاية
+
+814
+01:00:46,110 --> 01:00:52,230
+واضح الان التانية بتنطبق عليها اللي هي Gamma 1 Q
+
+815
+01:00:52,230 --> 01:00:56,690
+على Gamma 1 وهذا بيصير عبارة عن Gamma 2 Q على
+
+816
+01:00:56,690 --> 01:01:01,050
+Gamma 2 provided that مش صفر والباقي أشمالهم صفر
+
+817
+01:01:01,050 --> 01:01:07,940
+صفر صفر صفر واضحمعايا الـ N الجامعة إكسا XN هتكون
+
+818
+01:01:07,940 --> 01:01:12,660
+الأول الجامعة واحد أقصى Q على جامعة واحد لما أصل
+
+819
+01:01:12,660 --> 01:01:18,300
+لعند ال .. لعند ال .. ال N تبعتها جامعة N Q على
+
+820
+01:01:18,300 --> 01:01:25,220
+جامعة N والباقي إيش مانه؟ هيتصفر واضح؟ طيب هذه مين
+
+821
+01:01:25,220 --> 01:01:29,880
+هي؟ هذه اللي هي الـ XN ال sequence اللي عندك هذه
+
+822
+01:01:29,880 --> 01:01:37,300
+سموها 6أذا من الخمسة احسبوه لان f of xn هي ال rule
+
+823
+01:01:37,300 --> 01:01:41,380
+تبع تحسيب الحسابات f of xn ايش بتساوي؟ اللي هو
+
+824
+01:01:41,380 --> 01:01:46,700
+summation xikn تبعتها تبعت ال xn هيها تبعت ال xn
+
+825
+01:01:46,700 --> 01:01:51,700
+في مين؟ في قامة k هذه تبعت ال x وهذه تبعت ال xn
+
+826
+01:01:51,700 --> 01:01:58,130
+اللي بتحسبلها في قامة k ويساويالان الجثة من عند
+
+827
+01:01:58,130 --> 01:02:01,070
+واحد لعند انا بيكون اللي لها قيمة اللي هي ايش
+
+828
+01:02:01,070 --> 01:02:04,750
+قيمتها؟ الباب سفارج فاهم من هنا اللي شفناها الباجي
+
+829
+01:02:04,750 --> 01:02:10,050
+سفارج ايش قيمتها؟ اللي هي SQ على Gamma K ومضروبة
+
+830
+01:02:10,050 --> 01:02:14,190
+في Gamma K بروحن مع بعض هذا provided مش سفر وفي
+
+831
+01:02:14,190 --> 01:02:17,670
+حالة سفر ماهو ال automatic المساواةAutomatic
+
+832
+01:02:17,670 --> 01:02:23,530
+متساوي إذا و يساوي هذا بالظبط بساوي لإنه هذا عبارة
+
+833
+01:02:23,530 --> 01:02:26,010
+عن مين absolute value يعني موجب إذا بساوي absolute
+
+834
+01:02:26,010 --> 01:02:31,320
+value لهأكيد و هذا إذن بيساوي ال absolute value ال
+
+835
+01:02:31,320 --> 01:02:35,460
+absolute value لمين هذا طلع اللي جوا هذا F of XN
+
+836
+01:02:35,460 --> 01:02:39,760
+ال absolute value هو absolute value لمين لل F of
+
+837
+01:02:39,760 --> 01:02:44,320
+XN هذا أكيد أصغر أو شامل مين أن F is bounded نورم
+
+838
+01:02:44,320 --> 01:02:50,120
+ال F و نورمين ال XN و يساوي نورم ال F هيه و نورم
+
+839
+01:02:50,120 --> 01:02:54,500
+ال XN لل XN هذه الآن ال XN من وين أنا بتاخد بتاخد
+
+840
+01:02:54,500 --> 01:03:01,620
+T من وينعند الـ F موجودة في الـ LB إبراهيم، ماشي؟
+
+841
+01:03:01,620 --> 01:03:05,320
+إذا الـ X تبعتها، الـ X تبعتها، اللي هي الـ X أو
+
+842
+01:03:05,320 --> 01:03:07,820
+الـ X1 و الـ X2 و الـ X3 و الـ X4 و الـ X5 و الـ
+
+843
+01:03:07,820 --> 01:03:08,000
+X6 و الـ X7 و الـ X8 و الـ X9 و الـ X10 و الـ X11
+
+844
+01:03:08,000 --> 01:03:10,900
+و الـ X12 و الـ X13 و الـ X14 و الـ X14 و الـ X15
+
+845
+01:03:10,900 --> 01:03:15,300
+و الـ X16 و الـ X20 و الـ X21 و الـ X22 و الـ X22
+
+846
+01:03:15,300 --> 01:03:15,840
+و الـ X22 و الـ X22 و الـ X22 و الـ X22 و الـ X22
+
+847
+01:03:15,840 --> 01:03:23,560
+و الـ X22 و الـ X22 و الـ X22 و الـ X22 و الـ X22
+
+848
+01:03:23,560 --> 01:03:26,190
+و الـ X22 و الـ X22 و الـ X22 و الـ X22 وفبصير
+
+849
+01:03:26,190 --> 01:03:29,610
+norm الـ F هيو في ال summation هذا كم ان عند واحد
+
+850
+01:03:29,610 --> 01:03:33,310
+عند N والباقي بتتصفر بحط القيمة تبعي تهدي اللي هي
+
+851
+01:03:33,310 --> 01:03:39,610
+Xi K SQ على مين براما K الكل أس مين أس بين و الكل
+
+852
+01:03:39,610 --> 01:03:46,150
+أس مين أس واحد على بينإذا اللي عملته يا جماعة نورم
+
+853
+01:03:46,150 --> 01:03:50,470
+الـ xn كتبته نورم الـ xn الـ xn وين موجود؟ في الـ
+
+854
+01:03:50,470 --> 01:03:55,050
+Lp اللي هي ال interest بتبعته xikn يعني نورم تبعه
+
+855
+01:03:55,050 --> 01:03:58,310
+ال absolute value الو أس بي الكل أس واحد على بي ال
+
+856
+01:03:58,310 --> 01:04:04,040
+summation هيولأن شيلت هدولة وحط قيمها قيم هدولة
+
+857
+01:04:04,040 --> 01:04:09,900
+اللي هي كلهم بيكون هيها جامعة واحد Q على جامعة
+
+858
+01:04:09,900 --> 01:04:18,020
+واحد لما أصل عند جامعة Q SQ على جامعة N والباقي
+
+859
+01:04:18,020 --> 01:04:23,120
+سفر سفر سفر سفربتسفر إذا الـ Submission هيجف عند
+
+860
+01:04:23,120 --> 01:04:26,760
+الأمن والباقي بتسفر لما نيجي في حد الأمن بشيل هذا
+
+861
+01:04:26,760 --> 01:04:29,680
+قيمته هي هذا على هذا و أس بيه و أس واحد على بيه
+
+862
+01:04:29,680 --> 01:04:35,260
+يلّا نحسب الآنهو يساوي norm of هذا الكلام هذا
+
+863
+01:04:35,260 --> 01:04:38,980
+الأنصار عنده عبارة عن اللي هو هذا واحد وهذا اللي
+
+864
+01:04:38,980 --> 01:04:43,400
+هو عبارة عن إيش عن ال Q فبصير Q نقص واحد قص مين قص
+
+865
+01:04:43,400 --> 01:04:46,080
+بي لإن هذا ال absolute value اللي دي هتان هيه هذا
+
+866
+01:04:46,080 --> 01:04:48,780
+ال absolute value موجود فهياخد للتحت و اللي فوق
+
+867
+01:04:48,780 --> 01:04:52,580
+absolute value أو مضلص بطلع Q ماينس واحد الكل
+
+868
+01:04:52,580 --> 01:04:56,140
+مضروف في مين في بيو في واحد على بيه هذا المقدر
+
+869
+01:04:56,140 --> 01:05:00,940
+اللي هو عبارة عن مين ال Qالـ Q ليش؟ لأن واحد على B
+
+870
+01:05:00,940 --> 01:05:06,280
+واحد على B زائد واحد على Q بساوي واحد اضربه كله في
+
+871
+01:05:06,280 --> 01:05:11,080
+الـ BQ فبتطلع Q زائد B بساوي B في Q إذا الـ Q
+
+872
+01:05:11,080 --> 01:05:17,840
+بيساوي BQ ناقص B، ماشي؟ واضح، أه؟ ماشي الحالة لأن
+
+873
+01:05:17,840 --> 01:05:22,570
+هذا QB ناقص Q اللي هي عبارة عن مين؟ عن الـ Qصار
+
+874
+01:05:22,570 --> 01:05:27,450
+عنده هذا المقدار Q وهذا S1 على B إذا صار عنده الآن
+
+875
+01:05:27,450 --> 01:05:32,670
+اللي وصلت إليه عنده ال F of Xn أصغر أو يساوي هذا
+
+876
+01:05:32,670 --> 01:05:41,610
+المقدار إذا ال F of Xn بساوي ال summation هيه F of
+
+877
+01:05:41,610 --> 01:05:46,150
+Xn بساوي ال summation هذا معاها و في النهاية وصلنا
+
+878
+01:05:46,150 --> 01:05:50,230
+أصغر أو ساوي هذاهي اللي بدك تبهن بس f of xn و اللي
+
+879
+01:05:50,230 --> 01:05:53,370
+بيساوي هذا و أصغر يبساوي هذا أصغر يبساوي norm of f
+
+880
+01:05:53,370 --> 01:05:59,450
+في هذا المقدر الآن من التنتين مع بعض صار عندي اللي
+
+881
+01:05:59,450 --> 01:06:05,090
+هو ال summation ال summation اللي هو انجلوه على
+
+882
+01:06:05,090 --> 01:06:11,890
+الجهة الثانية انجلوه هنا هذا يعني ده اسمهبصير هذا
+
+883
+01:06:11,890 --> 01:06:15,550
+أسوء Q هنقص واحد و هذا أسوء واحد على بيه بيصير
+
+884
+01:06:15,550 --> 01:06:18,450
+واحد ناقصه بيصير واحد ناقص واحد على بيه أصغر أو
+
+885
+01:06:18,450 --> 01:06:23,430
+ساوي مين نورم ال F إذا صار عندي اللي هو هذا طبعا
+
+886
+01:06:23,430 --> 01:06:27,830
+هو واحد على Q صار هذا أصغر أو ساوي نورم ال F يعني
+
+887
+01:06:27,830 --> 01:06:34,590
+هذا صار finite يعني صار ال element هذا وين موجود
+
+888
+01:06:34,590 --> 01:06:41,840
+في القلة Q وهذا اللي بديه أصلا بدي الآن أخد TT من
+
+889
+01:06:41,840 --> 01:06:52,460
+LB' لعند LQ الـ T الآن of IF بساوي المقدار اللي
+
+890
+01:06:52,460 --> 01:06:58,240
+حصلت عليه اللي عندي اللي جابله شوية since طبعا
+
+891
+01:06:58,240 --> 01:07:01,700
+الان since and بس بتكمل الجثة أساسا هو تكتمل
+
+892
+01:07:01,700 --> 01:07:05,930
+الصورةSince N is arbitrary, I N بودي N من لما
+
+893
+01:07:05,930 --> 01:07:09,270
+لنهاية، then by letting N تروح لما لنهاية، بيصير
+
+894
+01:07:09,270 --> 01:07:12,390
+هذا المقدار من واحد لما لنهاية أصغر أو ساوى F.
+
+895
+01:07:12,750 --> 01:07:15,990
+Normal F إذا صارت الجامعة كي وين موجودة في ال LQ.
+
+896
+01:07:16,210 --> 01:07:23,620
+Now اللي روحت عليه God, Now اطلع لفوقT Define T من
+
+897
+01:07:23,620 --> 01:07:27,860
+الـ B' لعند الـ LQ by T of F أيش بيساوي الـ F of
+
+898
+01:07:27,860 --> 01:07:32,120
+EK اللي هو جامعة K اتجهزناها وين قاعدة في الـ LQ
+
+899
+01:07:32,120 --> 01:07:38,160
+to show الآن .. الآن بدنا نثبت أنه T is onto مافي
+
+900
+01:07:38,160 --> 01:07:43,020
+الحال أخر شوية هو أثبات اللي هو ب reserve the norm
+
+901
+01:07:43,020 --> 01:07:46,720
+بس عشان نثبته onto و بعدين نرجع لل norm لكن بنفع
+
+902
+01:07:46,720 --> 01:07:47,080
+نثبته
+
+903
+01:07:49,890 --> 01:07:54,410
+طيب صلوا على النبي عليه الصلاة والسلام نشف طريقي
+
+904
+01:07:54,410 --> 01:07:59,710
+هو لأ هو عشان الدنيا رمضان هذا هيتسجل تسجيل فالناس
+
+905
+01:07:59,710 --> 01:08:02,490
+هتسمع أنه احنا كنا نشرح في رمضان عشان يقولك رمضان
+
+906
+01:08:02,490 --> 01:08:06,370
+طيب صلوا على النبي عليه الصلاة والسلام الان هو
+
+907
+01:08:06,370 --> 01:08:09,130
+اليوم هذا اصلا اليوم احنا عارفين ان الدنيا رمضان
+
+908
+01:08:09,130 --> 01:08:11,550
+لكن يمكن اللي بسمعه يسمعه كمان عشر سنين خمس عشر
+
+909
+01:08:11,550 --> 01:08:15,530
+سنة ويقول الله يرحمهم كانوا يشرحوا في رمضان طيب
+
+910
+01:08:15,530 --> 01:08:19,130
+صلوا على النبي عليه الصلاة والسلامالحمد لله جميعا
+
+911
+01:08:19,130 --> 01:08:23,330
+الـ Enhance Gamma K Element لـ LQ ماشي الان Now
+
+912
+01:08:23,330 --> 01:08:28,670
+define T-LB' لعند LQ by T of F ال element هنا
+
+913
+01:08:28,670 --> 01:08:32,330
+بيسوي F of EK سواء Gamma K اللي قعدناها to show
+
+914
+01:08:32,330 --> 01:08:36,770
+that T is onto خط B arbitrary element في مين في LQ
+
+915
+01:08:36,770 --> 01:08:42,130
+هنجح مش .. في شبه من اللي فات عرفلي G-LB لعند L ..
+
+916
+01:08:42,130 --> 01:08:45,190
+لعند K function بدي ألاقي function عشان .. عشان
+
+917
+01:08:45,190 --> 01:08:47,630
+اللي هو A لاجي صورتها تسوي مين اللي بدأت فيه
+
+918
+01:08:48,060 --> 01:08:51,720
+كمبليكس أوريال بي جي of X بيساوي بـ Psi K Gamma K
+
+919
+01:08:51,720 --> 01:08:54,480
+Beta K K من 1 لإنفينتي بالظبط زي اللي أحكي الأول
+
+920
+01:08:54,480 --> 01:08:57,240
+يعني for any X و إيه الموجودة بـPsi K و إيه
+
+921
+01:08:57,240 --> 01:09:00,980
+الموجود الآن في الـL بي then as in the previous
+
+922
+01:09:00,980 --> 01:09:05,340
+example G is linear مش هيختلف ماعرف أقول إنها ده G
+
+923
+01:09:05,340 --> 01:09:09,560
+is linear moreover by holder in quality الآن هقول
+
+924
+01:09:09,560 --> 01:09:13,410
+لأبسليوت وينه للـG of Xبساوي الـ Absolute Value
+
+925
+01:09:13,410 --> 01:09:16,550
+لهذه والـ Absolute Value لهذه اللي هي أصغر أو
+
+926
+01:09:16,550 --> 01:09:21,990
+يساوي هذه بيقص واحد على بيقص واحد على بيقص واحد
+
+927
+01:09:21,990 --> 01:09:22,550
+على بيقص واحد على بيقص واحد على بيقص واحد على بيقص
+
+928
+01:09:22,550 --> 01:09:22,690
+واحد على بيقص واحد على بيقص واحد على بيقص واحد على
+
+929
+01:09:22,690 --> 01:09:22,750
+بيقص واحد على بيقص واحد على بيقص واحد على بيقص
+
+930
+01:09:22,750 --> 01:09:22,770
+واحد على بيقص واحد على بيقص واحد على بيقص واحد على
+
+931
+01:09:22,770 --> 01:09:23,970
+بيقص واحد على بيقص واحد على بيقص واحد على بيقص
+
+932
+01:09:23,970 --> 01:09:26,370
+واحد على بيقص واحد على بيقص واحد على بيقص واحد على
+
+933
+01:09:26,370 --> 01:09:35,810
+بيقص واحد على بيقص واحد على بيقص واحد
+
+934
+01:09:35,810 --> 01:09:39,750
+على بيقص
+
+935
+01:09:39,990 --> 01:09:44,890
+and so ومنها الـ G of X بالساوي الـ summation صارت
+
+936
+01:09:44,890 --> 01:09:48,610
+bound to be linear إذا بقدر أدخل من الـ G جوا زي
+
+937
+01:09:48,610 --> 01:09:51,170
+ما بدها لإنه صارت ال limit تدخل و تطلع لإنه
+
+938
+01:09:51,170 --> 01:09:53,530
+continuous بيصير عند الـ G of X بالساوي الـ
+
+939
+01:09:53,530 --> 01:09:56,550
+summation X I K و G of E K ونظرا لإن ال
+
+940
+01:09:56,550 --> 01:09:59,570
+representation واحد إذا الـ G of E K هي الـ BK
+
+941
+01:09:59,570 --> 01:10:02,290
+اللي غالط إذا زي الحكية الأولى بالظبط then T G
+
+942
+01:10:02,290 --> 01:10:06,810
+أشها تساوي G of E K من التعريف هذا T G بالساوي G
+
+943
+01:10:06,810 --> 01:10:10,890
+of E K اللي عرفناها في الأصل هناالـ T بيساوي اللي
+
+944
+01:10:10,890 --> 01:10:15,150
+هو Beta K إذا Therefore T is Onto مصر علينه الكلام
+
+945
+01:10:15,150 --> 01:10:21,070
+بتكرر نفس اللي حكيته قبل شوية الآن صارت T Onto
+
+946
+01:10:21,070 --> 01:10:26,240
+بدنا اللي هو نثبت إنها preserve the Northالان اذا
+
+947
+01:10:26,240 --> 01:10:29,600
+اثبتنا بـ Reservoir norm و T on two بيبقى هو ال
+
+948
+01:10:29,600 --> 01:10:32,440
+linear بس هو ال linear سهل الان by holder
+
+949
+01:10:32,440 --> 01:10:36,180
+inequality احسبوني ال absolute value ل F of X ال
+
+950
+01:10:36,180 --> 01:10:38,660
+absolute value ل F of X بيساوي ال absolute value
+
+951
+01:10:38,660 --> 01:10:42,490
+of summation X I K بقى ما كال هي F of E K هذهماشي
+
+952
+01:10:42,490 --> 01:10:46,310
+اللي هي أصغر أو يساوي اللي هو by holder اللي هو
+
+953
+01:10:46,310 --> 01:10:48,970
+أصغر أو يساوي ال summation ب أصواح ده ل بي ال
+
+954
+01:10:48,970 --> 01:10:52,890
+summation of q أصواح ده ل q هذا مين هو نورم ال X
+
+955
+01:10:52,890 --> 01:10:56,490
+وهذا زي ما هو اللي عندى اللي بعد شوية هصير نورم
+
+956
+01:10:56,490 --> 01:10:59,850
+ينقل Gamma K ماشي إذا صارت ال absolute value of f
+
+957
+01:10:59,850 --> 01:11:03,730
+of X أصغر أو يساوي هذا المقدار ومنه على طور اللي
+
+958
+01:11:03,730 --> 01:11:07,170
+ناخد اللي هو ال supremum النورمات اللي بيساوي واحد
+
+959
+01:11:07,170 --> 01:11:11,470
+بطلع ال absolute value النورم لل F فاهمينأه يعني
+
+960
+01:11:11,470 --> 01:11:14,630
+هذه بنجيبها بالسيرة هذا على هذه أصغر أو يساوي هذا
+
+961
+01:11:14,630 --> 01:11:17,210
+ياخد ال supermom على ال Xات اللي بتساوي انيش سفر
+
+962
+01:11:17,210 --> 01:11:20,030
+وإذا بدكم على ال Xات اللي بتساوي واحد نورمهن
+
+963
+01:11:20,030 --> 01:11:22,590
+وبيطلع نفس الاشي نورم ال F أصغر أو يساوي هذا
+
+964
+01:11:22,590 --> 01:11:25,650
+المقدار لأن من سبعة اللي جابت اللي بشوية قولنا
+
+965
+01:11:25,650 --> 01:11:29,510
+حطوها في الذاكرة هذا أصغر أو يساوي نورم وهذا ال
+
+966
+01:11:29,510 --> 01:11:32,850
+norm أصغر أو يساويهن إذا ال team team together صار
+
+967
+01:11:32,850 --> 01:11:38,150
+ال norm بساوي هذا therefore صار ال norm لل TFما هو
+
+968
+01:11:38,150 --> 01:11:40,870
+الـ TF ايش بيساوي، ما عارفين واحنا، بيساوي الـ
+
+969
+01:11:40,870 --> 01:11:45,610
+Gamma K أدات التغريف نورم الـ TF بيساوي نورم Gamma
+
+970
+01:11:45,610 --> 01:11:49,920
+K ونورم Gamma K في الواقع هو هذااللي هو بساوى هذا
+
+971
+01:11:49,920 --> 01:11:52,540
+و هو أثبتنا بساوية norm of
+
+972
+01:12:18,310 --> 01:12:22,750
+أف اف اي كي اللي هي الـ Gamma K Element in LQ و
+
+973
+01:12:22,750 --> 01:12:26,370
+Preserve the Normal 1 to 1 و Unto و Linear إذن
+
+974
+01:12:26,370 --> 01:12:30,250
+صارت Isomorphism إذن ده Dual Space of الـ B هو الـ
+
+975
+01:12:30,250 --> 01:12:33,570
+LQ و بارك الله فيكم و إلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/wdHX26yF5r4.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/wdHX26yF5r4.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b4a31d17fbb627de695f074f4707f93576a708ce
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/wdHX26yF5r4.srt
@@ -0,0 +1,2203 @@
+1
+00:00:05,150 --> 00:00:07,670
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,670 --> 00:00:10,590
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:10,590 --> 00:00:17,290
+آله وصحبه أجمعين هذه المحاضرة رقم 35 مساق تحليل 
+
+4
+00:00:17,290 --> 00:00:20,010
+اقتران أو تحليل دالي طلاب وطالبات الجامعة 
+
+5
+00:00:20,010 --> 00:00:26,990
+الإسلامية ماجستير رياضية حكينا المحاضرة الماضية عن
+
+6
+00:00:26,990 --> 00:00:31,930
+اللي هو الـ Open Mapping Theorem اللي هي النظرية 
+
+7
+00:00:31,930 --> 00:00:35,830
+الأساسية الثالثة اليوم نحكي عن آخر نظرية أساسية في
+
+8
+00:00:35,830 --> 00:00:38,350
+اللي هو الـ Functional Analysis اللي هي اسمها
+
+9
+00:00:38,350 --> 00:00:44,070
+Closed Graph Theorem Closed Graph Theorem الآن 
+
+10
+00:00:44,070 --> 00:00:51,780
+العنوان تحت Closed Linear Operators عنا احنا الـ ..
+
+11
+00:00:51,780 --> 00:00:54,620
+الـ .. الـ .. واضح اللي احنا اهتمينا فيه كبير كثير
+
+12
+00:00:54,620 --> 00:00:57,040
+اللي هو الـ Bounded Linear Operators اللي هو الـ 
+
+13
+00:00:57,040 --> 00:01:00,360
+Continuous Linear Operators وبعدين اهتمينا شوية في 
+
+14
+00:01:00,360 --> 00:01:04,500
+الـ .. في الـ Open Mapping في الـ Open Operators الآن 
+
+15
+00:01:04,500 --> 00:01:10,340
+في اللي هو Operator آخر ومش شرط يكون Bounded
+
+16
+00:01:10,340 --> 00:01:14,200
+Linear Operator هنا قبل شوية قولنا احنا الـ .. الـ
+
+17
+00:01:14,200 --> 00:01:16,920
+.. الـ .. الـ Bounded Linear Operator ممكن يكون Open
+
+18
+00:01:16,920 --> 00:01:21,570
+تحت الشروط اللي حكيناها الآن لـ Closed Linear 
+
+19
+00:01:21,570 --> 00:01:27,570
+Operators، سنجد أن ليس كل الـ bounded linear
+
+20
+00:01:27,570 --> 00:01:33,110
+operators اللي في الدنيا هتكون bounded linear 
+
+21
+00:01:33,110 --> 00:01:35,710
+operators يعني ممكن unbounded linear operators
+
+22
+00:01:36,870 --> 00:01:40,230
+ومهمة زي اللي هو اللي خدناها اللي هو الـ .. الـ ..
+
+23
+00:01:40,230 --> 00:01:45,990
+الـ .. الـ operator اللي كان يرسل الـ X للـ X' هذا الـ
+
+24
+00:01:45,990 --> 00:01:50,690
+unbounded .. unbounded و هذا له استخدامات كثيرة و
+
+25
+00:01:50,690 --> 00:01:59,150
+.. و فيه له خلّيني أقول خواص معينة بتأهله أن يكون 
+
+26
+00:01:59,150 --> 00:02:05,730
+مهمو تطبيقات كثيرة بتاهله أن يكون مهم اللي هو هذا
+
+27
+00:02:05,730 --> 00:02:12,810
+النوع من الـ operators عادة يتمتع بخاصية الـ 
+
+28
+00:02:12,810 --> 00:02:17,870
+closedness يعني بنسميه closed operator ده نشوف إيش
+
+29
+00:02:17,870 --> 00:02:22,810
+معناته closed operator فهذا اللي هو استدعى أن يكون 
+
+30
+00:02:22,810 --> 00:02:26,750
+اللي هو الـ closed operator مهمنظراً لهو لوجود
+
+31
+00:02:26,750 --> 00:02:30,430
+Unbounded Linear Operator وهو في نفس الوقت Closed
+
+32
+00:02:30,430 --> 00:02:35,410
+وقاله تطبيقات أعتقد في الـ Quantum Mechanics في 
+
+33
+00:02:35,410 --> 00:02:43,690
+أمور هندسية وفيزيائية في شباتر قدام موجود حتى
+
+34
+00:02:43,690 --> 00:02:46,610
+الحديث عنه لما نحكي عن الـ Spectral Theory
+
+35
+00:02:46,610 --> 00:02:52,610
+لـClosed Linear Operators هو نحكي عن سيجما و روه 
+
+36
+00:02:52,610 --> 00:02:56,450
+الهنو .. طيب شوفوا نعرف إيش معناه closed linear
+
+37
+00:02:56,450 --> 00:03:00,790
+operator let X and Y be normed spaces T من domain
+
+38
+00:03:00,790 --> 00:03:03,670
+of T لعند مين؟ لعند Y بيقى linear operator و الـ
+
+39
+00:03:03,670 --> 00:03:07,170
+domain of T جزء من مين؟ من X يعني أنا جاعد في اللي
+
+40
+00:03:07,170 --> 00:03:10,890
+هو normed space then T is called closed linear
+
+41
+00:03:10,890 --> 00:03:15,190
+operator إذا كانت الـ graph .. الـ graph زي ما
+
+42
+00:03:15,190 --> 00:03:17,650
+نتخيل الـ graph تبع الـ function العادية اللي ..
+
+43
+00:03:17,650 --> 00:03:21,170
+اللي هي المجموعة من الـ ordered pairs للعنصر و
+
+44
+00:03:21,170 --> 00:03:25,610
+صورته للعنصر و صورته لأن g of t هذا اللي هو عبارة 
+
+45
+00:03:25,610 --> 00:03:28,670
+عن كل الـ x و y حيث الـ x في الـ domain و الـ y و
+
+46
+00:03:28,670 --> 00:03:32,410
+ما له صورته فين؟ في الـ range اللي هي x واحد و x في
+
+47
+00:03:32,410 --> 00:03:35,850
+الـ domain of t و y بساوة x is closed in the normed
+
+48
+00:03:35,850 --> 00:03:40,300
+space x cross y إذن الآن where two algebraic
+
+49
+00:03:40,300 --> 00:03:42,780
+operations of the vector space are defined إلى آخر
+
+50
+00:03:42,780 --> 00:03:49,480
+فالن بعدين يعني عند T في الـ domain of T لعند Y هذا
+
+51
+00:03:49,480 --> 00:03:52,500
+جزء من X و احنا بنحكي عن norm of the space الآن 
+
+52
+00:03:52,500 --> 00:03:55,480
+بتقول إن T is a closed linear operator
+
+53
+00:03:57,760 --> 00:04:00,560
+وكان اللي هو الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+54
+00:04:00,560 --> 00:04:00,760
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+55
+00:04:00,760 --> 00:04:00,780
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+56
+00:04:00,780 --> 00:04:01,140
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+57
+00:04:01,140 --> 00:04:01,160
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+58
+00:04:01,160 --> 00:04:01,180
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+59
+00:04:01,180 --> 00:04:01,640
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+60
+00:04:01,640 --> 00:04:02,340
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+61
+00:04:02,340 --> 00:04:03,160
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+62
+00:04:03,160 --> 00:04:03,220
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+63
+00:04:03,220 --> 00:04:04,260
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ 
+
+64
+00:04:04,260 --> 00:04:04,320
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+65
+00:04:04,320 --> 00:04:07,960
+الـ ..
+
+66
+00:04:07,960 --> 00:04:08,920
+الـ
+
+67
+00:04:12,530 --> 00:04:16,510
+معناته احنا بنقصد مين؟ الـ T is a closed set طبعاً 
+
+68
+00:04:16,510 --> 00:04:19,850
+هذي closed set في مين؟ في الـ space تبعها، هذي جزء
+
+69
+00:04:19,850 --> 00:04:23,950
+من الـ space اللي هو X across me and Y فبتكون اللي
+
+70
+00:04:23,950 --> 00:04:29,170
+هي G of T closed تعني في هذه الحالة أنه اللي هو الـ
+
+71
+00:04:29,170 --> 00:04:33,650
+operator اللي عند T is a closed linear operator
+
+72
+00:04:35,250 --> 00:04:38,110
+اللي هان .. إيش العمليات اللي على الـ .. الـ ..
+
+73
+00:04:38,110 --> 00:04:40,850
+العمليات الجبريعية الـ X cross Y اللي خلتـه vector 
+
+74
+00:04:40,850 --> 00:04:43,670
+space اللي عمليات العادية اللي أنتم عارفينها الـ 
+
+75
+00:04:43,670 --> 00:04:46,870
+.. الـ pointwise addition و اللي هو الـ scalar
+
+76
+00:04:46,870 --> 00:04:49,350
+multiplication برضه pointwise في الأولى و في
+
+77
+00:04:49,350 --> 00:04:54,220
+التانية هذه بتعملية vector space ولو أخدنا اللي هو 
+
+78
+00:04:54,220 --> 00:04:58,000
+الـ Norm عرفناه Normal X Y بيسوا Normal X زائد 
+
+79
+00:04:58,000 --> 00:05:02,120
+Normal Y هنجيها برضه تعمل ليه أشماله؟ Normed Space 
+
+80
+00:05:02,120 --> 00:05:08,080
+كامل يعني X cross Y هتعمل Vector Space وNorm تبحها 
+
+81
+00:05:08,080 --> 00:05:11,140
+اللي عرفناها قبل بشوية هتعملنها عبارة عن Normed
+
+82
+00:05:11,140 --> 00:05:15,260
+Space لأن لو كانت هذه Closed فيه هذا معنى إيه؟
+
+83
+00:05:15,260 --> 00:05:19,100
+اللي هو الـ T is a Closed Linear Operator أو It is
+
+84
+00:05:19,100 --> 00:05:25,200
+a Closed Operator اطلع على اللي فوق طيب الآن نجي لـ 
+
+85
+00:05:25,200 --> 00:05:27,660
+Closed Graph Theorem Closed Graph Theorem لطيفة 
+
+86
+00:05:27,660 --> 00:05:32,640
+يعني فبرهنها لطيف let X and Y be Banach Spaces 
+
+87
+00:05:32,640 --> 00:05:37,080
+شايفين؟ and let T من domain of T لعند Y be a 
+
+88
+00:05:37,080 --> 00:05:40,980
+closed linear operator with domain of T جزء من X
+
+89
+00:05:40,980 --> 00:05:46,580
+if domain of T is closed in X then T إيش مالها؟ is
+
+90
+00:05:46,580 --> 00:05:52,520
+bounded وكأنه بقولك إن أي عامل عامل عامل عامل عامل 
+
+91
+00:05:52,520 --> 00:05:53,360
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل 
+
+92
+00:05:53,360 --> 00:05:56,300
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل 
+
+93
+00:05:56,300 --> 00:05:56,660
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل 
+
+94
+00:05:56,660 --> 00:05:57,000
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+95
+00:05:57,000 --> 00:05:57,020
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+96
+00:05:57,020 --> 00:05:58,250
+عامل عامل عامل عامل عامل عامل عامل عامل عامل أن لو
+
+97
+00:05:58,250 --> 00:06:02,450
+كانت domain of T closed أكيد automatic حيصير اللي
+
+98
+00:06:02,450 --> 00:06:08,510
+هو إيش؟ closed subspace من Banach space X إذا أكيد 
+
+99
+00:06:08,510 --> 00:06:11,910
+حيكون Banach space يعني بالمعنى الآخر لو كانت T من Banach
+
+100
+00:06:11,910 --> 00:06:15,270
+space لـ Banach space وكانت bounded linear operator كل
+
+101
+00:06:15,270 --> 00:06:19,170
+سنة متسلمين على طول إيش بده يطلع؟ اللي هو عبارة عن 
+
+102
+00:06:19,170 --> 00:06:27,740
+Robin عبارة عن closed آسف .. bounded .. bounded إذن 
+
+103
+00:06:27,740 --> 00:06:32,640
+الآن الـ .. الـ .. الـ .. الـ .. الـ open mapping 
+
+104
+00:06:32,640 --> 00:06:36,720
+theorem كانت تاخد من Banach space لـ Banach space و قلته
+
+105
+00:06:36,720 --> 00:06:43,740
+أعطتكم اللي هي الـ .. الـ bounded open هنا الآن الـ 
+
+106
+00:06:43,740 --> 00:06:48,820
+closed أعطانا mean bounded تحت نفس الظروف وأقل
+
+107
+00:06:48,820 --> 00:06:53,160
+شوية ما فيش قنته هنا مش لازم قنته يعني T من X لعند 
+
+108
+00:06:53,160 --> 00:06:57,420
+Y تكون closed in our operator من Banach space لـ Banach
+
+109
+00:06:57,420 --> 00:07:02,260
+space أعطتك إيه أشماله؟ الـ T إيه أشماله؟ is bounded
+
+110
+00:07:02,260 --> 00:07:10,320
+واضح أه أي سؤال؟ أي سؤال؟ طيب
+
+111
+00:07:12,850 --> 00:07:18,890
+بتثبت أنه T is bounded خلّينا بس نحضر لما نصل لـ T
+
+112
+00:07:18,890 --> 00:07:24,850
+is bounded لتزد أن بانيكوشي سيكوينس X across Y
+
+113
+00:07:28,280 --> 00:07:32,440
+بدأ أثبت لكم أول حاجة إن X×Y نفسها complete ماشي
+
+114
+00:07:32,440 --> 00:07:36,700
+الحاجة أول حاجة لإنه بتلزمني بعد شوية عشان أثبت أن
+
+115
+00:07:36,700 --> 00:07:41,840
+T is bounded let ZN be any Cauchy sequence in X×Y
+
+116
+00:07:41,840 --> 00:07:45,980
+where ZN بسوء XN و YN أخد الـ sequence فيها كلام سلس 
+
+117
+00:07:45,980 --> 00:07:50,600
+و سهل وسهل سريع then then for or therefore
+
+118
+00:07:50,600 --> 00:07:54,380
+therefore for every epsilon أو then for every
+
+119
+00:07:54,380 --> 00:07:58,060
+epsilon أكبر من صفر there exist k limited to n
+
+120
+00:07:58,060 --> 00:08:02,300
+such that for all m و n أكبر من n و أكبر من k هكون 
+
+121
+00:08:02,300 --> 00:08:06,880
+norm اللي هو الذد أنمك الذد أم أشماله أصغر من 
+
+122
+00:08:06,880 --> 00:08:10,540
+epsilon اللي ماياخد الـ E دي أشماله is Cauchy طيب
+
+123
+00:08:10,540 --> 00:08:15,980
+الـ ZM نقص الـ ZN الـ ZN XN و YN إذا الـ ZN اللي
+
+124
+00:08:15,980 --> 00:08:20,700
+هي عبارة هي .. و الـ ZM اللي هي .. قصدي هذه و الـ
+
+125
+00:08:20,700 --> 00:08:25,800
+ZM هي .. و طرحتهم من بعض طلعت XN نقص XM و YN نقص
+
+126
+00:08:25,800 --> 00:08:30,180
+YM في دا عملها سهلة الآن norm هذا حسب اللي عرفناه 
+
+127
+00:08:30,180 --> 00:08:33,360
+قبل و شوية هان الـ norm هذا عبارة عن norm هذه زي
+
+128
+00:08:33,360 --> 00:08:38,290
+norm هذه هي norm هذه زي norm هذه إذا واضح إن لما 
+
+129
+00:08:38,290 --> 00:08:43,630
+كانت Z انكوشي سيكوانس أعطتلي هذه زائد هذه أصغر من
+
+130
+00:08:43,630 --> 00:08:49,930
+مين؟ من إبسل يعني أكيد طلع عندي اللي هو الـ XN ماقص
+
+131
+00:08:49,930 --> 00:08:55,850
+XN و الـ YN ناقص YN مدى إن مجموحه أصغر من إبسلون فكل
+
+132
+00:08:55,850 --> 00:09:00,650
+واحدة فيه أصغر من مين؟ من إبسلون for every m و n 
+
+133
+00:09:00,650 --> 00:09:04,590
+أشمالهن أكبر من k إذا صارت هذه اللي هي الـ sequence 
+
+134
+00:09:04,590 --> 00:09:09,830
+تبعتها XN كوشي في الـ X و الـ YN كوشي في مين؟ في الـ Y
+
+135
+00:09:09,830 --> 00:09:13,250
+أو كوشي حتى في الـ domain و الـ domain ما هو closed
+
+136
+00:09:13,250 --> 00:09:19,910
+فأكيد أشماله complete إذاً صار هذه كوشي في complete
+
+137
+00:09:19,910 --> 00:09:23,190
+و Y and كوشي في complete إذاً كل واحدة فيها limit
+
+138
+00:09:23,190 --> 00:09:29,240
+ماشي؟ طيب و هذا اللي هو اللي بدويا إذا Hence x and y
+
+139
+00:09:29,240 --> 00:09:31,960
+and are Cauchy sequences in x and y respectively
+
+140
+00:09:31,960 --> 00:09:35,440
+أو حتى في الـ domain of T however x and y are
+
+141
+00:09:35,440 --> 00:09:38,360
+complete وكمان الـ domain of T complete then there
+
+142
+00:09:38,360 --> 00:09:41,160
+exist x element in X and y element in Y such that
+
+143
+00:09:41,160 --> 00:09:44,780
+x and .. بتروح للـ X و Y and إيش ما لها؟ بتروح للـ Y
+
+144
+00:09:44,780 --> 00:09:50,460
+الآن وابحث هذه تعالوا لواحد هذا وودوه لأم تروح إلى
+
+145
+00:09:50,460 --> 00:09:55,410
+ما لنهاية طبعا أنا ماخدين M أكبر من N عمدا على أساس
+
+146
+00:09:55,410 --> 00:09:58,430
+M تروح لما لا نهاية تطير و M هي حرة بتظهر زي ما هي
+
+147
+00:09:58,430 --> 00:10:03,530
+إذا M واحدة إلى ما لا نهاية صار عندي XM ناقص X و
+
+148
+00:10:03,530 --> 00:10:09,970
+YM ناقص Y أصغر اللي هو من مين من إرسلون صار عندي
+
+149
+00:10:09,970 --> 00:10:17,000
+تنتين مع بعض ZM ناقص XY حصلت الـ limit هي X لهذه و Y
+
+150
+00:10:17,000 --> 00:10:21,040
+لهذه صارت واحدة في X واحدة في Y صار عندي ZN ناقص X
+
+151
+00:10:21,040 --> 00:10:25,500
+و Y بيساوي normal XN ناقص X زي YN ناقص mean Y
+
+152
+00:10:25,500 --> 00:10:30,360
+التنتين أصغر من مين من يبسلون إذا صار عندي this
+
+153
+00:10:30,360 --> 00:10:34,820
+means that ZN converts the mean لـ X و Y therefore
+
+154
+00:10:34,820 --> 00:10:39,940
+X cross Y is complete إذا انتهينا من X x Y is
+
+155
+00:10:39,940 --> 00:10:42,360
+complete و لو حتى خدنا الـ domain برضه بيبقى لها 
+
+156
+00:10:42,360 --> 00:10:48,940
+complete لأن الـ domain is a closed subspace طيب يا
+
+157
+00:10:48,940 --> 00:10:57,320
+جماعة أطلع لفور الآن عندي T is closed T is closed
+
+158
+00:10:57,320 --> 00:11:01,920
+إذن أكيد الـ G of T أشماله closed in X cross Y و
+
+159
+00:11:01,920 --> 00:11:04,380
+الـ domain of T closed in X إذن الاتنين صاروا
+
+160
+00:11:04,380 --> 00:11:06,960
+incomplete لأن هذا بنخ space و هذا بنخ space اللي
+
+161
+00:11:06,960 --> 00:11:10,680
+هم جزء منه هذا بنخ space و هذا بنخ space إذا على
+
+162
+00:11:10,680 --> 00:11:14,680
+طول G of T and D of T are complete spaces Now
+
+163
+00:11:14,680 --> 00:11:18,300
+consider the mapping خدها الـ mapping الآن B من G
+
+164
+00:11:18,300 --> 00:11:23,040
+of T لعين 2 لعين D of T Defined by .. كله بده أصلهش
+
+165
+00:11:23,040 --> 00:11:26,100
+أنما .. بده أصلكم أن الـ T is bounded يعني نورم
+
+166
+00:11:26,100 --> 00:11:29,140
+الـ T of X أصغر يساوي إيش some number في مين في
+
+167
+00:11:29,140 --> 00:11:31,960
+نورم الـ X هي اللي بده أصله فخلّيني أشوف عبر إيش
+
+168
+00:11:31,960 --> 00:11:35,440
+نصله Now consider the mapping B من G من G of T
+
+169
+00:11:35,440 --> 00:11:39,020
+لعين Domain of T that defined by projection map
+
+170
+00:11:39,020 --> 00:11:44,540
+projection سقاط بسقط الأول B X و T X بسقطوا على
+
+171
+00:11:44,540 --> 00:11:49,570
+مين؟ على X لأن it is left to the reader to show
+
+172
+00:11:49,570 --> 00:11:53,990
+that P is linear P is linear سهل حتى linear بنقدر
+
+173
+00:11:53,990 --> 00:12:06,910
+نثبتها وإحنا مرتاحين عندي P of X و TX اللي هو طبعا
+
+174
+00:12:06,910 --> 00:12:14,670
+بساوي من؟ بساوي X لأن P of الـ element اللي في الـ
+
+175
+00:12:14,670 --> 00:12:16,790
+element اللي في الـ G of T هتديروا بالك أين موجود
+
+176
+00:12:16,790 --> 00:12:22,010
+في الـ G of T الـ element راحة alpha X زائد اللي هو
+
+177
+00:12:22,010 --> 00:12:26,310
+مثلا X prime هيكون ال .. ال .. ال .. ال .. ال
+
+178
+00:12:26,310 --> 00:12:28,590
+element عشان يكون في الـ G of T بدي يكون صورته
+
+179
+00:12:28,590 --> 00:12:35,330
+اللي هو T of alpha X زائد X prime صح؟ ويساوي هدي
+
+180
+00:12:35,330 --> 00:12:41,630
+بيه مش بدنا في ال .. معايا أه ويساوي alpha X زايد X
+
+181
+00:12:41,630 --> 00:12:53,330
+prime ويساوي Alpha بي of X و TX زايد بي of X prime
+
+182
+00:12:53,330 --> 00:12:59,950
+و TX prime حسب التاريخ على طول صارت عندي الـ B is
+
+183
+00:12:59,950 --> 00:13:04,670
+linear أي سؤال معايا
+
+184
+00:13:09,630 --> 00:13:12,750
+الآن خدوا الـ norm الـ norm هي واضح هذه ما هي على
+
+185
+00:13:12,750 --> 00:13:20,030
+طول نورم هذه هو norm الـ X، مظبوط؟ طيب، إذا الها ده
+
+186
+00:13:20,030 --> 00:13:23,390
+هتوديني على الـ boundedness تبعت مين؟ تبع الـ B اللي
+
+187
+00:13:23,390 --> 00:13:27,810
+هو الـ norm الـ B of X و T X اللي هو بيساوي نورم الـ
+
+188
+00:13:27,810 --> 00:13:33,970
+X وراء الـ X، then B is bounded اللي هي أكيد هذه
+
+189
+00:13:35,150 --> 00:13:40,650
+نورم الـ X الـ BX و TX بيساوي نورم الـ X بتخليلي
+
+190
+00:13:40,650 --> 00:13:47,070
+اللي هو هذا is bounded كيف طيب؟ لأ مهو ده اللي
+
+191
+00:13:47,070 --> 00:13:53,350
+منتبهها بشير أصغر أو شاوى اللي هو نورم الـ X زائد
+
+192
+00:13:53,350 --> 00:13:59,290
+نورمين الـ TX صح ولا؟ و هذا إيش بيساوي نورم الـ X و
+
+193
+00:13:59,290 --> 00:14:04,620
+TX إذا صار عندي B of العمصر تبعها هذا اللي بترسله
+
+194
+00:14:04,620 --> 00:14:07,860
+أصغر أو شوية اللي بترسله وانت تعرف اللي هو النور
+
+195
+00:14:07,860 --> 00:14:12,600
+يعني الـ B هنا واحد الثابت فبصير B أشماله is
+
+196
+00:14:12,600 --> 00:14:20,920
+bounded هذا سبب الـ boundedness طيب الآن then اللي
+
+197
+00:14:20,920 --> 00:14:24,300
+هو B is bounded it is easy to see that B is
+
+198
+00:14:24,300 --> 00:14:29,320
+bijective بيواجيكتيف أصلا أكيد B is bijective or
+
+199
+00:14:29,320 --> 00:14:29,820
+one to one
+
+200
+00:14:38,740 --> 00:14:40,920
+معايا ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+201
+00:14:40,920 --> 00:14:42,100
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+202
+00:14:42,100 --> 00:14:42,540
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+203
+00:14:42,540 --> 00:14:42,580
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+204
+00:14:42,580 --> 00:14:42,880
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+205
+00:14:42,880 --> 00:14:42,900
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+206
+00:14:42,900 --> 00:14:43,000
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+207
+00:14:43,000 --> 00:14:48,480
+ال ال ال ال ال ال ال ال ال ال ال ال الت بي
+
+208
+00:14:48,480 --> 00:14:50,200
+of X
+
+209
+00:14:56,260 --> 00:15:02,160
+أكس برايم و TX أشماله أبرايم بظبط هذه X برايم X
+
+210
+00:15:02,160 --> 00:15:07,360
+بيساوي X مين أبرايم بناء عليه TX هيساوي TX برايم
+
+211
+00:15:07,360 --> 00:15:12,020
+عشان T function إذا صارت one to one الآن أنتم
+
+212
+00:15:12,020 --> 00:15:16,540
+خدوا أي من وين لوين جاية الـ B اللي هي الجاية الـ B
+
+213
+00:15:16,540 --> 00:15:20,500
+من اللي هو وينها وينها وينها هي من G of T لـ domain
+
+214
+00:15:20,500 --> 00:15:26,220
+of T خد أي element هنا شكله X إذاً أكيد فيه إله TX
+
+215
+00:15:26,220 --> 00:15:32,320
+إذاً there exist X هو و TX لأن TX موجودة لإنه الـ T
+
+216
+00:15:32,320 --> 00:15:35,420
+function X و TX هنا such that بيه كده مثلًا وكده
+
+217
+00:15:35,420 --> 00:15:40,660
+إذاً الأمطوا برضه أشماله واضحة أشوف التقباتات
+
+218
+00:15:47,740 --> 00:15:57,420
+للعدي بي من من من G of T لعين domain of T خد الآن
+
+219
+00:15:57,420 --> 00:16:04,880
+أي X element in domain of T then there exist X و T
+
+220
+00:16:04,880 --> 00:16:11,140
+X element in domain of T لأن T is a function G of
+
+221
+00:16:11,140 --> 00:16:19,120
+T such that P of X و TX هو مين اللي بدأت فيها X إذا
+
+222
+00:16:19,120 --> 00:16:28,280
+أنتوا معايا؟ إذا B is onto إذا كل شي فيها صارت عندي
+
+223
+00:16:28,280 --> 00:16:34,660
+الآن B bounded أو one to one onto و linear إذا B
+
+224
+00:16:34,660 --> 00:16:38,060
+inverse من domain of T إلى G of T أشماله exist and
+
+225
+00:16:38,060 --> 00:16:42,440
+is defined by B inverse X إيش هيروح للـ X و صورة مين
+
+226
+00:16:42,440 --> 00:16:47,840
+اللي هي الـ X under T اللي هي TX الآن since D of D
+
+227
+00:16:47,840 --> 00:16:50,580
+and D of D are complete then by open mapping
+
+228
+00:16:50,580 --> 00:16:54,760
+theorem اللي قبل بشوية المرة المحادرة اللي فاتت
+
+229
+00:16:54,760 --> 00:16:58,740
+اللي هو هيكون الـ B inverse إيش ماله is bounded
+
+230
+00:16:58,740 --> 00:17:02,920
+خلينا نقول مدام B inverse bounded نقول norm الـ B
+
+231
+00:17:02,920 --> 00:17:07,000
+inverse للـ X أصغر سوى B في مين؟ في norm الـ X طب هو
+
+232
+00:17:07,000 --> 00:17:11,490
+B inverse of X إيش بسوى norm الـ X و TX معايا؟ إذا
+
+233
+00:17:11,490 --> 00:17:16,910
+صار عندي هذا المقدار أصغر أو أشهر هذا ومنه على طول
+
+234
+00:17:16,910 --> 00:17:21,370
+norm of TX أنا بعرف أصغر أو أشهر norm of TX زائد
+
+235
+00:17:21,370 --> 00:17:25,170
+مين؟ زائد norm of X زي اللي عملتها وهذا هو مين؟
+
+236
+00:17:25,170 --> 00:17:28,970
+norm of X و TX هيه اللي هو أصغر أو أشهر من B في X
+
+237
+00:17:28,970 --> 00:17:31,730
+إذا صار عندي norm of TX أصغر أو أشهر بيه في norm
+
+238
+00:17:31,730 --> 00:17:39,030
+of X وهذا يعني أن الـ T is bounded أي شؤال اللي
+
+239
+00:17:39,030 --> 00:17:39,490
+بعده
+
+240
+00:17:43,930 --> 00:17:47,410
+إذن هذا أعطاني condition الـ closed graph theorem
+
+241
+00:17:47,410 --> 00:17:54,650
+أعطاني إعلان إن T من بنخ space إلى بنخ space اللي
+
+242
+00:17:54,650 --> 00:18:00,390
+هو closed إذا كان closed بيعطيني إيه شماله؟
+
+243
+00:18:00,390 --> 00:18:08,030
+bounded T is bounded طيب شوفوا
+
+244
+00:18:08,030 --> 00:18:13,890
+الآن اللي بعدها النظرية اللي بعدها بتقول للـ T من
+
+245
+00:18:13,890 --> 00:18:16,890
+domain of T لعند Y بيه a linear operator و الـ
+
+246
+00:18:16,890 --> 00:18:20,390
+domain of T X معلق crazing على اللي هو انه ياخد الـ
+
+247
+00:18:20,390 --> 00:18:24,770
+domain of T للـ X يا جماعة هرايحنا و خد من X لعند Y
+
+248
+00:18:24,770 --> 00:18:28,630
+واشتغلونه وحط خاص الـ domain of T في الـ X يا سيدة
+
+249
+00:18:28,630 --> 00:18:35,130
+مش مشكلة كتيرة يعني بشعر أنه هي كأعام كتير
+
+250
+00:18:35,130 --> 00:18:37,550
+من الكتب خلاص مش بتبقى في domain of T علشان تبقى
+
+251
+00:18:37,550 --> 00:18:40,510
+تعتبر X لعند Y وتعتبر X هو الـ domain وهو norm of
+
+252
+00:18:40,510 --> 00:18:44,330
+this base الأخرى أو إذا كان بديها هي كمليت بتعطيه
+
+253
+00:18:44,330 --> 00:18:47,690
+كمليت ومتعاشر وكذا الأخرى بيقالين ياروبيرت لو الـ
+
+254
+00:18:47,690 --> 00:18:50,590
+domain of T subset من X and X and Y لكن رائع هو
+
+255
+00:18:50,590 --> 00:18:56,210
+عموما في العرض and X and Y be normed this basis ثم
+
+256
+00:18:56,210 --> 00:18:59,410
+T is closed if and only if it has the following
+
+257
+00:18:59,410 --> 00:19:03,390
+properties أنتم اللي بقولوا هال properties XN
+
+258
+00:19:03,390 --> 00:19:06,390
+بتروح للـ X where XN المتن دومين of T for all n and
+
+259
+00:19:06,390 --> 00:19:09,410
+T XN بتروح للـ Y دون X المتن دومين of T and T X
+
+260
+00:19:09,410 --> 00:19:17,980
+يشبه لها بتسوى Y هذا يستوجب الوقوف نحكي عنه يعني
+
+261
+00:19:17,980 --> 00:19:23,900
+بمعنى آخر يترجم .. يترجم إحنا زمان .. زمان أخدنا T
+
+262
+00:19:23,900 --> 00:19:31,700
+اه .. قولوا معايا T من عند X لعند Y أنها
+
+263
+00:19:31,700 --> 00:19:37,500
+continuous أو bounded إذا حققت الشرط التالي أنه
+
+264
+00:19:37,500 --> 00:19:44,130
+لما XN بتروح للـ X ماشي الحال يعني XN من وين؟ XN من
+
+265
+00:19:44,130 --> 00:19:47,950
+الـ X والـ X من الـ X من رأس الدورة و XN روحت للـ 
+
+266
+00:19:47,950 --> 00:19:54,010
+X إذا هذا أعطاني إن الـ TXN بتروح للـ TX على طول
+
+267
+00:19:54,010 --> 00:19:57,990
+بنقول عن الـ T أشماله is continuous إذن التعبير
+
+268
+00:19:57,990 --> 00:20:00,770
+عن الـ continuity أو الـ boundedness للـ linear
+
+269
+00:20:00,770 --> 00:20:05,030
+operator عن طريق الـ sequence إن sequence converges
+
+270
+00:20:05,030 --> 00:20:09,420
+في X في داخل كله في داخل X بيعطيني إذا أعطاني أن
+
+271
+00:20:09,420 --> 00:20:13,500
+الـ TX بتروح لـ TX في داخل الـ Y معناته أنه انتهى
+
+272
+00:20:13,500 --> 00:20:16,800
+الأمر صار إيش ماله continuous هنا الآن بده يعطي
+
+273
+00:20:16,800 --> 00:20:21,620
+condition يكافئ لـ closedness اللي closed برضه عن
+
+274
+00:20:21,620 --> 00:20:24,940
+طريق الـ sequences بس ديروا بالكم هنا ماخد اللي هو
+
+275
+00:20:24,940 --> 00:20:28,690
+الـ X و الـ Y normed spaces مضارة normed spaces الـ N
+
+276
+00:20:28,690 --> 00:20:32,270
+يعني خرّين إحنا T is closed if and only if T has
+
+277
+00:20:32,270 --> 00:20:36,090
+the following property إيش بييجي بيقول إذا كانت
+
+278
+00:20:36,090 --> 00:20:43,350
+إذا كانت XN element in X لكل N و الـ XN عاملها
+
+279
+00:20:43,350 --> 00:20:52,050
+راحت للـ X و أيضا اللي هو TXN راحت للـ Y و TXN TXN
+
+280
+00:20:52,050 --> 00:20:59,850
+راحت للـ Y و الـ TXM طبيعي هتكون موجودة في الـ Y ما 
+
+281
+00:20:59,850 --> 00:21:03,510
+حكى شيء لا عن X ولا عن Y يعني ما قالش أن X موجودة
+
+282
+00:21:03,510 --> 00:21:08,490
+في الـ X وما فرضش هذه الحالة لأ هو الـ N يعني قال
+
+283
+00:21:08,490 --> 00:21:13,250
+XN بتروح لصنف X ماجاش موجودة في الـ X وقال أن الـ
+
+284
+00:21:13,250 --> 00:21:17,570
+TXN بتروح للـ Y هنا استنتجناها في الـ Continuity
+
+285
+00:21:17,570 --> 00:21:21,170
+TXN راحت للـ X وكانت هذه موقف شرط أن تكون هنا،
+
+286
+00:21:21,170 --> 00:21:26,070
+هنا مش شرط لكن شرط شيء هنا أن TXN تروح للـ Y هنا مش
+
+287
+00:21:26,070 --> 00:21:31,490
+شرط تطلع من جواب الشرط TXN بتروح لمين؟ لـ TX أعطال
+
+288
+00:21:31,490 --> 00:21:37,670
+الـ Continuity هذا لو حدث كلّه على بعضه أو أعطاني أن
+
+289
+00:21:37,670 --> 00:21:42,310
+الـ X في الـ X والـ TX هي الـ Y معناته وين موجودة
+
+290
+00:21:42,310 --> 00:21:47,010
+في الـ Y معناته إذا حدث هذا بيكون الـ T is a
+
+291
+00:21:47,010 --> 00:21:51,910
+closed operator is a closed operator إذن if XN
+
+292
+00:21:51,910 --> 00:21:57,140
+بتروح للـ X و XN في Domain T والـ T X N بتروح للـ Y
+
+293
+00:21:57,140 --> 00:22:02,360
+إذا هذا مع بعضه أعطاني أنه X في دومين الـ T والـ T
+
+294
+00:22:02,360 --> 00:22:06,560
+X بتساوي Y Automatic هذا إيش معناه أنه هتكون الـ
+
+295
+00:22:06,560 --> 00:22:13,560
+T is closed واضح الفرق بين ال continuity بدلالة 
+
+296
+00:22:13,560 --> 00:22:17,700
+اللي هو ال sequences و ال closedness للـ T بدلالة
+
+297
+00:22:17,700 --> 00:22:21,340
+ال sequences هاي الفرق بين أنه هاي الأمور واضحة
+
+298
+00:22:25,070 --> 00:22:30,770
+خليني بس نكمل اللي بنحكيه suppose
+
+299
+00:22:30,770 --> 00:22:35,090
+that T 
+
+300
+00:22:35,090 --> 00:22:36,630
+is closed
+
+301
+00:22:40,870 --> 00:22:46,790
+الـ openness بتحكي علاقة بين T inverse و T إذا
+
+302
+00:22:46,790 --> 00:22:50,430
+بدنا نترجم على T inverse بيصير كلام ثاني then T is
+
+303
+00:22:50,430 --> 00:22:55,810
+closed إذا دول اللي ده property صحيحة نجي الآن
+
+304
+00:22:55,810 --> 00:23:00,350
+نبرهن suppose that T is closed إذا G of T إيش
+
+305
+00:23:00,350 --> 00:23:07,820
+ماله؟ Closed الآن بدي أثبت لك آخذ هذه وهذه وأوصلك 
+
+306
+00:23:07,820 --> 00:23:11,120
+لهذه المجموعة ماشي؟ ممكن خلصنا الـ visual أول طيب
+
+307
+00:23:11,120 --> 00:23:15,480
+إذا بدي آخذ ما أعطينيه عشان أستعمله بدي أقول له let
+
+308
+00:23:15,480 --> 00:23:19,620
+xn بتروح للـx هيها و الـxn في domain الـT وخلينا 
+
+309
+00:23:19,620 --> 00:23:25,440
+نأخذ Txn بتروح لمين؟ للـY من الحديث هذا أكيد الـxn
+
+310
+00:23:25,440 --> 00:23:31,220
+و Txn وين موجود؟ في الـ G of D ماشي و ال XN و ال T
+
+311
+00:23:31,220 --> 00:23:36,060
+XN وين بتروح للـ X و Y لأنّه مضلل الـ X عن وين ومضلل 
+
+312
+00:23:36,060 --> 00:23:39,680
+أيها الـ X عن ... على الـ X ومضلل الـ T XN على 
+
+313
+00:23:39,680 --> 00:23:46,060
+مين؟ على الـ T X إذا عند X و Y هتكون وين موجودة؟ في 
+
+314
+00:23:46,060 --> 00:23:52,580
+الـ G of D معايا؟ ليش؟ لأن الـ T is closed ما هو شو 
+
+315
+00:23:52,580 --> 00:23:56,220
+معناه الـ T is closed؟ أنه الآن الـ G of T is
+
+316
+00:23:56,220 --> 00:23:59,180
+closed إيش معناه الـ G of T is closed؟ يعني أي
+
+317
+00:23:59,180 --> 00:24:04,120
+sequence فيه converts to some element ستكون في الـ
+
+318
+00:24:04,120 --> 00:24:08,600
+G of T إذا صار عندي Xn وT Xn بتروح للـ X و Y قطعًا 
+
+319
+00:24:08,600 --> 00:24:12,900
+X و Y هتكون في الـ G of T عشان الـ G of T is
+
+320
+00:24:12,900 --> 00:24:16,420
+closed لأن الـ T في الأصل is closed this means
+
+321
+00:24:16,420 --> 00:24:20,620
+that إن ما دامت الـ X Y في الـ G of T إذن X في الـ
+
+322
+00:24:20,620 --> 00:24:25,100
+domain of T والـ T X أشماله بسوء Y لأن الـ G of T
+
+323
+00:24:25,100 --> 00:24:28,520
+هي عبارة عن ال order pairs بين اللي هو عناصر ال
+
+324
+00:24:28,520 --> 00:24:33,160
+domain of T و الصور اللي هي لهذا ال domain إذن هذا
+
+325
+00:24:33,160 --> 00:24:37,820
+بيعني أن X في domain T و T X بسوء Y لأن conversely
+
+326
+00:24:39,630 --> 00:24:43,530
+suppose that اتنين holds هي هذه الخاصية إيش ما لها
+
+327
+00:24:43,530 --> 00:24:48,150
+تتحقق الآن بدنا نثبت لكم أن هو g of t is closed
+
+328
+00:24:48,150 --> 00:24:51,770
+كيف بدنا نثبت أنها closed؟ بدي آخذ x y في ال g of
+
+329
+00:24:51,770 --> 00:24:54,910
+t closure وأثبت لكم ال x y في ال g of t وخلصنا
+
+330
+00:24:54,910 --> 00:24:57,150
+صار ال g of t is closed اللي بيساوي ال g of t يعني 
+
+331
+00:24:57,150 --> 00:25:01,700
+أن ال g of t is closed ثم مادام الـ G of T مقفلة 
+
+332
+00:25:01,700 --> 00:25:04,980
+الـ X Y في الـ G of T مقفلة إذا تتمتع بالخاصية 
+
+333
+00:25:04,980 --> 00:25:08,600
+التالية أن أنا بقدر ألاقي الـ sequence XN و TXN في
+
+334
+00:25:08,600 --> 00:25:13,420
+الـ G of T convolutionally للـ XY إذا there exists
+
+335
+00:25:13,420 --> 00:25:16,820
+this sequence of elements in G of T such that XN و
+
+336
+00:25:16,820 --> 00:25:21,030
+TXN تروح لمين للـ XY وهذا يعني Xn بتروح للـ X و Tx
+
+337
+00:25:21,030 --> 00:25:24,990
+بتروح لمين؟ للـ Y و Xn من وين جاية؟ من ال domain of
+
+338
+00:25:24,990 --> 00:25:28,390
+T يعني كل الشروط اللي جاب المتحققة then by
+
+339
+00:25:28,390 --> 00:25:31,690
+assumption اللي هو the property 2 X هذه هتكون في 
+
+340
+00:25:31,690 --> 00:25:36,150
+domain T و Tx بالساوية Y وهذا يعني ال X و Y موجودة
+
+341
+00:25:36,150 --> 00:25:40,170
+في G of T وهذا يعني أنه بدأنا بهذه وانتهينا بهذه 
+
+342
+00:25:40,170 --> 00:25:44,710
+أنه therefore G of D is closed وهذا يعني أنه T is
+
+343
+00:25:44,710 --> 00:25:45,830
+closed اللي بعده يلا
+
+344
+00:25:50,340 --> 00:25:54,340
+الآن مثال اللي وعدناكم فيه هو الأول اللي قلنا احنا
+
+345
+00:25:54,340 --> 00:25:58,160
+احنا يعني في bounded linear operators أو في عندي
+
+346
+00:25:58,160 --> 00:26:01,740
+closed linear operators which is not bounded
+
+347
+00:26:01,740 --> 00:26:05,440
+والمثال المشهور اللي هو example differential 
+
+348
+00:26:05,440 --> 00:26:11,020
+operator I differential operator let X بتساوي C01
+
+349
+00:26:11,020 --> 00:26:15,690
+على ال continuous functions وT من الـ domain of T
+
+350
+00:26:15,690 --> 00:26:19,950
+لعند مين؟ لعند X بي such that الـ TX بتساوي إيش ما
+
+351
+00:26:19,950 --> 00:26:24,620
+لها X' و X' is the derivative of X طيب ما هو هذا
+
+352
+00:26:24,620 --> 00:26:28,140
+الـ X إيش ما لها عبارة عن continuous functions مش 
+
+353
+00:26:28,140 --> 00:26:30,480
+كل ال continuous functions كان بيه إيش ما لها
+
+354
+00:26:30,480 --> 00:26:34,060
+مشتقاته إذا أكيد اللي هو بده يكون ال domain
+
+355
+00:26:34,060 --> 00:26:38,820
+of T of proper subspace من مين؟ من ال X إذا هذا ال
+
+356
+00:26:38,820 --> 00:26:42,280
+proper subspace اللي هو of functions اللي بيديها
+
+357
+00:26:42,280 --> 00:26:45,780
+كمان مش بس ما مشتقاته اللي هو domain of T is a
+
+358
+00:26:45,780 --> 00:26:49,060
+subspace of functions ياك بديها X element in X
+
+359
+00:26:49,060 --> 00:26:51,980
+which have a continuous derivative يعني اللي بتطلع
+
+360
+00:26:51,980 --> 00:26:55,480
+برضه تطلع أي شمالها continuous عشان أقدر أرسلها
+
+361
+00:26:55,480 --> 00:26:58,460
+وين في حالة فتطلع continuous مش هاد ال X
+
+362
+00:26:58,460 --> 00:27:02,260
+continuous فالآن اللي أنا أخذش domain of T هو ال
+
+363
+00:27:02,260 --> 00:27:09,200
+domain اللي جزء من الـ C01 و اللي دواله اللي
+
+364
+00:27:09,200 --> 00:27:15,200
+بتتفاضل وتفاضلها بتطلع أي شمالها continuous الآن 
+
+365
+00:27:15,200 --> 00:27:20,580
+أحدّن T is not bounded بط إيش ماله is closed
+
+366
+00:27:20,580 --> 00:27:25,320
+أثبتناها not bounded زمان اللي هو by اثنين سبعة
+
+367
+00:27:25,320 --> 00:27:30,720
+خمسة بالظبط T is linear بط not bounded بدنا نثبت
+
+368
+00:27:30,720 --> 00:27:35,570
+أنها إيش لأن أنّه closed شوفوا كيف بعد أن نثبت أنها 
+
+369
+00:27:35,570 --> 00:27:40,090
+قريبة نستخدم الخاصية اللي قبل بشوية let XN element
+
+370
+00:27:40,090 --> 00:27:44,650
+in domain of T for all N such that XN بتروح للـ X و
+
+371
+00:27:44,650 --> 00:27:50,390
+TXN إيش معناها سموها XN برايم بتروح لمين للـ Y ماشي
+
+372
+00:27:50,390 --> 00:27:53,890
+الحالة XN برايم اللي هي إيش معناه ال derivative
+
+373
+00:27:53,890 --> 00:27:59,090
+مش هي اتفجن اللي هو بريطان هو اللي بفاضل إذا TXN
+
+374
+00:27:59,090 --> 00:28:02,050
+برايم هو سمّيه إيش اسمه XN برايم اللي هي derivative
+
+375
+00:28:02,050 --> 00:28:08,010
+لمين للـ XN معايا احنا هي اللي بدنا هيها نفترض هذه
+
+376
+00:28:08,010 --> 00:28:11,590
+بتروح لهذه وهذه بتروح لمين لـ some y يعني ال xn
+
+377
+00:28:11,590 --> 00:28:15,150
+بتروح للـ x و ال xn بتروح لمين للـ y بدنا نثبت لكم
+
+378
+00:28:15,150 --> 00:28:19,590
+أن الـ x في الـ domain of T ونثبت أن هو الـ y إيش
+
+379
+00:28:19,590 --> 00:28:25,960
+معناه تي اكس هي الـ y بتكون مقفلة طيب by 155 the
+
+380
+00:28:25,960 --> 00:28:29,720
+convergence in the norm space أخذناها برضه الـ C زي
+
+381
+00:28:29,720 --> 00:28:33,380
+اللي كنا نقول convergence في C01 أنه uniform
+
+382
+00:28:33,380 --> 00:28:37,640
+convergence إيش يعني uniform convergence يعني لو 
+
+383
+00:28:37,640 --> 00:28:41,540
+عندي sequence of continuous functions هذا في
+
+384
+00:28:41,540 --> 00:28:44,280
+الدنيا العادية تبع ال real analysis تبع اثنين تبع
+
+385
+00:28:44,280 --> 00:28:49,240
+الـ baccalaureate لو xn sequence of functions
+
+386
+00:28:51,780 --> 00:28:55,680
+continuous functions that converge to some x وكان
+
+387
+00:28:55,680 --> 00:28:59,480
+الـ convergence اللي هو point y يسمّى y مش شرط أنّه
+
+388
+00:28:59,480 --> 00:29:02,800
+تطلع x continuous لكن إذا uniform قطعًا أنّه تطلع 
+
+389
+00:29:02,800 --> 00:29:06,240
+أي شمالها continuous وعنا الـ convergence uniform
+
+390
+00:29:06,240 --> 00:29:11,380
+and since the convergence is uniform then اللي هو 
+
+391
+00:29:11,380 --> 00:29:14,980
+هتكون الـ limit تبعتنا اللي هو في داخل هذا هتكون
+
+392
+00:29:14,980 --> 00:29:20,730
+continuous طيب خلوه في الذاكرة إذا الـ integration
+
+393
+00:29:20,730 --> 00:29:27,240
+لـ 0 لـ T Y of T DT بساوي طبعًا و الـ Limit مدام
+
+394
+00:29:27,240 --> 00:29:29,780
+ينظم convergence الـ Limit بطلع وبنزل زي ما بده
+
+395
+00:29:29,780 --> 00:29:35,260
+من الهدف هو عبارة عن Limit من 0 لـ T لـ X N prime of
+
+396
+00:29:35,260 --> 00:29:39,220
+T لأنه اتفجن أن X N prime of T أشمال ل X N prime
+
+397
+00:29:39,220 --> 00:29:43,660
+بتروح لمين لـ Y فبيصير عند الـ Limit ده يتاو الـ Limit
+
+398
+00:29:43,660 --> 00:29:46,860
+بنطلحها برا بيصير X N prime of T dt من صفر اللي عند
+
+399
+00:29:46,860 --> 00:29:52,280
+T وهي ساوي الـ Limit الآن التفاضل .. التكامل هذه ..
+
+400
+00:29:52,280 --> 00:29:55,940
+مجرد هذا .. اللي هو ال derivative على طول هي عبارة
+
+401
+00:29:55,940 --> 00:30:02,540
+عن مين؟ xn of t ماقص xn of mean of zero xn of t
+
+402
+00:30:02,540 --> 00:30:07,700
+اللي هي أشمالها اللي هي limitها اللي هو x of t لأنه 
+
+403
+00:30:07,700 --> 00:30:13,540
+ماخد مين أنا الـ limit حسبتها حسبت هذه طلعت هذه ال
+
+404
+00:30:13,540 --> 00:30:17,700
+limit اللي أنا لها هي الـ limit limit لهذه x of t و
+
+405
+00:30:17,700 --> 00:30:22,800
+limit لهذه إيش ماله x of zero لإنه xn بتروح لل x 
+
+406
+00:30:22,800 --> 00:30:25,900
+uniformly إذا أكيد point twice إيش يعني point
+
+407
+00:30:25,900 --> 00:30:29,740
+twice يعني xn of t بتروح لل x of t و ال xn of zero
+
+408
+00:30:29,740 --> 00:30:33,200
+بتروح لمين لل zero هذا for every t إذا صار عندي ال
+
+409
+00:30:33,200 --> 00:30:37,800
+integration هذا بيساوي xn of t نقص x of zero that
+
+410
+00:30:37,800 --> 00:30:42,240
+is x of t إيش بتساوي؟ x of zero زائد ال integration
+
+411
+00:30:42,240 --> 00:30:47,760
+ماشي الحال إذا طلعت عند ال x إيش مالها؟ اللي على 
+
+412
+00:30:47,760 --> 00:30:51,940
+الصورة هذه اللي هي عبارة عن continuous أيّهاش؟ اللي
+
+413
+00:30:51,940 --> 00:30:58,080
+هي ال derivative اللي موجودة و continuous الـ
+
+414
+00:30:58,080 --> 00:31:02,660
+derivative لهذه موجودة و continuous هذه بتكون x في
+
+415
+00:31:02,660 --> 00:31:06,800
+domain of t لأن ال derivative لهذه ثابت ال
+
+416
+00:31:06,800 --> 00:31:09,640
+derivative لهذه zero و ال derivative لهذه أشمالها 
+
+417
+00:31:09,640 --> 00:31:13,580
+اللي هي بتطلع y of t صح نقص y of zero و y of t ما 
+
+418
+00:31:13,580 --> 00:31:18,690
+هي أشمالها اللي هي continuous YOM ماذا يعني إذا 
+
+419
+00:31:18,690 --> 00:31:22,350
+كنتنيواص فانكشن لأننا قلنا اللي هو ال uniform
+
+420
+00:31:22,350 --> 00:31:25,570
+convergence بوات ديناميين ال continuous ل
+
+421
+00:31:25,570 --> 00:31:29,470
+continuous ماشي الحال لأن هذه continuous والـ 
+
+422
+00:31:29,470 --> 00:31:32,750
+convergence uniform إذا أكيد هذه أيش معناها؟
+
+423
+00:31:32,750 --> 00:31:36,030
+continuous من وين إكس أن إبراهيم continuous ما هو؟
+
+424
+00:31:36,030 --> 00:31:38,530
+إيه إحنا الـ x unwell موجودة في الـ domain والـ T
+
+425
+00:31:38,530 --> 00:31:41,490
+الـ domain والـ T هو عبارة عن الدوال اللي الـ
+
+426
+00:31:41,490 --> 00:31:45,070
+derivative إلها continuous فطبيعي كل الأمور مبررة
+
+427
+00:31:45,070 --> 00:31:48,730
+فبتصير عندي x of T بتساوي هذا الكلام اللي هي is a
+
+428
+00:31:48,730 --> 00:31:52,110
+continuous function يعني x في الـ domain والـ T و
+
+429
+00:31:52,110 --> 00:31:56,970
+الـ Tx إيش بتساوي؟ اللي هو الـ X' الـ Tx اللي هي الـ X'
+
+430
+00:31:57,250 --> 00:32:01,750
+بالـ X' إيش بتساوي الـ Y then by theorem كده T is
+
+431
+00:32:01,750 --> 00:32:06,430
+closed إذن هذا مثال على اللي هو closed linear
+
+432
+00:32:06,430 --> 00:32:13,290
+operator which is not bounded يلاّ
+
+433
+00:32:13,290 --> 00:32:20,570
+أطلع على فوق الـ dot بتقول domain of T ليس مغلقًا
+
+434
+00:32:20,570 --> 00:32:24,570
+لأن .. لا طبعًا أكيد domain of T ليس مغلقًا domain 
+
+435
+00:32:24,570 --> 00:32:27,090
+of T اللي فوق .. اللي فوق هذا domain of T اللي
+
+436
+00:32:27,090 --> 00:32:30,370
+أخدناه اللي هو main domain of T the space أو the
+
+437
+00:32:30,370 --> 00:32:33,610
+subspace of all continuous .. اللي هو of all
+
+438
+00:32:33,610 --> 00:32:37,400
+functions that has a continuous derivative هذا is
+
+439
+00:32:37,400 --> 00:32:42,480
+not closed لأنه لو كان closed automatic من النظرية
+
+440
+00:32:42,480 --> 00:32:46,220
+اللي جابلها in example كذا is not closed because
+
+441
+00:32:46,220 --> 00:32:50,660
+if it is closed then by theorem أربعة تلتاشت اتنين 
+
+442
+00:32:50,660 --> 00:32:55,540
+T is bounded because T is closed then we have a
+
+443
+00:32:55,540 --> 00:32:58,500
+contradiction with T is not bounded اللي أثبتناها
+
+444
+00:33:04,230 --> 00:33:13,890
+تعني المثال اللي فوق ببرهن لك أن الـ subspace of
+
+445
+00:33:13,890 --> 00:33:18,130
+all the functions that has a continuous derivative
+
+446
+00:33:18,130 --> 00:33:26,330
+is not a closed subspace طيب .. الآن قلنا الـ 
+
+447
+00:33:26,330 --> 00:33:30,070
+Closedness does not imply boundedness of linear
+
+448
+00:33:30,070 --> 00:33:33,610
+operator من اللي فوق يعني Closed مش شرط يعطيه
+
+449
+00:33:33,610 --> 00:33:38,430
+شماله bounded الآن برضه boundedness does not imply
+
+450
+00:33:38,430 --> 00:33:41,430
+the closeness of linear operator يعني بدي أديبلك
+
+451
+00:33:41,430 --> 00:33:47,690
+اللي هو bounded linear operator which is not
+
+452
+00:33:47,690 --> 00:33:50,870
+closed بدي أديب bounded linear operator which is
+
+453
+00:33:50,870 --> 00:33:58,700
+not closed طيب، نشوف لـ I الـ Identity من domain of
+
+454
+00:33:58,700 --> 00:34:01,220
+T لـ domain of T Be the identity operator on domain
+
+455
+00:34:01,220 --> 00:34:03,720
+of T يعني أي domain of T من عند X لعندك نور من الـ
+
+456
+00:34:03,720 --> 00:34:05,200
+space لعندك نور من الـ space أو جزء من نور من الـ
+
+457
+00:34:05,200 --> 00:34:09,300
+space Where D of T is .. بقى أسف بدي أقول هو
+
+458
+00:34:09,300 --> 00:34:12,960
+domain of T proper dense subspace of a normed
+
+459
+00:34:12,960 --> 00:34:17,760
+space من X يعني أخد الآن ال identity function الـ
+
+460
+00:34:17,760 --> 00:34:23,160
+identity function من domain of T لعند domain of T
+
+461
+00:34:24,330 --> 00:34:28,950
+اللي بيرسل الـ Element لمين؟ لنفسه، Identity هش
+
+462
+00:34:28,950 --> 00:34:35,190
+بدّو domain of T بدّو domain of T Dense من X الـ
+
+463
+00:34:35,190 --> 00:34:42,810
+Space اللي هو Normed Space وDomain of T بدّي بربر
+
+464
+00:34:42,810 --> 00:34:51,270
+subset من X بربر subset من X يعني في Element في
+
+465
+00:34:51,270 --> 00:34:55,830
+الـ X مش موجود وين؟ في الـ Domain of T وهذا وهذا
+
+466
+00:34:55,830 --> 00:34:59,940
+اللي هو مفتاح انها تثبت ان T is not closed طيب أو
+
+467
+00:34:59,940 --> 00:35:03,040
+الـ identity is not closed let T من domain of T يا
+
+468
+00:35:03,040 --> 00:35:05,320
+domain of B be the indented operator on domain of
+
+469
+00:35:05,320 --> 00:35:09,080
+T where domain of T is a proper dense subspace of
+
+470
+00:35:09,080 --> 00:35:12,900
+a known D space X زي ما قلت it is clear that T is
+
+471
+00:35:12,900 --> 00:35:15,980
+linear and bounded اللي هو ال .. اللي هو مين؟ اللي
+
+472
+00:35:15,980 --> 00:35:18,580
+هو ال identity function اثبتناها مرات انه bounded
+
+473
+00:35:18,580 --> 00:35:23,000
+و .. و .. و linear but T is not closed ليش T مش
+
+474
+00:35:23,000 --> 00:35:27,580
+closed؟ شوفوا this follows from theorem 4.13 اللي
+
+475
+00:35:27,580 --> 00:35:32,660
+قبل شوية if we take an x element in main خدوا x x
+
+476
+00:35:32,660 --> 00:35:43,090
+x element in x نقص و main of T ماشي الحال و أكيد في
+
+477
+00:35:43,090 --> 00:35:50,790
+X لأننا ماخدينه بربر الان و sequence Xn element
+
+478
+00:35:50,790 --> 00:35:57,300
+in domain of T which converts لمن؟ لمن؟ لل X بنقدر
+
+479
+00:35:57,300 --> 00:36:01,400
+نعمل هيك عندي أكيد بنقدر نعمل X في ال .. في ال ..
+
+480
+00:36:01,400 --> 00:36:04,640
+في ال X إذا في Sequence موجودة في domain of T
+
+481
+00:36:04,640 --> 00:36:09,720
+Converse لها إذا صار عندي X N بتروح لل X و ال X مش
+
+482
+00:36:09,720 --> 00:36:14,240
+في domain T ال X أشماله is not element in domain
+
+483
+00:36:14,240 --> 00:36:21,030
+of mean of T إذا صار عندي هذا متحققهذا متحقق
+
+484
+00:36:21,030 --> 00:36:25,570
+خلّيني هذه أحطها وين؟ برا X is not element in
+
+485
+00:36:25,570 --> 00:36:31,570
+domain of T هذا متحقق و I X M X N له هو عبارة عن I
+
+486
+00:36:31,570 --> 00:36:37,850
+X لانها دي function يعني هذه ال X وهذه ال X M من
+
+487
+00:36:37,850 --> 00:36:41,390
+فوق هي متحققة إذا ال I X M اللي هو ال X M
+
+488
+00:36:41,390 --> 00:36:48,820
+converges لل X اللي هي I X واضح أنه لو بدها تكون
+
+489
+00:36:48,820 --> 00:36:53,460
+closed بدوا يكون عندكم ال X في domain ال T و ال I
+
+490
+00:36:53,460 --> 00:36:59,240
+X هو ال X اللي هي اسمها ال I X هي ال Y لكن ال X
+
+491
+00:36:59,240 --> 00:37:05,100
+مالها؟ مش في domain ال T إذا ال I is not closed أي
+
+492
+00:37:05,100 --> 00:37:11,280
+سؤال اللي بعده يلاّ نيجي الآن للمّا اطلع لفوق
+
+493
+00:37:11,280 --> 00:37:16,540
+الأخيرة الـ let T من الـ domain of T لعند YB a
+
+494
+00:37:16,540 --> 00:37:22,020
+bounded linear operator Subset of X where X and Y
+
+495
+00:37:22,020 --> 00:37:26,560
+are non-disbases then if domain of T is closed
+
+496
+00:37:26,560 --> 00:37:32,220
+subset of X then T is closed إذا كانت domain of T
+
+497
+00:37:32,220 --> 00:37:35,920
+is closed ستكون T is closed هاي واحد هذا إيش ماله
+
+498
+00:37:35,920 --> 00:37:39,820
+bounded linear operator تانية if T is closed and Y
+
+499
+00:37:39,820 --> 00:37:42,480
+is complete then domain of T is closed subset من
+
+500
+00:37:42,480 --> 00:37:47,120
+من من اللي هو ال X البروف لأ بدنا نبره اللي بروف
+
+501
+00:37:47,120 --> 00:37:53,900
+وافتحلي على الكتاب يالا البرهان هو .. عند .. زي ما
+
+502
+00:37:53,900 --> 00:37:57,560
+قلنا إذا كان domain of T closed subset of X إذا T
+
+503
+00:37:57,560 --> 00:38:00,640
+أشمالها is closed بالـ data between الـ T is
+
+504
+00:38:00,640 --> 00:38:03,180
+closed كيف ال data between ال T is closed؟ بقى عن
+
+505
+00:38:03,180 --> 00:38:05,540
+طريق الـ sequences بناخد Xn وين؟ موجودة في domain
+
+506
+00:38:05,540 --> 00:38:10,920
+of T ونفترض إنها Xn converged من X ونفترض إن T Xn
+
+507
+00:38:10,920 --> 00:38:13,820
+برضه أشماله converged converged to some اللي هو
+
+508
+00:38:13,820 --> 00:38:19,620
+element Y الآن مدام xn in domain of T اذا أكيد الـ
+
+509
+00:38:19,620 --> 00:38:22,900
+.. ال .. ال .. ال .. ال .. ال xn convergence اللي
+
+510
+00:38:22,900 --> 00:38:25,660
+هيكون هو الموجود في الـ domain of T closure لكن
+
+511
+00:38:25,660 --> 00:38:29,320
+احنا بنقول دي domain of T أشماله اللي هو عبارة عن
+
+512
+00:38:29,320 --> 00:38:32,680
+closed اه مقاطينها closed اذا أكيد الـ domain of T
+
+513
+00:38:32,680 --> 00:38:34,940
+closure هو .. هو نفس الـ domain of T يعني ال x هو
+
+514
+00:38:34,940 --> 00:38:38,540
+الموجودة في الـ domain of T لأن since the domain of
+
+515
+00:38:38,540 --> 00:38:41,860
+T is closed زي ما قلنا إذا صار عندي ال X ال X
+
+516
+00:38:41,860 --> 00:38:47,940
+موجودة في domain of T و ال T X N هتروح ل T X لأن T
+
+517
+00:38:47,940 --> 00:38:51,280
+أشمالها is continuous يعني صار عندي الآن بمعنى أخر
+
+518
+00:38:51,280 --> 00:38:57,880
+X N راحت لل X و ال X في domain T هي واحد و T X N
+
+519
+00:38:57,880 --> 00:39:01,900
+converge مزام converge وعندي T is continuous إذا
+
+520
+00:39:01,900 --> 00:39:06,680
+هذا بيعطينا ال T X N بتروح لمين؟ ل T X فبكون اكتملت
+
+521
+00:39:06,960 --> 00:39:11,160
+اللي هو ما استلزم أن يكون closed إذا صارت T إيش ما
+
+522
+00:39:11,160 --> 00:39:17,620
+لها is closed اللي بعده يلاّ if T is closed ايوة T
+
+523
+00:39:17,620 --> 00:39:22,120
+is closed and اللي هو ال code domain اللي هو Y is
+
+524
+00:39:22,120 --> 00:39:25,180
+complete then domain of T is a closed subset of
+
+525
+00:39:25,180 --> 00:39:28,740
+main of X إذا بيشترط أنه يكون main Y is complete
+
+526
+00:39:28,740 --> 00:39:32,720
+تطلع ال domain of T is closed لكن هذا ماشترطش
+
+527
+00:39:32,720 --> 00:39:35,700
+علشان جالك domain of T closed على طول بتعطيك إيش T
+
+528
+00:39:35,700 --> 00:39:39,830
+is closed عشان تبين الـ domain of T is closed
+
+529
+00:39:39,830 --> 00:39:44,950
+كالعادة بناخد X وين؟ موجودة في الـ domain of T مدام
+
+530
+00:39:44,950 --> 00:39:47,130
+في الـ domain of T موجودة نوصلها إلى X في الـ
+
+531
+00:39:47,130 --> 00:39:50,370
+domain of T كي بنوصلها؟ إذا في سيكوانس من الـ
+
+532
+00:39:50,370 --> 00:39:52,950
+elements اللي في الـ domain of T اللي هو converged
+
+533
+00:39:52,950 --> 00:39:58,130
+من الـ main للـ X Since T is bounded، إذا اطلع لفوق،
+
+534
+00:39:58,130 --> 00:40:02,150
+احسبلي الـ T X N نقص T X M، اللي هو بيساوي T X N
+
+535
+00:40:02,150 --> 00:40:05,630
+نقص T X M، اللي هي أصغر شهر نورم الـ T في نورم X N
+
+536
+00:40:05,630 --> 00:40:10,530
+نقص X M، الآن هذه من هنا، X N بتروح للـ X، إذا هذه
+
+537
+00:40:10,530 --> 00:40:14,030
+كوشي، مدام هذه كوشي، إذا بزخرها زي ما بدي، أصغر من
+
+538
+00:40:14,030 --> 00:40:17,370
+Y عن نورم الـ T مثلا، إذا هيكون هذه أشمالها أصغر
+
+539
+00:40:17,370 --> 00:40:21,150
+من Y، يعني بمعنى أخر صارت الـ T X N كوشي هي
+
+540
+00:40:21,150 --> 00:40:23,690
+الاستدعى Y is complete تي اكس ان كوشي Y is
+
+541
+00:40:23,690 --> 00:40:26,930
+complete يدا نكون verbs يدا تي اكس ان بتروح لمين؟
+
+542
+00:40:26,930 --> 00:40:30,870
+لل Y لأن Y is complete صار عندي تي اكس ان بتروح لل
+
+543
+00:40:30,870 --> 00:40:35,410
+Y وبما ان T is closed وعندي اكس ان بتروح لل X و تي
+
+544
+00:40:35,410 --> 00:40:40,490
+اكس ان راحت لل Y يدا هيكون ال Y هي مين؟ ال T X هو
+
+545
+00:40:40,490 --> 00:40:44,450
+ال X موجودة في دومين T يدا since T is closed يدا X
+
+546
+00:40:44,450 --> 00:40:48,750
+في دومين T اللي هو صار عندي لان X في domain of T
+
+547
+00:40:48,750 --> 00:40:52,150
+closure وانتهيت ب X في domain of T لذا صار عندي
+
+548
+00:40:52,150 --> 00:40:57,070
+اللي هو ال domain of T is closed وبقول هي كذا
+
+549
+00:40:57,070 --> 00:41:00,730
+خلصنا الورهان النظرية وانهينا chapter اللي هو
+
+550
+00:41:00,730 --> 00:41:04,850
+أربعة عشر .. chapter أربعة وإلى لقاء آخر السلام
+
+551
+00:41:04,850 --> 00:41:06,130
+عليكم ورحمة الله وبركاته
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/wdHX26yF5r4_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/wdHX26yF5r4_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..29f49342dd43dd19c9524523151961ef047682fe
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/wdHX26yF5r4_postprocess.srt
@@ -0,0 +1,2204 @@
+1
+00:00:05,150 --> 00:00:07,670
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,670 --> 00:00:10,590
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,590 --> 00:00:17,290
+آله وصحبه أجمعين هذه المحاضرة رقم 35 مساق تحليل
+
+4
+00:00:17,290 --> 00:00:20,010
+اقتران أو تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:20,010 --> 00:00:26,990
+الإسلامية ماجستير رياضيةحكينا المحاضرة الماضية عن
+
+6
+00:00:26,990 --> 00:00:31,930
+اللي هو الـ Open Mapping Theorem اللي هي النظرية
+
+7
+00:00:31,930 --> 00:00:35,830
+الأساسية الثالثة اليوم نحكي عن آخر نظرية أساسية في
+
+8
+00:00:35,830 --> 00:00:38,350
+اللي هو الـ Functional Analysis اللي هي اسمها
+
+9
+00:00:38,350 --> 00:00:44,070
+Closed Graph Theorem Closed Graph Theorem الآن
+
+10
+00:00:44,070 --> 00:00:51,780
+العنوان تحت Closed Linear Operatorsعنا احنا ال ..
+
+11
+00:00:51,780 --> 00:00:54,620
+ال .. ال .. واضح اللي احنا اهتمينا فيه كبير كثير
+
+12
+00:00:54,620 --> 00:00:57,040
+اللي هو الـ Bounded Linear Operators اللي هو الـ
+
+13
+00:00:57,040 --> 00:01:00,360
+Continuous Linear Operators وبعدين اهتمينا شوية في
+
+14
+00:01:00,360 --> 00:01:04,500
+ال .. في ال Open Mapping في ال Open Operators الآن
+
+15
+00:01:04,500 --> 00:01:10,340
+في اللي هو Operator آخر ومش شرط يكون Bounded
+
+16
+00:01:10,340 --> 00:01:14,200
+Linear Operator هنا قبل شوية قولنا احنا ال .. ال
+
+17
+00:01:14,200 --> 00:01:16,920
+.. ال .. ال Bounded Linear Operator ممكن يكون Open
+
+18
+00:01:16,920 --> 00:01:21,570
+تحت الشروط اللي حكيناهاالان لـ Closed Linear
+
+19
+00:01:21,570 --> 00:01:27,570
+Operators ، سنجد ان ليس كل الـ bounded linear
+
+20
+00:01:27,570 --> 00:01:33,110
+operators اللي في الدنيا هتكون bounded linear
+
+21
+00:01:33,110 --> 00:01:35,710
+operators يعني ممكن unbounded linear operators
+
+22
+00:01:36,870 --> 00:01:40,230
+ومهمة زي اللي هو اللي خدناها اللي هو ال .. ال ..
+
+23
+00:01:40,230 --> 00:01:45,990
+ال .. ال operator اللي كان يرسل ال X لل X' هذا ال
+
+24
+00:01:45,990 --> 00:01:50,690
+unbounded .. unbounded و هذا له استخدامات كثيرة و
+
+25
+00:01:50,690 --> 00:01:59,150
+.. و فيه له خلّيني أقول خواص معينة بتأهله أن يكون
+
+26
+00:01:59,150 --> 00:02:05,730
+مهمو تطبيقات كثيرة بتاهله أن يكون مهم اللي هو هذا
+
+27
+00:02:05,730 --> 00:02:12,810
+النوع من ال operators عادة يتمتع بخاصية ال
+
+28
+00:02:12,810 --> 00:02:17,870
+closedness يعني بنسميه closed operator ده نشوف إيش
+
+29
+00:02:17,870 --> 00:02:22,810
+معناته closed operator فهذا اللي هو استدعى أن يكون
+
+30
+00:02:22,810 --> 00:02:26,750
+اللي هو ال closed operator مهمنظراً لهو لوجود
+
+31
+00:02:26,750 --> 00:02:30,430
+Unbounded Linear Operator وهو في نفس الوقت Closed
+
+32
+00:02:30,430 --> 00:02:35,410
+وقاله تطبيقات أعتقد في الـ Quantum Mechanics في
+
+33
+00:02:35,410 --> 00:02:43,690
+أمور هندسية وفيزيائية في شباتر قدام موجود حتى
+
+34
+00:02:43,690 --> 00:02:46,610
+الحديث عنه لما نحكي عن الـ Spectral Theory
+
+35
+00:02:46,610 --> 00:02:52,610
+لـClosed Linear Operatorsهو نحكي عن سيجما و روه
+
+36
+00:02:52,610 --> 00:02:56,450
+الهنو .. طيب شوفوا نعرف ايش معناه closed linear
+
+37
+00:02:56,450 --> 00:03:00,790
+operator let X and Y be normed spaces T من domain
+
+38
+00:03:00,790 --> 00:03:03,670
+of T لعند مين لعند Y بيقى linear operator و ال
+
+39
+00:03:03,670 --> 00:03:07,170
+domain of T جزء من مين من X يعني أنا جاعد في اللي
+
+40
+00:03:07,170 --> 00:03:10,890
+هو normed space then T is called closed linear
+
+41
+00:03:10,890 --> 00:03:15,190
+operatorإذا كانت الـ graph .. الـ graph زي ما
+
+42
+00:03:15,190 --> 00:03:17,650
+نتخيل الـ graph تبع الـ function العادية اللي ..
+
+43
+00:03:17,650 --> 00:03:21,170
+اللي هي المجموعة من الـ ordered pairs للعنصر و
+
+44
+00:03:21,170 --> 00:03:25,610
+صورته للعنصر و صورته لأن g of t هذا اللي هو عبارة
+
+45
+00:03:25,610 --> 00:03:28,670
+عن كل الـ x و y حيث الـ x في ال domain و الـ y و
+
+46
+00:03:28,670 --> 00:03:32,410
+ما له صورته فين؟ في ال range اللي هي x واحد و x في
+
+47
+00:03:32,410 --> 00:03:35,850
+ال domain of t و y بساوة x is closed in the normed
+
+48
+00:03:35,850 --> 00:03:40,300
+space x cross yإذن الان where two algebraic
+
+49
+00:03:40,300 --> 00:03:42,780
+operations of the vector space are defined إلى أخر
+
+50
+00:03:42,780 --> 00:03:49,480
+فالن بعدين يعني عند T في ال domain of T لعند Y هذا
+
+51
+00:03:49,480 --> 00:03:52,500
+جزء من X و احنا بنحكي عن norm of the space الان
+
+52
+00:03:52,500 --> 00:03:55,480
+بتقول ان T is a closed linear operator
+
+53
+00:03:57,760 --> 00:04:00,560
+وكان اللي هو ال .. ال .. ال .. ال .. ال .. ال ..
+
+54
+00:04:00,560 --> 00:04:00,760
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+55
+00:04:00,760 --> 00:04:00,780
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+56
+00:04:00,780 --> 00:04:01,140
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+57
+00:04:01,140 --> 00:04:01,160
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+58
+00:04:01,160 --> 00:04:01,180
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+59
+00:04:01,180 --> 00:04:01,640
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+60
+00:04:01,640 --> 00:04:02,340
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+61
+00:04:02,340 --> 00:04:03,160
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+62
+00:04:03,160 --> 00:04:03,220
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+63
+00:04:03,220 --> 00:04:04,260
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+64
+00:04:04,260 --> 00:04:04,320
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+65
+00:04:04,320 --> 00:04:07,960
+ال ..
+
+66
+00:04:07,960 --> 00:04:08,920
+ال
+
+67
+00:04:12,530 --> 00:04:16,510
+معناته احنا بنقصد مين الـ T is a closed set طبعاً
+
+68
+00:04:16,510 --> 00:04:19,850
+هذي closed set في مين؟ في ال space تبعها، هذي جزء
+
+69
+00:04:19,850 --> 00:04:23,950
+من ال space اللي هو X across me and Y فبتكون اللي
+
+70
+00:04:23,950 --> 00:04:29,170
+هي G of T closed تعني في هذه الحالة أنه اللي هو ال
+
+71
+00:04:29,170 --> 00:04:33,650
+operator اللي عند T is a closed linear operator
+
+72
+00:04:35,250 --> 00:04:38,110
+اللي هان .. إيش العمليات اللي على ال .. ال ..
+
+73
+00:04:38,110 --> 00:04:40,850
+العمليات الجبريعية الـ X cross Y اللي خلّته vector
+
+74
+00:04:40,850 --> 00:04:43,670
+space اللي عمليات العادية اللي أنتوا عارفينها ال
+
+75
+00:04:43,670 --> 00:04:46,870
+.. ال pointwise addition و اللي هو ال scalar
+
+76
+00:04:46,870 --> 00:04:49,350
+multiplication برضه pointwise في الأولى و في
+
+77
+00:04:49,350 --> 00:04:54,220
+التانية هذه بتعملية vector spaceولو أخدنا اللي هو
+
+78
+00:04:54,220 --> 00:04:58,000
+الـ Norm عرفناه Normal X Y بيسوا Normal X زاد
+
+79
+00:04:58,000 --> 00:05:02,120
+Normal Y هنجيها برضه تعمل ليه أشماله؟ Normed Space
+
+80
+00:05:02,120 --> 00:05:08,080
+كامل يعني X cross Y هتعمل Vector Space وNorm تبحها
+
+81
+00:05:08,080 --> 00:05:11,140
+اللي عرفناها قبل بشوية هتعملنها عبارة عن Normed
+
+82
+00:05:11,140 --> 00:05:15,260
+Space لأن لو كانت هذه Closed فيه هذا معنى إيه؟
+
+83
+00:05:15,260 --> 00:05:19,100
+اللي هو الـ T is a Closed Linear Operator او It is
+
+84
+00:05:19,100 --> 00:05:25,200
+a Closed Operator اطلع على اللي فوقطيب الان نجي لـ
+
+85
+00:05:25,200 --> 00:05:27,660
+Closed Graph Theorem Closed Graph Theorem لطيفة
+
+86
+00:05:27,660 --> 00:05:32,640
+يعني فبرهنها لطيف let X and Y be بنخ Spaces
+
+87
+00:05:32,640 --> 00:05:37,080
+شايفين؟ and let T من domain of T لعند Y be a
+
+88
+00:05:37,080 --> 00:05:40,980
+closed linear operator with domain of T جزء من X
+
+89
+00:05:40,980 --> 00:05:46,580
+if domain of T is closed in X then T إيش مالها is
+
+90
+00:05:46,580 --> 00:05:52,520
+bounded وكأنه بقولكإن أي عامل عامل عامل عامل عامل
+
+91
+00:05:52,520 --> 00:05:53,360
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+92
+00:05:53,360 --> 00:05:56,300
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+93
+00:05:56,300 --> 00:05:56,660
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+94
+00:05:56,660 --> 00:05:57,000
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+95
+00:05:57,000 --> 00:05:57,020
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+96
+00:05:57,020 --> 00:05:58,250
+عامل عامل عامل عامل عامل عامل عامل عامل عاملأن لو
+
+97
+00:05:58,250 --> 00:06:02,450
+كانت domain of T closed أكيد automatic حيصير اللي
+
+98
+00:06:02,450 --> 00:06:08,510
+هو إيش closed subspace من بنخ space X إذا أكيد
+
+99
+00:06:08,510 --> 00:06:11,910
+حيكون بنخ space يعني بالمعنى أخر لو كانت T من بنخ
+
+100
+00:06:11,910 --> 00:06:15,270
+space لبنخ space وكانت bounded linear operator كل
+
+101
+00:06:15,270 --> 00:06:19,170
+سنة متسلمين على طول إيش بده يطلع اللي هو عبارة عن
+
+102
+00:06:19,170 --> 00:06:27,740
+Robin عبارة عن closedأسف .. bounded .. bounded إذن
+
+103
+00:06:27,740 --> 00:06:32,640
+الآن ال .. ال .. ال .. ال .. ال open mapping
+
+104
+00:06:32,640 --> 00:06:36,720
+theorem كانت تاخد من بلغ space لبلغ space و قلته
+
+105
+00:06:36,720 --> 00:06:43,740
+أعطتكم اللي هي ال .. ال bounded openهنا الآن الـ
+
+106
+00:06:43,740 --> 00:06:48,820
+closed أعطانا mean bounded تحت نفس الظروف وأقل
+
+107
+00:06:48,820 --> 00:06:53,160
+شوية مافيش قنته هنا مش لازم قنته يعني T من X لعند
+
+108
+00:06:53,160 --> 00:06:57,420
+Y تكون closed in our operator من بناخ space لبناخ
+
+109
+00:06:57,420 --> 00:07:02,260
+space أعطتك إيه أشماله الـ T إيه أشماله is bounded
+
+110
+00:07:02,260 --> 00:07:10,320
+واضح أه أي سؤال أي سؤال طيب
+
+111
+00:07:12,850 --> 00:07:18,890
+بتثبت أنه T is bounded خلّينا بس نحضر لما نصل لـ T
+
+112
+00:07:18,890 --> 00:07:24,850
+is bounded لتزد أن بانيكوشي سيكوينس X across Y
+
+113
+00:07:28,280 --> 00:07:32,440
+بدأ أثبت لكم أول حاجة إن X×Y نفسها complete ماشي
+
+114
+00:07:32,440 --> 00:07:36,700
+الحاجة أول حاجة لإنه بتلزمني بعد شوية عشان أثبت أن
+
+115
+00:07:36,700 --> 00:07:41,840
+T is bounded let ZN be any Cauchy sequence in X×Y
+
+116
+00:07:41,840 --> 00:07:45,980
+where ZN بسوء XN و YN أخد ال sequence فيهاكلام سلس
+
+117
+00:07:45,980 --> 00:07:50,600
+و سهل وسهل سريع then then for or therefore
+
+118
+00:07:50,600 --> 00:07:54,380
+therefore for every epsilon او then for every
+
+119
+00:07:54,380 --> 00:07:58,060
+epsilon أكبر من سفر there exist k limited to n
+
+120
+00:07:58,060 --> 00:08:02,300
+such that for all m و n أكبر من n و أكبر من k هكون
+
+121
+00:08:02,300 --> 00:08:06,880
+norm اللي هو الذد أنمك الذد أم أشماله أصغر من
+
+122
+00:08:06,880 --> 00:08:10,540
+epsilon اللي ماياخد ال E دي أشمالها is Cauchyطيب
+
+123
+00:08:10,540 --> 00:08:15,980
+الـ ZM نقص الـ ZM الـ ZN XN و YN إذا الـ ZN اللي
+
+124
+00:08:15,980 --> 00:08:20,700
+هي عبارة هي .. و الـ ZM اللي هي .. قصدي هذه و الـ
+
+125
+00:08:20,700 --> 00:08:25,800
+ZM هي .. و طرحتهم من بعض طلعت XN نقص XM و YN نقص
+
+126
+00:08:25,800 --> 00:08:30,180
+YM في دا عملها سهلة الان norm هذا حسب اللي عرفناه
+
+127
+00:08:30,180 --> 00:08:33,360
+قبل و شوية هان ال norm هذا عبارة عن norm هذه زي
+
+128
+00:08:33,360 --> 00:08:38,290
+norm هذه هي norm هذه زي norm هذه إذا واضحإن لما
+
+129
+00:08:38,290 --> 00:08:43,630
+كانت Z انكوشي سيكوانس أعطتلي هذه زائد هذه أصغر من
+
+130
+00:08:43,630 --> 00:08:49,930
+مين من إبسل يعني أكيد طلع عندي اللي هو ال XN ماقص
+
+131
+00:08:49,930 --> 00:08:55,850
+XNوالـ yn ناقص yn مدى أن مجموحه أصغر من إبسلون فكل
+
+132
+00:08:55,850 --> 00:09:00,650
+واحدة فيه أصغر من مين من إبسلون for every m و n
+
+133
+00:09:00,650 --> 00:09:04,590
+أشمالهن أكبر من k إذا صارت هذه اللي هي ال sequence
+
+134
+00:09:04,590 --> 00:09:09,830
+تبعتها xn كوشي في ال x و ال yn كوشي في مين في ال y
+
+135
+00:09:09,830 --> 00:09:13,250
+أو كوشي حتى في ال domain و ال domain ما هو closed
+
+136
+00:09:13,250 --> 00:09:19,910
+فأكيد أشماله completeإذاً صار هذه كوشي في complete
+
+137
+00:09:19,910 --> 00:09:23,190
+و y and كوشي في complete إذاً كل واحدة فيها limit
+
+138
+00:09:23,190 --> 00:09:29,240
+ماشي طيب و هذا اللي هو اللي بدويا إذاHence x and y
+
+139
+00:09:29,240 --> 00:09:31,960
+and are Cauchy sequences in x and y respectively
+
+140
+00:09:31,960 --> 00:09:35,440
+أو حتى في الـ domain of T however x and y are
+
+141
+00:09:35,440 --> 00:09:38,360
+complete وكمان ال domain of T complete then there
+
+142
+00:09:38,360 --> 00:09:41,160
+exist x element in x and y element in y such that
+
+143
+00:09:41,160 --> 00:09:44,780
+x and .. بتروح لل x و y and إيش ما لها؟ بتروح لل y
+
+144
+00:09:44,780 --> 00:09:50,460
+الآن وابحث هذه تعالوا لواحد هذا وودوه لأم تروح إلى
+
+145
+00:09:50,460 --> 00:09:55,410
+ما لنهايةطبعا أنا ماخدين M أكبر من N عمدا على أساس
+
+146
+00:09:55,410 --> 00:09:58,430
+M تروح لما لا نهاية تطير و M هي حرة بتظهر زي ما هي
+
+147
+00:09:58,430 --> 00:10:03,530
+إذا M واحدة إلى ما لا نهاية صار عندي XM ناقص X و
+
+148
+00:10:03,530 --> 00:10:09,970
+YM ناقص Y أصغر اللي هو من مين من إرسلون صار عندي
+
+149
+00:10:09,970 --> 00:10:17,000
+تنتين مع بعض ZM ناقص XYحصلت ال limit هي x لهذه و y
+
+150
+00:10:17,000 --> 00:10:21,040
+لهذه صارت واحدة في x واحدة في y صار عندي zn نقص x
+
+151
+00:10:21,040 --> 00:10:25,500
+و y بيساوي normal xn نقص x زي yn نقص mean y
+
+152
+00:10:25,500 --> 00:10:30,360
+التنتين أصغر من مين من يبسلون إذا صار عندي this
+
+153
+00:10:30,360 --> 00:10:34,820
+means that zn converts the mean ل x و y therefore
+
+154
+00:10:34,820 --> 00:10:39,940
+x cross y is completeإذا انتهينا من X x Y is
+
+155
+00:10:39,940 --> 00:10:42,360
+complete و لو حتى خدنا ال domain برضه بيبقى لها
+
+156
+00:10:42,360 --> 00:10:48,940
+complete لأن ال domain is a closed subspace طيب يا
+
+157
+00:10:48,940 --> 00:10:57,320
+جماعة أطلع لفور الآن عندي T is closedT is closed
+
+158
+00:10:57,320 --> 00:11:01,920
+إذن أكيد الـ G of T أشماله closed in X cross Y و
+
+159
+00:11:01,920 --> 00:11:04,380
+ال domain of T closed in X إذن الاتنين صاروا
+
+160
+00:11:04,380 --> 00:11:06,960
+incomplete لأن هذا بنخ space و هذا بنخ space اللي
+
+161
+00:11:06,960 --> 00:11:10,680
+هم جزء منه هذا بنخ space و هذا بنخ space إذا على
+
+162
+00:11:10,680 --> 00:11:14,680
+طول G of T and D of T are complete spaces Now
+
+163
+00:11:14,680 --> 00:11:18,300
+consider the mapping خدها ال mapping الآن B من G
+
+164
+00:11:18,300 --> 00:11:23,040
+of T لعين 2 لعين D of TDefined by .. كله بده أصلهش
+
+165
+00:11:23,040 --> 00:11:26,100
+أنما .. بده أصلكم أن الـT is bounded يعني نورم
+
+166
+00:11:26,100 --> 00:11:29,140
+الـT of X أصغر يساوي إيش some number في مين في
+
+167
+00:11:29,140 --> 00:11:31,960
+نورم الـX هى اللي بده أصله فخلّيني أشوف عبر إيش
+
+168
+00:11:31,960 --> 00:11:35,440
+نصله Now consider the mapping B من G من G of T
+
+169
+00:11:35,440 --> 00:11:39,020
+لعين Domain of T that defined by projection map
+
+170
+00:11:39,020 --> 00:11:44,540
+projection سقاط بسقط الأول B X و T X بسقطوا على
+
+171
+00:11:44,540 --> 00:11:49,570
+مين؟ على Xلأن it is left to the reader to show
+
+172
+00:11:49,570 --> 00:11:53,990
+that P is linear P is linear سهل حتى linear بنقدر
+
+173
+00:11:53,990 --> 00:12:06,910
+نثبتها وإحنا مرتاحين عندي P of X و TX اللي هو طبعا
+
+174
+00:12:06,910 --> 00:12:14,670
+بساوي من؟ بساوي X لأن Pof الـ element اللي في الـ
+
+175
+00:12:14,670 --> 00:12:16,790
+element اللي في الـ g of t هتديروا بالك أين موجود
+
+176
+00:12:16,790 --> 00:12:22,010
+في الـ g of t ال element راحة alpha x زائد اللي هو
+
+177
+00:12:22,010 --> 00:12:26,310
+مثلا x prime هيكون ال .. ال .. ال .. ال .. ال
+
+178
+00:12:26,310 --> 00:12:28,590
+element عشان يكون في الـ g of t بدي يكون صورته
+
+179
+00:12:28,590 --> 00:12:35,330
+اللي هو t of alpha x زائد x prime صح؟ ويساوي هدي
+
+180
+00:12:35,330 --> 00:12:41,630
+بيه مش بدنا في ال .. معايا أه ويساوي alpha xزايد x
+
+181
+00:12:41,630 --> 00:12:53,330
+prime ويساوي Alpha بي of x وTx زايد بي of x prime
+
+182
+00:12:53,330 --> 00:12:59,950
+وTx prime حسب التاريخ على طول صارت عندي ال b is
+
+183
+00:12:59,950 --> 00:13:04,670
+linear أي سؤال معايا
+
+184
+00:13:09,630 --> 00:13:12,750
+الآن خدوا ال norm ال norm هي واضح هذه ما هي على
+
+185
+00:13:12,750 --> 00:13:20,030
+طول نورم هذه هو norm ال X، مظبوط؟ طيب، إذا الها ده
+
+186
+00:13:20,030 --> 00:13:23,390
+هتوديني على ال boundedness تبعت مين؟ تبع ال B اللي
+
+187
+00:13:23,390 --> 00:13:27,810
+هو ال norm ال B of X و T X اللي هو بيساوي نورم ال
+
+188
+00:13:27,810 --> 00:13:33,970
+X وراء ال X، then B is bounded اللي هي أكيد هذه
+
+189
+00:13:35,150 --> 00:13:40,650
+نورم الـ X الـ BX و TX بيساوي نورم الـ X بتخليلي
+
+190
+00:13:40,650 --> 00:13:47,070
+اللي هو هذا is bounded كيف طيب؟ لأ مهو ده اللي
+
+191
+00:13:47,070 --> 00:13:53,350
+منتبهها بشير أصغر أو شاوي اللي هو نورم ال X زائد
+
+192
+00:13:53,350 --> 00:13:59,290
+نورمين ال TX صح ولا؟ و هذا إيش بيساوي نورم ال X و
+
+193
+00:13:59,290 --> 00:14:04,620
+TXإذا صار عندي B of العمصر تبعها هذا اللي بترسله
+
+194
+00:14:04,620 --> 00:14:07,860
+أصغر أو شوية اللي بترسله وانت تعرف اللي هو النور
+
+195
+00:14:07,860 --> 00:14:12,600
+يعني الـB هنا واحد الثابت فبصير B أشمالها is
+
+196
+00:14:12,600 --> 00:14:20,920
+bounded هذا سبب الـboundedness طيب الآن then اللي
+
+197
+00:14:20,920 --> 00:14:24,300
+هو B is bounded it is easy to see that B is
+
+198
+00:14:24,300 --> 00:14:29,320
+bijective بيواجектив أصلا أكيد B is bijective or
+
+199
+00:14:29,320 --> 00:14:29,820
+one to one
+
+200
+00:14:38,740 --> 00:14:40,920
+معايا ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+201
+00:14:40,920 --> 00:14:42,100
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+202
+00:14:42,100 --> 00:14:42,540
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+203
+00:14:42,540 --> 00:14:42,580
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+204
+00:14:42,580 --> 00:14:42,880
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+205
+00:14:42,880 --> 00:14:42,900
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+206
+00:14:42,900 --> 00:14:43,000
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+207
+00:14:43,000 --> 00:14:48,480
+ال ال ال ال ال ال ال ال ال ال ال ال الت بي
+
+208
+00:14:48,480 --> 00:14:50,200
+of x
+
+209
+00:14:56,260 --> 00:15:02,160
+أكس برايم و TX أشماله أبرايم بظبط هذه X برايم X
+
+210
+00:15:02,160 --> 00:15:07,360
+بيساوي X مين أبرايم بناء عليه TX هيساوي TX برايم
+
+211
+00:15:07,360 --> 00:15:12,020
+عشان T function إذا صارت one to one الان انتوا
+
+212
+00:15:12,020 --> 00:15:16,540
+خدوا أي من وين لوين جاية ال B اللي هي الجاية ال B
+
+213
+00:15:16,540 --> 00:15:20,500
+من اللي هو وينها وينها وينها هي من G of T ل domain
+
+214
+00:15:20,500 --> 00:15:26,220
+of T خد أي element هنا شكله Xإذاً أكيد فيه إله TX
+
+215
+00:15:26,220 --> 00:15:32,320
+إذاً there exist X هو وTX لأن TX موجودة لإنه الـ T
+
+216
+00:15:32,320 --> 00:15:35,420
+function X وTX هنا such that بيه كده مثلًا وكده
+
+217
+00:15:35,420 --> 00:15:40,660
+إذاً الأمطوا برضه أشمالها واضحة أشوف التقباتات
+
+218
+00:15:47,740 --> 00:15:57,420
+للعدي بي من من من g of T لعين domain of T خد الآن
+
+219
+00:15:57,420 --> 00:16:04,880
+أي x element in domain of T then there exist x و T
+
+220
+00:16:04,880 --> 00:16:11,140
+x element in domain of T لأن T is a function جي of
+
+221
+00:16:11,140 --> 00:16:19,120
+TSuch that P of X و TX هو مين اللي بدأت فيها X إذا
+
+222
+00:16:19,120 --> 00:16:28,280
+أنتوامعايا؟ اذا B is onto اذا كل شي فيها صارت عندي
+
+223
+00:16:28,280 --> 00:16:34,660
+الان B bounded او one to one onto وlinear اذا B
+
+224
+00:16:34,660 --> 00:16:38,060
+inverse من domain of T الى U of T اشماله exist and
+
+225
+00:16:38,060 --> 00:16:42,440
+is defined by B inverse X ايش هيروح لل X وصورة مين
+
+226
+00:16:42,440 --> 00:16:47,840
+اللي هي ال X under T اللي هي TXالان since D of D
+
+227
+00:16:47,840 --> 00:16:50,580
+and D of D are complete then by open mapping
+
+228
+00:16:50,580 --> 00:16:54,760
+theorem اللي قبل بشوية المرة المحادرة اللي فاتت
+
+229
+00:16:54,760 --> 00:16:58,740
+اللي هو هيكون ال B inverse إيش ماله is bounded
+
+230
+00:16:58,740 --> 00:17:02,920
+خلينا نقول مدام B inverse bounded نقول norm ال B
+
+231
+00:17:02,920 --> 00:17:07,000
+inverse لل X أصغر سوى B في مين؟ في norm ال X طب هو
+
+232
+00:17:07,000 --> 00:17:11,490
+B inverse of X إيش بسوى norm ال X و TXمعايا؟ إذا
+
+233
+00:17:11,490 --> 00:17:16,910
+صار عندي هذا المقدار أصغر أو أشهر هذا ومنه على طول
+
+234
+00:17:16,910 --> 00:17:21,370
+norm of TX انا بعرف أصغر أو أشهر norm of TX زائد
+
+235
+00:17:21,370 --> 00:17:25,170
+مين؟ زائد norm of X زي اللي عملتها وهذا هو مين؟
+
+236
+00:17:25,170 --> 00:17:28,970
+norm of X وTX هيه اللي هو أصغر أو أشهر من B في X
+
+237
+00:17:28,970 --> 00:17:31,730
+إذا صار عندي norm of TX أصغر أو أشهر بيه في norm
+
+238
+00:17:31,730 --> 00:17:39,030
+of X وهذا يعني أن الـ T is bounded أي شؤال اللي
+
+239
+00:17:39,030 --> 00:17:39,490
+بعده
+
+240
+00:17:43,930 --> 00:17:47,410
+إذن هذا أعطاني condition الـ closed graph theorem
+
+241
+00:17:47,410 --> 00:17:54,650
+أعطاني إعلان إن T من بنخ space إلى بنخ space اللي
+
+242
+00:17:54,650 --> 00:18:00,390
+هو closed إذا كان closed بيعطيني إيه شماله؟
+
+243
+00:18:00,390 --> 00:18:08,030
+bounded T is bounded طيب شوفوا
+
+244
+00:18:08,030 --> 00:18:13,890
+الآن اللي بعدهاالنظرية اللي بعدها بتقول لل T من
+
+245
+00:18:13,890 --> 00:18:16,890
+domain of T لعند Y بيه a linear operator و ال
+
+246
+00:18:16,890 --> 00:18:20,390
+domain of T X معلق crazing على اللي هو انه ياخد ال
+
+247
+00:18:20,390 --> 00:18:24,770
+domain of T لل X يا جماعة هرايحنا و خد من X لعند Y
+
+248
+00:18:24,770 --> 00:18:28,630
+و اشتغلونه و حط خاص ال domain of T في ال X يا سيدة
+
+249
+00:18:28,630 --> 00:18:35,130
+مش مشكلة كتيرهو يعني بشعر أنه هي كأعام كتير
+
+250
+00:18:35,130 --> 00:18:37,550
+من الكتب خلاص مش بتبقى في domain of T علشان تبقى
+
+251
+00:18:37,550 --> 00:18:40,510
+تعتبر X لعند Y وتعتبر X هو ال domain وهو norm of
+
+252
+00:18:40,510 --> 00:18:44,330
+this base الاخرى أو إذا كان بديها هي كمليت بتعطيه
+
+253
+00:18:44,330 --> 00:18:47,690
+كمليت ومتعاشر وكذا الاخرى بيقالين ياروبيرت لو ال
+
+254
+00:18:47,690 --> 00:18:50,590
+domain of T subset من X and X and Y لكن رائع هو
+
+255
+00:18:50,590 --> 00:18:56,210
+عموما في العرض and X and Y be normed this basisثم
+
+256
+00:18:56,210 --> 00:18:59,410
+T is closed if and only if it has the following
+
+257
+00:18:59,410 --> 00:19:03,390
+properties انتوا اللي بقولوا هال properties Xn
+
+258
+00:19:03,390 --> 00:19:06,390
+بتروح لل X where Xn المتن دومين of T for all n and
+
+259
+00:19:06,390 --> 00:19:09,410
+T Xn بتروح لل Y دون X المتن دومين of T and T X
+
+260
+00:19:09,410 --> 00:19:17,980
+يشبه لها بتسوى Y هذا يستوجب الوقوفونحكي عنه يعني
+
+261
+00:19:17,980 --> 00:19:23,900
+بمعنى آخر يترجم .. يترجم احنا زمان .. زمان أخدنا T
+
+262
+00:19:23,900 --> 00:19:31,700
+اه .. قولوا معايا T من عند X لعند Y انها
+
+263
+00:19:31,700 --> 00:19:37,500
+continuous او bounded اذا حققت الشرط التالي انه
+
+264
+00:19:37,500 --> 00:19:44,130
+لما XNبتروح للـ X ماشي الحال يعني Xn من وين؟ Xn من
+
+265
+00:19:44,130 --> 00:19:47,950
+الـ X والـ X من الـ X من رأس الدورة و Xn روحت للـ
+
+266
+00:19:47,950 --> 00:19:54,010
+X إذا هذا أعطاني إن الـ TXn بتروح للـ TX على طول
+
+267
+00:19:54,010 --> 00:19:57,990
+بنقول عن الـ T أشمالها is continuous إذن التعبير
+
+268
+00:19:57,990 --> 00:20:00,770
+عن ال continuity أو ال boundedness للـ linear
+
+269
+00:20:00,770 --> 00:20:05,030
+operator عن طريق ال sequence إن sequence converges
+
+270
+00:20:05,030 --> 00:20:09,420
+في X في داخل كله في داخل Xبيعطيني اذا اعطاني ان
+
+271
+00:20:09,420 --> 00:20:13,500
+الـ TX بتروح لـ TX في داخل الـ Y معناته انه انتهى
+
+272
+00:20:13,500 --> 00:20:16,800
+الامر صار إيش ماله continuous هنا الان بده يعطي
+
+273
+00:20:16,800 --> 00:20:21,620
+condition يكافئ لclosedness اللي closed برضه عن
+
+274
+00:20:21,620 --> 00:20:24,940
+طريق ال sequences بس ديروا بالكم هنا ماخد اللي هو
+
+275
+00:20:24,940 --> 00:20:28,690
+ال X و ال Y normed spaces مضارة normed spacesالـ N
+
+276
+00:20:28,690 --> 00:20:32,270
+يعني خرّين نحنا T is closed if and only if T has
+
+277
+00:20:32,270 --> 00:20:36,090
+the following property إيش بييجي بيقول إذا كانت
+
+278
+00:20:36,090 --> 00:20:43,350
+إذا كانت XN element in X لكل N و الـ XN عاملها
+
+279
+00:20:43,350 --> 00:20:52,050
+راحت لل X و أيضا اللي هو TXN راحت لل Y و TXN TXN
+
+280
+00:20:52,050 --> 00:20:59,850
+راحت لل Yوالـ TXM طبيعي هتكون موجودة في الـ Y ما
+
+281
+00:20:59,850 --> 00:21:03,510
+حكى اشي لا عن X ولا عن Y يعني ما قالش ان X موجودة
+
+282
+00:21:03,510 --> 00:21:08,490
+في الـ X وما فرضش هذا الحالة لأ هو الـ N يعني جال
+
+283
+00:21:08,490 --> 00:21:13,250
+XN بتروح لصن X ماجالش موجودة في الـ Xوقال إن الـ
+
+284
+00:21:13,250 --> 00:21:17,570
+TXN بتروح للـ Y هن استنتجناها في الـ Continuity
+
+285
+00:21:17,570 --> 00:21:21,170
+TXN روحت للـ X وكانت هذه موقف شرط إنها تكون هنا،
+
+286
+00:21:21,170 --> 00:21:26,070
+هن مش شرط لكن شرط إشي هنا إن TXN تروح للـ Y هن مش
+
+287
+00:21:26,070 --> 00:21:31,490
+شرط تطلع من جواب الشرط TXN بتروح لمين؟ لـ TX أعطال
+
+288
+00:21:31,490 --> 00:21:37,670
+الـ Continuity هذا لو حدث كله على بعض أو أعطاني إن
+
+289
+00:21:37,670 --> 00:21:42,310
+الـ X في الـ Xوالـ TX هي الـ Y معناته وين موجودة
+
+290
+00:21:42,310 --> 00:21:47,010
+في الـ Y معناته إذا حدث هذا بيكون الـ T is a
+
+291
+00:21:47,010 --> 00:21:51,910
+closed operator is a closed operator إذن if XN
+
+292
+00:21:51,910 --> 00:21:57,140
+بتروح لل X و XN في Domain Tوالـ T X N بتروح للـ Y
+
+293
+00:21:57,140 --> 00:22:02,360
+إذا هذا مع بعض أعطاني إنه X في دومين الـ T والـ T
+
+294
+00:22:02,360 --> 00:22:06,560
+X بتساوي Y Automatic هذا إيش معناته إنه هتكون الـ
+
+295
+00:22:06,560 --> 00:22:13,560
+T is closed واضح الفرق بين ال continuity بتلالة
+
+296
+00:22:13,560 --> 00:22:17,700
+اللي هو ال sequences و ال closedness للـ T بدلالة
+
+297
+00:22:17,700 --> 00:22:21,340
+ال sequences هاي الفرق بين إنه هاي الأمور واضحة
+
+298
+00:22:25,070 --> 00:22:30,770
+خلّيني بس نكمل اللي بنحكيه suppose
+
+299
+00:22:30,770 --> 00:22:35,090
+that T
+
+300
+00:22:35,090 --> 00:22:36,630
+is closed
+
+301
+00:22:40,870 --> 00:22:46,790
+الـ openness بتحكي علاقة بين T inverse و T إذا
+
+302
+00:22:46,790 --> 00:22:50,430
+بدنا نترجم على T inverse بيصير كلام تاني then T is
+
+303
+00:22:50,430 --> 00:22:55,810
+closed إذا دول اللي ده property صحيحة نيجي الآن
+
+304
+00:22:55,810 --> 00:23:00,350
+إبرهن suppose that T is closed إذا G of T إيش
+
+305
+00:23:00,350 --> 00:23:07,820
+ماله؟ Closedالان بدي اثبت لك اخد هذه و هذه و اصلك
+
+306
+00:23:07,820 --> 00:23:11,120
+لهذه المجموعه ماشي؟ ممكن خلصنا الـ visual اول طيب
+
+307
+00:23:11,120 --> 00:23:15,480
+اذا بدي اخد ماعطينيه عشان استعمله بدي اقول له let
+
+308
+00:23:15,480 --> 00:23:19,620
+xn بتروح للـx هيها و الـxn في domain الـT و خلينا
+
+309
+00:23:19,620 --> 00:23:25,440
+ناخد Txn بتروح لمين؟ للـY من الحديث هذا اكيد الـxn
+
+310
+00:23:25,440 --> 00:23:31,220
+و Txn وين موجود؟فى الـ G of D ماشي و ال XN و ال T
+
+311
+00:23:31,220 --> 00:23:36,060
+XN وين بتروح لل X و Y لإن هو مضّيل ال X عن وين و
+
+312
+00:23:36,060 --> 00:23:39,680
+مضّيل إيها ال X عن .. على ال X و مضّيل ال T XN على
+
+313
+00:23:39,680 --> 00:23:46,060
+مين؟ على ال T X إذا عند X و Y هتكون وين موجودة؟ فى
+
+314
+00:23:46,060 --> 00:23:52,580
+ال G of D معايا؟ ليش؟ لإن ال T is closedما هو شو
+
+315
+00:23:52,580 --> 00:23:56,220
+معناه الـ T is closed؟ انه الآن الـ G of T is
+
+316
+00:23:56,220 --> 00:23:59,180
+closed ايش معناه الـ G of T is closed؟ يعني أي
+
+317
+00:23:59,180 --> 00:24:04,120
+sequence فيه converts to some element ستكون في الـ
+
+318
+00:24:04,120 --> 00:24:08,600
+G of T إذا صار عندي Xn وT Xn بتروح لل X و Y قطعًا
+
+319
+00:24:08,600 --> 00:24:12,900
+X و Y هتكون في الـ G of T عشان الـ G of T is
+
+320
+00:24:12,900 --> 00:24:16,420
+closed لأن الـ T في الأصل is closed this means
+
+321
+00:24:16,420 --> 00:24:20,620
+thatإن ما دامت الـ X Y في الـ G of T إذن X في الـ
+
+322
+00:24:20,620 --> 00:24:25,100
+domain of T والـ T X أشماله بسوء Y لأن الـ G of T
+
+323
+00:24:25,100 --> 00:24:28,520
+هي عبارة عن ال order pairs بين اللي هو أعناصر ال
+
+324
+00:24:28,520 --> 00:24:33,160
+domain of T و الصور اللي هي لهذا ال domain إذن هذا
+
+325
+00:24:33,160 --> 00:24:37,820
+بيعني إن X في domain T و T X بسوء Y لأن conversely
+
+326
+00:24:39,630 --> 00:24:43,530
+suppose that اتنين holds هي هذه الخاصية ايش ما لها
+
+327
+00:24:43,530 --> 00:24:48,150
+تتحقق الان بدنا نثبت لكم ان هو g of t is closed
+
+328
+00:24:48,150 --> 00:24:51,770
+كيف بدنا نثبت انها closed؟ بدي اخد x y في ال g of
+
+329
+00:24:51,770 --> 00:24:54,910
+t closure و اثبت لكم ال x y في ال g of t و خلصنا
+
+330
+00:24:54,910 --> 00:24:57,150
+صار ال g of t is closed اللي بيساوي ال g of t يعني
+
+331
+00:24:57,150 --> 00:25:01,700
+ان ال g of t is closedثم مادام الـ G of T مقفلة
+
+332
+00:25:01,700 --> 00:25:04,980
+الـ X Y في الـ G of T مقفلة إذا تتمتع بالخاصية
+
+333
+00:25:04,980 --> 00:25:08,600
+التالية إن أنا بقدر ألاقي الـ sequence XN و TXN في
+
+334
+00:25:08,600 --> 00:25:13,420
+الـ G of T convolutionally للـ XY إذا there exists
+
+335
+00:25:13,420 --> 00:25:16,820
+this sequence of elements in G of T such that XN و
+
+336
+00:25:16,820 --> 00:25:21,030
+TXN تروح لمين للـ XYوهذا يعني Xn بتروح لل X و Tx
+
+337
+00:25:21,030 --> 00:25:24,990
+بتروح لمين؟ لل Y و Xn من وين جاية؟ من ال domain of
+
+338
+00:25:24,990 --> 00:25:28,390
+T يعني كل الشروط اللي جاب المتحققة then by
+
+339
+00:25:28,390 --> 00:25:31,690
+assumption اللي هو the property 2 X هذه هتكون في
+
+340
+00:25:31,690 --> 00:25:36,150
+domain T و Tx بالساوية Y وهذا يعني ال X و Y موجودة
+
+341
+00:25:36,150 --> 00:25:40,170
+في G of T وهذا يعني أنه بدأنا بهذه وانتهينا بهذه
+
+342
+00:25:40,170 --> 00:25:44,710
+أنه therefore G of D is closed وهذا يعني أنه T is
+
+343
+00:25:44,710 --> 00:25:45,830
+closed اللي بعده يلا
+
+344
+00:25:50,340 --> 00:25:54,340
+الان مثال اللى عدناكم فيه هو الأول اللى قلنا احنا
+
+345
+00:25:54,340 --> 00:25:58,160
+احنا يعني فى bounded linear operators او فى عندى
+
+346
+00:25:58,160 --> 00:26:01,740
+closed linear operators which is not bounded
+
+347
+00:26:01,740 --> 00:26:05,440
+والمثال المشهور اللى هو example differential
+
+348
+00:26:05,440 --> 00:26:11,020
+operator I differential operator let X بتساوى C01
+
+349
+00:26:11,020 --> 00:26:15,690
+على ال continuous functionsوT من الـ domain of T
+
+350
+00:26:15,690 --> 00:26:19,950
+لعند مين؟ لعند X بي such that الـ TX بتاوى إيش ما
+
+351
+00:26:19,950 --> 00:26:24,620
+لها X' و X' is the derivative of Xطيب ما هو هذا
+
+352
+00:26:24,620 --> 00:26:28,140
+الـ X إيش ما لها عبارة عن continuous functions مش
+
+353
+00:26:28,140 --> 00:26:30,480
+كل ال continuous functions كان بيه إيش ما لها
+
+354
+00:26:30,480 --> 00:26:34,060
+دفعانشياتي ده إذا أكيد اللي هو بده يكون ال domain
+
+355
+00:26:34,060 --> 00:26:38,820
+of T of روبر subspace من مين؟ من ال X إذا هذا ال
+
+356
+00:26:38,820 --> 00:26:42,280
+proper subspace اللي هو of functions اللي بيديها
+
+357
+00:26:42,280 --> 00:26:45,780
+كمان مش بس ما دفعانشيابلاللي هو domain of T is a
+
+358
+00:26:45,780 --> 00:26:49,060
+subspace of functions ياك بديها X element in X
+
+359
+00:26:49,060 --> 00:26:51,980
+which have a continuous derivative يعني اللي بتطلع
+
+360
+00:26:51,980 --> 00:26:55,480
+برضه تطلع أي شمالها continuous عشان أقدر أرسلها
+
+361
+00:26:55,480 --> 00:26:58,460
+وين في حالة فتطلع continuous مش هاد ال X
+
+362
+00:26:58,460 --> 00:27:02,260
+continuous فالآن اللي أنا أخدش domain of T هو ال
+
+363
+00:27:02,260 --> 00:27:09,200
+domain اللي جزء من الـ C01 و اللي دواله اللي
+
+364
+00:27:09,200 --> 00:27:15,200
+بتتفاضل و تفاضلها بتطلع أي شماله continuousالأن
+
+365
+00:27:15,200 --> 00:27:20,580
+احدين T is not bounded بط ايش ماله is closed
+
+366
+00:27:20,580 --> 00:27:25,320
+اثبتناها not bounded زمان اللي هو by اثنين سبعة
+
+367
+00:27:25,320 --> 00:27:30,720
+خمسة بالظبط T is linear بط not bounded بدنا نثبت
+
+368
+00:27:30,720 --> 00:27:35,570
+انها ايش لان انها closed شوفوا كيفبعد أن نثبت أنها
+
+369
+00:27:35,570 --> 00:27:40,090
+قريبة نستخدم الخاصية اللي قبل بشوية let XN element
+
+370
+00:27:40,090 --> 00:27:44,650
+in domain of T for all N such that XN بتروح لل X و
+
+371
+00:27:44,650 --> 00:27:50,390
+TXN ايش معناها سموها XN برايم بتروح لمين لل Y ماشي
+
+372
+00:27:50,390 --> 00:27:53,890
+الحالة XN برايم اللي هي ايش معناته ال derivative
+
+373
+00:27:53,890 --> 00:27:59,090
+مش هي اتفجن اللي هو بريطان هو اللي بفاضل اذا TXN
+
+374
+00:27:59,090 --> 00:28:02,050
+برايم هو سميه ايش اسمه XN برايم اللي هي derivative
+
+375
+00:28:02,050 --> 00:28:08,010
+لمين لل XNمعايا احنا هي اللي بدنا هيها نفترض هذه
+
+376
+00:28:08,010 --> 00:28:11,590
+بتروح لهذه وهذه بتروح لمين ل some y يعني ال xn
+
+377
+00:28:11,590 --> 00:28:15,150
+بتروح لل x و ال xn بتروح لمين لل y بدنا نثبت لكم
+
+378
+00:28:15,150 --> 00:28:19,590
+ان ال x في ال domain of T و نثبت ان هو ال y ايش
+
+379
+00:28:19,590 --> 00:28:25,960
+معناه تي اكس هي ال yبتكون مقفلة طيب by 155 the
+
+380
+00:28:25,960 --> 00:28:29,720
+convergence in the norm space أخدناها برضه ال C زي
+
+381
+00:28:29,720 --> 00:28:33,380
+اللي كنا قولنا convergence في C01 انه uniform
+
+382
+00:28:33,380 --> 00:28:37,640
+convergence ايش يعني uniform convergence يعني لو
+
+383
+00:28:37,640 --> 00:28:41,540
+عندي sequence of continuous functions هذا في
+
+384
+00:28:41,540 --> 00:28:44,280
+الدنيا العادية تبع ال real analysis تبع اتنين تبع
+
+385
+00:28:44,280 --> 00:28:49,240
+ال baccalaureate لو xn sequence of functions
+
+386
+00:28:51,780 --> 00:28:55,680
+continuous functions that converge to some x وكان
+
+387
+00:28:55,680 --> 00:28:59,480
+ال convergence اللي هو point y يسمى y مش شرط انها
+
+388
+00:28:59,480 --> 00:29:02,800
+تطلع x continuous لكن اذا uniform قطعا انها تطلع
+
+389
+00:29:02,800 --> 00:29:06,240
+اي شمالها continuous وعنا ال convergence uniform
+
+390
+00:29:06,240 --> 00:29:11,380
+and since the convergence is uniform then اللي هو
+
+391
+00:29:11,380 --> 00:29:14,980
+هتكون ال limit تبعتنا اللي هو في داخل هذا هتكون
+
+392
+00:29:14,980 --> 00:29:20,730
+continuous طيب خلوه في الذاكرةإذا الـ integration
+
+393
+00:29:20,730 --> 00:29:27,240
+لـ 0 لـ T Y of T DT بساويطبعاً و الـ Limit مدام
+
+394
+00:29:27,240 --> 00:29:29,780
+ينظم convergence الـ Limit بطلع و بنزل زي ما بده
+
+395
+00:29:29,780 --> 00:29:35,260
+من الهدف هو عبارة عن Limit من 0 ل T ل X N prime of
+
+396
+00:29:35,260 --> 00:29:39,220
+T لأنه اتفجنا ان X N prime of T اشمل ل X N prime
+
+397
+00:29:39,220 --> 00:29:43,660
+بتروح لمين ل Y فبصير عند ال Limit ده يتاو ال Limit
+
+398
+00:29:43,660 --> 00:29:46,860
+بنطلحها برا بصير X N prime of T dt من سفر اللي عند
+
+399
+00:29:46,860 --> 00:29:52,280
+T و هي ساوة ال Limitالان التفاضل .. التكامل هذه ..
+
+400
+00:29:52,280 --> 00:29:55,940
+مجرد هذا .. اللي هو ال derivative على طول هي عبارة
+
+401
+00:29:55,940 --> 00:30:02,540
+عن مين؟ xn of t ماقص xn of mean of zero xn of t
+
+402
+00:30:02,540 --> 00:30:07,700
+اللي هي أشمالها اللي هي limitها اللي هو x of tلأنه
+
+403
+00:30:07,700 --> 00:30:13,540
+ماخد مين أنا ال limit حسبتها حسبت هذه طلعت هذه ال
+
+404
+00:30:13,540 --> 00:30:17,700
+limit اللي أنا لها هي ال limit limit لهذه x of t و
+
+405
+00:30:17,700 --> 00:30:22,800
+limit لهذه ايش ماله x of zero لإنه xn بتروح لل x
+
+406
+00:30:22,800 --> 00:30:25,900
+uniformly اذا اكيد point twice ايش يعني point
+
+407
+00:30:25,900 --> 00:30:29,740
+twice يعني xn of t بتروح لل x of t و ال xn of zero
+
+408
+00:30:29,740 --> 00:30:33,200
+بتروح لمين لل zero هذا for every tإذا صار عندي ال
+
+409
+00:30:33,200 --> 00:30:37,800
+integration هذا بيساوي xn of t نقص x of zero that
+
+410
+00:30:37,800 --> 00:30:42,240
+is x of t إيش بتساوي؟ x of zero زاد ال integration
+
+411
+00:30:42,240 --> 00:30:47,760
+ماشي الحال إذا طلعت عند ال x إيش مالها؟ اللي على
+
+412
+00:30:47,760 --> 00:30:51,940
+الصورة هذه اللي هي عبارة عن continuous إيهاش؟ اللي
+
+413
+00:30:51,940 --> 00:30:58,080
+هي ال derivative اللي موجودة و continuousالـ
+
+414
+00:30:58,080 --> 00:31:02,660
+derivative لهذه موجودة و continuous هذه بتكون x في
+
+415
+00:31:02,660 --> 00:31:06,800
+domain of t لأن ال derivative لهذه ثابت ال
+
+416
+00:31:06,800 --> 00:31:09,640
+derivative لهذه zero و ال derivative لهذه إشمالها
+
+417
+00:31:09,640 --> 00:31:13,580
+اللي هي بتطلع y of t صح نقص y of zero و y of t ما
+
+418
+00:31:13,580 --> 00:31:18,690
+هي إشمالها اللي هي continuousYOM ماذا يعني إذا
+
+419
+00:31:18,690 --> 00:31:22,350
+كنتنيواص فانكشن لأننا قلنا اللي هو ال uniform
+
+420
+00:31:22,350 --> 00:31:25,570
+convergence بوات ديناميين ال continuous ل
+
+421
+00:31:25,570 --> 00:31:29,470
+continuous ماشي الحال لأن هذه continuous و ال
+
+422
+00:31:29,470 --> 00:31:32,750
+convergence uniform إذا أكيد هذه أيش معناها
+
+423
+00:31:32,750 --> 00:31:36,030
+continuous من وين إكس أن إبراهيم continuousما هو
+
+424
+00:31:36,030 --> 00:31:38,530
+إيه إحنا الـ x unwell موجودة في الـ domain والـ T
+
+425
+00:31:38,530 --> 00:31:41,490
+ال domain والـ T هو عبارة عن الدوال اللي ال
+
+426
+00:31:41,490 --> 00:31:45,070
+derivative إلها continuous فطبيعي كل الأمور مبررة
+
+427
+00:31:45,070 --> 00:31:48,730
+فبتصير عندي x of T بتساوي هذا الكلام اللي هي is a
+
+428
+00:31:48,730 --> 00:31:52,110
+continuous function يعني x في ال domain والـ T و
+
+429
+00:31:52,110 --> 00:31:56,970
+ال Tx إيش بتساوي اللي هو ال X' ال Tx اللي هي ال X'
+
+430
+00:31:57,250 --> 00:32:01,750
+بال X' إيش بتساوي ال Y then by theorem كده T is
+
+431
+00:32:01,750 --> 00:32:06,430
+closedإذن هذا مثال على اللي هو closed linear
+
+432
+00:32:06,430 --> 00:32:13,290
+operator which is not bounded يلّا
+
+433
+00:32:13,290 --> 00:32:20,570
+أطلع على فوق ال dot بتقولdomain of T ليس مغلقًا
+
+434
+00:32:20,570 --> 00:32:24,570
+لأن .. لا طبعًا أكيد domain of T ليس مغلقًا domain
+
+435
+00:32:24,570 --> 00:32:27,090
+of T اللي فوق .. اللي فوق هذا domain of T اللي
+
+436
+00:32:27,090 --> 00:32:30,370
+أخدناه اللي هو main domain of T the space أو the
+
+437
+00:32:30,370 --> 00:32:33,610
+subspace of all continuous .. اللي هو of all
+
+438
+00:32:33,610 --> 00:32:37,400
+functions that has a continuous derivativeهذا is
+
+439
+00:32:37,400 --> 00:32:42,480
+not closed لأنه لو كان closed automatic من النظرية
+
+440
+00:32:42,480 --> 00:32:46,220
+اللي جابلها in example كذا is not closed because
+
+441
+00:32:46,220 --> 00:32:50,660
+if it is closed then by theorem أربعة تلتاشت اتنين
+
+442
+00:32:50,660 --> 00:32:55,540
+T is bounded because T is closed then we have a
+
+443
+00:32:55,540 --> 00:32:58,500
+contradiction with T is not bounded اللي أثبتناها
+
+444
+00:33:04,230 --> 00:33:13,890
+تعني المثال اللي فوق ببرهن لك أن الـ subspace of
+
+445
+00:33:13,890 --> 00:33:18,130
+all the functions that has a continuous derivative
+
+446
+00:33:18,130 --> 00:33:26,330
+is not a closed subspace طيب .. الآن قلناالـ
+
+447
+00:33:26,330 --> 00:33:30,070
+Closedness does not imply boundedness of linear
+
+448
+00:33:30,070 --> 00:33:33,610
+operator من اللي فوق يعني Closed مش شرط يعطيه
+
+449
+00:33:33,610 --> 00:33:38,430
+شماله bounded الآن برضه boundedness does not imply
+
+450
+00:33:38,430 --> 00:33:41,430
+the closeness of linear operator يعني بدي أديبلك
+
+451
+00:33:41,430 --> 00:33:47,690
+اللي هو bounded linear operator which is not
+
+452
+00:33:47,690 --> 00:33:50,870
+closed بدي أديب bounded linear operator which is
+
+453
+00:33:50,870 --> 00:33:58,700
+not closed طيب، نشوفلت I الـ Identity من domain of
+
+454
+00:33:58,700 --> 00:34:01,220
+T لdomain of T Be the identity operator on domain
+
+455
+00:34:01,220 --> 00:34:03,720
+of T يعني أي domain of T من عند X لعندك نور من الـ
+
+456
+00:34:03,720 --> 00:34:05,200
+space لعندك نور من الـ space أو جزء من نور من الـ
+
+457
+00:34:05,200 --> 00:34:09,300
+space Where D of T is .. بقى أسف بدي أقول هو
+
+458
+00:34:09,300 --> 00:34:12,960
+domain of T proper dense subspace of a normed
+
+459
+00:34:12,960 --> 00:34:17,760
+space من X يعني أخد الآن ال identity function ال
+
+460
+00:34:17,760 --> 00:34:23,160
+identity function من domain of T لعند domain of T
+
+461
+00:34:24,330 --> 00:34:28,950
+اللي بيرسل الـElement لمين؟ لنفسه، Identity هش
+
+462
+00:34:28,950 --> 00:34:35,190
+بدّو domain of T بدّو domain of TDense من X الـ
+
+463
+00:34:35,190 --> 00:34:42,810
+Space اللي هو Normed Space وDomain of T بدّي بربر
+
+464
+00:34:42,810 --> 00:34:51,270
+subset من X بربر subset من X يعني في Element في
+
+465
+00:34:51,270 --> 00:34:55,830
+الـ X مش موجود وين في الـDomain of T وهذا وهذا
+
+466
+00:34:55,830 --> 00:34:59,940
+اللي هو مفتاح انها تثبت ان T is not closedطيب او
+
+467
+00:34:59,940 --> 00:35:03,040
+الـ identity is not closed let T من domain of T يا
+
+468
+00:35:03,040 --> 00:35:05,320
+domain of B be the indented operator on domain of
+
+469
+00:35:05,320 --> 00:35:09,080
+T where domain of T is a proper dense subspace of
+
+470
+00:35:09,080 --> 00:35:12,900
+a known D space X زي ما قلت it is clear that T is
+
+471
+00:35:12,900 --> 00:35:15,980
+linear and bounded اللي هو ال .. اللي هو مين؟ اللي
+
+472
+00:35:15,980 --> 00:35:18,580
+هو ال identity function اثبتناها مرات انه bounded
+
+473
+00:35:18,580 --> 00:35:23,000
+و .. و .. و linear but T is not closed ليش T مش
+
+474
+00:35:23,000 --> 00:35:27,580
+closed؟ شوفواthis follows from theorem 4.13 اللي
+
+475
+00:35:27,580 --> 00:35:32,660
+قبل شوية if we take an x element in main خدوا x x
+
+476
+00:35:32,660 --> 00:35:43,090
+x element in x نقص و main of T ماشي الحالوأكيد في
+
+477
+00:35:43,090 --> 00:35:50,790
+X لأننا ماخدينه بربر الان و sequence Xn element
+
+478
+00:35:50,790 --> 00:35:57,300
+in domain of T which converts لمن لمن لل Xبنقدر
+
+479
+00:35:57,300 --> 00:36:01,400
+نعمل هيك عندي أكيد بنقدر نعمل X في ال .. في ال ..
+
+480
+00:36:01,400 --> 00:36:04,640
+في ال X إذا في Sequence موجودة في domain of T
+
+481
+00:36:04,640 --> 00:36:09,720
+Converse لها إذا صار عندي X N بتروح لل X و ال X مش
+
+482
+00:36:09,720 --> 00:36:14,240
+في domain T ال X أشماله is not element in domain
+
+483
+00:36:14,240 --> 00:36:21,030
+of mean of T إذا صار عندي هذا متحققهذا متحقق
+
+484
+00:36:21,030 --> 00:36:25,570
+خلّيني هذه أحطها وين برا X is not element in
+
+485
+00:36:25,570 --> 00:36:31,570
+domain of T هذا متحقق و I X M X N له هو عبارة عن I
+
+486
+00:36:31,570 --> 00:36:37,850
+X لانها دي function يعني هذه ال X وهذه ال X M من
+
+487
+00:36:37,850 --> 00:36:41,390
+فوق هي متحققة إذا ال I X M اللي هو ال X M
+
+488
+00:36:41,390 --> 00:36:48,820
+converges لل X اللي هي I Xواضح أنه لو بدها تكون
+
+489
+00:36:48,820 --> 00:36:53,460
+closed بدوا يكون عندكم ال X في domain ال T و ال I
+
+490
+00:36:53,460 --> 00:36:59,240
+X هو ال X اللي هي اسمها ال I X هي ال Y لكن ال X
+
+491
+00:36:59,240 --> 00:37:05,100
+مالها مش في domain ال T إذا ال I is not closed أي
+
+492
+00:37:05,100 --> 00:37:11,280
+سؤال اللي بعده يلّا نيجي الآن للمّا اطلع لفوق
+
+493
+00:37:11,280 --> 00:37:16,540
+الأخيرةالـ let T من الـ domain of T لعند YB a
+
+494
+00:37:16,540 --> 00:37:22,020
+bounded linear operatorSubset of X where X and Y
+
+495
+00:37:22,020 --> 00:37:26,560
+are non-disbases then if domain of T is closed
+
+496
+00:37:26,560 --> 00:37:32,220
+subset of X then T is closed إذا كانت domain of T
+
+497
+00:37:32,220 --> 00:37:35,920
+is closed ستكون T is closed هاي واحد هذا إيش ماله
+
+498
+00:37:35,920 --> 00:37:39,820
+bounded linear operator تانية if T is closed and Y
+
+499
+00:37:39,820 --> 00:37:42,480
+is complete then domain of T is closed subset من
+
+500
+00:37:42,480 --> 00:37:47,120
+من من اللي هو ال X البروف لأ بدنا نبره اللي بروف
+
+501
+00:37:47,120 --> 00:37:53,900
+وافتحلي على الكتاب يالاالبرمان هو .. عند .. زي ما
+
+502
+00:37:53,900 --> 00:37:57,560
+قلنا إذا كان domain of T closed subset of X إذا T
+
+503
+00:37:57,560 --> 00:38:00,640
+أشمالها is closed بالـ data between الـ T is
+
+504
+00:38:00,640 --> 00:38:03,180
+closed كيف ال data between ال T is closed؟ بقى عن
+
+505
+00:38:03,180 --> 00:38:05,540
+طريق الـ sequences بناخد Xn وين موجودة في domain
+
+506
+00:38:05,540 --> 00:38:10,920
+of T ونفترض إنها Xn converged من X ونفترض إن T Xn
+
+507
+00:38:10,920 --> 00:38:13,820
+برضه أشماله converged converged to some اللي هو
+
+508
+00:38:13,820 --> 00:38:19,620
+element Yالان مدام xn in domain of T اذا اكيد ال
+
+509
+00:38:19,620 --> 00:38:22,900
+.. ال .. ال .. ال .. ال .. ال xn convergence اللي
+
+510
+00:38:22,900 --> 00:38:25,660
+هيكون هو الموجود في ال domain of T closure لكن
+
+511
+00:38:25,660 --> 00:38:29,320
+احنا بنقول دي domain of T أشماله اللي هو عبارة عن
+
+512
+00:38:29,320 --> 00:38:32,680
+closed اه مقاطينها closed اذا اكيد ال domain of T
+
+513
+00:38:32,680 --> 00:38:34,940
+closure هو .. هو نفس ال domain of T يعني ال x هو
+
+514
+00:38:34,940 --> 00:38:38,540
+الموجودة في ال domain of Tلأن since the domain of
+
+515
+00:38:38,540 --> 00:38:41,860
+T is closed زي ما قلنا إذا صار عندي ال X ال X
+
+516
+00:38:41,860 --> 00:38:47,940
+موجودة في domain of T و ال T X N هتروح ل T X لأن T
+
+517
+00:38:47,940 --> 00:38:51,280
+أشمالها is continuous يعني صار عندي الآن بمعنى أخر
+
+518
+00:38:51,280 --> 00:38:57,880
+X N راحت لل X و ال X في domain T هي واحد و T X N
+
+519
+00:38:57,880 --> 00:39:01,900
+converge مزام converge و عندي T is continuous إذا
+
+520
+00:39:01,900 --> 00:39:06,680
+هذا بيعطينا ال T X N بتروح لمين ل T X فبكون اكتملت
+
+521
+00:39:06,960 --> 00:39:11,160
+اللي هو ما استلزم أن يكون closed إذا صارت T إيش ما
+
+522
+00:39:11,160 --> 00:39:17,620
+لها is closed اللي بعده يالا if T is closed ايوة T
+
+523
+00:39:17,620 --> 00:39:22,120
+is closed and اللي هو ال code domain اللي هو Y is
+
+524
+00:39:22,120 --> 00:39:25,180
+complete then domain of T is a closed subset of
+
+525
+00:39:25,180 --> 00:39:28,740
+main of X إذا بيشترط أنه يكون main Y is complete
+
+526
+00:39:28,740 --> 00:39:32,720
+تطلع ال domain of T is closed لكن هذا ماشترطش
+
+527
+00:39:32,720 --> 00:39:35,700
+علشان جالك domain of T closed على طول بتعطيك إيش T
+
+528
+00:39:35,700 --> 00:39:39,830
+is closedعشان تبين الـ domain of T is closed
+
+529
+00:39:39,830 --> 00:39:44,950
+كالعادة بناخد X وين موجودة في الـ domain of T مدام
+
+530
+00:39:44,950 --> 00:39:47,130
+في الـ domain of T موجودة نوصلها إلى X في الـ
+
+531
+00:39:47,130 --> 00:39:50,370
+domain of T كي بنوصلها إذا في سيكوانس من الـ
+
+532
+00:39:50,370 --> 00:39:52,950
+elements اللي في الـ domain of T اللي هو converged
+
+533
+00:39:52,950 --> 00:39:58,130
+من الـmain للـ XSince T is bounded، إذا اطلع لفوق،
+
+534
+00:39:58,130 --> 00:40:02,150
+احسبلي الـ T X N نقص T X M، اللي هو بيساوي T X N
+
+535
+00:40:02,150 --> 00:40:05,630
+نقص T X M، اللي هي أصغر شهر نورم الـ T في نورم X N
+
+536
+00:40:05,630 --> 00:40:10,530
+نقص X M، الآن هذه من هنا، X N بتروح للـ X، إذا هذه
+
+537
+00:40:10,530 --> 00:40:14,030
+كوشي، مدام هذه كوشي، إذا بزخرها زي ما بدي، أصغر من
+
+538
+00:40:14,030 --> 00:40:17,370
+Y عن نورم الـ T مثلا، إذا هيكون هذه أشمالها أصغر
+
+539
+00:40:17,370 --> 00:40:21,150
+من Y، يعني بمعنى أخر صارت الـ T X N كوشيهي
+
+540
+00:40:21,150 --> 00:40:23,690
+الاستدعى Y is complete تي اكس ان كوشي Y is
+
+541
+00:40:23,690 --> 00:40:26,930
+complete يدا نكون verbs يدا تي اكس ان بتروح لمين
+
+542
+00:40:26,930 --> 00:40:30,870
+لل Y لأن Y is complete صار عندي تي اكس ان بتروح لل
+
+543
+00:40:30,870 --> 00:40:35,410
+Y وبما ان T is closed وعندي اكس ان بتروح لل X و تي
+
+544
+00:40:35,410 --> 00:40:40,490
+اكس ان راحت لل Y يدا هيكون ال Y هي مين ال T X هو
+
+545
+00:40:40,490 --> 00:40:44,450
+ال X موجودة في دومين T يدا since T is closed يدا X
+
+546
+00:40:44,450 --> 00:40:48,750
+في دومين Tاللي هو صار عندي لان X في domain of T
+
+547
+00:40:48,750 --> 00:40:52,150
+closure وانتهيت ب X في domain of T لذا صار عندي
+
+548
+00:40:52,150 --> 00:40:57,070
+اللي هو ال domain of T is closed وبقول هي كذا
+
+549
+00:40:57,070 --> 00:41:00,730
+خلصنا الورهان النظرية وانهينا chapter اللي هو
+
+550
+00:41:00,730 --> 00:41:04,850
+أربعة عشر .. chapter أربعة وإلى لقاء آخر السلام
+
+551
+00:41:04,850 --> 00:41:06,130
+عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/wdHX26yF5r4_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/wdHX26yF5r4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..174d2c93c1be2d5d4ddcb037526bede3890ce0d3
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/wdHX26yF5r4_raw.srt
@@ -0,0 +1,2232 @@
+1
+00:00:05,150 --> 00:00:07,670
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,670 --> 00:00:10,590
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,590 --> 00:00:17,290
+آله وصحبه أجمعين هذه المحاضرة رقم 35 مساق تحليل
+
+4
+00:00:17,290 --> 00:00:20,010
+اقتران أو تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:20,010 --> 00:00:26,990
+الإسلامية ماجستير رياضيةحكينا المحاضرة الماضية عن
+
+6
+00:00:26,990 --> 00:00:31,930
+اللي هو الـ Open Mapping Theorem اللي هي النظرية
+
+7
+00:00:31,930 --> 00:00:35,830
+الأساسية الثالثة اليوم نحكي عن آخر نظرية أساسية في
+
+8
+00:00:35,830 --> 00:00:38,350
+اللي هو الـ Functional Analysis اللي هي اسمها
+
+9
+00:00:38,350 --> 00:00:44,070
+Closed Graph Theorem Closed Graph Theorem الآن
+
+10
+00:00:44,070 --> 00:00:51,780
+العنوان تحت Closed Linear Operatorsعنا احنا ال ..
+
+11
+00:00:51,780 --> 00:00:54,620
+ال .. ال .. واضح اللي احنا اهتمينا فيه كبير كثير
+
+12
+00:00:54,620 --> 00:00:57,040
+اللي هو الـ Bounded Linear Operators اللي هو الـ
+
+13
+00:00:57,040 --> 00:01:00,360
+Continuous Linear Operators وبعدين اهتمينا شوية في
+
+14
+00:01:00,360 --> 00:01:04,500
+ال .. في ال Open Mapping في ال Open Operators الآن
+
+15
+00:01:04,500 --> 00:01:10,340
+في اللي هو Operator آخر ومش شرط يكون Bounded
+
+16
+00:01:10,340 --> 00:01:14,200
+Linear Operator هنا قبل شوية قولنا احنا ال .. ال
+
+17
+00:01:14,200 --> 00:01:16,920
+.. ال .. ال Bounded Linear Operator ممكن يكون Open
+
+18
+00:01:16,920 --> 00:01:21,570
+تحت الشروط اللي حكيناهاالان لـ Closed Linear
+
+19
+00:01:21,570 --> 00:01:27,570
+Operators ، سنجد ان ليس كل الـ bounded linear
+
+20
+00:01:27,570 --> 00:01:33,110
+operators اللي في الدنيا هتكون bounded linear
+
+21
+00:01:33,110 --> 00:01:35,710
+operators يعني ممكن unbounded linear operators
+
+22
+00:01:36,870 --> 00:01:40,230
+ومهمة زي اللي هو اللي خدناها اللي هو ال .. ال ..
+
+23
+00:01:40,230 --> 00:01:45,990
+ال .. ال operator اللي كان يرسل ال X لل X' هذا ال
+
+24
+00:01:45,990 --> 00:01:50,690
+unbounded .. unbounded و هذا له استخدامات كثيرة و
+
+25
+00:01:50,690 --> 00:01:59,150
+.. و فيه له خلّيني أقول خواص معينة بتأهله أن يكون
+
+26
+00:01:59,150 --> 00:02:05,730
+مهمو تطبيقات كثيرة بتاهله أن يكون مهم اللي هو هذا
+
+27
+00:02:05,730 --> 00:02:12,810
+النوع من ال operators عادة يتمتع بخاصية ال
+
+28
+00:02:12,810 --> 00:02:17,870
+closedness يعني بنسميه closed operator ده نشوف إيش
+
+29
+00:02:17,870 --> 00:02:22,810
+معناته closed operator فهذا اللي هو استدعى أن يكون
+
+30
+00:02:22,810 --> 00:02:26,750
+اللي هو ال closed operator مهمنظراً لهو لوجود
+
+31
+00:02:26,750 --> 00:02:30,430
+Unbounded Linear Operator وهو في نفس الوقت Closed
+
+32
+00:02:30,430 --> 00:02:35,410
+وقاله تطبيقات أعتقد في الـ Quantum Mechanics في
+
+33
+00:02:35,410 --> 00:02:43,690
+أمور هندسية وفيزيائية في شباتر قدام موجود حتى
+
+34
+00:02:43,690 --> 00:02:46,610
+الحديث عنه لما نحكي عن الـ Spectral Theory
+
+35
+00:02:46,610 --> 00:02:52,610
+لـClosed Linear Operatorsهو نحكي عن سيجما و روه
+
+36
+00:02:52,610 --> 00:02:56,450
+الهنو .. طيب شوفوا نعرف ايش معناه closed linear
+
+37
+00:02:56,450 --> 00:03:00,790
+operator let X and Y be normed spaces T من domain
+
+38
+00:03:00,790 --> 00:03:03,670
+of T لعند مين لعند Y بيقى linear operator و ال
+
+39
+00:03:03,670 --> 00:03:07,170
+domain of T جزء من مين من X يعني أنا جاعد في اللي
+
+40
+00:03:07,170 --> 00:03:10,890
+هو normed space then T is called closed linear
+
+41
+00:03:10,890 --> 00:03:15,190
+operatorإذا كانت الـ graph .. الـ graph زي ما
+
+42
+00:03:15,190 --> 00:03:17,650
+نتخيل الـ graph تبع الـ function العادية اللي ..
+
+43
+00:03:17,650 --> 00:03:21,170
+اللي هي المجموعة من الـ ordered pairs للعنصر و
+
+44
+00:03:21,170 --> 00:03:25,610
+صورته للعنصر و صورته لأن g of t هذا اللي هو عبارة
+
+45
+00:03:25,610 --> 00:03:28,670
+عن كل الـ x و y حيث الـ x في ال domain و الـ y و
+
+46
+00:03:28,670 --> 00:03:32,410
+ما له صورته فين؟ في ال range اللي هي x واحد و x في
+
+47
+00:03:32,410 --> 00:03:35,850
+ال domain of t و y بساوة x is closed in the normed
+
+48
+00:03:35,850 --> 00:03:40,300
+space x cross yإذن الان where two algebraic
+
+49
+00:03:40,300 --> 00:03:42,780
+operations of the vector space are defined إلى أخر
+
+50
+00:03:42,780 --> 00:03:49,480
+فالن بعدين يعني عند T في ال domain of T لعند Y هذا
+
+51
+00:03:49,480 --> 00:03:52,500
+جزء من X و احنا بنحكي عن norm of the space الان
+
+52
+00:03:52,500 --> 00:03:55,480
+بتقول ان T is a closed linear operator
+
+53
+00:03:57,760 --> 00:04:00,560
+وكان اللي هو ال .. ال .. ال .. ال .. ال .. ال ..
+
+54
+00:04:00,560 --> 00:04:00,760
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+55
+00:04:00,760 --> 00:04:00,780
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+56
+00:04:00,780 --> 00:04:01,140
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+57
+00:04:01,140 --> 00:04:01,160
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+58
+00:04:01,160 --> 00:04:01,180
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+59
+00:04:01,180 --> 00:04:01,640
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+60
+00:04:01,640 --> 00:04:01,640
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+61
+00:04:01,640 --> 00:04:02,340
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+62
+00:04:02,340 --> 00:04:03,160
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+63
+00:04:03,160 --> 00:04:03,220
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+64
+00:04:03,220 --> 00:04:04,260
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+65
+00:04:04,260 --> 00:04:04,320
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+66
+00:04:04,320 --> 00:04:07,960
+ال ..
+
+67
+00:04:07,960 --> 00:04:08,920
+ال
+
+68
+00:04:12,530 --> 00:04:16,510
+معناته احنا بنقصد مين الـ T is a closed set طبعاً
+
+69
+00:04:16,510 --> 00:04:19,850
+هذي closed set في مين؟ في ال space تبعها، هذي جزء
+
+70
+00:04:19,850 --> 00:04:23,950
+من ال space اللي هو X across me and Y فبتكون اللي
+
+71
+00:04:23,950 --> 00:04:29,170
+هي G of T closed تعني في هذه الحالة أنه اللي هو ال
+
+72
+00:04:29,170 --> 00:04:33,650
+operator اللي عند T is a closed linear operator
+
+73
+00:04:35,250 --> 00:04:38,110
+اللي هان .. إيش العمليات اللي على ال .. ال ..
+
+74
+00:04:38,110 --> 00:04:40,850
+العمليات الجبريعية الـ X cross Y اللي خلّته vector
+
+75
+00:04:40,850 --> 00:04:43,670
+space اللي عمليات العادية اللي أنتوا عارفينها ال
+
+76
+00:04:43,670 --> 00:04:46,870
+.. ال pointwise addition و اللي هو ال scalar
+
+77
+00:04:46,870 --> 00:04:49,350
+multiplication برضه pointwise في الأولى و في
+
+78
+00:04:49,350 --> 00:04:54,220
+التانية هذه بتعملية vector spaceولو أخدنا اللي هو
+
+79
+00:04:54,220 --> 00:04:58,000
+الـ Norm عرفناه Normal X Y بيسوا Normal X زاد
+
+80
+00:04:58,000 --> 00:05:02,120
+Normal Y هنجيها برضه تعمل ليه أشماله؟ Normed Space
+
+81
+00:05:02,120 --> 00:05:08,080
+كامل يعني X cross Y هتعمل Vector Space وNorm تبحها
+
+82
+00:05:08,080 --> 00:05:11,140
+اللي عرفناها قبل بشوية هتعملنها عبارة عن Normed
+
+83
+00:05:11,140 --> 00:05:15,260
+Space لأن لو كانت هذه Closed فيه هذا معنى إيه؟
+
+84
+00:05:15,260 --> 00:05:19,100
+اللي هو الـ T is a Closed Linear Operator او It is
+
+85
+00:05:19,100 --> 00:05:25,200
+a Closed Operator اطلع على اللي فوقطيب الان نجي لـ
+
+86
+00:05:25,200 --> 00:05:27,660
+Closed Graph Theorem Closed Graph Theorem لطيفة
+
+87
+00:05:27,660 --> 00:05:32,640
+يعني فبرهنها لطيف let X and Y be بنخ Spaces
+
+88
+00:05:32,640 --> 00:05:37,080
+شايفين؟ and let T من domain of T لعند Y be a
+
+89
+00:05:37,080 --> 00:05:40,980
+closed linear operator with domain of T جزء من X
+
+90
+00:05:40,980 --> 00:05:46,580
+if domain of T is closed in X then T إيش مالها is
+
+91
+00:05:46,580 --> 00:05:52,520
+bounded وكأنه بقولكإن أي عامل عامل عامل عامل عامل
+
+92
+00:05:52,520 --> 00:05:53,360
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+93
+00:05:53,360 --> 00:05:56,300
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+94
+00:05:56,300 --> 00:05:56,660
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+95
+00:05:56,660 --> 00:05:57,000
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+96
+00:05:57,000 --> 00:05:57,020
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+97
+00:05:57,020 --> 00:05:57,020
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+98
+00:05:57,020 --> 00:05:58,250
+عامل عامل عامل عامل عامل عامل عامل عامل عاملأن لو
+
+99
+00:05:58,250 --> 00:06:02,450
+كانت domain of T closed أكيد automatic حيصير اللي
+
+100
+00:06:02,450 --> 00:06:08,510
+هو إيش closed subspace من بنخ space X إذا أكيد
+
+101
+00:06:08,510 --> 00:06:11,910
+حيكون بنخ space يعني بالمعنى أخر لو كانت T من بنخ
+
+102
+00:06:11,910 --> 00:06:15,270
+space لبنخ space وكانت bounded linear operator كل
+
+103
+00:06:15,270 --> 00:06:19,170
+سنة متسلمين على طول إيش بده يطلع اللي هو عبارة عن
+
+104
+00:06:19,170 --> 00:06:27,740
+Robin عبارة عن closedأسف .. bounded .. bounded إذن
+
+105
+00:06:27,740 --> 00:06:32,640
+الآن ال .. ال .. ال .. ال .. ال open mapping
+
+106
+00:06:32,640 --> 00:06:36,720
+theorem كانت تاخد من بلغ space لبلغ space و قلته
+
+107
+00:06:36,720 --> 00:06:43,740
+أعطتكم اللي هي ال .. ال bounded openهنا الآن الـ
+
+108
+00:06:43,740 --> 00:06:48,820
+closed أعطانا mean bounded تحت نفس الظروف وأقل
+
+109
+00:06:48,820 --> 00:06:53,160
+شوية مافيش قنته هنا مش لازم قنته يعني T من X لعند
+
+110
+00:06:53,160 --> 00:06:57,420
+Y تكون closed in our operator من بناخ space لبناخ
+
+111
+00:06:57,420 --> 00:07:02,260
+space أعطتك إيه أشماله الـ T إيه أشماله is bounded
+
+112
+00:07:02,260 --> 00:07:10,320
+واضح أه أي سؤال أي سؤال طيب
+
+113
+00:07:12,850 --> 00:07:18,890
+بتثبت أنه T is bounded خلّينا بس نحضر لما نصل لـ T
+
+114
+00:07:18,890 --> 00:07:24,850
+is bounded لتزد أن بانيكوشي سيكوينس X across Y
+
+115
+00:07:28,280 --> 00:07:32,440
+بدأ أثبت لكم أول حاجة إن X×Y نفسها complete ماشي
+
+116
+00:07:32,440 --> 00:07:36,700
+الحاجة أول حاجة لإنه بتلزمني بعد شوية عشان أثبت أن
+
+117
+00:07:36,700 --> 00:07:41,840
+T is bounded let ZN be any Cauchy sequence in X×Y
+
+118
+00:07:41,840 --> 00:07:45,980
+where ZN بسوء XN و YN أخد ال sequence فيهاكلام سلس
+
+119
+00:07:45,980 --> 00:07:50,600
+و سهل وسهل سريع then then for or therefore
+
+120
+00:07:50,600 --> 00:07:54,380
+therefore for every epsilon او then for every
+
+121
+00:07:54,380 --> 00:07:58,060
+epsilon أكبر من سفر there exist k limited to n
+
+122
+00:07:58,060 --> 00:08:02,300
+such that for all m و n أكبر من n و أكبر من k هكون
+
+123
+00:08:02,300 --> 00:08:06,880
+norm اللي هو الذد أنمك الذد أم أشماله أصغر من
+
+124
+00:08:06,880 --> 00:08:10,540
+epsilon اللي ماياخد ال E دي أشمالها is Cauchyطيب
+
+125
+00:08:10,540 --> 00:08:15,980
+الـ ZM نقص الـ ZM الـ ZN XN و YN إذا الـ ZN اللي
+
+126
+00:08:15,980 --> 00:08:20,700
+هي عبارة هي .. و الـ ZM اللي هي .. قصدي هذه و الـ
+
+127
+00:08:20,700 --> 00:08:25,800
+ZM هي .. و طرحتهم من بعض طلعت XN نقص XM و YN نقص
+
+128
+00:08:25,800 --> 00:08:30,180
+YM في دا عملها سهلة الان norm هذا حسب اللي عرفناه
+
+129
+00:08:30,180 --> 00:08:33,360
+قبل و شوية هان ال norm هذا عبارة عن norm هذه زي
+
+130
+00:08:33,360 --> 00:08:38,290
+norm هذه هي norm هذه زي norm هذه إذا واضحإن لما
+
+131
+00:08:38,290 --> 00:08:43,630
+كانت Z انكوشي سيكوانس أعطتلي هذه زائد هذه أصغر من
+
+132
+00:08:43,630 --> 00:08:49,930
+مين من إبسل يعني أكيد طلع عندي اللي هو ال XN ماقص
+
+133
+00:08:49,930 --> 00:08:55,850
+XNوالـ yn ناقص yn مدى أن مجموحه أصغر من إبسلون فكل
+
+134
+00:08:55,850 --> 00:09:00,650
+واحدة فيه أصغر من مين من إبسلون for every m و n
+
+135
+00:09:00,650 --> 00:09:04,590
+أشمالهن أكبر من k إذا صارت هذه اللي هي ال sequence
+
+136
+00:09:04,590 --> 00:09:09,830
+تبعتها xn كوشي في ال x و ال yn كوشي في مين في ال y
+
+137
+00:09:09,830 --> 00:09:13,250
+أو كوشي حتى في ال domain و ال domain ما هو closed
+
+138
+00:09:13,250 --> 00:09:19,910
+فأكيد أشماله completeإذاً صار هذه كوشي في complete
+
+139
+00:09:19,910 --> 00:09:23,190
+و y and كوشي في complete إذاً كل واحدة فيها limit
+
+140
+00:09:23,190 --> 00:09:29,240
+ماشي طيب و هذا اللي هو اللي بدويا إذاHence x and y
+
+141
+00:09:29,240 --> 00:09:31,960
+and are Cauchy sequences in x and y respectively
+
+142
+00:09:31,960 --> 00:09:35,440
+أو حتى في الـ domain of T however x and y are
+
+143
+00:09:35,440 --> 00:09:38,360
+complete وكمان ال domain of T complete then there
+
+144
+00:09:38,360 --> 00:09:41,160
+exist x element in x and y element in y such that
+
+145
+00:09:41,160 --> 00:09:44,780
+x and .. بتروح لل x و y and إيش ما لها؟ بتروح لل y
+
+146
+00:09:44,780 --> 00:09:50,460
+الآن وابحث هذه تعالوا لواحد هذا وودوه لأم تروح إلى
+
+147
+00:09:50,460 --> 00:09:55,410
+ما لنهايةطبعا أنا ماخدين M أكبر من N عمدا على أساس
+
+148
+00:09:55,410 --> 00:09:58,430
+M تروح لما لا نهاية تطير و M هي حرة بتظهر زي ما هي
+
+149
+00:09:58,430 --> 00:10:03,530
+إذا M واحدة إلى ما لا نهاية صار عندي XM ناقص X و
+
+150
+00:10:03,530 --> 00:10:09,970
+YM ناقص Y أصغر اللي هو من مين من إرسلون صار عندي
+
+151
+00:10:09,970 --> 00:10:17,000
+تنتين مع بعض ZM ناقص XYحصلت ال limit هي x لهذه و y
+
+152
+00:10:17,000 --> 00:10:21,040
+لهذه صارت واحدة في x واحدة في y صار عندي zn نقص x
+
+153
+00:10:21,040 --> 00:10:25,500
+و y بيساوي normal xn نقص x زي yn نقص mean y
+
+154
+00:10:25,500 --> 00:10:30,360
+التنتين أصغر من مين من يبسلون إذا صار عندي this
+
+155
+00:10:30,360 --> 00:10:34,820
+means that zn converts the mean ل x و y therefore
+
+156
+00:10:34,820 --> 00:10:39,940
+x cross y is completeإذا انتهينا من X x Y is
+
+157
+00:10:39,940 --> 00:10:42,360
+complete و لو حتى خدنا ال domain برضه بيبقى لها
+
+158
+00:10:42,360 --> 00:10:48,940
+complete لأن ال domain is a closed subspace طيب يا
+
+159
+00:10:48,940 --> 00:10:57,320
+جماعة أطلع لفور الآن عندي T is closedT is closed
+
+160
+00:10:57,320 --> 00:11:01,920
+إذن أكيد الـ G of T أشماله closed in X cross Y و
+
+161
+00:11:01,920 --> 00:11:04,380
+ال domain of T closed in X إذن الاتنين صاروا
+
+162
+00:11:04,380 --> 00:11:06,960
+incomplete لأن هذا بنخ space و هذا بنخ space اللي
+
+163
+00:11:06,960 --> 00:11:10,680
+هم جزء منه هذا بنخ space و هذا بنخ space إذا على
+
+164
+00:11:10,680 --> 00:11:14,680
+طول G of T and D of T are complete spaces Now
+
+165
+00:11:14,680 --> 00:11:18,300
+consider the mapping خدها ال mapping الآن B من G
+
+166
+00:11:18,300 --> 00:11:23,040
+of T لعين 2 لعين D of TDefined by .. كله بده أصلهش
+
+167
+00:11:23,040 --> 00:11:26,100
+أنما .. بده أصلكم أن الـT is bounded يعني نورم
+
+168
+00:11:26,100 --> 00:11:29,140
+الـT of X أصغر يساوي إيش some number في مين في
+
+169
+00:11:29,140 --> 00:11:31,960
+نورم الـX هى اللي بده أصله فخلّيني أشوف عبر إيش
+
+170
+00:11:31,960 --> 00:11:35,440
+نصله Now consider the mapping B من G من G of T
+
+171
+00:11:35,440 --> 00:11:39,020
+لعين Domain of T that defined by projection map
+
+172
+00:11:39,020 --> 00:11:44,540
+projection سقاط بسقط الأول B X و T X بسقطوا على
+
+173
+00:11:44,540 --> 00:11:49,570
+مين؟ على Xلأن it is left to the reader to show
+
+174
+00:11:49,570 --> 00:11:53,990
+that P is linear P is linear سهل حتى linear بنقدر
+
+175
+00:11:53,990 --> 00:12:06,910
+نثبتها وإحنا مرتاحين عندي P of X و TX اللي هو طبعا
+
+176
+00:12:06,910 --> 00:12:14,670
+بساوي من؟ بساوي X لأن Pof الـ element اللي في الـ
+
+177
+00:12:14,670 --> 00:12:16,790
+element اللي في الـ g of t هتديروا بالك أين موجود
+
+178
+00:12:16,790 --> 00:12:22,010
+في الـ g of t ال element راحة alpha x زائد اللي هو
+
+179
+00:12:22,010 --> 00:12:26,310
+مثلا x prime هيكون ال .. ال .. ال .. ال .. ال
+
+180
+00:12:26,310 --> 00:12:28,590
+element عشان يكون في الـ g of t بدي يكون صورته
+
+181
+00:12:28,590 --> 00:12:35,330
+اللي هو t of alpha x زائد x prime صح؟ ويساوي هدي
+
+182
+00:12:35,330 --> 00:12:41,630
+بيه مش بدنا في ال .. معايا أه ويساوي alpha xزايد x
+
+183
+00:12:41,630 --> 00:12:53,330
+prime ويساوي Alpha بي of x وTx زايد بي of x prime
+
+184
+00:12:53,330 --> 00:12:59,950
+وTx prime حسب التاريخ على طول صارت عندي ال b is
+
+185
+00:12:59,950 --> 00:13:04,670
+linear أي سؤال معايا
+
+186
+00:13:09,630 --> 00:13:12,750
+الآن خدوا ال norm ال norm هي واضح هذه ما هي على
+
+187
+00:13:12,750 --> 00:13:20,030
+طول نورم هذه هو norm ال X، مظبوط؟ طيب، إذا الها ده
+
+188
+00:13:20,030 --> 00:13:23,390
+هتوديني على ال boundedness تبعت مين؟ تبع ال B اللي
+
+189
+00:13:23,390 --> 00:13:27,810
+هو ال norm ال B of X و T X اللي هو بيساوي نورم ال
+
+190
+00:13:27,810 --> 00:13:33,970
+X وراء ال X، then B is bounded اللي هي أكيد هذه
+
+191
+00:13:35,150 --> 00:13:40,650
+نورم الـ X الـ BX و TX بيساوي نورم الـ X بتخليلي
+
+192
+00:13:40,650 --> 00:13:47,070
+اللي هو هذا is bounded كيف طيب؟ لأ مهو ده اللي
+
+193
+00:13:47,070 --> 00:13:53,350
+منتبهها بشير أصغر أو شاوي اللي هو نورم ال X زائد
+
+194
+00:13:53,350 --> 00:13:59,290
+نورمين ال TX صح ولا؟ و هذا إيش بيساوي نورم ال X و
+
+195
+00:13:59,290 --> 00:14:04,620
+TXإذا صار عندي B of العمصر تبعها هذا اللي بترسله
+
+196
+00:14:04,620 --> 00:14:07,860
+أصغر أو شوية اللي بترسله وانت تعرف اللي هو النور
+
+197
+00:14:07,860 --> 00:14:12,600
+يعني الـB هنا واحد الثابت فبصير B أشمالها is
+
+198
+00:14:12,600 --> 00:14:20,920
+bounded هذا سبب الـboundedness طيب الآن then اللي
+
+199
+00:14:20,920 --> 00:14:24,300
+هو B is bounded it is easy to see that B is
+
+200
+00:14:24,300 --> 00:14:29,320
+bijective بيواجектив أصلا أكيد B is bijective or
+
+201
+00:14:29,320 --> 00:14:29,820
+one to one
+
+202
+00:14:38,740 --> 00:14:40,920
+معايا ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+203
+00:14:40,920 --> 00:14:42,100
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+204
+00:14:42,100 --> 00:14:42,540
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+205
+00:14:42,540 --> 00:14:42,580
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+206
+00:14:42,580 --> 00:14:42,880
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+207
+00:14:42,880 --> 00:14:42,900
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+208
+00:14:42,900 --> 00:14:43,000
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+209
+00:14:43,000 --> 00:14:43,000
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+210
+00:14:43,000 --> 00:14:43,000
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+211
+00:14:43,000 --> 00:14:43,000
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+212
+00:14:43,000 --> 00:14:43,000
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+213
+00:14:43,000 --> 00:14:43,000
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+214
+00:14:43,000 --> 00:14:48,480
+ال ال ال ال ال ال ال ال ال ال ال ال الت بي
+
+215
+00:14:48,480 --> 00:14:50,200
+of x
+
+216
+00:14:56,260 --> 00:15:02,160
+أكس برايم و TX أشماله أبرايم بظبط هذه X برايم X
+
+217
+00:15:02,160 --> 00:15:07,360
+بيساوي X مين أبرايم بناء عليه TX هيساوي TX برايم
+
+218
+00:15:07,360 --> 00:15:12,020
+عشان T function إذا صارت one to one الان انتوا
+
+219
+00:15:12,020 --> 00:15:16,540
+خدوا أي من وين لوين جاية ال B اللي هي الجاية ال B
+
+220
+00:15:16,540 --> 00:15:20,500
+من اللي هو وينها وينها وينها هي من G of T ل domain
+
+221
+00:15:20,500 --> 00:15:26,220
+of T خد أي element هنا شكله Xإذاً أكيد فيه إله TX
+
+222
+00:15:26,220 --> 00:15:32,320
+إذاً there exist X هو وTX لأن TX موجودة لإنه الـ T
+
+223
+00:15:32,320 --> 00:15:35,420
+function X وTX هنا such that بيه كده مثلًا وكده
+
+224
+00:15:35,420 --> 00:15:40,660
+إذاً الأمطوا برضه أشمالها واضحة أشوف التقباتات
+
+225
+00:15:47,740 --> 00:15:57,420
+للعدي بي من من من g of T لعين domain of T خد الآن
+
+226
+00:15:57,420 --> 00:16:04,880
+أي x element in domain of T then there exist x و T
+
+227
+00:16:04,880 --> 00:16:11,140
+x element in domain of T لأن T is a function جي of
+
+228
+00:16:11,140 --> 00:16:19,120
+TSuch that P of X و TX هو مين اللي بدأت فيها X إذا
+
+229
+00:16:19,120 --> 00:16:28,280
+أنتوامعايا؟ اذا B is onto اذا كل شي فيها صارت عندي
+
+230
+00:16:28,280 --> 00:16:34,660
+الان B bounded او one to one onto وlinear اذا B
+
+231
+00:16:34,660 --> 00:16:38,060
+inverse من domain of T الى U of T اشماله exist and
+
+232
+00:16:38,060 --> 00:16:42,440
+is defined by B inverse X ايش هيروح لل X وصورة مين
+
+233
+00:16:42,440 --> 00:16:47,840
+اللي هي ال X under T اللي هي TXالان since D of D
+
+234
+00:16:47,840 --> 00:16:50,580
+and D of D are complete then by open mapping
+
+235
+00:16:50,580 --> 00:16:54,760
+theorem اللي قبل بشوية المرة المحادرة اللي فاتت
+
+236
+00:16:54,760 --> 00:16:58,740
+اللي هو هيكون ال B inverse إيش ماله is bounded
+
+237
+00:16:58,740 --> 00:17:02,920
+خلينا نقول مدام B inverse bounded نقول norm ال B
+
+238
+00:17:02,920 --> 00:17:07,000
+inverse لل X أصغر سوى B في مين؟ في norm ال X طب هو
+
+239
+00:17:07,000 --> 00:17:11,490
+B inverse of X إيش بسوى norm ال X و TXمعايا؟ إذا
+
+240
+00:17:11,490 --> 00:17:16,910
+صار عندي هذا المقدار أصغر أو أشهر هذا ومنه على طول
+
+241
+00:17:16,910 --> 00:17:21,370
+norm of TX انا بعرف أصغر أو أشهر norm of TX زائد
+
+242
+00:17:21,370 --> 00:17:25,170
+مين؟ زائد norm of X زي اللي عملتها وهذا هو مين؟
+
+243
+00:17:25,170 --> 00:17:28,970
+norm of X وTX هيه اللي هو أصغر أو أشهر من B في X
+
+244
+00:17:28,970 --> 00:17:31,730
+إذا صار عندي norm of TX أصغر أو أشهر بيه في norm
+
+245
+00:17:31,730 --> 00:17:39,030
+of X وهذا يعني أن الـ T is bounded أي شؤال اللي
+
+246
+00:17:39,030 --> 00:17:39,490
+بعده
+
+247
+00:17:43,930 --> 00:17:47,410
+إذن هذا أعطاني condition الـ closed graph theorem
+
+248
+00:17:47,410 --> 00:17:54,650
+أعطاني إعلان إن T من بنخ space إلى بنخ space اللي
+
+249
+00:17:54,650 --> 00:18:00,390
+هو closed إذا كان closed بيعطيني إيه شماله؟
+
+250
+00:18:00,390 --> 00:18:08,030
+bounded T is bounded طيب شوفوا
+
+251
+00:18:08,030 --> 00:18:13,890
+الآن اللي بعدهاالنظرية اللي بعدها بتقول لل T من
+
+252
+00:18:13,890 --> 00:18:16,890
+domain of T لعند Y بيه a linear operator و ال
+
+253
+00:18:16,890 --> 00:18:20,390
+domain of T X معلق crazing على اللي هو انه ياخد ال
+
+254
+00:18:20,390 --> 00:18:24,770
+domain of T لل X يا جماعة هرايحنا و خد من X لعند Y
+
+255
+00:18:24,770 --> 00:18:28,630
+و اشتغلونه و حط خاص ال domain of T في ال X يا سيدة
+
+256
+00:18:28,630 --> 00:18:35,130
+مش مشكلة كتيرهو يعني بشعر أنه هي كأعام كتير
+
+257
+00:18:35,130 --> 00:18:37,550
+من الكتب خلاص مش بتبقى في domain of T علشان تبقى
+
+258
+00:18:37,550 --> 00:18:40,510
+تعتبر X لعند Y وتعتبر X هو ال domain وهو norm of
+
+259
+00:18:40,510 --> 00:18:44,330
+this base الاخرى أو إذا كان بديها هي كمليت بتعطيه
+
+260
+00:18:44,330 --> 00:18:47,690
+كمليت ومتعاشر وكذا الاخرى بيقالين ياروبيرت لو ال
+
+261
+00:18:47,690 --> 00:18:50,590
+domain of T subset من X and X and Y لكن رائع هو
+
+262
+00:18:50,590 --> 00:18:56,210
+عموما في العرض and X and Y be normed this basisثم
+
+263
+00:18:56,210 --> 00:18:59,410
+T is closed if and only if it has the following
+
+264
+00:18:59,410 --> 00:19:03,390
+properties انتوا اللي بقولوا هال properties Xn
+
+265
+00:19:03,390 --> 00:19:06,390
+بتروح لل X where Xn المتن دومين of T for all n and
+
+266
+00:19:06,390 --> 00:19:09,410
+T Xn بتروح لل Y دون X المتن دومين of T and T X
+
+267
+00:19:09,410 --> 00:19:17,980
+يشبه لها بتسوى Y هذا يستوجب الوقوفونحكي عنه يعني
+
+268
+00:19:17,980 --> 00:19:23,900
+بمعنى آخر يترجم .. يترجم احنا زمان .. زمان أخدنا T
+
+269
+00:19:23,900 --> 00:19:31,700
+اه .. قولوا معايا T من عند X لعند Y انها
+
+270
+00:19:31,700 --> 00:19:37,500
+continuous او bounded اذا حققت الشرط التالي انه
+
+271
+00:19:37,500 --> 00:19:44,130
+لما XNبتروح للـ X ماشي الحال يعني Xn من وين؟ Xn من
+
+272
+00:19:44,130 --> 00:19:47,950
+الـ X والـ X من الـ X من رأس الدورة و Xn روحت للـ
+
+273
+00:19:47,950 --> 00:19:54,010
+X إذا هذا أعطاني إن الـ TXn بتروح للـ TX على طول
+
+274
+00:19:54,010 --> 00:19:57,990
+بنقول عن الـ T أشمالها is continuous إذن التعبير
+
+275
+00:19:57,990 --> 00:20:00,770
+عن ال continuity أو ال boundedness للـ linear
+
+276
+00:20:00,770 --> 00:20:05,030
+operator عن طريق ال sequence إن sequence converges
+
+277
+00:20:05,030 --> 00:20:09,420
+في X في داخل كله في داخل Xبيعطيني اذا اعطاني ان
+
+278
+00:20:09,420 --> 00:20:13,500
+الـ TX بتروح لـ TX في داخل الـ Y معناته انه انتهى
+
+279
+00:20:13,500 --> 00:20:16,800
+الامر صار إيش ماله continuous هنا الان بده يعطي
+
+280
+00:20:16,800 --> 00:20:21,620
+condition يكافئ لclosedness اللي closed برضه عن
+
+281
+00:20:21,620 --> 00:20:24,940
+طريق ال sequences بس ديروا بالكم هنا ماخد اللي هو
+
+282
+00:20:24,940 --> 00:20:28,690
+ال X و ال Y normed spaces مضارة normed spacesالـ N
+
+283
+00:20:28,690 --> 00:20:32,270
+يعني خرّين نحنا T is closed if and only if T has
+
+284
+00:20:32,270 --> 00:20:36,090
+the following property إيش بييجي بيقول إذا كانت
+
+285
+00:20:36,090 --> 00:20:43,350
+إذا كانت XN element in X لكل N و الـ XN عاملها
+
+286
+00:20:43,350 --> 00:20:52,050
+راحت لل X و أيضا اللي هو TXN راحت لل Y و TXN TXN
+
+287
+00:20:52,050 --> 00:20:59,850
+راحت لل Yوالـ TXM طبيعي هتكون موجودة في الـ Y ما
+
+288
+00:20:59,850 --> 00:21:03,510
+حكى اشي لا عن X ولا عن Y يعني ما قالش ان X موجودة
+
+289
+00:21:03,510 --> 00:21:08,490
+في الـ X وما فرضش هذا الحالة لأ هو الـ N يعني جال
+
+290
+00:21:08,490 --> 00:21:13,250
+XN بتروح لصن X ماجالش موجودة في الـ Xوقال إن الـ
+
+291
+00:21:13,250 --> 00:21:17,570
+TXN بتروح للـ Y هن استنتجناها في الـ Continuity
+
+292
+00:21:17,570 --> 00:21:21,170
+TXN روحت للـ X وكانت هذه موقف شرط إنها تكون هنا،
+
+293
+00:21:21,170 --> 00:21:26,070
+هن مش شرط لكن شرط إشي هنا إن TXN تروح للـ Y هن مش
+
+294
+00:21:26,070 --> 00:21:31,490
+شرط تطلع من جواب الشرط TXN بتروح لمين؟ لـ TX أعطال
+
+295
+00:21:31,490 --> 00:21:37,670
+الـ Continuity هذا لو حدث كله على بعض أو أعطاني إن
+
+296
+00:21:37,670 --> 00:21:42,310
+الـ X في الـ Xوالـ TX هي الـ Y معناته وين موجودة
+
+297
+00:21:42,310 --> 00:21:47,010
+في الـ Y معناته إذا حدث هذا بيكون الـ T is a
+
+298
+00:21:47,010 --> 00:21:51,910
+closed operator is a closed operator إذن if XN
+
+299
+00:21:51,910 --> 00:21:57,140
+بتروح لل X و XN في Domain Tوالـ T X N بتروح للـ Y
+
+300
+00:21:57,140 --> 00:22:02,360
+إذا هذا مع بعض أعطاني إنه X في دومين الـ T والـ T
+
+301
+00:22:02,360 --> 00:22:06,560
+X بتساوي Y Automatic هذا إيش معناته إنه هتكون الـ
+
+302
+00:22:06,560 --> 00:22:13,560
+T is closed واضح الفرق بين ال continuity بتلالة
+
+303
+00:22:13,560 --> 00:22:17,700
+اللي هو ال sequences و ال closedness للـ T بدلالة
+
+304
+00:22:17,700 --> 00:22:21,340
+ال sequences هاي الفرق بين إنه هاي الأمور واضحة
+
+305
+00:22:25,070 --> 00:22:30,770
+خلّيني بس نكمل اللي بنحكيه suppose
+
+306
+00:22:30,770 --> 00:22:35,090
+that T
+
+307
+00:22:35,090 --> 00:22:36,630
+is closed
+
+308
+00:22:40,870 --> 00:22:46,790
+الـ openness بتحكي علاقة بين T inverse و T إذا
+
+309
+00:22:46,790 --> 00:22:50,430
+بدنا نترجم على T inverse بيصير كلام تاني then T is
+
+310
+00:22:50,430 --> 00:22:55,810
+closed إذا دول اللي ده property صحيحة نيجي الآن
+
+311
+00:22:55,810 --> 00:23:00,350
+إبرهن suppose that T is closed إذا G of T إيش
+
+312
+00:23:00,350 --> 00:23:07,820
+ماله؟ Closedالان بدي اثبت لك اخد هذه و هذه و اصلك
+
+313
+00:23:07,820 --> 00:23:11,120
+لهذه المجموعه ماشي؟ ممكن خلصنا الـ visual اول طيب
+
+314
+00:23:11,120 --> 00:23:15,480
+اذا بدي اخد ماعطينيه عشان استعمله بدي اقول له let
+
+315
+00:23:15,480 --> 00:23:19,620
+xn بتروح للـx هيها و الـxn في domain الـT و خلينا
+
+316
+00:23:19,620 --> 00:23:25,440
+ناخد Txn بتروح لمين؟ للـY من الحديث هذا اكيد الـxn
+
+317
+00:23:25,440 --> 00:23:31,220
+و Txn وين موجود؟فى الـ G of D ماشي و ال XN و ال T
+
+318
+00:23:31,220 --> 00:23:36,060
+XN وين بتروح لل X و Y لإن هو مضّيل ال X عن وين و
+
+319
+00:23:36,060 --> 00:23:39,680
+مضّيل إيها ال X عن .. على ال X و مضّيل ال T XN على
+
+320
+00:23:39,680 --> 00:23:46,060
+مين؟ على ال T X إذا عند X و Y هتكون وين موجودة؟ فى
+
+321
+00:23:46,060 --> 00:23:52,580
+ال G of D معايا؟ ليش؟ لإن ال T is closedما هو شو
+
+322
+00:23:52,580 --> 00:23:56,220
+معناه الـ T is closed؟ انه الآن الـ G of T is
+
+323
+00:23:56,220 --> 00:23:59,180
+closed ايش معناه الـ G of T is closed؟ يعني أي
+
+324
+00:23:59,180 --> 00:24:04,120
+sequence فيه converts to some element ستكون في الـ
+
+325
+00:24:04,120 --> 00:24:08,600
+G of T إذا صار عندي Xn وT Xn بتروح لل X و Y قطعًا
+
+326
+00:24:08,600 --> 00:24:12,900
+X و Y هتكون في الـ G of T عشان الـ G of T is
+
+327
+00:24:12,900 --> 00:24:16,420
+closed لأن الـ T في الأصل is closed this means
+
+328
+00:24:16,420 --> 00:24:20,620
+thatإن ما دامت الـ X Y في الـ G of T إذن X في الـ
+
+329
+00:24:20,620 --> 00:24:25,100
+domain of T والـ T X أشماله بسوء Y لأن الـ G of T
+
+330
+00:24:25,100 --> 00:24:28,520
+هي عبارة عن ال order pairs بين اللي هو أعناصر ال
+
+331
+00:24:28,520 --> 00:24:33,160
+domain of T و الصور اللي هي لهذا ال domain إذن هذا
+
+332
+00:24:33,160 --> 00:24:37,820
+بيعني إن X في domain T و T X بسوء Y لأن conversely
+
+333
+00:24:39,630 --> 00:24:43,530
+suppose that اتنين holds هي هذه الخاصية ايش ما لها
+
+334
+00:24:43,530 --> 00:24:48,150
+تتحقق الان بدنا نثبت لكم ان هو g of t is closed
+
+335
+00:24:48,150 --> 00:24:51,770
+كيف بدنا نثبت انها closed؟ بدي اخد x y في ال g of
+
+336
+00:24:51,770 --> 00:24:54,910
+t closure و اثبت لكم ال x y في ال g of t و خلصنا
+
+337
+00:24:54,910 --> 00:24:57,150
+صار ال g of t is closed اللي بيساوي ال g of t يعني
+
+338
+00:24:57,150 --> 00:25:01,700
+ان ال g of t is closedثم مادام الـ G of T مقفلة
+
+339
+00:25:01,700 --> 00:25:04,980
+الـ X Y في الـ G of T مقفلة إذا تتمتع بالخاصية
+
+340
+00:25:04,980 --> 00:25:08,600
+التالية إن أنا بقدر ألاقي الـ sequence XN و TXN في
+
+341
+00:25:08,600 --> 00:25:13,420
+الـ G of T convolutionally للـ XY إذا there exists
+
+342
+00:25:13,420 --> 00:25:16,820
+this sequence of elements in G of T such that XN و
+
+343
+00:25:16,820 --> 00:25:21,030
+TXN تروح لمين للـ XYوهذا يعني Xn بتروح لل X و Tx
+
+344
+00:25:21,030 --> 00:25:24,990
+بتروح لمين؟ لل Y و Xn من وين جاية؟ من ال domain of
+
+345
+00:25:24,990 --> 00:25:28,390
+T يعني كل الشروط اللي جاب المتحققة then by
+
+346
+00:25:28,390 --> 00:25:31,690
+assumption اللي هو the property 2 X هذه هتكون في
+
+347
+00:25:31,690 --> 00:25:36,150
+domain T و Tx بالساوية Y وهذا يعني ال X و Y موجودة
+
+348
+00:25:36,150 --> 00:25:40,170
+في G of T وهذا يعني أنه بدأنا بهذه وانتهينا بهذه
+
+349
+00:25:40,170 --> 00:25:44,710
+أنه therefore G of D is closed وهذا يعني أنه T is
+
+350
+00:25:44,710 --> 00:25:45,830
+closed اللي بعده يلا
+
+351
+00:25:50,340 --> 00:25:54,340
+الان مثال اللى عدناكم فيه هو الأول اللى قلنا احنا
+
+352
+00:25:54,340 --> 00:25:58,160
+احنا يعني فى bounded linear operators او فى عندى
+
+353
+00:25:58,160 --> 00:26:01,740
+closed linear operators which is not bounded
+
+354
+00:26:01,740 --> 00:26:05,440
+والمثال المشهور اللى هو example differential
+
+355
+00:26:05,440 --> 00:26:11,020
+operator I differential operator let X بتساوى C01
+
+356
+00:26:11,020 --> 00:26:15,690
+على ال continuous functionsوT من الـ domain of T
+
+357
+00:26:15,690 --> 00:26:19,950
+لعند مين؟ لعند X بي such that الـ TX بتاوى إيش ما
+
+358
+00:26:19,950 --> 00:26:24,620
+لها X' و X' is the derivative of Xطيب ما هو هذا
+
+359
+00:26:24,620 --> 00:26:28,140
+الـ X إيش ما لها عبارة عن continuous functions مش
+
+360
+00:26:28,140 --> 00:26:30,480
+كل ال continuous functions كان بيه إيش ما لها
+
+361
+00:26:30,480 --> 00:26:34,060
+دفعانشياتي ده إذا أكيد اللي هو بده يكون ال domain
+
+362
+00:26:34,060 --> 00:26:38,820
+of T of روبر subspace من مين؟ من ال X إذا هذا ال
+
+363
+00:26:38,820 --> 00:26:42,280
+proper subspace اللي هو of functions اللي بيديها
+
+364
+00:26:42,280 --> 00:26:45,780
+كمان مش بس ما دفعانشيابلاللي هو domain of T is a
+
+365
+00:26:45,780 --> 00:26:49,060
+subspace of functions ياك بديها X element in X
+
+366
+00:26:49,060 --> 00:26:51,980
+which have a continuous derivative يعني اللي بتطلع
+
+367
+00:26:51,980 --> 00:26:55,480
+برضه تطلع أي شمالها continuous عشان أقدر أرسلها
+
+368
+00:26:55,480 --> 00:26:58,460
+وين في حالة فتطلع continuous مش هاد ال X
+
+369
+00:26:58,460 --> 00:27:02,260
+continuous فالآن اللي أنا أخدش domain of T هو ال
+
+370
+00:27:02,260 --> 00:27:09,200
+domain اللي جزء من الـ C01 و اللي دواله اللي
+
+371
+00:27:09,200 --> 00:27:15,200
+بتتفاضل و تفاضلها بتطلع أي شماله continuousالأن
+
+372
+00:27:15,200 --> 00:27:20,580
+احدين T is not bounded بط ايش ماله is closed
+
+373
+00:27:20,580 --> 00:27:25,320
+اثبتناها not bounded زمان اللي هو by اثنين سبعة
+
+374
+00:27:25,320 --> 00:27:30,720
+خمسة بالظبط T is linear بط not bounded بدنا نثبت
+
+375
+00:27:30,720 --> 00:27:35,570
+انها ايش لان انها closed شوفوا كيفبعد أن نثبت أنها
+
+376
+00:27:35,570 --> 00:27:40,090
+قريبة نستخدم الخاصية اللي قبل بشوية let XN element
+
+377
+00:27:40,090 --> 00:27:44,650
+in domain of T for all N such that XN بتروح لل X و
+
+378
+00:27:44,650 --> 00:27:50,390
+TXN ايش معناها سموها XN برايم بتروح لمين لل Y ماشي
+
+379
+00:27:50,390 --> 00:27:53,890
+الحالة XN برايم اللي هي ايش معناته ال derivative
+
+380
+00:27:53,890 --> 00:27:59,090
+مش هي اتفجن اللي هو بريطان هو اللي بفاضل اذا TXN
+
+381
+00:27:59,090 --> 00:28:02,050
+برايم هو سميه ايش اسمه XN برايم اللي هي derivative
+
+382
+00:28:02,050 --> 00:28:08,010
+لمين لل XNمعايا احنا هي اللي بدنا هيها نفترض هذه
+
+383
+00:28:08,010 --> 00:28:11,590
+بتروح لهذه وهذه بتروح لمين ل some y يعني ال xn
+
+384
+00:28:11,590 --> 00:28:15,150
+بتروح لل x و ال xn بتروح لمين لل y بدنا نثبت لكم
+
+385
+00:28:15,150 --> 00:28:19,590
+ان ال x في ال domain of T و نثبت ان هو ال y ايش
+
+386
+00:28:19,590 --> 00:28:25,960
+معناه تي اكس هي ال yبتكون مقفلة طيب by 155 the
+
+387
+00:28:25,960 --> 00:28:29,720
+convergence in the norm space أخدناها برضه ال C زي
+
+388
+00:28:29,720 --> 00:28:33,380
+اللي كنا قولنا convergence في C01 انه uniform
+
+389
+00:28:33,380 --> 00:28:37,640
+convergence ايش يعني uniform convergence يعني لو
+
+390
+00:28:37,640 --> 00:28:41,540
+عندي sequence of continuous functions هذا في
+
+391
+00:28:41,540 --> 00:28:44,280
+الدنيا العادية تبع ال real analysis تبع اتنين تبع
+
+392
+00:28:44,280 --> 00:28:49,240
+ال baccalaureate لو xn sequence of functions
+
+393
+00:28:51,780 --> 00:28:55,680
+continuous functions that converge to some x وكان
+
+394
+00:28:55,680 --> 00:28:59,480
+ال convergence اللي هو point y يسمى y مش شرط انها
+
+395
+00:28:59,480 --> 00:29:02,800
+تطلع x continuous لكن اذا uniform قطعا انها تطلع
+
+396
+00:29:02,800 --> 00:29:06,240
+اي شمالها continuous وعنا ال convergence uniform
+
+397
+00:29:06,240 --> 00:29:11,380
+and since the convergence is uniform then اللي هو
+
+398
+00:29:11,380 --> 00:29:14,980
+هتكون ال limit تبعتنا اللي هو في داخل هذا هتكون
+
+399
+00:29:14,980 --> 00:29:20,730
+continuous طيب خلوه في الذاكرةإذا الـ integration
+
+400
+00:29:20,730 --> 00:29:27,240
+لـ 0 لـ T Y of T DT بساويطبعاً و الـ Limit مدام
+
+401
+00:29:27,240 --> 00:29:29,780
+ينظم convergence الـ Limit بطلع و بنزل زي ما بده
+
+402
+00:29:29,780 --> 00:29:35,260
+من الهدف هو عبارة عن Limit من 0 ل T ل X N prime of
+
+403
+00:29:35,260 --> 00:29:39,220
+T لأنه اتفجنا ان X N prime of T اشمل ل X N prime
+
+404
+00:29:39,220 --> 00:29:43,660
+بتروح لمين ل Y فبصير عند ال Limit ده يتاو ال Limit
+
+405
+00:29:43,660 --> 00:29:46,860
+بنطلحها برا بصير X N prime of T dt من سفر اللي عند
+
+406
+00:29:46,860 --> 00:29:52,280
+T و هي ساوة ال Limitالان التفاضل .. التكامل هذه ..
+
+407
+00:29:52,280 --> 00:29:55,940
+مجرد هذا .. اللي هو ال derivative على طول هي عبارة
+
+408
+00:29:55,940 --> 00:30:02,540
+عن مين؟ xn of t ماقص xn of mean of zero xn of t
+
+409
+00:30:02,540 --> 00:30:07,700
+اللي هي أشمالها اللي هي limitها اللي هو x of tلأنه
+
+410
+00:30:07,700 --> 00:30:13,540
+ماخد مين أنا ال limit حسبتها حسبت هذه طلعت هذه ال
+
+411
+00:30:13,540 --> 00:30:17,700
+limit اللي أنا لها هي ال limit limit لهذه x of t و
+
+412
+00:30:17,700 --> 00:30:22,800
+limit لهذه ايش ماله x of zero لإنه xn بتروح لل x
+
+413
+00:30:22,800 --> 00:30:25,900
+uniformly اذا اكيد point twice ايش يعني point
+
+414
+00:30:25,900 --> 00:30:29,740
+twice يعني xn of t بتروح لل x of t و ال xn of zero
+
+415
+00:30:29,740 --> 00:30:33,200
+بتروح لمين لل zero هذا for every tإذا صار عندي ال
+
+416
+00:30:33,200 --> 00:30:37,800
+integration هذا بيساوي xn of t نقص x of zero that
+
+417
+00:30:37,800 --> 00:30:42,240
+is x of t إيش بتساوي؟ x of zero زاد ال integration
+
+418
+00:30:42,240 --> 00:30:47,760
+ماشي الحال إذا طلعت عند ال x إيش مالها؟ اللي على
+
+419
+00:30:47,760 --> 00:30:51,940
+الصورة هذه اللي هي عبارة عن continuous إيهاش؟ اللي
+
+420
+00:30:51,940 --> 00:30:58,080
+هي ال derivative اللي موجودة و continuousالـ
+
+421
+00:30:58,080 --> 00:31:02,660
+derivative لهذه موجودة و continuous هذه بتكون x في
+
+422
+00:31:02,660 --> 00:31:06,800
+domain of t لأن ال derivative لهذه ثابت ال
+
+423
+00:31:06,800 --> 00:31:09,640
+derivative لهذه zero و ال derivative لهذه إشمالها
+
+424
+00:31:09,640 --> 00:31:13,580
+اللي هي بتطلع y of t صح نقص y of zero و y of t ما
+
+425
+00:31:13,580 --> 00:31:18,690
+هي إشمالها اللي هي continuousYOM ماذا يعني إذا
+
+426
+00:31:18,690 --> 00:31:22,350
+كنتنيواص فانكشن لأننا قلنا اللي هو ال uniform
+
+427
+00:31:22,350 --> 00:31:25,570
+convergence بوات ديناميين ال continuous ل
+
+428
+00:31:25,570 --> 00:31:29,470
+continuous ماشي الحال لأن هذه continuous و ال
+
+429
+00:31:29,470 --> 00:31:32,750
+convergence uniform إذا أكيد هذه أيش معناها
+
+430
+00:31:32,750 --> 00:31:36,030
+continuous من وين إكس أن إبراهيم continuousما هو
+
+431
+00:31:36,030 --> 00:31:38,530
+إيه إحنا الـ x unwell موجودة في الـ domain والـ T
+
+432
+00:31:38,530 --> 00:31:41,490
+ال domain والـ T هو عبارة عن الدوال اللي ال
+
+433
+00:31:41,490 --> 00:31:45,070
+derivative إلها continuous فطبيعي كل الأمور مبررة
+
+434
+00:31:45,070 --> 00:31:48,730
+فبتصير عندي x of T بتساوي هذا الكلام اللي هي is a
+
+435
+00:31:48,730 --> 00:31:52,110
+continuous function يعني x في ال domain والـ T و
+
+436
+00:31:52,110 --> 00:31:56,970
+ال Tx إيش بتساوي اللي هو ال X' ال Tx اللي هي ال X'
+
+437
+00:31:57,250 --> 00:32:01,750
+بال X' إيش بتساوي ال Y then by theorem كده T is
+
+438
+00:32:01,750 --> 00:32:06,430
+closedإذن هذا مثال على اللي هو closed linear
+
+439
+00:32:06,430 --> 00:32:13,290
+operator which is not bounded يلّا
+
+440
+00:32:13,290 --> 00:32:20,570
+أطلع على فوق ال dot بتقولdomain of T ليس مغلقًا
+
+441
+00:32:20,570 --> 00:32:24,570
+لأن .. لا طبعًا أكيد domain of T ليس مغلقًا domain
+
+442
+00:32:24,570 --> 00:32:27,090
+of T اللي فوق .. اللي فوق هذا domain of T اللي
+
+443
+00:32:27,090 --> 00:32:30,370
+أخدناه اللي هو main domain of T the space أو the
+
+444
+00:32:30,370 --> 00:32:33,610
+subspace of all continuous .. اللي هو of all
+
+445
+00:32:33,610 --> 00:32:37,400
+functions that has a continuous derivativeهذا is
+
+446
+00:32:37,400 --> 00:32:42,480
+not closed لأنه لو كان closed automatic من النظرية
+
+447
+00:32:42,480 --> 00:32:46,220
+اللي جابلها in example كذا is not closed because
+
+448
+00:32:46,220 --> 00:32:50,660
+if it is closed then by theorem أربعة تلتاشت اتنين
+
+449
+00:32:50,660 --> 00:32:55,540
+T is bounded because T is closed then we have a
+
+450
+00:32:55,540 --> 00:32:58,500
+contradiction with T is not bounded اللي أثبتناها
+
+451
+00:33:04,230 --> 00:33:13,890
+تعني المثال اللي فوق ببرهن لك أن الـ subspace of
+
+452
+00:33:13,890 --> 00:33:18,130
+all the functions that has a continuous derivative
+
+453
+00:33:18,130 --> 00:33:26,330
+is not a closed subspace طيب .. الآن قلناالـ
+
+454
+00:33:26,330 --> 00:33:30,070
+Closedness does not imply boundedness of linear
+
+455
+00:33:30,070 --> 00:33:33,610
+operator من اللي فوق يعني Closed مش شرط يعطيه
+
+456
+00:33:33,610 --> 00:33:38,430
+شماله bounded الآن برضه boundedness does not imply
+
+457
+00:33:38,430 --> 00:33:41,430
+the closeness of linear operator يعني بدي أديبلك
+
+458
+00:33:41,430 --> 00:33:47,690
+اللي هو bounded linear operator which is not
+
+459
+00:33:47,690 --> 00:33:50,870
+closed بدي أديب bounded linear operator which is
+
+460
+00:33:50,870 --> 00:33:58,700
+not closed طيب، نشوفلت I الـ Identity من domain of
+
+461
+00:33:58,700 --> 00:34:01,220
+T لdomain of T Be the identity operator on domain
+
+462
+00:34:01,220 --> 00:34:03,720
+of T يعني أي domain of T من عند X لعندك نور من الـ
+
+463
+00:34:03,720 --> 00:34:05,200
+space لعندك نور من الـ space أو جزء من نور من الـ
+
+464
+00:34:05,200 --> 00:34:09,300
+space Where D of T is .. بقى أسف بدي أقول هو
+
+465
+00:34:09,300 --> 00:34:12,960
+domain of T proper dense subspace of a normed
+
+466
+00:34:12,960 --> 00:34:17,760
+space من X يعني أخد الآن ال identity function ال
+
+467
+00:34:17,760 --> 00:34:23,160
+identity function من domain of T لعند domain of T
+
+468
+00:34:24,330 --> 00:34:28,950
+اللي بيرسل الـElement لمين؟ لنفسه، Identity هش
+
+469
+00:34:28,950 --> 00:34:35,190
+بدّو domain of T بدّو domain of TDense من X الـ
+
+470
+00:34:35,190 --> 00:34:42,810
+Space اللي هو Normed Space وDomain of T بدّي بربر
+
+471
+00:34:42,810 --> 00:34:51,270
+subset من X بربر subset من X يعني في Element في
+
+472
+00:34:51,270 --> 00:34:55,830
+الـ X مش موجود وين في الـDomain of T وهذا وهذا
+
+473
+00:34:55,830 --> 00:34:59,940
+اللي هو مفتاح انها تثبت ان T is not closedطيب او
+
+474
+00:34:59,940 --> 00:35:03,040
+الـ identity is not closed let T من domain of T يا
+
+475
+00:35:03,040 --> 00:35:05,320
+domain of B be the indented operator on domain of
+
+476
+00:35:05,320 --> 00:35:09,080
+T where domain of T is a proper dense subspace of
+
+477
+00:35:09,080 --> 00:35:12,900
+a known D space X زي ما قلت it is clear that T is
+
+478
+00:35:12,900 --> 00:35:15,980
+linear and bounded اللي هو ال .. اللي هو مين؟ اللي
+
+479
+00:35:15,980 --> 00:35:18,580
+هو ال identity function اثبتناها مرات انه bounded
+
+480
+00:35:18,580 --> 00:35:23,000
+و .. و .. و linear but T is not closed ليش T مش
+
+481
+00:35:23,000 --> 00:35:27,580
+closed؟ شوفواthis follows from theorem 4.13 اللي
+
+482
+00:35:27,580 --> 00:35:32,660
+قبل شوية if we take an x element in main خدوا x x
+
+483
+00:35:32,660 --> 00:35:43,090
+x element in x نقص و main of T ماشي الحالوأكيد في
+
+484
+00:35:43,090 --> 00:35:50,790
+X لأننا ماخدينه بربر الان و sequence Xn element
+
+485
+00:35:50,790 --> 00:35:57,300
+in domain of T which converts لمن لمن لل Xبنقدر
+
+486
+00:35:57,300 --> 00:36:01,400
+نعمل هيك عندي أكيد بنقدر نعمل X في ال .. في ال ..
+
+487
+00:36:01,400 --> 00:36:04,640
+في ال X إذا في Sequence موجودة في domain of T
+
+488
+00:36:04,640 --> 00:36:09,720
+Converse لها إذا صار عندي X N بتروح لل X و ال X مش
+
+489
+00:36:09,720 --> 00:36:14,240
+في domain T ال X أشماله is not element in domain
+
+490
+00:36:14,240 --> 00:36:21,030
+of mean of T إذا صار عندي هذا متحققهذا متحقق
+
+491
+00:36:21,030 --> 00:36:25,570
+خلّيني هذه أحطها وين برا X is not element in
+
+492
+00:36:25,570 --> 00:36:31,570
+domain of T هذا متحقق و I X M X N له هو عبارة عن I
+
+493
+00:36:31,570 --> 00:36:37,850
+X لانها دي function يعني هذه ال X وهذه ال X M من
+
+494
+00:36:37,850 --> 00:36:41,390
+فوق هي متحققة إذا ال I X M اللي هو ال X M
+
+495
+00:36:41,390 --> 00:36:48,820
+converges لل X اللي هي I Xواضح أنه لو بدها تكون
+
+496
+00:36:48,820 --> 00:36:53,460
+closed بدوا يكون عندكم ال X في domain ال T و ال I
+
+497
+00:36:53,460 --> 00:36:59,240
+X هو ال X اللي هي اسمها ال I X هي ال Y لكن ال X
+
+498
+00:36:59,240 --> 00:37:05,100
+مالها مش في domain ال T إذا ال I is not closed أي
+
+499
+00:37:05,100 --> 00:37:11,280
+سؤال اللي بعده يلّا نيجي الآن للمّا اطلع لفوق
+
+500
+00:37:11,280 --> 00:37:16,540
+الأخيرةالـ let T من الـ domain of T لعند YB a
+
+501
+00:37:16,540 --> 00:37:22,020
+bounded linear operatorSubset of X where X and Y
+
+502
+00:37:22,020 --> 00:37:26,560
+are non-disbases then if domain of T is closed
+
+503
+00:37:26,560 --> 00:37:32,220
+subset of X then T is closed إذا كانت domain of T
+
+504
+00:37:32,220 --> 00:37:35,920
+is closed ستكون T is closed هاي واحد هذا إيش ماله
+
+505
+00:37:35,920 --> 00:37:39,820
+bounded linear operator تانية if T is closed and Y
+
+506
+00:37:39,820 --> 00:37:42,480
+is complete then domain of T is closed subset من
+
+507
+00:37:42,480 --> 00:37:47,120
+من من اللي هو ال X البروف لأ بدنا نبره اللي بروف
+
+508
+00:37:47,120 --> 00:37:53,900
+وافتحلي على الكتاب يالاالبرمان هو .. عند .. زي ما
+
+509
+00:37:53,900 --> 00:37:57,560
+قلنا إذا كان domain of T closed subset of X إذا T
+
+510
+00:37:57,560 --> 00:38:00,640
+أشمالها is closed بالـ data between الـ T is
+
+511
+00:38:00,640 --> 00:38:03,180
+closed كيف ال data between ال T is closed؟ بقى عن
+
+512
+00:38:03,180 --> 00:38:05,540
+طريق الـ sequences بناخد Xn وين موجودة في domain
+
+513
+00:38:05,540 --> 00:38:10,920
+of T ونفترض إنها Xn converged من X ونفترض إن T Xn
+
+514
+00:38:10,920 --> 00:38:13,820
+برضه أشماله converged converged to some اللي هو
+
+515
+00:38:13,820 --> 00:38:19,620
+element Yالان مدام xn in domain of T اذا اكيد ال
+
+516
+00:38:19,620 --> 00:38:22,900
+.. ال .. ال .. ال .. ال .. ال xn convergence اللي
+
+517
+00:38:22,900 --> 00:38:25,660
+هيكون هو الموجود في ال domain of T closure لكن
+
+518
+00:38:25,660 --> 00:38:29,320
+احنا بنقول دي domain of T أشماله اللي هو عبارة عن
+
+519
+00:38:29,320 --> 00:38:32,680
+closed اه مقاطينها closed اذا اكيد ال domain of T
+
+520
+00:38:32,680 --> 00:38:34,940
+closure هو .. هو نفس ال domain of T يعني ال x هو
+
+521
+00:38:34,940 --> 00:38:38,540
+الموجودة في ال domain of Tلأن since the domain of
+
+522
+00:38:38,540 --> 00:38:41,860
+T is closed زي ما قلنا إذا صار عندي ال X ال X
+
+523
+00:38:41,860 --> 00:38:47,940
+موجودة في domain of T و ال T X N هتروح ل T X لأن T
+
+524
+00:38:47,940 --> 00:38:51,280
+أشمالها is continuous يعني صار عندي الآن بمعنى أخر
+
+525
+00:38:51,280 --> 00:38:57,880
+X N راحت لل X و ال X في domain T هي واحد و T X N
+
+526
+00:38:57,880 --> 00:39:01,900
+converge مزام converge و عندي T is continuous إذا
+
+527
+00:39:01,900 --> 00:39:06,680
+هذا بيعطينا ال T X N بتروح لمين ل T X فبكون اكتملت
+
+528
+00:39:06,960 --> 00:39:11,160
+اللي هو ما استلزم أن يكون closed إذا صارت T إيش ما
+
+529
+00:39:11,160 --> 00:39:17,620
+لها is closed اللي بعده يالا if T is closed ايوة T
+
+530
+00:39:17,620 --> 00:39:22,120
+is closed and اللي هو ال code domain اللي هو Y is
+
+531
+00:39:22,120 --> 00:39:25,180
+complete then domain of T is a closed subset of
+
+532
+00:39:25,180 --> 00:39:28,740
+main of X إذا بيشترط أنه يكون main Y is complete
+
+533
+00:39:28,740 --> 00:39:32,720
+تطلع ال domain of T is closed لكن هذا ماشترطش
+
+534
+00:39:32,720 --> 00:39:35,700
+علشان جالك domain of T closed على طول بتعطيك إيش T
+
+535
+00:39:35,700 --> 00:39:39,830
+is closedعشان تبين الـ domain of T is closed
+
+536
+00:39:39,830 --> 00:39:44,950
+كالعادة بناخد X وين موجودة في الـ domain of T مدام
+
+537
+00:39:44,950 --> 00:39:47,130
+في الـ domain of T موجودة نوصلها إلى X في الـ
+
+538
+00:39:47,130 --> 00:39:50,370
+domain of T كي بنوصلها إذا في سيكوانس من الـ
+
+539
+00:39:50,370 --> 00:39:52,950
+elements اللي في الـ domain of T اللي هو converged
+
+540
+00:39:52,950 --> 00:39:58,130
+من الـmain للـ XSince T is bounded، إذا اطلع لفوق،
+
+541
+00:39:58,130 --> 00:40:02,150
+احسبلي الـ T X N نقص T X M، اللي هو بيساوي T X N
+
+542
+00:40:02,150 --> 00:40:05,630
+نقص T X M، اللي هي أصغر شهر نورم الـ T في نورم X N
+
+543
+00:40:05,630 --> 00:40:10,530
+نقص X M، الآن هذه من هنا، X N بتروح للـ X، إذا هذه
+
+544
+00:40:10,530 --> 00:40:14,030
+كوشي، مدام هذه كوشي، إذا بزخرها زي ما بدي، أصغر من
+
+545
+00:40:14,030 --> 00:40:17,370
+Y عن نورم الـ T مثلا، إذا هيكون هذه أشمالها أصغر
+
+546
+00:40:17,370 --> 00:40:21,150
+من Y، يعني بمعنى أخر صارت الـ T X N كوشيهي
+
+547
+00:40:21,150 --> 00:40:23,690
+الاستدعى Y is complete تي اكس ان كوشي Y is
+
+548
+00:40:23,690 --> 00:40:26,930
+complete يدا نكون verbs يدا تي اكس ان بتروح لمين
+
+549
+00:40:26,930 --> 00:40:30,870
+لل Y لأن Y is complete صار عندي تي اكس ان بتروح لل
+
+550
+00:40:30,870 --> 00:40:35,410
+Y وبما ان T is closed وعندي اكس ان بتروح لل X و تي
+
+551
+00:40:35,410 --> 00:40:40,490
+اكس ان راحت لل Y يدا هيكون ال Y هي مين ال T X هو
+
+552
+00:40:40,490 --> 00:40:44,450
+ال X موجودة في دومين T يدا since T is closed يدا X
+
+553
+00:40:44,450 --> 00:40:48,750
+في دومين Tاللي هو صار عندي لان X في domain of T
+
+554
+00:40:48,750 --> 00:40:52,150
+closure وانتهيت ب X في domain of T لذا صار عندي
+
+555
+00:40:52,150 --> 00:40:57,070
+اللي هو ال domain of T is closed وبقول هي كذا
+
+556
+00:40:57,070 --> 00:41:00,730
+خلصنا الورهان النظرية وانهينا chapter اللي هو
+
+557
+00:41:00,730 --> 00:41:04,850
+أربعة عشر .. chapter أربعة وإلى لقاء آخر السلام
+
+558
+00:41:04,850 --> 00:41:06,130
+عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/yeiwPsS60fU_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/yeiwPsS60fU_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ed1f9cec0e81c02a8619084556396e01dd37fd13
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/yeiwPsS60fU_postprocess.srt
@@ -0,0 +1,3284 @@
+1
+00:00:05,110 --> 00:00:08,030
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,030 --> 00:00:11,930
+الصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:11,930 --> 00:00:17,350
+آله وصحبه أجمعين هذه هي المحاضرة رقم 19 مساق تحليل
+
+4
+00:00:17,350 --> 00:00:20,930
+اقتراني او تحليل دالي طلاب طالبات الجامعة
+
+5
+00:00:20,930 --> 00:00:26,170
+الإسلامية ماجستير الرياضيات وصلنا لعند اللي هو ال
+
+6
+00:00:26,170 --> 00:00:28,350
+section الثالث تلاتة تلاتة اللي هو orthogonal
+
+7
+00:00:28,350 --> 00:00:30,450
+complement and direct sum
+
+8
+00:00:33,360 --> 00:00:37,900
+عشان اللي هو ندخل للموضوع اللي أمامنا بنزمنا بعض
+
+9
+00:00:37,900 --> 00:00:43,040
+التعريفات السريعة نذكركم فيها لو كان عندي اللي هو
+
+10
+00:00:43,040 --> 00:00:48,440
+X metric space عليها metric D ومن ثم لو كان عندي X
+
+11
+00:00:48,440 --> 00:00:52,640
+norm of space عليها norm وكانت M اللي هي مجموعة
+
+12
+00:00:52,640 --> 00:00:56,960
+جزئية من X وعندي هذا X space أي إن كان هذا ال
+
+13
+00:00:56,960 --> 00:01:01,480
+space و ال M هي عبارة عن مجموعة جزئية من ال X
+
+14
+00:01:01,480 --> 00:01:07,850
+الكاملةبدنا نعرف شو معنات اللي هو المسافة بين نقطة
+
+15
+00:01:07,850 --> 00:01:14,590
+X جواة الـ X و بين الـ 6 اللي أمامنا اللي هي الـ M
+
+16
+00:01:14,590 --> 00:01:18,910
+هذه الـ X element in X و المسافة بينها و بين 100 و
+
+17
+00:01:18,910 --> 00:01:22,410
+بين الـ M المسافة هذه بتقول عنها بسميها Delta
+
+18
+00:01:22,410 --> 00:01:30,370
+عبارة عن الـ infimum للمسافة بين X هذه و أي نقطة Y
+
+19
+00:01:30,750 --> 00:01:35,470
+والـ Y موخودة من الـ M أو يمكن أن يكتبها Y تلدة
+
+20
+00:01:35,470 --> 00:01:41,370
+إذا الـ infimum للمسافة بين X و6 هي المسافة Delta
+
+21
+00:01:41,370 --> 00:01:44,930
+عن
+
+22
+00:01:44,930 --> 00:01:50,270
+الـ M هذا الكلام in general ويعني في أي metric
+
+23
+00:01:50,270 --> 00:01:55,980
+spaceأطلع لفوق وده كان بيتعامل مع norm فبيصير
+
+24
+00:01:55,980 --> 00:02:00,260
+عندها ال delta بتساوي ال infimum بدل اللي هو
+
+25
+00:02:00,260 --> 00:02:05,200
+المسافة المسافة بتصير يرمز إليها X minus Y حيث Y
+
+26
+00:02:05,200 --> 00:02:08,340
+element in M وهذه تمثل المسافة بين المبطأ X اللي
+
+27
+00:02:08,340 --> 00:02:12,240
+في ال space X وبينها اللي هي ال M subset من X
+
+28
+00:02:12,870 --> 00:02:19,690
+السؤال المهم اللى .. اللى بنحكى دايما هل احنا
+
+29
+00:02:19,690 --> 00:02:27,460
+بنقدر نلاقي لقطةاللي هي في ال M بحيث انه اللي هو
+
+30
+00:02:27,460 --> 00:02:32,560
+هذا النقطة لو سمناها Y not مثلا هي اللي تمثل ال
+
+31
+00:02:32,560 --> 00:02:37,100
+Delta اللي بتساوي اللي هو ال infimum يعني نورما X
+
+32
+00:02:37,100 --> 00:02:40,760
+minus Y not هو اللي يمثل Delta يعني هل بنقدر نلاقي
+
+33
+00:02:40,760 --> 00:02:44,320
+ال infimum عند نقطة Y not في ال M يعني نورما X
+
+34
+00:02:44,320 --> 00:02:48,300
+minus Y not بساوية Delta اللي هي بساوية مسافة يعني
+
+35
+00:02:48,300 --> 00:02:51,960
+يعني نلاقي النقطة اللي في ال M اللي بتكون هي
+
+36
+00:02:51,960 --> 00:02:52,980
+الأقرب
+
+37
+00:02:57,270 --> 00:02:59,910
+سؤال هذا طبعا مطروح سؤال كبير
+
+38
+00:03:02,610 --> 00:03:06,130
+السؤال من شقين وجود النقطة هل النقطة فينا اللي
+
+39
+00:03:06,130 --> 00:03:10,350
+موجودة ولا النقطة لو كانت موجودة هل ممكن نلاقيها
+
+40
+00:03:10,350 --> 00:03:14,330
+واحدة ولا ممكن نلاقي اللي هو اكثر من هي حنلاقي ان
+
+41
+00:03:14,330 --> 00:03:19,810
+هذا الكلام حتى حتى في ال space السهل اللي هو ال R
+
+42
+00:03:19,810 --> 00:03:24,070
+تربيع العادى ال R تربيع اللي هو في ال Cartesian
+
+43
+00:03:24,070 --> 00:03:30,400
+plane العادى هنلاقي اللي هو الأمر مختلفأو يعني له
+
+44
+00:03:30,400 --> 00:03:35,240
+اختلافات أو له حالات يعني هنلاقي بعض ال 6 فعلا
+
+45
+00:03:35,240 --> 00:03:38,860
+اللي هو بنلاقي نقطة وحيدة بعض ال 6 مابنلاقيش
+
+46
+00:03:38,860 --> 00:03:42,680
+بالمرة من أصله وبعض ال 6 بنلاقي عدد لانهائي من
+
+47
+00:03:42,680 --> 00:03:46,650
+النقط أو اللي هو نقطة مش وحيدةخلينا ناخد أمثلة على
+
+48
+00:03:46,650 --> 00:03:49,210
+السريع اللي هي الأمثلة اللي أنتوا أصلا عارفينها
+
+49
+00:03:49,210 --> 00:03:53,610
+اطلع لفوق شويه عندى اطلع لفوق كمان كمان كمان لو
+
+50
+00:03:53,610 --> 00:03:57,470
+جينا أخدنا كمان كمان لو جينا أخدنا هي اللي هي الست
+
+51
+00:03:57,470 --> 00:04:02,290
+أخدنا الست الأولى اللي هي مين اللي هي الست M هذه
+
+52
+00:04:02,290 --> 00:04:04,950
+وهي النقطة X هذه بحكي عن إيه عشان في أرض تربيع
+
+53
+00:04:04,950 --> 00:04:08,210
+ونفترض أن النقطة هذه اللي هي open يعني ال .. ال ..
+
+54
+00:04:08,210 --> 00:04:11,210
+ال .. الست اللي أخدتها عبارة عن ال open ال
+
+55
+00:04:11,210 --> 00:04:14,510
+interval من النقطة هذه مثلا واحد إلى مال نهاية
+
+56
+00:04:15,870 --> 00:04:20,890
+النقطة هذه الـ set هذه الان ال set هذه هل فعلا
+
+57
+00:04:20,890 --> 00:04:26,050
+بنلاقي نقطة في داخلها تكون هذه اللي هو من X لهنا
+
+58
+00:04:26,050 --> 00:04:30,370
+تمثل هي ال .. ال .. ال delta لو جينا اتطلعنا اللي
+
+59
+00:04:30,370 --> 00:04:34,470
+هو بالنظر العادي المسافة اللي هي اقل المسافة هي من
+
+60
+00:04:34,470 --> 00:04:36,690
+هال لهال عنده نقطة هذه بس هذه النقطة أصلا مش
+
+61
+00:04:36,690 --> 00:04:41,770
+موجودة بناء عليه اللي هو ال infimumبين النقطة هذه
+
+62
+00:04:41,770 --> 00:04:45,570
+وبين اللي هي ال 6 هذه does not exist إذا مش موجودة
+
+63
+00:04:45,570 --> 00:04:49,590
+من أصله اللي هي نقطة في داخل ال M بحيث أن ال Delta
+
+64
+00:04:49,590 --> 00:04:54,910
+تساوي ال normal X minus اللي هو X note هنا أو Y
+
+65
+00:04:54,910 --> 00:04:59,540
+note اللي هيالحالة الثانية لو جينا أخدنا اللي هو
+
+66
+00:04:59,540 --> 00:05:04,380
+الـ 6 اللي أمامي هنا وأخدت النقطة X أعلاها بس
+
+67
+00:05:04,380 --> 00:05:08,960
+أعلاها بحيث أنه أنا لو نزلت عمود اللي هو يكون وين
+
+68
+00:05:08,960 --> 00:05:13,260
+موجود النقطة موجودة فيها واحنا بنعرف أنه أقل اللي
+
+69
+00:05:13,260 --> 00:05:16,800
+هو بعض اللي هو العمود بين طبعا احنا بنحكي فيه في
+
+70
+00:05:16,800 --> 00:05:19,160
+space عادي و في earth تربيع اللي بنشغل فيه عادي
+
+71
+00:05:19,690 --> 00:05:23,330
+فبتكون الـ X أخد العمود بتلاقي هذا النقطة اللي
+
+72
+00:05:23,330 --> 00:05:26,850
+بلتقي فيها العمود هذا مع هذا اللي هو الموجودة في
+
+73
+00:05:26,850 --> 00:05:31,430
+داخل المجموعة M فعشان هي كهذه Y not هي فعلاً Delta
+
+74
+00:05:31,430 --> 00:05:35,890
+هتساوي اللي هو norm الـ X minus Y not حيث الـ X
+
+75
+00:05:35,890 --> 00:05:41,450
+هيها والـ Y not هي مكان الإسقاط من الـ X عالمياً
+
+76
+00:05:41,450 --> 00:05:46,390
+على اللي هو الخط المستقيم أو القطعة المستقيمة اللي
+
+77
+00:05:46,390 --> 00:05:51,080
+هنعمللو جينا أخدنا اللي هو الجزء هذا اللي هو جزء
+
+78
+00:05:51,080 --> 00:05:56,000
+من محيط دائرة وهذا بيمثل مين المركز هاي الست عندى
+
+79
+00:05:56,000 --> 00:06:01,260
+M لو جيت أخدته النقطة ال X هنا ال N كلهم على نفس
+
+80
+00:06:01,260 --> 00:06:05,440
+البعدفبناء على الـ Delta اللي هي ال Infimum هي
+
+81
+00:06:05,440 --> 00:06:08,860
+عبارة عن كل النقاط لأن في عدد لا نهاية من النقاط
+
+82
+00:06:08,860 --> 00:06:14,000
+بتمثل اللي هو ايه شماله اللي هو ال Delta اللي ببحث
+
+83
+00:06:14,000 --> 00:06:17,920
+عنها اللي هي المسافة بين ال X و بين ال 6 اللي عندي
+
+84
+00:06:18,230 --> 00:06:22,550
+إذا بالرغم من سهولة ال space اللي عندنا ومنبسطه
+
+85
+00:06:22,550 --> 00:06:26,090
+اللي احنا بنعرفه إلا إنه لجينا هذه المسألة اللي هو
+
+86
+00:06:26,090 --> 00:06:29,390
+البحث عن ال .. عن وجود النقطة اللي هي y naught
+
+87
+00:06:29,390 --> 00:06:33,270
+اللي بتمثل ال .. اللي هي هي اللي هتكون النقطة التي
+
+88
+00:06:33,270 --> 00:06:38,630
+تبعد أقل ما يمكن عن مين عن ال set اللي هي من
+
+89
+00:06:38,630 --> 00:06:44,030
+النقطة x لل set اللي هي اللي بنبحث عنها طيب ارجعلي
+
+90
+00:06:44,030 --> 00:06:44,930
+للتلخيص الآن
+
+91
+00:06:47,900 --> 00:06:52,120
+نأتي الآن لتلخيصنا نكمل عليه a subset remark اللي
+
+92
+00:06:52,120 --> 00:06:55,500
+هو a subset M of a vector space X set to be convex
+
+93
+00:06:55,500 --> 00:07:00,380
+هي لازم هذا التعريف انها تكون convex if for all x,
+
+94
+00:07:00,500 --> 00:07:05,340
+y element in M ال linear combination بين ال X والY
+
+95
+00:07:05,340 --> 00:07:09,180
+لازم يكون في M بس هنا combination بإيش؟ بال scalar
+
+96
+00:07:09,180 --> 00:07:13,510
+Alphaواللي هي واحد ناقص Alpha يكون Alpha X يعني
+
+97
+00:07:13,510 --> 00:07:18,470
+الخط المقطع المستقيمة بين X و بين Y اللي هي Alpha
+
+98
+00:07:18,470 --> 00:07:21,910
+X زاد واحد ميز Alpha Y وY بتكون موجودة في M إذا
+
+99
+00:07:21,910 --> 00:07:26,090
+اتحققت هذه الخاصية بيكون عندي A شماله ال Set M
+
+100
+00:07:26,090 --> 00:07:31,100
+بتكون Convex بناء عليهأي subspace من X هيكون
+
+101
+00:07:31,100 --> 00:07:34,540
+convex لأن subspace مايعنيش subspace بيكون اللي هو
+
+102
+00:07:34,540 --> 00:07:37,440
+أنه أي linear combination بين أنه خطي لازم يكون في
+
+103
+00:07:37,440 --> 00:07:41,240
+main يعني لو كانت X و Y في ال space لازم في
+
+104
+00:07:41,240 --> 00:07:44,200
+subspace اللي بنحكي عنه عشان يكون subspace لازم
+
+105
+00:07:44,200 --> 00:07:48,500
+يكون Alpha X زائد Beta Y يكون في داخل ال Y لكل X و
+
+106
+00:07:48,500 --> 00:07:53,580
+Y موجودة في ال subspace X عشان هيك نسميه subspace
+
+107
+00:07:54,590 --> 00:07:58,730
+إذا أي subspace من X هيكون أشماله convex ومش هيك و
+
+108
+00:07:58,730 --> 00:08:02,130
+the intersection of convex sets is convex يعني لو
+
+109
+00:08:02,130 --> 00:08:08,130
+كان عندي اللي هو تقاطع اللي هوC و الـ C هدول عبارة
+
+110
+00:08:08,130 --> 00:08:13,130
+عن convex sets C α مثلا نسميها هيكون برضه هذا
+
+111
+00:08:13,130 --> 00:08:18,170
+التقاطع أشماله عبارة عن convex خدوا .. خدوا أي X و
+
+112
+00:08:18,170 --> 00:08:24,850
+Y في داخل التقاطع للـ C α أكيد هيعطينا أنه الآن
+
+113
+00:08:24,850 --> 00:08:29,010
+اللي هو كل ال X و ال Y هدولة موجودة في الـ C α for
+
+114
+00:08:29,010 --> 00:08:33,620
+every α صح ولا لأ؟من تعريف الطفافة و بما أن كل
+
+115
+00:08:33,620 --> 00:08:38,140
+واحدة منهم C Alpha Convex إذا حيكون عندي الآن X أو
+
+116
+00:08:38,140 --> 00:08:40,980
+سأسميها C Beta عشان ما أخلطش بين ال Alpha تبعت الـ
+
+117
+00:08:40,980 --> 00:08:47,460
+C Beta Beta لكل Beta الآن بدأنا عليه مدامة C Beta
+
+118
+00:08:47,460 --> 00:08:52,760
+is Convex حيكون CX في Alphaزائد واحد ناقص Alpha في
+
+119
+00:08:52,760 --> 00:08:57,880
+Y والموجودات في الـC Beta لكل Beta معناته صار عندي
+
+120
+00:08:57,880 --> 00:09:02,320
+أكيد هذا بيعطينا ان X Alpha زائد واحد ماينس Alpha
+
+121
+00:09:02,320 --> 00:09:07,540
+في Y اللي هو موجود في التقاطع لـC Beta وبناء عليه
+
+122
+00:09:07,540 --> 00:09:12,760
+أخدنا هذه arbitrary لAlpha Element 01 وجدنا ان
+
+123
+00:09:12,760 --> 00:09:15,640
+اللي هو الـLinear Combination هذا موجود في التقاطع
+
+124
+00:09:15,640 --> 00:09:21,970
+إذا التقاطع هيكون أي تقاطع is convex pipeنجي الآن
+
+125
+00:09:21,970 --> 00:09:26,710
+لنظريتنا الأولى اللي احنا قبل بشوية بدينا نحكي
+
+126
+00:09:26,710 --> 00:09:31,110
+عنهالأن النظرية بتقول let X be an inner product
+
+127
+00:09:31,110 --> 00:09:37,090
+space and M be a non-empty non-empty convex set
+
+128
+00:10:07,080 --> 00:10:12,720
+النظرية بتقول ان لو كان عندك X inner product space
+
+129
+00:10:12,720 --> 00:10:18,710
+و M non-emptyو Convex و Complete إذا التلات شروط
+
+130
+00:10:18,710 --> 00:10:24,790
+هذه تكون موجودة بضمنك أنه لكل X في ال X بقدر ألاقي
+
+131
+00:10:24,790 --> 00:10:30,870
+Y موجودة في M اللي هي normها ال X minus Y بعيد عن
+
+132
+00:10:30,870 --> 00:10:35,490
+ال X هو اللي اللي بيمثل المسافة بين اللي هو ال M و
+
+133
+00:10:35,490 --> 00:10:39,550
+بين ال L ال M و ال X يعني الآن
+
+134
+00:10:44,010 --> 00:10:50,710
+الان اضمننا اخدنا الان اللي هو شروط معينة على ال M
+
+135
+00:10:50,710 --> 00:10:57,550
+اللي هي لا تسوى Phi او convex او complete بحيث ان
+
+136
+00:10:57,550 --> 00:11:03,390
+هذا بضمنك انه لو اخدت اي X في ال Xو جيت هي ال M
+
+137
+00:11:03,390 --> 00:11:09,350
+هتلاقي نقطة في داخل ال M وحيدة اللي هي هيتمثل
+
+138
+00:11:09,350 --> 00:11:14,550
+المسافة بينها و بين اللي هي ال X اللي هي X minus Y
+
+139
+00:11:14,550 --> 00:11:21,050
+هي اللي تكون Delta المسافة بين X و بين مين اللي هي
+
+140
+00:11:21,050 --> 00:11:26,860
+ال M نيجي الأن للبرهاننقسم البرهان لجزءين جزء أثبت
+
+141
+00:11:26,860 --> 00:11:31,020
+ال existence وجود النقطة وقسم أخر يمثل ال
+
+142
+00:11:31,020 --> 00:11:35,400
+uniqueness أو وحدانية النقطة أو النقطة واحدةأطلع
+
+143
+00:11:35,400 --> 00:11:39,340
+لفوق خلّينا نشوف ال existence أول اشي احنا ال
+
+144
+00:11:39,340 --> 00:11:42,860
+delta بساوي ال infimum من norm ال X minus Y حيث Y
+
+145
+00:11:42,860 --> 00:11:46,420
+تل ده Y نقص تل ده حيث Y تل ده element من مين هذا
+
+146
+00:11:46,420 --> 00:11:51,800
+تعريف من اللي هي المسافة بينه نقطة X وبين اللي هي
+
+147
+00:11:51,800 --> 00:11:57,760
+ال set ال infimum هذا طبعا لما نتعريف ال infimumلو
+
+148
+00:11:57,760 --> 00:12:00,340
+الـ infimum هو عبارة عن مين يا جماعة؟ ال greatest
+
+149
+00:12:00,340 --> 00:12:04,880
+lower bound ماشي الحين ال infimum هو اللي بيمثل لي
+
+150
+00:12:04,880 --> 00:12:09,720
+ال greatest lower bound طيب انتبهوا كيف عندى ال
+
+151
+00:12:09,720 --> 00:12:15,800
+delta بسوء ال infimum ل norm ال X minus Y تلده و Y
+
+152
+00:12:15,800 --> 00:12:21,910
+تلده element in مين؟ in Mالان الـ Greatest Lower
+
+153
+00:12:21,910 --> 00:12:25,770
+Bound اول اشي Lower Bound و اكبر Lower Bound لو
+
+154
+00:12:25,770 --> 00:12:30,110
+ضفنا اشي بسيط لانه جولنا جولنا Delta زائد واحد ال
+
+155
+00:12:30,110 --> 00:12:35,330
+Delta زائد واحد بيبطل Lower Bound اه مادام بيبطل
+
+156
+00:12:35,330 --> 00:12:41,410
+Lower Bound اذا بلاجي اللي هو Y واحد في الان بحيث
+
+157
+00:12:41,410 --> 00:12:44,910
+انه Delta زائد واحد يبطل Lower Bound بيصير اكبر او
+
+158
+00:12:44,910 --> 00:12:51,580
+يسوى Normal X minus Y واحدماشي الحال لو اجيت اخدت
+
+159
+00:12:51,580 --> 00:12:58,820
+دلتا ضفتلها نص مش واحد برضه بلاجيلها اللي هو Y2
+
+160
+00:12:58,820 --> 00:13:04,300
+بحيث انه يكون اللي هو هذا اكبر او يساوي X minus Y2
+
+161
+00:13:04,300 --> 00:13:08,660
+لانه بتبطل معلها معلها بتبطل اللي هو lower bound
+
+162
+00:13:09,210 --> 00:13:14,630
+الأن in general لو ضفت عدل تواحد على n لأي n في
+
+163
+00:13:14,630 --> 00:13:19,130
+الدنيا حاليا دي بناء عليه هدف but lower bound ومن
+
+164
+00:13:19,130 --> 00:13:24,970
+ثم there exists xn في ال M يعني يوجد xn في ال M
+
+165
+00:13:25,580 --> 00:13:30,200
+بحيث ان دلتا زياد واحد على ان اتبطل ال power bomb
+
+166
+00:13:30,200 --> 00:13:35,700
+يعني تكون اكبر او يساوي هذه ال X ناقص YN هذه سموها
+
+167
+00:13:35,700 --> 00:13:40,360
+دلتا واحد هذه سموها دلتا اتنين هذه سموها دلتا ان
+
+168
+00:13:40,360 --> 00:13:46,660
+in general اذا الان لكل ان في الدنيا بقدر الاجي
+
+169
+00:13:46,660 --> 00:13:53,920
+اللي هو sequence من ال YN بحيث ان اللي هو دلتا ان
+
+170
+00:13:54,870 --> 00:14:01,350
+يكون أكبر أو يساوي norm الـ X minus Y N الـ Delta
+
+171
+00:14:01,350 --> 00:14:06,920
+N اللي هي عبارة عن Delta زائد واحد على Nوالـ Delta
+
+172
+00:14:06,920 --> 00:14:10,720
+نفسها عبارة عن lower bound إذن هتكون هذه أكبر أو
+
+173
+00:14:10,720 --> 00:14:14,900
+يساوي الـ Delta صح ولا لأ؟ لأن الـ Delta إيش
+
+174
+00:14:14,900 --> 00:14:18,140
+مالها؟ ال greatest lower bound يعني lower bound،
+
+175
+00:14:18,140 --> 00:14:23,000
+ماشي؟ إذن as n goes to infinity هذه هتروح لـ Delta
+
+176
+00:14:23,000 --> 00:14:28,160
+وهذه هتروح لـ Delta ويكون limit ال normal x minus
+
+177
+00:14:28,160 --> 00:14:31,140
+y n صار محصور بين الـ Delta والـ Delta يعني إيش
+
+178
+00:14:31,140 --> 00:14:38,060
+بساوي؟ بساوي Delta يعني بمعنى آخرلجيت sequence yn
+
+179
+00:14:38,060 --> 00:14:41,680
+بحيث أنه الدل تبسو ال limit normal x minus yn هذه
+
+180
+00:14:41,680 --> 00:14:46,200
+ال sequence شوفوا كيف بدا أقولكم إيش بتطلع بالظبط
+
+181
+00:14:46,200 --> 00:14:51,020
+نشوف نرجع لبرهانناالان ساديك على جنب عشان تفسير
+
+182
+00:14:51,020 --> 00:14:54,900
+بعض الأمور انا الان بقوللي مدام ان ال Delta بيساوي
+
+183
+00:14:54,900 --> 00:14:59,020
+ال infimum لل norm هذا اذا بقدر الاجي sequence yn
+
+184
+00:14:59,020 --> 00:15:03,660
+in M هي اللي لجيتها هناك قبل بشوية such that Delta
+
+185
+00:15:03,660 --> 00:15:08,160
+N بتروح لمين لل Delta و Delta N ايش بتساوي norm ال
+
+186
+00:15:08,160 --> 00:15:13,660
+X minus YN الان هذه ال sequence اللي لجيتها YN بده
+
+187
+00:15:13,660 --> 00:15:17,100
+اثبتلك اول حاجة و ي show that YN is اكوشي sequence
+
+188
+00:15:17,760 --> 00:15:20,660
+ماشي انت بقى خلّيكوا معايا خلّيني أشوف كيف نانيت
+
+189
+00:15:20,660 --> 00:15:24,820
+بتنهي كوشي سيكوانس خلّيني نسمي اللي هو ال V1
+
+190
+00:15:24,820 --> 00:15:30,660
+بيساوي Y1 ناقص X V2 Y2 ناقص X in general VN بدي
+
+191
+00:15:30,660 --> 00:15:35,000
+أسميها YN ناقص 200 ناقص X من وين جبتها هذه ال X
+
+192
+00:15:35,000 --> 00:15:37,560
+اللي بدأنا فيها اللي بدنا نبحث عن المسافة بينها و
+
+193
+00:15:37,560 --> 00:15:41,260
+بين ال 6 و ال YN هي ال sequence اللي ركبتها اللي
+
+194
+00:15:41,260 --> 00:15:46,420
+فوق ماشي الحالإذن الآن خدوا سمولي صارت عند الـ Δن
+
+195
+00:15:46,420 --> 00:15:51,940
+هذه هي عبارة عن norm من الـ Vm ماشي طيب و لو أجيت
+
+196
+00:15:51,940 --> 00:15:57,760
+حسبت norm ال Vm زائد Vm ال Vm هذي اللي هي مين
+
+197
+00:15:57,760 --> 00:16:05,410
+هتكون ال Vm هيها Ym ناقص X زائد Ym ناقص Xها دي
+
+198
+00:16:05,410 --> 00:16:10,350
+بيساوي اللي هو norm الـ yn زاد yn ناقص مين اتنين x
+
+199
+00:16:10,350 --> 00:16:15,250
+ويساوي واضح اه اسحبولي اللي هو اتنين عامل مشترك من
+
+200
+00:16:15,250 --> 00:16:18,730
+هنا بيصير عندى اللي هو انا طبعا مافيش فيه عامل
+
+201
+00:16:18,730 --> 00:16:22,990
+فبصير نص و بطلع برا فبصير اتنين في نص yn ناقص y
+
+202
+00:16:22,990 --> 00:16:27,230
+زاد yn ناقص x احنا بنقول انها convex اصلا ماشي
+
+203
+00:16:27,230 --> 00:16:33,890
+الحال الان ynYN في ال .. في ال .. في الست M من
+
+204
+00:16:33,890 --> 00:16:37,330
+جبتها من وين ال YN ؟ هذي YN وين جبتها ؟ هذي بقى
+
+205
+00:16:37,330 --> 00:16:39,850
+قاعد بقول there exist Y واحد element in M و Y
+
+206
+00:16:39,850 --> 00:16:43,900
+اتنين element in M مشان باخد ال M في وم عليهاواضح
+
+207
+00:16:43,900 --> 00:16:47,860
+هاه؟ إذا الـ sequence yn من الـ M مدامت M convex
+
+208
+00:16:47,860 --> 00:16:52,900
+إذا بضمنلكم أنه مصف yn زاد yn مشيكون في الـ Y
+
+209
+00:16:52,900 --> 00:16:57,120
+نفسها، مظبوط؟ إذا هذه صارت element في ال .. آسف في
+
+210
+00:16:57,120 --> 00:17:01,480
+الـ M هذه صارت element وين في الـ M فالان norm
+
+211
+00:17:01,480 --> 00:17:05,340
+element في الـ M ناقص X أكيد .. أكيد .. أكيد هيكون
+
+212
+00:17:05,340 --> 00:17:09,140
+أكبر أو يسوى من Delta لأن دلتا هي لين ثم من لين،
+
+213
+00:17:09,140 --> 00:17:13,070
+ماشيإذا صارت الاتنين في هذا المقدار أكبر أو يساوي
+
+214
+00:17:13,070 --> 00:17:17,250
+مين؟ اتنين دلتا أو بمعنى أخر هذا المقدار أكبر أو
+
+215
+00:17:17,250 --> 00:17:21,790
+يساوي اتنين دلتا زي ما قلت لكم where نصف YN زي ال
+
+216
+00:17:21,790 --> 00:17:26,590
+YM element in M because M إشمالها is convex خلّي
+
+217
+00:17:26,590 --> 00:17:31,170
+هذه في الذاكرة خلّينا نكمل اللي بدناهاFurthermore
+
+218
+00:17:31,170 --> 00:17:39,130
+لو جيت حسبة YM-YM تراحت من بعض اللي هو YM-X فبسيط
+
+219
+00:17:39,130 --> 00:17:43,270
+تروح ال X مع ال X فبتظهر عندي VN ناقص من VM يعني
+
+220
+00:17:43,270 --> 00:17:47,870
+VN ناقص VM هتطلع هذه ناقص اللي هي تبع ال YM ناقص X
+
+221
+00:17:47,870 --> 00:17:51,350
+فبروح مع بعض فبظهر YM ناقص YM احسب أحسابات سهلة
+
+222
+00:17:52,020 --> 00:17:55,060
+الان بدي استخدم باستخدام Parallelogram Equality
+
+223
+00:17:55,060 --> 00:17:57,540
+نحن لدينا الـ Parallelogram Equality اللي هي في
+
+224
+00:17:57,540 --> 00:18:01,960
+نورم ديسمبرز جائزة مظبوط او متحققة اللي هي عبارة
+
+225
+00:18:01,960 --> 00:18:07,250
+عن تخد الان YN نقص و YM من كل تربيع ايش هيساوي؟هي
+
+226
+00:18:07,250 --> 00:18:12,590
+احنا yn ناقص ym ايش لقينها بتساوي عبارة عن vn ناقص
+
+227
+00:18:12,590 --> 00:18:16,630
+vm فبالصحيح انهم تربيع وإيه ساوي احنا بنعرف ال
+
+228
+00:18:16,630 --> 00:18:20,870
+program equality ايش معناتها الطرح والجمع تربيع
+
+229
+00:18:20,870 --> 00:18:24,130
+بساوي اتنين فطول الضلع الأول زي الضلعة الثانية
+
+230
+00:18:24,130 --> 00:18:28,610
+الأقطار ولا ايش ولا ولا ولا واضع المستطيل فاهمين
+
+231
+00:18:29,230 --> 00:18:33,030
+فبصير عندي النورم هذا بساوي ناقص النورم هذا زائد
+
+232
+00:18:33,030 --> 00:18:35,690
+اللي هو اتنين في هذه النورمين هذه اللي هي
+
+233
+00:18:35,690 --> 00:18:41,490
+البروغرام البرلوغرام اللي هي main equality طيب هذا
+
+234
+00:18:41,490 --> 00:18:44,810
+اصغر او ساوي بدنا نستخدم اللي فوق اثبتنا ان هذا
+
+235
+00:18:44,810 --> 00:18:50,830
+المقدار اكبر او اتنين دلتا هذا اللي هو عبارة عن vn
+
+236
+00:18:50,830 --> 00:18:54,750
+زائد vm اكبر او اتنين دلتا واضح فبصير عندي اصغر او
+
+237
+00:18:54,750 --> 00:19:00,690
+ساويالأن هذا ناقص اللي هي هذه هي شايفينها ناقص
+
+238
+00:19:00,690 --> 00:19:03,730
+اتنين ديلتا تربيع لإنه لما نضرب اللي هو المقدار
+
+239
+00:19:03,730 --> 00:19:07,750
+هذا VN زائد VN بناقص من برا هذه بتصير اشمالها
+
+240
+00:19:07,750 --> 00:19:11,150
+بتنجلب الإشارة فبصير أصغر أو يساوي ناقص اتنين
+
+241
+00:19:11,150 --> 00:19:16,470
+ديلتا لكل تربيع واضح ها طيب زائد ال norm ال VN
+
+242
+00:19:16,470 --> 00:19:20,230
+تربيع اللي هو أصغر أو يساوي ال VN لحق لل norm ال
+
+243
+00:19:20,230 --> 00:19:25,480
+VN اللي هي عبارة عن مين ديلتا N هيهاوها delta M
+
+244
+00:19:25,480 --> 00:19:29,940
+التانية فبصير زيادة 2 delta N تربيع زيادة delta M
+
+245
+00:19:29,940 --> 00:19:34,900
+من تربيع إذا صار عندي المقدار اللي هو Y N نقص وين
+
+246
+00:19:34,900 --> 00:19:39,660
+رايح أنا أنا رايحت بين ال Y نكوشي يعني إيش Y نكوشي
+
+247
+00:19:39,660 --> 00:19:43,420
+يعني for large N و M هيقول هذا المقدار السفرة و
+
+248
+00:19:43,420 --> 00:19:46,920
+هيكون أصغر من Y في الدنيا معايا إذا صار هذا
+
+249
+00:19:46,920 --> 00:19:53,760
+المقدارالان اصغر او يساوي هذه الكمية الان as n و n
+
+250
+00:19:53,760 --> 00:19:58,200
+goes to infinity delta n بتروح لدلتا و delta n
+
+251
+00:19:58,200 --> 00:20:02,100
+بتروح لدلتا اذا هذا هيصير اتنين في اتنين اربعة
+
+252
+00:20:02,100 --> 00:20:06,620
+دلتا تربية و انا اربعة دلتا تربية اذا هذا المقدار
+
+253
+00:20:06,620 --> 00:20:10,920
+as n و n goes to infinity هيصير very very small
+
+254
+00:20:10,920 --> 00:20:14,810
+لدرجة ان احنا مينللسفر وهذا معنى as n goes و M
+
+255
+00:20:14,810 --> 00:20:17,710
+goes وهذا المقدر روح السفر hence for every epsilon
+
+256
+00:20:17,710 --> 00:20:21,430
+أكبر من سفر there is K sufficiently large such
+
+257
+00:20:21,430 --> 00:20:25,430
+that ال Ym نقص Ym هتكون إيه شمالها أصغر من إبسلون
+
+258
+00:20:25,430 --> 00:20:31,070
+for all n و M أكبر من K وهذا أثبت لنا اطلع لفوق ال
+
+259
+00:20:31,070 --> 00:20:35,320
+Ym is a Cauchy sequence in Mالان وي ان كوشي
+
+260
+00:20:35,320 --> 00:20:37,720
+سيكوينس في الام و احنا اصلا اخدنا الام complete
+
+261
+00:20:37,720 --> 00:20:41,500
+عشان نقدر نكمل برهاننا الان مادام ات ام complete
+
+262
+00:20:41,500 --> 00:20:46,060
+وعندي كوشي سيكوينس اذا اكيد اكيد بط ام is complete
+
+263
+00:20:46,060 --> 00:20:51,080
+then وي ان converge says ان وي ان converge لمين ل
+
+264
+00:20:51,080 --> 00:20:57,360
+Y element in Mمدام Y في الـ M إذا أكيد نورم X
+
+265
+00:20:57,360 --> 00:21:01,580
+minus Y لكونها نقطة في الـ M أكبر أو يساوي اللي هو
+
+266
+00:21:01,580 --> 00:21:04,640
+الـ Delta اللي هي عبارة عن ال .. ال .. ال Infimum
+
+267
+00:21:04,640 --> 00:21:07,440
+أو ال .. ال .. greatest lower bound يعني في الأخر
+
+268
+00:21:07,440 --> 00:21:11,280
+lower bound هذه بتكون أصغر أو يساوي نورم X minus Y
+
+269
+00:21:11,870 --> 00:21:15,470
+However من جهة أخرى لو جينا أخدنا Normal X minus Y
+
+270
+00:21:15,470 --> 00:21:19,130
+هتكون أصغر أو يساوي بالـ Triangling Quality X ناقص
+
+271
+00:21:19,130 --> 00:21:23,310
+YN زي YN ناقص Y الأولى عبارة عن Delta N والتانية
+
+272
+00:21:23,310 --> 00:21:27,990
+اللى هي Normal YN ناقص Min ناقص Y لأن من فوق as N
+
+273
+00:21:27,990 --> 00:21:30,650
+goes to infinity احنا اتفاجن أن هذا هتروح لمين
+
+274
+00:21:30,650 --> 00:21:34,950
+للزفر و Delta N هتروح لمين للدلتا يعني بمعنى أخر
+
+275
+00:21:34,950 --> 00:21:40,780
+Normal X minus Y هيصير أصغر أو يساوي Deltaوعندي
+
+276
+00:21:40,780 --> 00:21:44,720
+دائما الـ X minus Y أكبر بساوي Delta إذا صار عندي
+
+277
+00:21:44,720 --> 00:21:48,560
+بالظبط الـ Normal X minus Y بساوي Delta يعني بمعنى
+
+278
+00:21:48,560 --> 00:21:53,160
+أخر لجينا الـ Y اللي البعد الـ X عنها هو اللي
+
+279
+00:21:53,160 --> 00:22:01,280
+بيمثل البعد الـ X عن اللي هي الـ M ككل طيب نثبت
+
+280
+00:22:01,280 --> 00:22:05,310
+إنه اللي هي هذه النقطة واحدةإتبعت إن واحدها سهلة
+
+281
+00:22:05,310 --> 00:22:08,370
+suppose that there are y و y not element in M
+
+282
+00:22:08,370 --> 00:22:14,570
+والتنتين اللي بيكون البعد بينهم و بين Y بينهم و
+
+283
+00:22:14,570 --> 00:22:18,510
+بين X هو بمثل الـ Delta هذه Delta وهذه Delta لنشوف
+
+284
+00:22:18,510 --> 00:22:25,170
+كيف نثبت أن y not هي بتساوي ال Yالنقطة واحدة by
+
+285
+00:22:25,170 --> 00:22:30,070
+parallelogram equality برضه اللي هي عبارة عن
+
+286
+00:22:30,070 --> 00:22:35,330
+اطبقها على ال y و ال y not يعني او على ال y minus
+
+287
+00:22:35,330 --> 00:22:39,530
+y not كل تربيع بساوي y minus x ناقص y minus y not
+
+288
+00:22:39,530 --> 00:22:44,600
+ال x كل تربيعأه فاهمين طرحت وضفت أطبقها عليهم
+
+289
+00:22:44,600 --> 00:22:49,760
+هدولة على اللي هي الجهتين هدول بساوي اتنين هيطرحن
+
+290
+00:22:49,760 --> 00:22:55,160
+ومجوحن اتنين في اتنين في الأولى y minus x في كل
+
+291
+00:22:55,160 --> 00:23:00,670
+تربيع هدول اللي اطلعزاد اتنين في yy not ناقص x لكل
+
+292
+00:23:00,670 --> 00:23:05,630
+تربيع ناقص اللي هو قطر التالي اللي هو عبارة عن
+
+293
+00:23:05,630 --> 00:23:09,270
+اللي هو بدّي الطرح اشماله الموجب لان عارفين اللي
+
+294
+00:23:09,270 --> 00:23:11,250
+هو القطرين
+
+295
+00:23:13,100 --> 00:23:18,260
+والاربعة طلعة المفروض أنكم مذكرين يعني بساوي هذا
+
+296
+00:23:18,260 --> 00:23:24,120
+زائد هذا هو يساوي الأولاني عبارة عن احنا فرضين انه
+
+297
+00:23:24,120 --> 00:23:27,620
+اللي هو ادمثل Delta فبصير اتنين Delta تربيعه وهذه
+
+298
+00:23:27,620 --> 00:23:30,180
+فرضينها بيساوي Delta برضه مش قولنا جدتين why why
+
+299
+00:23:30,180 --> 00:23:34,100
+notوها دي برضه اشملها اتنين دلده تربيع ناقص اللي
+
+300
+00:23:34,100 --> 00:23:38,340
+هو اربعة في نص Y نفس اللي عملت قبل شوية بدي اطلع
+
+301
+00:23:38,340 --> 00:23:43,420
+اللي هو الاتنين عامل مشترك فبطلع الاتنين من برة
+
+302
+00:23:43,420 --> 00:23:50,360
+التربيع اربعة عندي هي المقدار هذا شايفينه Yزائد y
+
+303
+00:23:50,360 --> 00:23:56,300
+not ناقص اتنين x طلعت الاتنين من عندها فصارت هذه y
+
+304
+00:23:56,300 --> 00:24:00,800
+minus زائد y not على اتنين يعني نص فيهم واتنين x
+
+305
+00:24:00,800 --> 00:24:04,040
+طلعت من هاتنين ضالت x لحالها ولمّا طلعته برا
+
+306
+00:24:04,040 --> 00:24:08,120
+التربية طلع باربعة فبصير عنده اربعة فنص y minus y
+
+307
+00:24:08,120 --> 00:24:11,800
+not ناقص x لكل تربية وهذا سمو ليه واحد خلّينا
+
+308
+00:24:11,800 --> 00:24:17,360
+نرجعله بعد شوية إذا اللي حصلته أن هذا normalتربيع
+
+309
+00:24:17,360 --> 00:24:20,780
+بيساوي اللي هو اتنين دلتة تربيع زاد اتنين دلتة
+
+310
+00:24:20,780 --> 00:24:25,680
+تربيع ناقص اللي هو اربع يعني اربع دلتة تربيع ناقص
+
+311
+00:24:29,150 --> 00:24:33,550
+since M is convex إذا أكيد هذه وين موجودة برضه في
+
+312
+00:24:33,550 --> 00:24:38,270
+الـ M وهذا معناته إنه نصف YY زاد Y not ناقص Normal
+
+313
+00:24:38,270 --> 00:24:42,590
+X أكبر يساوي مين؟ Delta، مظبوط ولا لأ؟ إذا ناقصه
+
+314
+00:24:42,590 --> 00:24:46,910
+أصغر يساوي Delta، أسالف Delta، إذن by this اللي هو
+
+315
+00:24:46,910 --> 00:24:52,360
+هذهو واحد بيكون عنده y minus y naught لكل تربيع
+
+316
+00:24:52,360 --> 00:24:56,820
+أصغر أو يساوي ماشي اللي هو اتنين دلتة تربيع زي ما
+
+317
+00:24:56,820 --> 00:24:59,960
+هي و اتنين دلتة تربيع زي ما هي و هذا بيصير أشمالها
+
+318
+00:24:59,960 --> 00:25:03,260
+أصغر أو يساوي ناقص أربع دلتة تربيع اللي هي ناقص
+
+319
+00:25:03,260 --> 00:25:07,400
+أربع دلتة تربيع و مجوح ان ايش بيساوي سفر اذا صار
+
+320
+00:25:07,400 --> 00:25:10,900
+عنده normal y minus y naught بيساوي سفر معناه y
+
+321
+00:25:10,900 --> 00:25:15,060
+بيساوي y naught و هذا بيثبت انه اللي هوالـ Y وحيدة
+
+322
+00:25:15,060 --> 00:25:18,440
+النقطة اللي بنحكي عليها إذا موجودة وحيدة بكون هي
+
+323
+00:25:18,440 --> 00:25:26,020
+خلصنا طيب الآن قبل شوية قبل شوية في سؤالنا المثال
+
+324
+00:25:26,020 --> 00:25:29,120
+اللي هو اللي أخدناه في الـ R تربيع لما أخدنا قطعة
+
+325
+00:25:29,120 --> 00:25:34,000
+مستقيمة و أخدنا فجيها اللي هي النقطة كان مين أقرب
+
+326
+00:25:34,000 --> 00:25:39,540
+بعض إلها العمودي؟العمودي الآن بدنا نروح بهذا
+
+327
+00:25:39,540 --> 00:25:43,680
+الاتجاه نشوف كيف نصل لإشي مشابه لهذا اللي بنحكيه
+
+328
+00:25:43,680 --> 00:25:48,900
+في العادى اللي هي نيجي للنمم اللي عندىبتقولي in
+
+329
+00:25:48,900 --> 00:25:53,700
+theorem تلاتة تلاتة واحد اللي قبله شوية نفترض M be
+
+330
+00:25:53,700 --> 00:25:58,860
+a complete subspace يعني مش اي subset يكون Y نفسه
+
+331
+00:25:58,860 --> 00:26:02,900
+ايه اشمالها او M اللي عندك تكون مش subset بس يعني
+
+332
+00:26:02,900 --> 00:26:06,120
+الـ M بالاضافة لشروط اللي كتبناها ال non-empty
+
+333
+00:26:07,940 --> 00:26:11,560
+وconvex و complete ونضيف لها انها تكون subspace في
+
+334
+00:26:11,560 --> 00:26:18,440
+هذه الحالة بقول لك انه then ال z اللي هي ال x
+
+335
+00:26:18,440 --> 00:26:21,560
+minus y اللي لجيتها انت قبل شوية اللي هي ال z هذه
+
+336
+00:26:21,560 --> 00:26:25,820
+هتكون is orthogonal to mean to y يعني الطول هذا
+
+337
+00:26:25,820 --> 00:26:28,950
+اللي قبل شوية اللي لجيناها هنااللي راجعناه هذا
+
+338
+00:26:28,950 --> 00:26:32,590
+الطول بين هال نهال هذا الطول المسافة بينهم هيكون
+
+339
+00:26:32,590 --> 00:26:39,430
+هذا orthogonal عالميا على ال Y ماشي الحالة نشوف
+
+340
+00:26:39,430 --> 00:26:44,470
+الآن هذا اللي هو نشوف كيف نثبت أنه orthogonal to Y
+
+341
+00:26:44,470 --> 00:26:49,580
+طيبsuppose that .. انه لأ suppose that Z بيساوي X
+
+342
+00:26:49,580 --> 00:26:53,040
+minus Y is not orthogonal to Y مدان مش عمودية على
+
+343
+00:26:53,040 --> 00:26:59,140
+Y اذا اكيد في نقطة بين اللي هو ال Y و بينها اللي
+
+344
+00:26:59,140 --> 00:27:01,740
+هي مش عمودية يعني ال inner product بين هنا شماله
+
+345
+00:27:01,740 --> 00:27:05,080
+مش صفر ماعرفشو معناته احنا ماعرفين شو معناته انه X
+
+346
+00:27:05,080 --> 00:27:09,740
+orthogonal to Y معناته inner product بين X و Y
+
+347
+00:27:09,740 --> 00:27:14,700
+بساوي صفر لكل Y وين موجودة في ال Y ماشي؟
+
+348
+00:27:17,380 --> 00:27:22,000
+طيب معايا طيب احنا طبعا شغلنا هان وين يا جماعة في
+
+349
+00:27:22,000 --> 00:27:25,640
+inner product space تنسوش بشتغل وين في inner
+
+350
+00:27:25,640 --> 00:27:28,860
+product space و احنا عرفنا ال orthogonality فيها
+
+351
+00:27:28,860 --> 00:27:33,240
+لان نفترض ان زد بيساوي x minus y is not orthogonal
+
+352
+00:27:33,240 --> 00:27:36,600
+to y مدام مش orthogonal اذا هلاجي y في ال y بحيث
+
+353
+00:27:36,600 --> 00:27:42,960
+ان زد و هذا النقطة اللي اشماله لايساوي سفرإذن then
+
+354
+00:27:42,960 --> 00:27:47,340
+there is y1 element in y such that z و y1 بيساوى
+
+355
+00:27:47,340 --> 00:27:53,100
+beta لاتساوى مين لاتساوى صفر clearly y1 لاتساوى
+
+356
+00:27:53,100 --> 00:27:56,400
+صفر أكيد لأن لو y1 بيساوى صفر معناته z و y1 بيساوى
+
+357
+00:27:56,400 --> 00:28:02,240
+صفر طيب الان otherwise z و y1 بيساوى صفر وهذا إيش
+
+358
+00:28:02,240 --> 00:28:06,940
+معله مش معجول ناشي و احنا لأنه مفترضين انه اللي هو
+
+359
+00:28:06,940 --> 00:28:11,200
+لايساوى صفر فاهمين طيبالأن furthermore for any
+
+360
+00:28:11,200 --> 00:28:15,360
+scalar α أحسبلي الآن لأي scalar α عشان بتصلكم
+
+361
+00:28:15,360 --> 00:28:18,440
+لتناقض احنا فرضنا العكس و بنصل لتناقض شوفوا كده
+
+362
+00:28:18,440 --> 00:28:21,880
+بتوصلكوا للتناقض خدوا ال Z ناقص Alpha Y واحد وكل
+
+363
+00:28:21,880 --> 00:28:25,300
+إيش ماله تربيع بنفك هذه بتعرفوا تفكوها عبارة عن
+
+364
+00:28:25,300 --> 00:28:28,240
+inner product بين هذه و بين نفسها و بنفك فكرة
+
+365
+00:28:28,240 --> 00:28:34,100
+بتطلع Z و Z ناقص أعملكم إياها ولا .. أو واضحة؟
+
+366
+00:28:34,100 --> 00:28:39,500
+الآن .. الآن .. هذه لأ خليني أعملها أحسنthe norm
+
+367
+00:28:39,500 --> 00:28:44,640
+of z-alpha y1 الكل تربية بساوي ال inner product
+
+368
+00:28:44,640 --> 00:28:52,440
+بين z-alpha y1 او z-alpha y1 مظبوط بفك الآن فكها
+
+369
+00:28:52,440 --> 00:28:57,540
+زي ما انتوا عارفين كيف بنفكها y ساوي z مع z
+
+370
+00:29:00,770 --> 00:29:07,610
+الان ناقص α y1 مع مين؟ مع الـ z اللي هي α y1 و مين
+
+371
+00:29:07,610 --> 00:29:12,890
+و z وهذه هتصير معاها بالنقص صح ولا لا؟ اذا الان
+
+372
+00:29:12,890 --> 00:29:17,750
+فكيت هذولة مع حاجة ديالأن بيدفك الآن هذولة مع مين
+
+373
+00:29:17,750 --> 00:29:21,870
+مع التانية Z مع اللي هي هذه ناقص ال Alpha لما تيجي
+
+374
+00:29:21,870 --> 00:29:24,590
+بتيجي أشمالها ال Alpha conjugate اللي Alpha
+
+375
+00:29:24,590 --> 00:29:30,810
+conjugate Z و Y1 وظل اللي هي هذه مع هذه مظبوط اللي
+
+376
+00:29:30,810 --> 00:29:33,850
+هي ناقص ناقص بيصير أشمالها زاد و Alpha في Alpha
+
+377
+00:29:33,850 --> 00:29:39,970
+conjugate فبصير مدرس لAlpha تربيع في Y1 و Y1 مظبوط
+
+378
+00:29:40,630 --> 00:29:45,270
+طيب إذا صار عندى عبارة عن Z و Z زى ما قولنا ناقص
+
+379
+00:29:45,270 --> 00:29:49,370
+Alpha conjugate في Z و Y1 ناقص الآن بدى أخد بين
+
+380
+00:29:49,370 --> 00:29:54,070
+اللي هي التنتين الأخرى التنتين هدولة بين هذه و هذه
+
+381
+00:29:54,070 --> 00:29:59,450
+بدأ أخد من على المشترك ال Alpha ماشي فبتضل Y1 و Z
+
+382
+00:29:59,450 --> 00:30:05,550
+و جوا أشمالها Alpha conjugate Y1 و Y Y1 واضح؟
+
+383
+00:30:05,550 --> 00:30:15,680
+بديها بعد شويةإذا أنا خدت أنا الآن ال alpha عامل
+
+384
+00:30:15,680 --> 00:30:20,300
+مشترك ضالت عندي هذه زي ما هي و هذه زي ما هي ناقص
+
+385
+00:30:20,300 --> 00:30:25,160
+alpha في هذه ناقص هذه طيب و إيه ساوي هذه نزلليها
+
+386
+00:30:25,160 --> 00:30:30,120
+زي ما هي و الآن alpha conjugate إيش أنا سميت z y1
+
+387
+00:30:30,120 --> 00:30:36,500
+z y1 هيها z y1 اللي هي beta هتطلع هذه y1 و z إيش
+
+388
+00:30:36,500 --> 00:30:42,380
+مالهاConjugate لها Beta Conjugate لأن هذه عبارة عن
+
+389
+00:30:42,380 --> 00:30:45,860
+زبد Y1 Conjugate وهذه كانت Beta اسمها إذا بصير
+
+390
+00:30:45,860 --> 00:30:50,740
+ناقص اللي هو Alpha فيه هذه بصير Beta Conjugate هنا
+
+391
+00:30:50,740 --> 00:30:57,910
+حطيتها ناقص Alpha Conjugate في Y1 ومنين؟ Y1بدي
+
+392
+00:30:57,910 --> 00:31:02,130
+أطير هذا الـ Turn فأخدت أنا Alpha conjugate هذه
+
+393
+00:31:02,130 --> 00:31:06,070
+بساوية يعني أنا بدي أسفره بساوية Beta conjugate
+
+394
+00:31:06,070 --> 00:31:11,070
+على Y1 ومين؟ Y1 أنا ضامن إن ال norm Y1 تربيه مش 0
+
+395
+00:31:11,070 --> 00:31:15,150
+لأن اضمنها إن Y1 ما لها مش 0 لذا بقسم عليه وانا
+
+396
+00:31:15,150 --> 00:31:18,790
+مرتاح لأن لما أخدت Alpha conjugate بساوية Beta
+
+397
+00:31:18,790 --> 00:31:22,030
+conjugate على هذه صار عندي الآن هذا المقدار اللي
+
+398
+00:31:22,030 --> 00:31:26,570
+بساوي هذا المقدارصار عبارة عن هذا زي ما هو بنزل
+
+399
+00:31:26,570 --> 00:31:34,790
+وهذا Alpha conjugate في Beta اللي هو ال Alpha
+
+400
+00:31:34,790 --> 00:31:39,710
+conjugate في Beta عنده بيصير عبارة عن norm ال Beta
+
+401
+00:31:39,710 --> 00:31:43,970
+تربيع على norm ال Y1 تربيع نشوف كيف .. كيف ال ..
+
+402
+00:31:43,970 --> 00:31:45,050
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+403
+00:31:45,050 --> 00:31:45,530
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+404
+00:31:45,530 --> 00:31:49,530
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+405
+00:31:49,530 --> 00:31:49,550
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+406
+00:31:49,550 --> 00:31:52,620
+.. ال .. ال ..الآن عندي اللي هو المقدار هذا لما
+
+407
+00:31:52,620 --> 00:31:55,620
+أخدنا Alpha conjugate عبارة عن Beta على هذا
+
+408
+00:31:55,620 --> 00:31:59,860
+المقدار هذا بيصير سفر صح ولا لأ معايا و Beta
+
+409
+00:31:59,860 --> 00:32:03,520
+conjugate مع Beta على هذه بيصير Beta في Beta
+
+410
+00:32:03,520 --> 00:32:07,000
+conjugate اللي هو هذا تربيع وينه؟ أه وعلى هذا اللي
+
+411
+00:32:07,000 --> 00:32:12,130
+هو Normal Y واحد تربيع واضح؟ ماضحش اللي صار؟عيد
+
+412
+00:32:12,130 --> 00:32:16,350
+طيب إذا صار عندي الان ال norm هذا بيساوي المقدار
+
+413
+00:32:16,350 --> 00:32:22,090
+هذا however norm ال z بيساوي norm ال x minus y و
+
+414
+00:32:22,090 --> 00:32:26,510
+هذا بيساوي مين ال delta و ال beta نفسها لا تساوي
+
+415
+00:32:26,510 --> 00:32:32,230
+سفر لا تساوي سفر إذا صار عندي الآن لما نشيل هذا
+
+416
+00:32:32,230 --> 00:32:37,730
+المقدارهذا المقدار اللي هو هذا المقدار Beta لا
+
+417
+00:32:37,730 --> 00:32:41,490
+تساوي سفر يعني Beta فيه رقم لما يصيرها بيصير هذا
+
+418
+00:32:41,490 --> 00:32:44,350
+المقدار لما نشيله اللي هو بيساوي هذا لما نشيله من
+
+419
+00:32:44,350 --> 00:32:47,710
+هذا المقدار بيصير strictly أصغر من مين من نورم الـ
+
+420
+00:32:47,710 --> 00:32:51,470
+Z تربية يعني نشيلنا منه رقم إذا بيصير أقل strictly
+
+421
+00:32:51,470 --> 00:32:56,350
+منه اللي هو هذا مين هو Delta تربية لأن نورم الـ Z
+
+422
+00:32:56,350 --> 00:32:59,790
+هو عبارة عن Delta لأن نورم الـ Z هو مين X minus Y
+
+423
+00:32:59,790 --> 00:33:04,880
+اللي هي اللي بيساوي Deltaمعايا إذا صار norm هذا
+
+424
+00:33:04,880 --> 00:33:09,880
+أصغر أو أسوأ من Delta تربيه لكن من جهة أخرى Y
+
+425
+00:33:09,880 --> 00:33:15,480
+subspace مظبوط إذا ال Y minus Alpha Y واحد هذه Y
+
+426
+00:33:15,480 --> 00:33:21,410
+نقص Alpha Y واحد في ال Yفي الـ Y لأن Y واحد في الـ
+
+427
+00:33:21,410 --> 00:33:24,370
+Y وY في الـ Y أي linear combination فيه في الـ Y
+
+428
+00:33:24,370 --> 00:33:30,410
+لأنها subspace بناء عليه Z ناقص Alpha Y واحد بساوي
+
+429
+00:33:30,410 --> 00:33:37,950
+بساوي norm الـ Z عبارة عن Xminus اللي هو Y ناقص
+
+430
+00:33:37,950 --> 00:33:42,850
+اطلع لفوق ناقص Alpha Y واحد وحطناها هتكون أشملها
+
+431
+00:33:42,850 --> 00:33:46,870
+أكبر أو ساوى Delta لإنه انزل انزل لإنه زي ما قلنا
+
+432
+00:33:46,870 --> 00:33:50,530
+عليا عليا لإنه هذا يقولنا هذا المقدار Y ناقص Alpha
+
+433
+00:33:50,530 --> 00:33:55,270
+Y واحد هذا المقدار في ال Y X ناقص اللي هو element
+
+434
+00:33:55,270 --> 00:33:58,910
+في ال Y أكبر أو ساوى من ال infimum اللي هو مين هو
+
+435
+00:33:58,910 --> 00:34:02,810
+ال Deltaإذا صار أكبر أو شويه Delta إذا صار في عندي
+
+436
+00:34:02,810 --> 00:34:08,550
+المقدار هذا مرة أكبر أو شويه Delta و مرة strictly
+
+437
+00:34:08,550 --> 00:34:12,550
+أصغر من Delta وهذا Contradiction معايا يا جماعة
+
+438
+00:34:12,550 --> 00:34:17,710
+هذا أكبر أو شويه Delta انزل و هنا اشماله أصغر
+
+439
+00:34:17,710 --> 00:34:22,130
+strictly من Delta حصلنا عليه أصغر strictly من مين؟
+
+440
+00:34:22,130 --> 00:34:25,530
+من Delta إذا مرة أصغر strictly من Delta لأن تربية
+
+441
+00:34:25,530 --> 00:34:28,510
+تربية بروحان مش أصغر strictly من Delta و مرة أكبر
+
+442
+00:34:28,510 --> 00:34:31,540
+أو شويه Deltaوهذا في Contradiction Therefore اللي
+
+443
+00:34:31,540 --> 00:34:37,260
+هو لازم تكون عندي اللي هي Z هذه Orthogonal على
+
+444
+00:34:37,260 --> 00:34:46,680
+اللي هي ال sub space Y طيب ننجي للوقت ده الآن
+
+445
+00:34:46,680 --> 00:34:57,150
+هذولة بأهلنا لا إشي أنه أقدر أجزء ال spaceأي space
+
+446
+00:34:57,150 --> 00:35:01,910
+أو inner product space أجزؤه إلى جزئين الجزء
+
+447
+00:35:01,910 --> 00:35:07,270
+والجزء الorthogonal عليه وبدأ أسميت اسمه الآن ماشي
+
+448
+00:35:07,270 --> 00:35:12,950
+الحالة let a vector space X is said to be the
+
+449
+00:35:12,950 --> 00:35:18,800
+direct sum of two subspaces Y and Z of Xأو written
+
+450
+00:35:18,800 --> 00:35:24,480
+X بتساوي Y زائد Z ماشي ال vector space X is said
+
+451
+00:35:24,480 --> 00:35:29,800
+to be direct sum of two subspaces Y and Z of X إذا
+
+452
+00:35:29,800 --> 00:35:33,660
+و بنكتبه على صورة X بتساوي direct sum Y زائد Z إذا
+
+453
+00:35:33,660 --> 00:35:38,920
+كل element في ال X فيه ال unique representation
+
+454
+00:35:38,920 --> 00:35:44,120
+يعني X بتساوي Y زائد Min زائد Z وهذا وحيد
+
+455
+00:35:55,680 --> 00:36:02,240
+واضح هذا بنسميه اللي هو كتبنا اللي هو ال X على
+
+456
+00:36:02,240 --> 00:36:06,800
+صورة direct sum Y زائد Z مركز عليه هذا الكلام لأن
+
+457
+00:36:06,800 --> 00:36:12,360
+هذا هي لازمنا نحتاج له بالتفصيل طيب الآن ال
+
+458
+00:36:12,360 --> 00:36:18,830
+theorem هذهبتحطلك النقاط على الحروف بالنسبة ل ..
+
+459
+00:36:18,830 --> 00:36:24,010
+اللي هي العلاقة بين اللي هو الـY والـY Orthogonal
+
+460
+00:36:24,010 --> 00:36:29,330
+احنا اذا .. خلّيني أسبق الأمور شوية في الـSpace
+
+461
+00:36:29,330 --> 00:36:36,170
+العادى، هي عندي اللي هو الـX Axis وهي الـY Axis،
+
+462
+00:36:36,170 --> 00:36:42,490
+مظبوط؟ عناصر هذولة Zero أو Xiو Zero أو إكساي واحد
+
+463
+00:36:42,490 --> 00:36:48,010
+و Zero خلّينا نسميها عناصرها نميل هي Zero و إكساي
+
+464
+00:36:48,010 --> 00:36:53,140
+اتنينوأي نقطة في ال space التانية Orthogonal على
+
+465
+00:36:53,140 --> 00:36:57,180
+بعض أي نقطة في ال space اللي هي XI واحد وXI اتنين
+
+466
+00:36:57,180 --> 00:37:03,080
+عبارة عن اللي هو النقاط الأولى زائد النقاط التانية
+
+467
+00:37:03,080 --> 00:37:06,960
+اللي هنا واللي هنا ماشي الحال وكأنه اللي هو ال
+
+468
+00:37:06,960 --> 00:37:11,380
+space X عند R تربيع اقدرنا نكتب على صورة direct
+
+469
+00:37:11,380 --> 00:37:20,190
+sum اللي هو R زائد مينR الـ N والـ R المقصود فيها
+
+470
+00:37:20,190 --> 00:37:23,750
+هنا أو خلّيني نقول مانعش نقول هذا isomorphic ل R
+
+471
+00:37:23,750 --> 00:37:29,950
+مش R خلّيني نقول إن هو ال space R اتحاد Zero
+
+472
+00:37:29,950 --> 00:37:35,730
+خلّيني نقول المزوج المرتبة بين R اتحاد Zero اللي
+
+473
+00:37:35,730 --> 00:37:39,610
+هي عبارة عن كل XI واحد و Zero such that XI واحد
+
+474
+00:37:39,610 --> 00:37:43,590
+element in R والتاني اللي هو الجهة التانيةوهذا ايش
+
+475
+00:37:43,590 --> 00:37:48,970
+معنى هنا orthogonal على بعض نشوف هذا الكلام ليش
+
+476
+00:37:48,970 --> 00:37:52,890
+علاقته باللي بنحكيه طيب projection theorem
+
+477
+00:37:52,890 --> 00:37:57,570
+projection theorem اللي بتقول اللي قلت y بيقال
+
+478
+00:37:57,570 --> 00:38:01,890
+close subspace of a Hilbert space H نفترض ان y أيش
+
+479
+00:38:01,890 --> 00:38:05,650
+معنى close subspace مفهوم ايش معنى close subspace
+
+480
+00:38:05,650 --> 00:38:12,140
+then H بيقول لك نقدر نكتب على صورة y زائد زدحيث
+
+481
+00:38:12,140 --> 00:38:16,720
+الـ Z هي مين الـ Y Orthogonal الـ Y Orthogonal
+
+482
+00:38:16,720 --> 00:38:19,740
+أخدنا إيش معنية الـ Y Orthogonal هي كل العناصر
+
+483
+00:38:19,740 --> 00:38:22,940
+اللي في الـ H اللي بتكون عمودية عالميا على الـ Y
+
+484
+00:38:22,940 --> 00:38:27,640
+يعني أي عنصر في الـ H و أكتبه على صورة اللي هو
+
+485
+00:38:27,640 --> 00:38:33,800
+حاصل جامع اللي هو direct sum من Y و Z حيث Y و Z
+
+486
+00:38:33,800 --> 00:38:38,220
+إيش ما هين متعامدين زي المثال للغاية ماشي الحالة
+
+487
+00:38:38,220 --> 00:38:45,340
+طيبالبرهن البرهن هذا الان اه اكيد هذا مبنع اللي
+
+488
+00:38:45,340 --> 00:38:48,600
+فات والبرهن هيكون جليل بناء على انه مبنع اللي فات
+
+489
+00:38:49,320 --> 00:38:53,980
+الان اللى دخلت على الخط جديد الان since Y is a
+
+490
+00:38:53,980 --> 00:38:57,960
+closed subspace of a Hilbert space H then Y ايش
+
+491
+00:38:57,960 --> 00:39:03,140
+ماله؟ اذا ان هي subspace من مين؟ دخلت انه H نفسها
+
+492
+00:39:03,140 --> 00:39:07,360
+تكون أيش معلها؟ Hilbert space احنا كنا نكون في
+
+493
+00:39:07,360 --> 00:39:11,100
+اللى جابلها انزل انزل عشان نقارن بين الجهتين عندى
+
+494
+00:39:11,100 --> 00:39:17,740
+في اللي هاناللي هي هيها X inner product space ماشي
+
+495
+00:39:17,740 --> 00:39:21,080
+الحال و بناء عليه اللي هو جلنا اللي هو بيكون فيه
+
+496
+00:39:21,080 --> 00:39:23,440
+نقطة واحدة و كده بناء على التلات شروط و من ثم
+
+497
+00:39:23,440 --> 00:39:28,160
+بتكون .. اللي هي النقطة هذه اللي هي اتلع لفوق
+
+498
+00:39:28,160 --> 00:39:32,560
+Orthogonal بناء على انه يكون Y subspace لأن لو
+
+499
+00:39:32,560 --> 00:39:36,600
+ضفنا على كل هالجثة انه ال space الأصلي H is
+
+500
+00:39:36,600 --> 00:39:39,600
+complete يصير أمورنا تمام اتتمام و نقدر نكتبه على
+
+501
+00:39:39,600 --> 00:39:45,040
+الصورة اللي أمامنا اتلع لفوقإذن الآن بما أن Y كله
+
+502
+00:39:45,040 --> 00:39:48,380
+ال subspace من Hilbert space H إذاً Y نفسه is H is
+
+503
+00:39:48,380 --> 00:39:50,700
+complete إذا مافيش داعي أن أفترض أن Y complete
+
+504
+00:39:50,700 --> 00:39:56,260
+بقول close subspace وH نفسه إيش ما لها complete
+
+505
+00:39:56,260 --> 00:40:00,120
+إذا ريح التراثي إذا حصلت على الشرط اللي بديها مدام
+
+506
+00:40:00,120 --> 00:40:04,180
+Y complete وY عندي since Y is convex لإنها اللي هي
+
+507
+00:40:04,180 --> 00:40:07,820
+subspacethen by theorem تلاتة تلاتة واحد اللي ..
+
+508
+00:40:07,820 --> 00:40:11,460
+اللي بدأنا فيها أو التانية and لما تلاتة تلاتة
+
+509
+00:40:11,460 --> 00:40:16,970
+اتنين imply that لكل X element in X في Y وحيدةأه
+
+510
+00:40:16,970 --> 00:40:20,730
+بحيث انه Z بتساوي او في Y في ال Y بحيث انه Z ايش
+
+511
+00:40:20,730 --> 00:40:24,650
+بتساوي X minus Y عمودي على مين على ال Y لقد
+
+512
+00:40:24,650 --> 00:40:28,490
+أثبتناها قبل شوية هذا إذا صارت عند ال X كتبتها على
+
+513
+00:40:28,490 --> 00:40:36,300
+صورة Y زائد مين زائد Z بدنا نثبت انه الآن حيثY
+
+514
+00:40:36,300 --> 00:40:40,420
+element in Y والـ Z وين موجودة في الـ Y Orthogonal
+
+515
+00:40:40,420 --> 00:40:44,880
+اللي هي الرمزنالها بالرمز مين Z Capital معايا؟ هذا
+
+516
+00:40:44,880 --> 00:40:48,380
+كله من وين؟ من النظرية الأولى الآن بدنا نفترض ..
+
+517
+00:40:48,380 --> 00:40:53,100
+بدنا نثبت أن هذه الصورة صورة إيه شمالها وحيدة يعني
+
+518
+00:40:53,100 --> 00:40:57,970
+الـ Y وحيدة والـ Z إيه شمالها؟ وحيدةنفترض الآن
+
+519
+00:40:57,970 --> 00:41:02,670
+suppose that there are y1 و y2 في ال y و z1 و z2
+
+520
+00:41:02,670 --> 00:41:07,330
+في ال y و ال x نقدر نكتبها على صورة x y1 زي z1 و
+
+521
+00:41:07,330 --> 00:41:12,350
+ال x نقدر نكتبها على صورة y2 زي z2 و نوصلكم أنه
+
+522
+00:41:12,350 --> 00:41:19,530
+لازم يكونين متساويتين ماشي الوصول سهل then احسبلي
+
+523
+00:41:19,530 --> 00:41:25,250
+الآنهذه بتساوي هذه خد ال Y على جهة و ال Z على جهة
+
+524
+00:41:25,250 --> 00:41:28,730
+بيصير Y واحد نقص Y اتنين بيساوي Z اتنين نقص Z واحد
+
+525
+00:41:28,730 --> 00:41:32,830
+however Y واحد نقص Y اتنين اللي موجودة في ال Y
+
+526
+00:41:32,830 --> 00:41:36,950
+مظبوط و هذه بتساوي هذه و هذه موجودة في ال Y
+
+527
+00:41:36,950 --> 00:41:41,170
+orthogonal اه إذا هذه صارت عمودية على هذه مظبوط
+
+528
+00:41:41,170 --> 00:41:46,920
+إذا صار عندي و Z اتنين في ال Y و Z واحد thenالـ Y1
+
+529
+00:41:46,920 --> 00:41:50,200
+والـ Y2 مدامت بالساوية هذه وهذه موجودة في الـ Y
+
+530
+00:41:50,200 --> 00:41:54,100
+أورثجونال ومن جهة أخرى هذه في الـ Y أورثجونال إذا
+
+531
+00:41:54,100 --> 00:41:58,960
+صارت هذه في الـ Y وبناء على المساوية اللي بتساويها
+
+532
+00:41:58,960 --> 00:42:00,960
+في الـ Y أورثجونال هتكون في الـ Y أورثجونال هي
+
+533
+00:42:00,960 --> 00:42:05,120
+برضه إذا صارت Y1 ناقص Y2 موجودة في الـ Y حسب هذه
+
+534
+00:42:05,120 --> 00:42:07,620
+وهتكون موجودة في الـ Y أورثجونال حسب هذه إذا
+
+535
+00:42:07,620 --> 00:42:11,800
+موجودة في التقاطع وبناء عليه فهتكون عمودية على
+
+536
+00:42:11,800 --> 00:42:16,180
+حالهاالاشي الوحيد اللي بين Y و Y Orthogonal هو مين
+
+537
+00:42:16,180 --> 00:42:19,920
+الصفر؟ ليش؟ لأن لو فرضنا إنه في عندنا Element اسمه
+
+538
+00:42:19,920 --> 00:42:25,780
+Y1-Y2 Element in Y تقاطع الـY Orthogonal معناته
+
+539
+00:42:25,780 --> 00:42:33,560
+هذا الـElement صار Y1-Y2 وY1-Y2 إيش هيساوي؟ صفر،
+
+540
+00:42:33,560 --> 00:42:36,680
+بناءً عليه هيكون هذا الـElement صفر، يعني إذا
+
+541
+00:42:36,680 --> 00:42:41,780
+دائمًا هذا التقاطع بيساوي مين؟الـ Zero إذا Y1-Y2
+
+542
+00:42:41,780 --> 00:42:50,680
+بيساوي 0 إذا Y1 بيساوي Y2 وبناء عليه بيصير عندي
+
+543
+00:42:50,680 --> 00:42:57,280
+اللي هو العنصر Y1 وحيد ومنه ما دام Y1 بيساوي Y2
+
+544
+00:42:57,280 --> 00:43:01,320
+إذا هذا صار سفر إذا Z2-Z1 بيساوي 0 إذا Z2 بيساوي
+
+545
+00:43:01,320 --> 00:43:06,580
+Z1 إذا صارت عندي اللي هي ال uniqueness تم إثباتها
+
+546
+00:43:07,090 --> 00:43:16,750
+نجي للملاحظة اللي بعدها ايش
+
+547
+00:43:16,750 --> 00:43:22,070
+الملاحظة بتقول from اتنين above
+
+548
+00:43:24,590 --> 00:43:28,650
+we can define a mapping called the orthogonal
+
+549
+00:43:28,650 --> 00:43:35,150
+projection of H onto Y صار عندي لان بقدر اعرف
+
+550
+00:43:35,150 --> 00:43:43,730
+mapping B من H اللي هو إيش بيساوي X أو آسف Y زائد
+
+551
+00:43:43,730 --> 00:43:51,880
+Y orthogonal، مظبوط؟ حاشي، لعند مين؟ لعند Yهذا الـ
+
+552
+00:43:51,880 --> 00:43:57,480
+projection بيجي بسقطلي اللي هو كل العناصر هنا
+
+553
+00:43:57,480 --> 00:44:02,780
+بسقطها العنصر على ال element 10 لنشوف كيف بدنا
+
+554
+00:44:02,780 --> 00:44:10,430
+نعرفه هو في الواقع العموداللي هو بي من أدش اللي
+
+555
+00:44:10,430 --> 00:44:16,790
+عند Y defined by بي X بتساوي Y where Y بتساوي X
+
+556
+00:44:16,790 --> 00:44:20,190
+زائد Z ياشي ال element .. Y element و Y و Z
+
+557
+00:44:20,190 --> 00:44:23,050
+element المين in Z this mass being has the
+
+558
+00:44:23,050 --> 00:44:26,490
+following properties شوفوا أمثلكم على اللي إحنا
+
+559
+00:44:26,490 --> 00:44:32,790
+بنعرفه هي عندي اللي هو ال X axis وهي مين ال Y axis
+
+560
+00:44:32,790 --> 00:44:36,390
+وخلّيني أقول .. يعني خلّيني أقول Roughly اللي هو R
+
+561
+00:44:36,390 --> 00:44:41,890
+تربيعبساوي الـ x-axis زائد مين ضايق صمت مع مين؟ مع
+
+562
+00:44:41,890 --> 00:44:47,370
+الـ y-axis ناشي الحال الان عندي ال projection قدوة
+
+563
+00:44:47,370 --> 00:44:53,310
+اي نقطة اي نقطة اللي هي x واحد و y واحد او زي ما
+
+564
+00:44:53,310 --> 00:44:56,590
+هو يسميها psi واحد وpsi اتنين هذا النقطة لما
+
+565
+00:44:56,590 --> 00:45:02,850
+اعملها projection بده نزلها هان صورتها مين؟X1 ماشي
+
+566
+00:45:02,850 --> 00:45:08,810
+الحال فالان بعملته projection X زي Y هو مسميها
+
+567
+00:45:08,810 --> 00:45:15,130
+طبعا هذه اللي هو اللي في الواقع اسمها Y عنده وهذه
+
+568
+00:45:15,130 --> 00:45:20,370
+ايش اسمها ال Z اللي هي ال Y Orthogonal معايافعملت
+
+569
+00:45:20,370 --> 00:45:24,530
+إسقاط صارت اللي هي صورة أي نقطة تاخد mean ال entry
+
+570
+00:45:24,530 --> 00:45:29,290
+الواحد الأول X واحد وكأنه صار له projection من ال
+
+571
+00:45:29,290 --> 00:45:36,020
+space اللي هو R تربيع لعند ال mean ال X axisأو
+
+572
+00:45:36,020 --> 00:45:39,640
+اللي هو مسميه هناك الـ Y ممكن أعمله حكامي وين؟ على
+
+573
+00:45:39,640 --> 00:45:42,300
+الجهة دي بعد شوية بنشوف اللي هو أعمله projection
+
+574
+00:45:42,300 --> 00:45:45,100
+وين؟ هنا بس الآن خلّينا على ال projection تبعنا
+
+575
+00:45:45,100 --> 00:45:49,580
+أنه عملنا projection من H Y زائد Y Orthogonal
+
+576
+00:45:49,580 --> 00:45:53,720
+عالمين على ال Y بعد شوية هنعمله عالمين على ال Y
+
+577
+00:45:53,720 --> 00:45:58,000
+Orthogonal كيف بدنا نعرفه هذا؟ بدنا نعرفه أن ال BX
+
+578
+00:45:58,000 --> 00:46:07,600
+BX اللي هي ال X إيش هتساويB of Y زائد مين؟ زائد Y
+
+579
+00:46:07,600 --> 00:46:14,860
+اللي هو الجزء الثاني أنا بسميها Z إيش بتساوي ال Y؟
+
+580
+00:46:14,860 --> 00:46:22,440
+واضح؟ أي سؤال؟ طيب الآن هذا ال projection has the
+
+581
+00:46:22,440 --> 00:46:27,310
+following propertiesمش احنا اتفاجنا قبل بشوية انه
+
+582
+00:46:27,310 --> 00:46:30,210
+اي X نقدر نكتبها على صورة Y زي Z من ال direct sum
+
+583
+00:46:30,210 --> 00:46:34,770
+هدف ال Y في ال Y و ال Z في ال Y ارتجونال الان ال
+
+584
+00:46:34,770 --> 00:46:37,690
+projection بده اعرفه من H لعند Y اللي هو بياخد ال
+
+585
+00:46:37,690 --> 00:46:42,070
+X و برميها لوين على ال Y الان P is linear and
+
+586
+00:46:42,070 --> 00:46:44,950
+bounded P is linear and bounded دوة دي سهلة P is
+
+587
+00:46:44,950 --> 00:46:52,490
+linear قلكم دي شجرة تفاصيلالان بي .. this mapping
+
+588
+00:46:52,490 --> 00:46:55,430
+has the following properties منها all bounded all
+
+589
+00:46:55,430 --> 00:46:58,890
+bounded برضه نفس الأشياء normal بي X هتصل to other
+
+590
+00:46:58,890 --> 00:47:04,130
+بساوي something في normal X بي maps H onto Y بياخد
+
+591
+00:47:04,130 --> 00:47:08,290
+H onto وين onto Y و هذا واضح بي و فاتش أشمالها خد
+
+592
+00:47:08,290 --> 00:47:11,670
+I X في هدا صورتها مين اللي هو Y خدوا I Y هنا
+
+593
+00:47:11,670 --> 00:47:15,010
+هتلاقوا element هنا بحيث انه صورته مين اللي هي هنا
+
+594
+00:47:16,380 --> 00:47:20,440
+أخدوا أي ويهان هتلاقوا اللي هو فيه element نهان
+
+595
+00:47:20,440 --> 00:47:25,700
+بحيث انه بي of اللي هي ال H بساوي اللي هو ال Y
+
+596
+00:47:29,260 --> 00:47:34,860
+الـ B of Y برضه إيش هتساوي اللي هي مين ال Y برضه
+
+597
+00:47:34,860 --> 00:47:37,360
+هذا كله بده إثبات يعني بس مش صعب إثباته دير بالكم
+
+598
+00:47:37,360 --> 00:47:42,140
+B of Y Orthogonal إيش هيساوي؟ هيساوي الصفر طبيعي
+
+599
+00:47:42,140 --> 00:47:46,040
+ما هو لإنه أي ال اللي هو element هنا في ال Y
+
+600
+00:47:46,040 --> 00:47:49,780
+Orthogonal اللي هو عبارة عن اللي هي في الآخر صورة
+
+601
+00:47:49,780 --> 00:47:52,780
+مين ال Y وعشان يكون في ال Y Orthogonal بيصير Zero
+
+602
+00:47:52,780 --> 00:47:55,540
+زائد ال element اللي في ال Y Orthogonal برميه على
+
+603
+00:47:55,540 --> 00:47:59,820
+ال Zero فبكون ده منصورة مش أي element هناهيصير أي
+
+604
+00:47:59,820 --> 00:48:03,840
+element Y أي element X في الـ Y Orthogonal هيكون
+
+605
+00:48:03,840 --> 00:48:09,800
+على صورة X بتساوي element اللي هو Zero زائد X والـ
+
+606
+00:48:09,800 --> 00:48:12,100
+X موجودة في الـ Y Orthogonal وهذا موجود في الـ Y
+
+607
+00:48:12,100 --> 00:48:18,500
+فهيكون ال projection له مين هو الـ Zero المهم الـ
+
+608
+00:48:18,500 --> 00:48:22,160
+B تربيه هيساوى مين؟ هيساوى الـ B خد الـ B تربيه في
+
+609
+00:48:22,160 --> 00:48:25,880
+Xو ال X طبعا على صورة هذه هتلاقيه وين هيروح في
+
+610
+00:48:25,880 --> 00:48:30,500
+الآخر لل P of X يعني P تربيع of X هتطلع P of X
+
+611
+00:48:30,500 --> 00:48:35,660
+ولكن سينا برضه يعني بمعنى آخر اللي هو هذا بنسميه
+
+612
+00:48:35,660 --> 00:48:40,100
+idempotent and the restriction of P on Y is the
+
+613
+00:48:40,100 --> 00:48:43,760
+identity operator on Y من هذه هي ال restriction
+
+614
+00:48:43,760 --> 00:48:46,800
+اللي فيه حتى تطلع ال identity operator هتاخد اللي
+
+615
+00:48:46,800 --> 00:48:50,560
+هو ال wire اللي بعد هذا left to the reader
+
+616
+00:48:50,560 --> 00:48:56,460
+homework معاكمالآن بناءً على اللي قبل بشوية اللي
+
+617
+00:48:56,460 --> 00:49:01,760
+هو the orthogonal complement of a closed subspace
+
+618
+00:49:01,760 --> 00:49:05,540
+Y of a Hilbert space H is the null space N of B of
+
+619
+00:49:05,540 --> 00:49:12,300
+the orthogonal projection of B onto Y يعني الآن مش
+
+620
+00:49:12,300 --> 00:49:20,890
+هحله بس يعني بعطيكم ال .. ال null space of Bالـ
+
+621
+00:49:20,890 --> 00:49:25,050
+null space of B أيش هيطلع عندك الـ null space of B
+
+622
+00:49:25,050 --> 00:49:32,190
+الـ null space of B هيطلع اللي هو مين هو the
+
+623
+00:49:32,190 --> 00:49:39,550
+orthogonal complement of Y in Hilbert
+
+624
+00:49:39,550 --> 00:49:42,370
+space is the null space of B يعني الـ N of B
+
+625
+00:49:42,370 --> 00:49:52,280
+هتساوي Y Orthogonal الـ N of B أيش تعريفهاهي عبارة
+
+626
+00:49:52,280 --> 00:49:57,520
+عن كل الإكسات اللي بيساوي Y زائد Z element معروف
+
+627
+00:49:57,520 --> 00:50:02,700
+اللي هي Z في ال Y Orthogonal و ال Y في ال Y such
+
+628
+00:50:02,700 --> 00:50:10,520
+that B of X بيساوي Zero يعني B of X ايش B of X في
+
+629
+00:50:10,520 --> 00:50:14,400
+هذه الحالة B of X اللي هي ال Y يعني ال Y ايش
+
+630
+00:50:14,400 --> 00:50:20,770
+بتساوي0 صح يعني النقاط هيصير X تساوي Z اللي وين
+
+631
+00:50:20,770 --> 00:50:23,050
+موجودة في ال Y ارتجونال يعني وين بتساوي ال Y
+
+632
+00:50:23,050 --> 00:50:26,770
+ارتجونال بس بده ترتيب يلا هاي سواء .. الآن اللي
+
+633
+00:50:26,770 --> 00:50:30,730
+بعده اللي بعده ال remark اللي بعده برضه exercises
+
+634
+00:50:30,730 --> 00:50:35,540
+بسيطة هذهإذا M is a non-empty subset of an inner
+
+635
+00:50:35,540 --> 00:50:39,460
+product space X إذا non-empty subset من subspace X
+
+636
+00:50:39,460 --> 00:50:45,960
+then M orthogonal is a closed vector subspace of
+
+637
+00:50:45,960 --> 00:50:52,160
+mean of X إذا حتى لو كانت M عبارة عن مجرد non
+
+638
+00:50:52,160 --> 00:50:55,460
+-empty subset of inner product space هتطلع ال M
+
+639
+00:50:55,460 --> 00:50:59,600
+orthogonal نفسها يشملها closed subspace يعني
+
+640
+00:50:59,600 --> 00:51:04,120
+subspace و closedماشي Sub-spacement عارفين تاخدوا
+
+641
+00:51:04,120 --> 00:51:09,060
+أي XY في الـ M Orthogonal و بتثبتوا أن Alpha X زي
+
+642
+00:51:09,060 --> 00:51:11,060
+الـ Y في الـ M Orthogonal وهذا بالـ Inner Product
+
+643
+00:51:11,060 --> 00:51:14,780
+على طول بتطلع و اللي هي Closed بتاخدوا Sequence X
+
+644
+00:51:14,780 --> 00:51:18,700
+and في الـ M Orthogonal بتكون Verged زي الـ X و
+
+645
+00:51:18,700 --> 00:51:21,300
+بتثبتوا أن الـ X موجودة في الـ M Orthogonal وهذا
+
+646
+00:51:21,300 --> 00:51:24,480
+هتستخدموا ال .. ال .. ال .. ال .. ال continuity لل
+
+647
+00:51:24,480 --> 00:51:27,640
+Inner Product و هتصلوا لنتيجة بسرعة بتثبتوا أن X
+
+648
+00:51:27,640 --> 00:51:31,890
+في الـ M Orthogonaland M is a subset of M
+
+649
+00:51:31,890 --> 00:51:35,370
+Orthogonal و Orthogonal الـ M نفسها هتكون جزئية من
+
+650
+00:51:35,370 --> 00:51:39,570
+مين؟ من M Orthogonal و Orthogonal واضح و برضه هدسي
+
+651
+00:51:39,570 --> 00:51:44,870
+اللي مش صعب .. طيب اللي هنلم اللي عندنا تلاتة
+
+652
+00:51:44,870 --> 00:51:49,830
+تلاتة ستة اطلع لفوق if Y is a closed subspace of a
+
+653
+00:51:49,830 --> 00:51:53,990
+Hilbert space H then هيطلع عند Y ايش متساوي؟ Y
+
+654
+00:51:53,990 --> 00:51:59,610
+Orthogonal و Orthogonal قبل قلنا ان Mجزئية من M
+
+655
+00:51:59,610 --> 00:52:03,570
+Orthogonal أو M Orthogonal لكن M Orthogonal
+
+656
+00:52:03,570 --> 00:52:10,430
+Orthogonal ليس شرطا أن يكون subset من M إلا خلّيني
+
+657
+00:52:10,430 --> 00:52:13,730
+أقول أو شرط أو أحد الشروط اللي بيخليها تتجرأ أن
+
+658
+00:52:13,730 --> 00:52:18,610
+تكون مسوائلها هو الشرط أنها تكون Y a closed
+
+659
+00:52:18,610 --> 00:52:22,130
+subspace وفي هذه الوقت subspace اتشدن Y بيستوي Y
+
+660
+00:52:22,130 --> 00:52:27,110
+Orthogonalخلّينا نبره انه by remark تلاتة y subset
+
+661
+00:52:27,110 --> 00:52:29,950
+من y Orthogonal Orthogonal وهذه سهلة اثباتها كمان
+
+662
+00:52:29,950 --> 00:52:35,390
+يعني لحالة بتثبتوها بشكل سريع طيب conversely ..
+
+663
+00:52:35,390 --> 00:52:39,510
+conversely let x element in y Orthogonal
+
+664
+00:52:39,510 --> 00:52:43,210
+Orthogonalماشي يعني اننا ناخد X في ال Y أرثجونال
+
+665
+00:52:43,210 --> 00:52:46,430
+أرثجونال تبتنها وين موجودة في ال Y by theorem اللي
+
+666
+00:52:46,430 --> 00:52:49,210
+جاب البشوية تلاتة تلاتة أربعة there exists a
+
+667
+00:52:49,210 --> 00:52:52,810
+unique Y element in Y بحيث ان X بتسوى مين Y زي ال
+
+668
+00:52:52,810 --> 00:52:58,610
+Z Y في ال Y و Z في مين في ال Y أرثجونال معايا لكن
+
+669
+00:52:58,610 --> 00:53:03,030
+ال Y جزئية من ال Y أرثجونال أرثجونال ماشي الحال
+
+670
+00:53:03,030 --> 00:53:07,310
+and Y أرثجونال أرثجونال نفسه اشمله is a vector
+
+671
+00:53:07,310 --> 00:53:10,760
+spaceأحنا اتفاجن الـ Y أرثوجونال اللي حالها في
+
+672
+00:53:10,760 --> 00:53:13,220
+vector space بغض النظر عن الـ Y تكون أه ولا لأ
+
+673
+00:53:13,220 --> 00:53:17,240
+الآن Y أرثوجونال أرثوجونال is a vector space إذا Z
+
+674
+00:53:17,240 --> 00:53:22,420
+بتساوي أي linear combination بين أي تنتين XY في
+
+675
+00:53:22,420 --> 00:53:24,640
+الـ Y أرثوجونال أرثوجونال لازم الـ linear
+
+676
+00:53:24,640 --> 00:53:29,860
+combination ماوجودش وين يكون فيها معايا؟ Y جزئية
+
+677
+00:53:29,860 --> 00:53:33,320
+من مين؟ من Y أرثوجونال أرثوجونال والـ Y موجودة
+
+678
+00:53:33,320 --> 00:53:39,850
+وين؟ في الـ Y معايا؟ معايا أهالان و ال .. و ال ..
+
+679
+00:53:39,850 --> 00:53:42,970
+و عندي .. الان حيصير عندي و ال Y Orthogonal
+
+680
+00:53:42,970 --> 00:53:47,170
+Orthogonal عبارة عن ماله عبارة عن subspace إذا
+
+681
+00:53:47,170 --> 00:53:50,770
+أكيد اللي هو Z بالسواء X minus Y برضه موجودة في ال
+
+682
+00:53:50,770 --> 00:53:55,450
+Y Orthogonal Orthogonal و ال .. و هذا معناته ..
+
+683
+00:53:55,450 --> 00:53:59,410
+إيش معناته Z في ال Y Orthogonal Orthogonal إنها
+
+684
+00:53:59,410 --> 00:54:02,790
+عمودية عالمياً على ال Y Orthogonal ولا ليش تكون في
+
+685
+00:54:02,790 --> 00:54:07,280
+ال Y Orthogonal Orthogonalعندى وصلت إن ال Z عمودية
+
+686
+00:54:07,280 --> 00:54:10,960
+على ال Y أرثجونال و ال Y is a closed subspace of a
+
+687
+00:54:10,960 --> 00:54:13,560
+Hilbert space then it is complete
+
+688
+00:54:35,010 --> 00:54:39,130
+والـ z عمودي على ال y orthogonal إذا صارت ال z
+
+689
+00:54:39,130 --> 00:54:42,830
+عمودي على حالها الواحدة منهم إذا صار ال z عمودي
+
+690
+00:54:42,830 --> 00:54:45,690
+على ال z ومن ثم اللي هو inner product بينهم سفر
+
+691
+00:54:45,690 --> 00:54:49,250
+يعني ال z أيش بتساوي سفر ومن ثم x أيش بتساوي y
+
+692
+00:54:49,250 --> 00:54:54,990
+ومدام x بتساوي y احنا بدأنا بxفي الـ Y Orthogonal
+
+693
+00:54:54,990 --> 00:54:58,950
+Orthogonal وانتهينا بالـ X موجودة في الـ Y إذا
+
+694
+00:54:58,950 --> 00:55:01,730
+صارت الـ Y Orthogonal Orthogonal subset من الـ Y و
+
+695
+00:55:01,730 --> 00:55:04,630
+الـ Y Orthogonal Orthogonal هتساوي Y بناء على هذه
+
+696
+00:55:04,630 --> 00:55:07,270
+subset من هذه و هذه أثباتها زي ما قلنا سهل لو
+
+697
+00:55:07,270 --> 00:55:09,930
+أخدتوا X في الـ Y هيكون ال inner product بين الـ X
+
+698
+00:55:09,930 --> 00:55:13,230
+و أي element في الـ Y Orthogonal بساوي سفر فبصير
+
+699
+00:55:13,230 --> 00:55:18,490
+اللي هو اللي هي منها بتقدر تصل لإنه الـ X نفسها
+
+700
+00:55:18,490 --> 00:55:26,870
+موجودة في الـ Y Orthogonalremark 4 if
+
+701
+00:55:26,870 --> 00:55:30,670
+Y is a closed subspace of a Hilbert space H and Z
+
+702
+00:55:30,670 --> 00:55:35,130
+بيساوي Y Orthogonal then
+
+703
+00:55:35,130 --> 00:55:40,850
+Z Orthogonal بيساوي Y Orthogonal Orthogonal بيساوي
+
+704
+00:55:40,850 --> 00:55:47,720
+Y ومن ثمصار انت بتكتب الـ H على صورة إيشي و عمودي
+
+705
+00:55:47,720 --> 00:55:54,320
+عليه مظبوط اللي هو Z زائد مين Z Orthogonal معايا
+
+706
+00:55:54,320 --> 00:56:00,120
+يا جماعة عندي Z بيساوي Y Orthogonal ماشي و Z
+
+707
+00:56:00,120 --> 00:56:04,410
+Orthogonal بيساوي Y Orthogonal Orthogonalاللي هو
+
+708
+00:56:04,410 --> 00:56:08,290
+أثبتناها مين واي هذا كله في حالة مين Y closed
+
+709
+00:56:08,290 --> 00:56:12,290
+subspace of Hilbert space إذا صارت عند أشكتها اللي
+
+710
+00:56:12,290 --> 00:56:16,230
+كاي بكتبها على صورة Z زائد Y صارت على صورة Z زائد
+
+711
+00:56:16,230 --> 00:56:20,170
+مين Z orthogonal لإن ال Y هي ال orthogonal ال
+
+712
+00:56:20,170 --> 00:56:24,070
+orthogonal هي Z orthogonal ماشي الحال إذا ومنه
+
+713
+00:56:24,070 --> 00:56:27,950
+بقدر على اللي حكيته قبل بشوية بنفس الأسلوب ولكن
+
+714
+00:56:27,950 --> 00:56:32,750
+بطبقها على هذه اللي هو direct sum
+
+715
+00:56:35,660 --> 00:56:40,360
+بكس او بكس او بكس او بكس او بكس او بكس او بكس او
+
+716
+00:56:40,360 --> 00:56:43,960
+بكس او بكس او بكس او بكس او بكس او بكس او بكس او
+
+717
+00:56:43,960 --> 00:56:47,860
+بكس او بكس او بكس او بكس او بكس او بكس او بكس او
+
+718
+00:56:47,860 --> 00:56:48,120
+بكس او بكس او بكس او بكس او بكس او بكس او بكس او
+
+719
+00:56:48,120 --> 00:56:48,160
+بكس او بكس او بكس او بكس او بكس او بكس او بكس او
+
+720
+00:56:48,160 --> 00:56:50,580
+بكس او بكس او بكس او بكس او بكس او بكس او بكس او
+
+721
+00:56:50,580 --> 00:56:56,720
+بكس او بكس
+
+722
+00:56:56,720 --> 00:57:04,030
+او بكس اعال Y Axis بسير Bx بدل ما هو عال Y ايش
+
+723
+00:57:04,030 --> 00:57:07,970
+بساوي؟ بساوي اللي هو Z limit in Z Define a
+
+724
+00:57:07,970 --> 00:57:13,590
+projection اللي هو من H لعند Z وهذا اللي هو بنفس
+
+725
+00:57:13,590 --> 00:57:16,870
+الأسلوب السابق نيجي للنمة الأخيرة
+
+726
+00:57:21,770 --> 00:57:26,690
+for any non-empty subset M of a Hilbert space H،
+
+727
+00:57:26,690 --> 00:57:32,930
+ده نرجعنا لمين؟ لمجرد non-empty subset من الـH،
+
+728
+00:57:32,930 --> 00:57:36,270
+the span of M is dense if and only if الامر تجهنا
+
+729
+00:57:36,270 --> 00:57:44,130
+الـH بساوي، بساوي اللي هو الـ0إذا الـ span لـ M هو
+
+730
+00:57:44,130 --> 00:57:47,450
+عبارة عن الـ set of all linear combinations of
+
+731
+00:57:47,450 --> 00:57:52,710
+element M هيكون dense إذا و فقط إذا الـ M مرتجونة
+
+732
+00:57:52,710 --> 00:58:03,370
+لش بتساوي؟ بتساوي سفر إذا
+
+733
+00:58:03,370 --> 00:58:08,170
+يا جماعة فيكم ما تصلوا على النبي بيصير عند الأقل
+
+734
+00:58:08,170 --> 00:58:15,780
+spanللـ M closure بيساوي الـ H او ايش بيسميه هو H
+
+735
+00:58:15,780 --> 00:58:22,000
+F and all F اللي هو الـ M orthogonal بيساوي مين
+
+736
+00:58:22,000 --> 00:58:27,620
+الـ 0 الـ M هذه مجرد مين subset من الـ H وهذه لا
+
+737
+00:58:27,620 --> 00:58:32,260
+تساوي سبق فاتر والـ H عبارة عن Hilbert S V S ماشي
+
+738
+00:58:32,260 --> 00:58:36,080
+تنثبت ناخد اول شي نفترض هذه و نوصل لهذه و نوصل
+
+739
+00:58:36,080 --> 00:58:41,800
+لهذه ماشي طيبلت X الان element of M Orthogonal
+
+740
+00:58:41,800 --> 00:58:46,220
+ونفترض ان V بيساوي ال span لـ M اللي حكيتها to be
+
+741
+00:58:46,220 --> 00:58:49,840
+dense in mean in H بدي اثبتلكم ان الـ X H لازم
+
+742
+00:58:49,840 --> 00:58:53,360
+تساوي السفر عشان اثبت الـ M Orthogonal بساوي الـ
+
+743
+00:58:53,360 --> 00:58:59,410
+Zero طيب صلى الله عليه الصلاة والسلامthen مادام
+
+744
+00:58:59,410 --> 00:59:02,450
+اللي هو ال V بتسوي ال span M، ال span M اللي هو
+
+745
+00:59:02,450 --> 00:59:06,050
+عبارة عن ال closure .. ال span لل M اللي هو ال
+
+746
+00:59:06,050 --> 00:59:09,490
+closure اللي بيسوي ال H يعني ال closure لل V بيسوي
+
+747
+00:59:09,490 --> 00:59:14,430
+ال H، من هيك بيسميه، إذا أكيد اللي هو ال V closure
+
+748
+00:59:14,430 --> 00:59:17,850
+هو ال H، لو أخدنا X في ال V closure، يعني X في ال
+
+749
+00:59:17,850 --> 00:59:21,130
+H، ماشي؟ أخدت X arbitrary element in H
+
+750
+00:59:23,950 --> 00:59:27,350
+الان X في الـ V يصار في الـ V closure مادام في الـ
+
+751
+00:59:27,350 --> 00:59:30,450
+V closure من تعريف الـ V closure إذا بقدر ألاقي
+
+752
+00:59:30,450 --> 00:59:34,390
+sequence XN of elements in mean in V such that XN
+
+753
+00:59:34,390 --> 00:59:40,450
+بيروح لمين؟ لل Xلكن أنا الآن هذي ال X طبعا هي اللي
+
+754
+00:59:40,450 --> 00:59:43,510
+في ال amygdala أسف أنا ال X هي نفس اللي في ال
+
+755
+00:59:43,510 --> 00:59:46,830
+amygdala ماشي اللي في ال amygdala أكيد و موجودة في
+
+756
+00:59:46,830 --> 00:59:50,790
+ال H الامور تجون أناسي في ال H اللي هي أكيد و
+
+757
+00:59:50,790 --> 00:59:54,760
+موجودة في ال VHفاهمين أه؟ يعني XX أخدتها في الـM
+
+758
+00:59:54,760 --> 00:59:58,180
+Orthogonal ومن ثم قلتلكم أكيد X هتكون في الـV
+
+759
+00:59:58,180 --> 01:00:02,260
+closure اللي هي في الـH إذا X نفسها بقدر أجيلها
+
+760
+01:00:02,260 --> 01:00:06,660
+Sequence Xn في الـV حيث Xn بتروح لمين؟ للـX لأن
+
+761
+01:00:06,660 --> 01:00:09,260
+since X element الـM closure then for all M
+
+762
+01:00:09,260 --> 01:00:12,460
+element الـM هيكون الـX و الـM إيش بتساوي؟ سفر
+
+763
+01:00:12,460 --> 01:00:17,300
+مدام الـX و الـM بتساوي سفر أكيد هذا بيعطيني الـX
+
+764
+01:00:17,300 --> 01:00:21,740
+و الـV برضه إيش هيساوي سفر؟ لكل V والموجودة في
+
+765
+01:00:21,740 --> 01:00:31,760
+الـVأسهل هذه عارفين ليش؟ فإنه عندي ال Vمزامة في
+
+766
+01:00:31,760 --> 01:00:40,580
+الـ V يعني الإسبان للـ N كيف شكلها؟ V بساوي Alpha
+
+767
+01:00:40,580 --> 01:00:48,140
+1 X 1 زائد Alpha N في X من الـ N مش V في الإسبان
+
+768
+01:00:48,140 --> 01:00:52,280
+كيف يكون V في الإسبان؟ عبارة عن Linear Combination
+
+769
+01:00:52,280 --> 01:00:54,780
+من الإنسبان في الـ N finite number of Linear
+
+770
+01:00:54,780 --> 01:01:00,210
+Combinations إذا بيصير عند الـ Nالـ X و الـ V
+
+771
+01:01:00,210 --> 01:01:06,770
+بيساوي لإن أنا قلتلك تبحكي عن الـ X و Alpha 1 X 1
+
+772
+01:01:06,770 --> 01:01:13,570
+زائد Alpha N X N صح ولا لأ؟ و يساوي Alpha 1 في X و
+
+773
+01:01:13,570 --> 01:01:19,830
+X 1 زائد لما أصل الأخر واحدة Alpha N في X و X N و
+
+774
+01:01:19,830 --> 01:01:22,810
+الآن الـ X 1 و الـ X 2 و الـ X N One هى الموجودات
+
+775
+01:01:22,810 --> 01:01:29,690
+كلها من الأمام مظبوط؟الـ V في الـ Span يعني V
+
+776
+01:01:29,690 --> 01:01:32,870
+Linear Combination من عناصر الـ M يعني الـ X1 و X2
+
+777
+01:01:32,870 --> 01:01:36,750
+و XN كلها من وين جوا من الـ M و أنا عمالي بقول X
+
+778
+01:01:36,750 --> 01:01:39,230
+وين موجودة في الـ M Orthogonal فما انها موجودة في
+
+779
+01:01:39,230 --> 01:01:41,790
+الـ M Orthogonal إذا الـ X و أي element في الـ M
+
+780
+01:01:41,790 --> 01:01:51,820
+صفر إذا هذا حيث سوى صفروهذا صحيح صحيح صحيح صحيح
+
+781
+01:01:51,820 --> 01:02:04,680
+صحيح صحيح صحيح صحيح صحيح
+
+782
+01:02:09,190 --> 01:02:12,770
+طيب ما احنا قلنا الـ xn من وين جاية sequence of
+
+783
+01:02:12,770 --> 01:02:16,830
+limits من مين في الـ V إذا ال inner product بين ال
+
+784
+01:02:16,830 --> 01:02:23,070
+X و ال Xn حيث أو Zero لكل N لإن هدولة من وين جاية
+
+785
+01:02:23,070 --> 01:02:26,710
+من مين الان by the continuity of inner product
+
+786
+01:02:26,710 --> 01:02:31,270
+بندخل ال limit على هذه ماشي الحال عند ال X و ال Xn
+
+787
+01:02:31,270 --> 01:02:37,210
+بتروح لمين لل X و ال X من هنا لكن هدولة كلها أسفار
+
+788
+01:02:38,010 --> 01:02:42,150
+إذا ال limit هنا صفر إذا هذه هتكون إيش؟ صفر إذا ال
+
+789
+01:02:42,150 --> 01:02:46,070
+X وال X هتساوي صفر ومنها ال X بتساوي صفر ومن ثم ال
+
+790
+01:02:46,070 --> 01:02:48,710
+X اللي بدأنا فيها في ال M Orthogonal طلعت Zero إذا
+
+791
+01:02:48,710 --> 01:02:52,090
+ال M Orthogonal بتساوي صفر نيجي لآخر نقطة
+
+792
+01:02:52,090 --> 01:02:56,250
+conversely suppose that أن ال M Orthogonal بتساوي
+
+793
+01:02:56,250 --> 01:03:02,390
+Zero element بس ماشي بس فيها Zeroالان ال M subset
+
+794
+01:03:02,390 --> 01:03:07,830
+من ال V closure أكيد لأن ال V حبارة عن من؟ عن
+
+795
+01:03:07,830 --> 01:03:11,730
+الإسبان و ال M subset من .. اللي هي من؟ اللي هو
+
+796
+01:03:11,730 --> 01:03:17,330
+الإسبان إذا الان بما أن M subset من V closure إذا
+
+797
+01:03:17,330 --> 01:03:20,090
+ال V closure orthogonal subset من مين؟ من ال M
+
+798
+01:03:20,090 --> 01:03:23,530
+orthogonal يعني لو كانت عندي على جهة هذه ال A
+
+799
+01:03:23,530 --> 01:03:28,920
+subset من ال Bهيعطينا الـ B Orthogonal subset من
+
+800
+01:03:28,920 --> 01:03:31,500
+مين؟ من ايه ال Orthogonal؟ ال Orthogonal ده سهل
+
+801
+01:03:31,500 --> 01:03:36,920
+خدوا .. عشان .. هذه تؤدي لهذه خدوا X هنا X في ال
+
+802
+01:03:36,920 --> 01:03:41,700
+.. او B خلينا ناخد X في مين في الـ B Orthogonal
+
+803
+01:03:41,700 --> 01:03:47,020
+إيش معناته هذا؟ هذا بيعطينا ال X والـ B بساوة 0
+
+804
+01:03:47,020 --> 01:03:52,140
+لكل بيوة موجودة في الـ Bطيب مدام ال inner product
+
+805
+01:03:52,140 --> 01:03:55,920
+بين X و ال B موجودة بساوي 0 لكل B في ال A إذا أكيد
+
+806
+01:03:55,920 --> 01:04:01,000
+في الجزئية منها بيكون صحيح إذا هذا بيعطينا X و B
+
+807
+01:04:01,000 --> 01:04:07,160
+بساوي 0 لكل B والموجودة في الآية لأنه إذا بنفعلها
+
+808
+01:04:07,160 --> 01:04:10,400
+كل اللي هي أنا أكيد بنفعلها الجزء منهم وهذا إيش
+
+809
+01:04:10,400 --> 01:04:14,820
+معناته؟ هذا معناته إن X element in A Orthogonal
+
+810
+01:04:21,300 --> 01:04:28,580
+بما أنه زي ما قلنام جزئية من الـV closure إذا
+
+811
+01:04:28,580 --> 01:04:31,940
+الـorthogonal لهذه جزئية من الـorthogonal لهذه إذا
+
+812
+01:04:31,940 --> 01:04:34,760
+صارت ال .. اللي هي V closure orthogonal subset من
+
+813
+01:04:34,760 --> 01:04:38,220
+M orthogonal اللي هي إيش بتساوي؟ سفر إذا صارت الـV
+
+814
+01:04:38,220 --> 01:04:41,840
+closure orthogonal بتساوي Zero إذا by theorem
+
+815
+01:04:41,840 --> 01:04:45,940
+تلاتة تلاتة أربعة إحنا عارفين إن الـH إيش بتساوي؟
+
+816
+01:04:45,940 --> 01:04:48,480
+V closure ليش أخدت الـV closure عشان أضمنها
+
+817
+01:04:48,480 --> 01:04:54,160
+closed؟V closure زائد V closure orthogonal هذه سفر
+
+818
+01:04:54,160 --> 01:04:58,020
+إذا V closure زائد ال zero element هتطلع مين ال V
+
+819
+01:04:58,020 --> 01:05:01,640
+closure إذا H هتطلع ايش بتساوي V closure يعني صارت
+
+820
+01:05:01,640 --> 01:05:06,840
+ال V نفسها dense in H وبارك الله فيكم وإلى لقاء
+
+821
+01:05:06,840 --> 01:05:07,300
+آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/yv5MMmcmY8k.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/yv5MMmcmY8k.srt
new file mode 100644
index 0000000000000000000000000000000000000000..30b9417bd306f7a1c598fc95c0722d444da298ea
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/yv5MMmcmY8k.srt
@@ -0,0 +1,2039 @@
+1
+00:00:05,230 --> 00:00:08,170
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,170 --> 00:00:10,790
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:10,790 --> 00:00:16,990
+أهله وصحبه أجمعين هذه المحاضرة رقم 31 مساق تحليل 
+
+4
+00:00:16,990 --> 00:00:19,630
+الاقتران أو تحليل جالي لطلاب وطالبات الجامعة
+
+5
+00:00:19,630 --> 00:00:24,950
+الإسلامية قسم الرياضيات  الـMagisterium الآن وصلنا
+
+6
+00:00:24,950 --> 00:00:29,890
+لعند اللي هي أربعة سبعة وهي تحت عنوان Category 
+
+7
+00:00:29,890 --> 00:00:32,930
+Theorem and Uniform Boundedness Theorem وهذه 
+
+8
+00:00:32,930 --> 00:00:35,610
+النظرية الأساسية الثانية بعد الـBanach Theorem
+
+9
+00:00:35,610 --> 00:00:40,090
+اللي هي التحليل 
+
+10
+00:00:40,090 --> 00:00:46,700
+الدوال عشان نصلها بدنا نبرهن الـRare Category 
+
+11
+00:00:46,700 --> 00:00:51,580
+Theorem وبدنا نعرف بعض التعريفات اللي هي طوبولوجية
+
+12
+00:00:51,580 --> 00:00:57,360
+ومن ثم نصلها اللي هي نظريتنا a subset M of a
+
+13
+00:00:57,360 --> 00:01:01,960
+metric space X is said to be واحدة بلان بنسمي الـ
+
+14
+00:01:01,960 --> 00:01:08,030
+M مجموعة جزئية من X أنَّها rare or nowhere dense rare
+
+15
+00:01:08,030 --> 00:01:12,250
+أو nowhere dense if الـM Closure إليها has no
+
+16
+00:01:12,250 --> 00:01:16,490
+interior point يعني بمعنى آخر إنه الـM Closure 
+
+17
+00:01:16,490 --> 00:01:23,970
+interior بتساوي فاي فهذه الحملة بنسمي الـM is rare 
+
+18
+00:01:23,970 --> 00:01:32,920
+is rare أو nowhere dense طيب الآن بنسمي اللي هو الـ
+
+19
+00:01:32,920 --> 00:01:41,320
+M is meager أو of first category in X if M is the
+
+20
+00:01:41,320 --> 00:01:46,180
+union of countably many sets each of which is rare
+
+21
+00:01:46,180 --> 00:01:57,410
+يعني بنسمي الـ  هو الآن الـsubset M is meager
+
+22
+00:01:57,410 --> 00:02:02,050
+in X إذا كنا نكتب الـM as a union أو countable
+
+23
+00:02:02,050 --> 00:02:06,910
+union of A I مثلاً I من عند واحد لعنده اللي هو
+
+24
+00:02:06,910 --> 00:02:11,510
+معناه نهاية countable union Each of which كل واحدة
+
+25
+00:02:11,510 --> 00:02:15,310
+من هدول ايش ما لها is rare يعني ايش ما لها كل 
+
+26
+00:02:15,310 --> 00:02:18,670
+واحدة من هدول اللي هو الـClosure لها interior 
+
+27
+00:02:18,670 --> 00:02:22,910
+بيساوي ايش بيساوي فاي يعني contains no open balls
+
+28
+00:02:23,490 --> 00:02:29,050
+يعني هذه معناته أن الـM Closure contains no open
+
+29
+00:02:29,050 --> 00:02:31,310
+balls لأن لو احتوت open balls معناته الـM 
+
+30
+00:02:31,310 --> 00:02:35,010
+interior يشملها الـClosure اللي الـInterior بيساوي ايش
+
+31
+00:02:35,010 --> 00:02:39,490
+في فاي طيب إلى الـNon-meager or of the second
+
+32
+00:02:39,490 --> 00:02:44,070
+category هذه of first category Non-meager or of the
+
+33
+00:02:44,070 --> 00:02:49,170
+second category in X إذا كانت مش Meager أو مش First
+
+34
+00:02:49,170 --> 00:02:52,870
+Category إذا الـSecond Category ما هي إلا نفي مين
+
+35
+00:02:52,870 --> 00:02:57,330
+للـFirst Category حلو  تقولنا Free Definitions بس حيث 
+
+36
+00:02:57,330 --> 00:03:03,460
+يلزمنك أدوات للوصول للي بدناها اطلع لفوق عنوان
+
+37
+00:03:03,460 --> 00:03:07,220
+الـBaire Category Theorem ما بتقول إذا metric
+
+38
+00:03:07,220 --> 00:03:10,820
+space X  لاتساوي  Y is complete إذا الـMetric Space
+
+39
+00:03:10,820 --> 00:03:15,340
+is complete إذا كان الـMetric Space X is complete
+
+40
+00:03:15,340 --> 00:03:22,040
+then it is Non-meager in itself يعني هيكون الـX الـ
+
+41
+00:03:22,040 --> 00:03:28,590
+Complete Space مش Meager في نفسه هنس اوتوماتيك إذا 
+
+42
+00:03:28,590 --> 00:03:32,510
+كانت اللي هو a Non-meager in itself if x لتساوي فيه
+
+43
+00:03:32,510 --> 00:03:36,870
+is complete and x بيساوي لينو للـ A K و A K is a 
+
+44
+00:03:36,870 --> 00:03:41,070
+closed for all k then at least one a k contains a
+
+45
+00:03:41,070 --> 00:03:44,690
+Non-empty subset اللي هو الجزء الثاني هذا سهل 
+
+46
+00:03:44,690 --> 00:03:49,250
+الآن بنقول الآن إذا كانت الـX لتساوي فيه complete
+
+47
+00:03:52,020 --> 00:03:56,240
+ماشي إذا ايه ايش ما هي اللي هتقول Non-meager مدام 
+
+48
+00:03:56,240 --> 00:04:00,900
+Non-meager إذا اللي هي can't be written as a
+
+49
+00:04:00,900 --> 00:04:05,300
+countable union of rare sets يعني في على الأقل
+
+50
+00:04:05,300 --> 00:04:09,480
+واحدة من هدول مش rare ايش يعني؟ يعني لو كان عندي
+
+51
+00:04:09,480 --> 00:04:12,840
+يعني خلّيني أقول لو كان عندي الـUnion للـAK X 
+
+52
+00:04:12,840 --> 00:04:15,720
+بيساوي الـUnion لـAK K من واحد لإنفينيتي وكل واحدة
+
+53
+00:04:15,720 --> 00:04:20,110
+فيه Closed إذا أكيد هذا مش rare واحدة من هنا على
+
+54
+00:04:20,110 --> 00:04:22,710
+الأقل مش rare ايش معناته واحدة من هنا مش rare يعني
+
+55
+00:04:22,710 --> 00:04:27,530
+الـAK Closure إلها Interior بيساوي ايش في يعني بمعنى 
+
+56
+00:04:27,530 --> 00:04:32,210
+الـAK Closure Interior واحدة من هنا على الأقل لا 
+
+57
+00:04:32,210 --> 00:04:38,230
+تساوي فاي بمعنى إنه AK Interior لا يساوي فاي لإنه
+
+58
+00:04:38,230 --> 00:04:41,670
+Closed احنا بنحكي عنه Closed يعني بمعنى آخر إنه الـ
+
+59
+00:04:41,670 --> 00:04:50,130
+AK contains open set فيها بس هذا اللي هو الجزء هذا 
+
+60
+00:04:50,130 --> 00:04:55,030
+لو برهنا اللي فوق هذا الجزء هذا لو برهنا اللي فوق 
+
+61
+00:04:55,030 --> 00:05:00,990
+إذا انطلنا برهين مين اللي فوق الآن Suppose that the
+
+62
+00:05:00,990 --> 00:05:04,250
+complete metric space X لتساوي فيه is not meager
+
+63
+00:05:04,250 --> 00:05:08,310
+is meager اصل الان طولوا رحكم عليها بنفرض أنه ايش 
+
+64
+00:05:08,310 --> 00:05:13,270
+معنى العكس أن X لتساوي فيه is meager in itself ايش 
+
+65
+00:05:13,270 --> 00:05:19,230
+معنى Meager then X بتساوي الـUnion خليني عشان نكتب 
+
+66
+00:05:19,230 --> 00:05:24,410
+هنا نرخص ما بنحصل عليه عشان نشوف كيف بنحصل على الـ
+
+67
+00:05:24,410 --> 00:05:28,250
+contradiction الآن
+
+68
+00:05:29,160 --> 00:05:32,860
+ثم X بيساوي الـUnion لـMK كام من واحد إلى مناهية
+
+69
+00:05:32,860 --> 00:05:36,740
+with each MK ازاي ايش؟ ايش rare؟ حيكون كل واحدة من
+
+70
+00:05:36,740 --> 00:05:41,960
+هنا إشمالها rare in X إذا بمعنى آخر الآن M Closure
+
+71
+00:05:41,960 --> 00:05:49,320
+واحد Interior إشماله بيساوي فاي الآن واحدة واحدة 
+
+72
+00:05:49,320 --> 00:05:53,900
+that means أن M1 Closure does not contain a non
+
+73
+00:05:53,900 --> 00:05:59,690
+-empty open sets مافيش فيها non-empty open sets But
+
+74
+00:05:59,690 --> 00:06:04,630
+X does But X ايش؟ Does إذا X نفسها احنا open set
+
+75
+00:06:04,630 --> 00:06:09,350
+إذا بتحتوي في داخلها عليا شمالها على open sets for
+
+76
+00:06:09,350 --> 00:06:14,410
+example X itself وممكن غيرها So that أم واحد
+
+77
+00:06:14,410 --> 00:06:19,980
+Closure مش هي الـX أكيد أكيد لأن هذي rare وهذه مش 
+
+78
+00:06:19,980 --> 00:06:24,580
+rare hence اللي هو الـComplement للـM1 Closure
+
+79
+00:06:24,580 --> 00:06:29,280
+اللي بيساوي X minus M1 Closure فيها نقاط لا تساوي 
+
+80
+00:06:29,280 --> 00:06:35,450
+فاي في نفس الوقت open ماشي هذه Closed مكملتها open 
+
+81
+00:06:35,450 --> 00:06:39,090
+ماشي الحال إذا هذه open و let's say if I is an
+
+82
+00:06:39,090 --> 00:06:44,830
+empty and open set so we can choose B ايش مالها 
+
+83
+00:06:44,830 --> 00:06:49,970
+إذا بنقدر نلاقي بي واحد element الـComplement للأم
+
+84
+00:06:49,970 --> 00:06:56,450
+واحد Closure ماشي نقدر نقدر نلاقي بي واحد ماشي and
+
+85
+00:06:56,450 --> 00:07:00,490
+an open ball about it و open ball كمان بيقدر نجي
+
+86
+00:07:00,490 --> 00:07:07,190
+about it خلّينا نسمي بي واحد بساوة بي of بي واحد و
+
+87
+00:07:07,190 --> 00:07:11,150
+إبسلون واحد هذه الـOpen Ball اللي وجناها حوالين الـ
+
+88
+00:07:11,150 --> 00:07:16,330
+بي واحد و جواها كده دي مظبوط؟ فاهمين عليها؟ اللي 
+
+89
+00:07:16,330 --> 00:07:24,470
+هي subset من الـ Knot M واحد Closure و أنا بقدر 
+
+90
+00:07:24,470 --> 00:07:28,170
+أزغيرها زي ما بدي بقدر أخد الـ Y واحد إشماله
+
+91
+00:07:28,170 --> 00:07:36,730
+أصغر من مين؟ من النص واضح هاه؟ طيب الآن since M2
+
+92
+00:07:36,730 --> 00:07:40,590
+is not nowhere dense ما هي زيها M2 is not nowhere dense، rare
+
+93
+00:07:40,590 --> 00:07:46,110
+يعني إذا أكيد الـM2 Closure does not contain a
+
+94
+00:07:46,110 --> 00:07:50,530
+non-empty open set تطلع على فوق برضه الـM2
+
+95
+00:07:50,530 --> 00:07:54,870
+Closure مابتحتويش open set إذا مش هتحتوي هذه
+
+96
+00:08:01,950 --> 00:08:06,570
+الـM2 is nowhere dense يعني غير موجود يعني بمعنى
+
+97
+00:08:06,570 --> 00:08:10,930
+آخر M2 Closure Interior بيساوي فاي معناته M2
+
+98
+00:08:10,930 --> 00:08:15,510
+Closure does not contain any open any non M2 open
+
+99
+00:08:15,510 --> 00:08:23,010
+set بالتالي B of B واحد و نص Y واحد ليس مجموعة من
+
+100
+00:08:23,010 --> 00:08:25,010
+ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة
+
+101
+00:08:25,010 --> 00:08:26,530
+ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة
+
+102
+00:08:26,530 --> 00:08:30,210
+ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة
+
+103
+00:08:30,210 --> 00:08:32,910
+ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة
+
+104
+00:08:32,910 --> 00:08:33,350
+ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة
+
+105
+00:08:33,350 --> 00:08:35,030
+ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة
+
+106
+00:08:35,030 --> 00:08:41,630
+ميان M2 مجموعة
+
+107
+00:08:41,630 --> 00:08:45,770
+مجموعة So we can choose B2 من مين من التقاطع إذا
+
+108
+00:08:45,770 --> 00:08:50,730
+بقدر ألاقي B2 من الموجودة B2 element in M2 Closure
+
+109
+00:08:50,730 --> 00:08:57,850
+Complement تقاطع اللي هو B of B1 و نص إبسلون واحد 
+
+110
+00:08:57,850 --> 00:09:06,610
+طيب and an open ball about it أكيد مدام هدولة open
+
+111
+00:09:07,460 --> 00:09:10,940
+و بي اتنين فيهم إذا بقدر لاجي open ball حوالين هذه
+
+112
+00:09:10,940 --> 00:09:17,620
+جوات هذه إذا سميها بي اتنين بي بي اتنين و إبسلون
+
+113
+00:09:17,620 --> 00:09:20,940
+اتنين Subset من مين من M اتنين الـClosure الـ
+
+114
+00:09:20,940 --> 00:09:24,800
+Complement لها تقاطع بي واحد بي بي واحد و نص 
+
+115
+00:09:24,800 --> 00:09:28,900
+إبسلون و اختار للإبسلون اتنين أصغر من مين من نص
+
+116
+00:09:28,900 --> 00:09:31,900
+إبسلون واحد طبعا نص إبسلون واحد ربع إبسلون واحد
+
+117
+00:09:31,900 --> 00:09:36,010
+عشان بيداخل حاجة Convergence بس الآن by induction
+
+118
+00:09:36,010 --> 00:09:40,430
+بقدر أكملها لأن احنا بنعرف الام واحد و الام اتنين
+
+119
+00:09:40,430 --> 00:09:44,290
+و الام تلاتة كلهن where و كلهن اللي سوناه على الام
+
+120
+00:09:44,290 --> 00:09:47,670
+واحد و الام اتنين بقدر أسويه على الباقية إذا by
+
+121
+00:09:47,670 --> 00:09:54,230
+induction we obtain a sequence of balls بك بساوي بك
+
+122
+00:09:54,230 --> 00:09:58,410
+إبسلون كه والإبسلون كه أخدتها أول واحد أصغر من 
+
+123
+00:09:58,410 --> 00:10:01,550
+إبسلون والتاني أصغر من نصها والتالت أصغر من نصها
+
+124
+00:10:01,550 --> 00:10:04,970
+ورابع إذا أكيد حاجة حصل على إبسلون كه أصغر من مين 
+
+125
+00:10:04,970 --> 00:10:10,150
+من اتنين أس minus كه وبحيث انه كل مرة باخد الـبك
+
+126
+00:10:10,150 --> 00:10:15,190
+زاد واحد جزئية من مين من اللي هي اللي جابلها بك نص 
+
+127
+00:10:15,190 --> 00:10:20,100
+إبسلون كه وهذه جزئية من مين اللي سميتها بك الآن و 
+
+128
+00:10:20,100 --> 00:10:25,520
+Epsilon K أصغر من مين؟ من 2 to the minus K إذا
+
+129
+00:10:25,520 --> 00:10:29,960
+بيصير عنده الآن المسافة بين أي بي ك و بي ك زائد
+
+130
+00:10:29,960 --> 00:10:37,260
+واحد اللي هو بيكون أصغر من اللي هو كل مرة أصغر من 
+
+131
+00:10:37,260 --> 00:10:39,700
+اللي هي الـEpsilon تبعته أصغر من الـEpsilon تبعته
+
+132
+00:10:39,700 --> 00:10:44,120
+إذا كل واحدة من هذول أصغر من 2 to the minus K الآن
+
+133
+00:10:44,120 --> 00:10:47,720
+بين bk و bk زائد واحد أصغر من two تقريبا minus k الـ
+
+134
+00:10:47,720 --> 00:10:50,480
+Summation اللي من k من واحد إلى نهاية أصغر شهو مين
+
+135
+00:10:50,480 --> 00:10:53,920
+الـSummation من سفر إلى مين إلى مانا نهاية صار 
+
+136
+00:10:53,920 --> 00:10:57,560
+عندي أنا Sequence من الـ Bees بي واحد و بي اتنين و
+
+137
+00:10:57,560 --> 00:11:02,600
+بي تلاتة و بي أربعة إلى آخره كل مرة اللي هو بديب
+
+138
+00:11:02,600 --> 00:11:05,480
+أكتر و بيصير كله موجودات في آخر واحدة موجودة فيهم
+
+139
+00:11:05,920 --> 00:11:10,200
+الآنفة بيصير ND اللي هو المسافات بينهم مجامع كل
+
+140
+00:11:10,200 --> 00:11:14,640
+واحدة أصغر من 2 إلى الأولى بين B1 وB2 أصغر من 2
+
+141
+00:11:14,640 --> 00:11:20,460
+إلى minus 1 بين B2 وB3 من 2 إلى minus 2 بين B4 وB5
+
+142
+00:11:20,460 --> 00:11:24,340
+إلى آخره إذا صار اللي هنا أصغر من الصفر إلى 2
+
+143
+00:11:24,340 --> 00:11:27,930
+إلى minus K الآن هذا convergence إذا قطعاً هذا
+
+144
+00:11:27,930 --> 00:11:32,310
+إشماله convergence صار إذا عندي sequence of
+
+145
+00:11:32,310 --> 00:11:36,150
+elements BK كوشي sequence in the complete metric
+
+146
+00:11:36,150 --> 00:11:40,760
+space X والـ Cauchy Sequence أكيد هتكون إيه إشمالها 
+
+147
+00:11:40,760 --> 00:11:45,820
+So it converges to limit BK إيش بيساوي B element in
+
+148
+00:11:45,820 --> 00:11:50,280
+X يعني الآن الـ Sequence هذه صارت Cauchy Sequence
+
+149
+00:11:50,280 --> 00:11:54,280
+في الـ
+
+150
+00:11:54,280 --> 00:11:58,420
+Complete Space X إذا أكيد هذه هتكون converges BK to
+
+151
+00:11:58,420 --> 00:12:03,220
+some element سميه مين؟ سميه B والـ B هتكون وموجودة
+
+152
+00:12:03,220 --> 00:12:09,280
+في الـ X تشوف الآن إذاً بي وان موجود في ال X الآن
+
+153
+00:12:09,280 --> 00:12:15,540
+اطلع لفوق بدي أوصل لك لإن بي مش في ال X اه ويصير
+
+154
+00:12:15,540 --> 00:12:20,940
+Contradiction شوف كده Also for all M and all N
+
+155
+00:12:20,940 --> 00:12:28,780
+أكبر من M we have ال بي and الأمات الصغيرة الـ Bm
+
+156
+00:12:28,780 --> 00:12:32,360
+كل ما كبرت الـ M إشمالها بتصغر الـ B الـ ball مش
+
+157
+00:12:32,360 --> 00:12:35,900
+أنا كل مرة بزغر ال ball فبتصير الـ Bm subset من ال
+
+158
+00:12:35,900 --> 00:12:40,520
+ball اللي بعدها اللي نقطتها مركزها بيبقى BM ونصف
+
+159
+00:12:40,520 --> 00:12:47,380
+قطرها نصف في EM إذا صارت المسافة بين BM و B أصغر أو
+
+160
+00:12:47,380 --> 00:12:56,900
+يساوي BM و BN و BM و B والمسافة بين BM و BN أصغر
+
+161
+00:12:56,900 --> 00:12:59,620
+من مين؟ من نفس N لأن هذه جزئية من مين؟ من التانية
+
+162
+00:12:59,620 --> 00:13:03,280
+اللي هنا فاضي فبصير عنده اللي هو المسافة أصغر من
+
+163
+00:13:03,280 --> 00:13:08,050
+مين؟ من أكيد من الصغيرة من الكبيرة مش الـ N هذه BM
+
+164
+00:13:08,050 --> 00:13:13,390
+BM موجودة هنا و BM أصلاً موجودة هنا لذا صارت ال BM
+
+165
+00:13:13,390 --> 00:13:17,330
+والـ BM فاضي على الأقل ماشي والمسافة بين أي نقطتين
+
+166
+00:13:17,330 --> 00:13:21,210
+فيه أصغر من مين؟ من نصف EM لذا صار عندي هذه المسافة
+
+167
+00:13:21,210 --> 00:13:27,890
+أصغر من نصف EM وهذه زائد D BN OB لأن هذه صارت أصغر
+
+168
+00:13:27,890 --> 00:13:31,090
+أو يساوي هذا المقدار وأنا ماخذ ال M أكبر من M
+
+169
+00:13:31,090 --> 00:13:34,130
+بطير ال M إلى ما لا نهاية زي ما بده وال M بتلغى
+
+170
+00:13:34,130 --> 00:13:38,130
+بيعدي زي ما هي إذا as M goes to infinity اللي هم
+
+171
+00:13:38,130 --> 00:13:44,650
+بيصير عندي المسافة بين ال B M والـ B هذي بتروح
+
+172
+00:13:44,650 --> 00:13:49,190
+للصفر لأن as n goes to infinity بيشهر بجد سير بسير
+
+173
+00:13:49,190 --> 00:13:54,170
+فيه بيه هاد ال bm والـ b بتروح لمين؟ للصفر فاهمين
+
+174
+00:13:54,170 --> 00:13:58,130
+اللي بحكيه؟ الآن هاد بتظل عند as n goes to
+
+175
+00:13:58,130 --> 00:14:01,690
+infinity ال distance بين ال bm والـ b أصغر من نصف
+
+176
+00:14:01,690 --> 00:14:05,570
+ال EM لأن هاد راح لمين؟ للصفر الآن هذا إيش معناه؟
+
+177
+00:14:05,570 --> 00:14:09,570
+أن المسافة بين ال bm والـ b أصغر من نصف ال EM؟
+
+178
+00:14:09,910 --> 00:14:14,790
+معناته أن الـ B موجودة في الـ BM لأن المسافة بين
+
+179
+00:14:14,790 --> 00:14:19,030
+الـ BM والـ B أصغر من نصف EM هذا المركز وهذا نصف
+
+180
+00:14:19,030 --> 00:14:22,850
+القطر إذن في الـ Bolt بيتهم إذا صارت الـ B موجودة
+
+181
+00:14:22,850 --> 00:14:28,810
+في الـ BM for all M إذا وعندي الـ BM جزئية من مين؟
+
+182
+00:14:28,810 --> 00:14:32,350
+من الـ complement في التركيبة كنت أخد الـ BM جزئية
+
+183
+00:14:32,350 --> 00:14:38,300
+من مين؟ هي rare جزء من هذه then B is not element in
+
+184
+00:14:38,300 --> 00:14:44,640
+main in اللي هو جزئية من وين؟ من مكملتها إذا أكيد
+
+185
+00:14:44,640 --> 00:14:47,420
+مش موجودة في الام أم إذا مش موجودة في الام أم
+
+186
+00:14:47,420 --> 00:14:53,370
+مكلوجر إذا مش موجودة في الـ MM إذا صارت عندي الـB مش
+
+187
+00:14:53,370 --> 00:14:57,250
+موجودة فيها طب ما هي مدام مش موجودة فيهن كلهن إذا
+
+188
+00:14:57,250 --> 00:15:00,650
+مش موجودة في ال union وال union هو ال X إذا صارت
+
+189
+00:15:00,650 --> 00:15:04,930
+ال B مش موجودة في من؟ في ال X وهذا معناه صار في
+
+190
+00:15:04,930 --> 00:15:08,330
+عندي contradiction لأن ال B من ال X إذا نفس ال X
+
+191
+00:15:08,330 --> 00:15:11,810
+هتصير إذا ما الفرضية الأولى اللي فرضناها مش صحيحة
+
+192
+00:15:11,810 --> 00:15:14,270
+إذا ال X must be non major
+
+193
+00:15:19,430 --> 00:15:24,550
+يلا لبعدها الـ Uniform Boundedness Theorem هي
+
+194
+00:15:24,550 --> 00:15:27,850
+النظرية اللي بنحكي عنها الأساسية التانية وألطف
+
+195
+00:15:27,850 --> 00:15:35,790
+برهانها من الأولى خلينا نشوف أيش اللي بتقوله اللي
+
+196
+00:15:35,790 --> 00:15:42,370
+بتقوله النظرية انه Uniform Boundedness Theorem
+
+197
+00:15:42,370 --> 00:15:47,670
+نشوف كيف let TN be a sequence of bounded linear
+
+198
+00:15:47,670 --> 00:15:52,530
+operators TN هي Sequence of Bounded Linear
+
+199
+00:15:52,530 --> 00:16:01,470
+Operators من بنخ X إلى بنخ Y من بنخ X إلى بنخ Y
+
+200
+00:16:04,690 --> 00:16:10,030
+Such that norm of TN is bounded for every X
+
+201
+00:16:10,030 --> 00:16:10,750
+element in X
+
+202
+00:16:23,660 --> 00:16:29,020
+اللي هي لكل X فيه الـ H ياش اللي هي بتجيلها ثابت
+
+203
+00:16:29,020 --> 00:16:33,660
+يعملها bound ثابت يعملها bound يعني بمعنى آخر TNX1
+
+204
+00:16:33,660 --> 00:16:40,080
+بتجيلها CX1 TNX2 بتجيلها CX2 TNX3 بتجيلها CX3 ماشي
+
+205
+00:16:40,080 --> 00:16:44,020
+الحال هذا اللي هو ياش ماله المُعطى بيقول لو كانت
+
+206
+00:16:44,020 --> 00:16:48,080
+ال sequence هذه تتمتع بالخاصية هذه بيقول لك الآن
+
+207
+00:16:48,770 --> 00:16:53,750
+بما انه هذه sequence of bounded اللي هي بالشكل هذا
+
+208
+00:16:53,750 --> 00:16:58,650
+وكانت من بنخ space ل Y اللي هو normed space أنا
+
+209
+00:16:58,650 --> 00:17:03,230
+بضمن لك الآن قوة النظرية بقول لك أنا بضمن لك أن ال
+
+210
+00:17:03,230 --> 00:17:06,070
+sequence هذا يكون ال boundedness uniform يعني لا
+
+211
+00:17:06,070 --> 00:17:09,190
+يعتمد على مين؟ على ال X عشان هي اسمها uniform
+
+212
+00:17:09,190 --> 00:17:12,280
+boundedness theorem uniform boundedness هذا يعني
+
+213
+00:17:12,280 --> 00:17:15,660
+بمعنى آخر بقدر ألاقي C بتنفع لكل شيء يعني norm ال
+
+214
+00:17:15,660 --> 00:17:20,900
+TN أصغر أو يساوي C لكل اللي هي ال Xات بغض النظر
+
+215
+00:17:20,900 --> 00:17:24,700
+يعني بل بقول لك norm ال TN نفسه أصغر أو يساوي مين؟
+
+216
+00:17:24,700 --> 00:17:29,480
+أصغر أو يساوي C لأنه لما نلاقي norm ال TN X أصغر أو
+
+217
+00:17:29,480 --> 00:17:32,740
+يساوي C في norm ال X خلاص على norm ال X بطلع norm
+
+218
+00:17:32,740 --> 00:17:38,280
+ال TN أصغر أو يساوي مين؟ some constant C نأتي الآن
+
+219
+00:17:38,280 --> 00:17:48,640
+لنثبت هذا اللي هو اتنين أكيد
+
+220
+00:17:48,640 --> 00:17:51,720
+بستخدم الكتاب البركاتو كوريو تيريم ولا ليش أصلاً
+
+221
+00:17:51,720 --> 00:17:59,880
+نثبتها and x is complete مظبوط؟ اه طيب for every k
+
+222
+00:17:59,880 --> 00:18:04,010
+element لانخليني أحضر بس سؤال برهان Let A K
+
+223
+00:18:04,010 --> 00:18:08,450
+subset من X أشهى A K be the set of all X such that
+
+224
+00:18:08,450 --> 00:18:12,750
+T N X أصغر شهو K for all N يعني بمعنى آخر خليني
+
+225
+00:18:12,750 --> 00:18:20,650
+أفسر أكثر أنه لو أخذنا A 1 هي عبارة عن كل الإكسات
+
+226
+00:18:20,650 --> 00:18:29,730
+such that T 1 X أصغر أو آسف T N X أصغر أو يساوي واحد
+
+227
+00:18:29,730 --> 00:18:35,530
+لكل N element in R A2
+
+228
+00:18:35,530 --> 00:18:43,430
+بساوي اللي هو كل ال X such that TNX أصغر أو يساوي
+
+229
+00:18:43,430 --> 00:18:50,090
+اتنين لكل N element in R AK in general هي عبارة عن
+
+230
+00:18:50,090 --> 00:18:55,470
+كل ال X such that TNX أصغر أو يساوي اللي هو الـ K
+
+231
+00:18:55,470 --> 00:19:04,910
+for every N element in N ماشي الحل ال
+
+232
+00:19:04,910 --> 00:19:08,790
+TNX اللي أصغر أو يساوي واحد أكيد هيكون إيه إشماله
+
+233
+00:19:08,790 --> 00:19:13,270
+أصغر أو يساوي اثنين يعني اللي لو أخذنا element 10
+
+234
+00:19:13,270 --> 00:19:19,810
+هلاجيه automatic element 10 صح؟ فبصير عندي ال .. ال
+
+235
+00:19:19,810 --> 00:19:21,610
+.. ال .. لو أخذنا .. يعني عندنا بصير ثانية الـ X
+
+236
+00:19:21,610 --> 00:19:24,130
+أصغر أصغر شوية واحد معناه أصغر شوية اثنين معناه
+
+237
+00:19:24,130 --> 00:19:28,030
+واحد يعني واحد جزء من اثنين جزء من اثنين طيب
+
+238
+00:19:28,030 --> 00:19:34,430
+مظبوط الحاجة تقولها طيب شوفوا لأن بس عشان أتعرف
+
+239
+00:19:34,430 --> 00:19:38,210
+عليها هنا to show that a k is closed ده أنت بتقول
+
+240
+00:19:38,210 --> 00:19:40,590
+انه a k مثلاً كل واحدة فيه نقش معناه closed set
+
+241
+00:19:40,590 --> 00:19:47,870
+خذوا X في مين؟ في ال a closure اه a k closure then
+
+242
+00:19:47,870 --> 00:19:51,890
+there exists a sequence xj بدأ اثبت لكم بلق ال
+
+243
+00:19:51,890 --> 00:19:54,410
+sequence xj في ال a كي a convert the mean لل x
+
+244
+00:19:54,410 --> 00:19:59,030
+بيكون خلصنا صح؟ then there is a sequence xj of
+
+245
+00:19:59,030 --> 00:20:04,010
+elements لأ اسف لان اثبتت اللي هي ال x في ال a كي
+
+246
+00:20:04,010 --> 00:20:09,310
+أخدت في ال a كلوجة بدأ اثبتها في ال a فبصير مش هوا
+
+247
+00:20:09,310 --> 00:20:14,030
+مشاكلكم ما أنتم معايا كي باثبت أن ال a كي is
+
+248
+00:20:14,030 --> 00:20:19,340
+closed الـ AK closure بيساوي الـ A كيف بياخدها؟
+
+249
+00:20:19,340 --> 00:20:23,320
+بياخد X في الـ AK closure وأثبتها أن X في 100 في
+
+250
+00:20:23,320 --> 00:20:28,040
+الـ AK لأن العكس صحيح دائماً اه ماشي بخير إذا
+
+251
+00:20:28,040 --> 00:20:34,450
+خلينا نشوف الآن نشوف الآن خدوا x في ال a k closure
+
+252
+00:20:34,450 --> 00:20:38,510
+إذا حسب تعريف الـ x في ال a k closure بقدر ألاقي
+
+253
+00:20:38,510 --> 00:20:42,530
+sequence xj of elements in a k such that limit الـ
+
+254
+00:20:42,530 --> 00:20:45,610
+xj إيش بيساوي؟ بيساوي ال x هذا تعريف ال x والي
+
+255
+00:20:45,610 --> 00:20:49,470
+موجودة في ال a closure في ال a k closure then for
+
+256
+00:20:49,470 --> 00:20:56,570
+any fixed n we have norm Tn xj هذا ال xj هذا ال 
+
+257
+00:20:56,570 --> 00:21:01,670
+xj أصغر أو يساوي مين؟ أصغر يساوي k اه من تعريفها لأن
+
+258
+00:21:01,670 --> 00:21:04,990
+الـ X هو الموجودة في .. آسف في الـ XJ هو
+
+259
+00:21:04,990 --> 00:21:11,570
+الموجودة في الـ AK وعلاصر الـ AK إيه إشمالها؟ XJ
+
+260
+00:21:11,570 --> 00:21:18,090
+فيها إذا TN XJ أظهر فيها OK ماشي الحال شوف شوية
+
+261
+00:21:18,090 --> 00:21:20,050
+علامة ما اعرفش علاقة بال convergence إذا انتبهوا
+
+262
+00:21:20,050 --> 00:21:27,370
+الآن عندي ال XJ هدولة من وين جاية؟ من ال AK مدام
+
+263
+00:21:27,370 --> 00:21:33,660
+ال XJ في ال AK إذا تحقق شروطها إيش شروطها أن
+
+264
+00:21:33,660 --> 00:21:39,760
+يكون TN هذي ال XJ أصغر يساوي مين؟ أصغر يساوي K صح؟
+
+265
+00:21:39,760 --> 00:21:44,700
+لكل N هذا الكلام طيب إذا صار عندي TN XJ أصغر يساوي
+
+266
+00:21:44,700 --> 00:21:48,880
+K لأن by the continuity of TN كل واحدة ما هي
+
+267
+00:21:48,880 --> 00:21:52,720
+bounded linear bounded then continuous and the
+
+268
+00:21:52,720 --> 00:21:55,480
+continuity of norm ويهب يعني ما نقدر ندخل ال limit
+
+269
+00:21:55,480 --> 00:22:00,520
+وين؟ جوا norm وجوا mean ال TN فبصير عنده اللي هو
+
+270
+00:22:00,520 --> 00:22:05,100
+limit دخل جوا ودخل على ال TN ودخل جوا الآن فبصير
+
+271
+00:22:05,100 --> 00:22:09,200
+عنده TN limit XJ وlimit XJ إيش بيساوي؟ بيصير X
+
+272
+00:22:09,200 --> 00:22:13,940
+إذا صار عنده norm TN X أصغر أو شوه مين؟ أصغر أو
+
+273
+00:22:13,940 --> 00:22:18,190
+شوه كام؟ معناه هذا؟ مدام ال TN X أصغر أو يساوي
+
+274
+00:22:18,190 --> 00:22:23,050
+K هذا أحلها أن تكون دوا ال AK إذا صار عند ال X
+
+275
+00:22:23,050 --> 00:22:29,030
+في ال AK معناه صارت A K is closed لأنه
+
+276
+00:22:29,030 --> 00:22:33,430
+حسب الكلام اللي حكيته قبل شوية طيب اللي بعده for
+
+277
+00:22:33,430 --> 00:22:38,690
+every X element in X there exists CX such that
+
+278
+00:22:38,690 --> 00:22:43,830
+norm TN X أصغر أو يساوي CX for all N هذا مقطع مقطع
+
+279
+00:22:43,830 --> 00:22:49,720
+ال N هلقن then for each x element in x belongs to
+
+280
+00:22:49,720 --> 00:22:54,420
+some a k لأن احنا مسترضين ان ال X ايش بتساوي احنا
+
+281
+00:22:54,420 --> 00:23:02,200
+الـ X انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+282
+00:23:02,200 --> 00:23:02,240
+انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+283
+00:23:02,240 --> 00:23:02,920
+انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+284
+00:23:02,920 --> 00:23:05,620
+انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+285
+00:23:05,620 --> 00:23:09,280
+انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+286
+00:23:09,280 --> 00:23:09,320
+انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+287
+00:23:22,360 --> 00:23:26,480
+ماشي الحال احنا ماشي الحال هذا أثبتنا 
+
+288
+00:23:29,810 --> 00:23:34,050
+الآن الـ I X element in X belongs to مين؟ to some A K
+
+289
+00:23:34,050 --> 00:23:37,270
+من مين؟ من اللي عرفناها لأنه في الآخر هيطلع اللي
+
+290
+00:23:37,270 --> 00:23:41,990
+هو T أن الـ X الها أصغر أو يساوي some number الواحد،
+
+291
+00:23:41,990 --> 00:23:43,890
+الثاني، الثالث، ما كانش من الواحد، من الثاني، من
+
+292
+00:23:43,890 --> 00:23:46,790
+البعيد، من الثالث، من البعيد وكذا وكأن الـ X يعذرها
+
+293
+00:23:46,790 --> 00:23:51,280
+عن union مين؟ ونقدر نكتبها union للـ A K إذا صار
+
+294
+00:23:51,280 --> 00:23:55,180
+عندي الآن الـ X belongs to some A K Hence X can be
+
+295
+00:23:55,180 --> 00:23:58,080
+written as الـ union لمن؟ للـ A K كمان واحدة عند من؟
+
+296
+00:23:58,080 --> 00:24:02,520
+لما أنت منها نهاية وكل واحدة منهم شمالها اللي هو
+
+297
+00:24:02,520 --> 00:24:08,660
+عبارة عن اللي هو closed كمان مرة يا جماعة الآن أي 
+
+298
+00:24:08,660 --> 00:24:16,790
+X في الـ X لو حسبنا لها T عن Xالـ T and X لأن T and
+
+299
+00:24:16,790 --> 00:24:24,370
+X هتكون الـ X يا أنا يا أنا يا أنا يا أنا يا أنا يا أنا يا أنا
+
+300
+00:24:24,370 --> 00:24:26,430
+يا أنا يا أنا يا أنا يا أنا يا أنا يا أنا يا أنا يا أنا يا أنا
+
+301
+00:24:26,430 --> 00:24:27,550
+يا أنا يا أنا يا أنا يا أنا يا أنا يا أنا يا أنا يا أنا يا أنا
+
+302
+00:24:27,550 --> 00:24:28,130
+يا أنا يا أنا يا أنا يا أنا يا أنا يا أنا يا أنا يا أنا يا أنا
+
+303
+00:24:28,130 --> 00:24:34,810
+يا أنا يا أنا يا أنا يا أنا يا أنا يا أنا يا أنا يا أنا يا أنا
+
+304
+00:24:34,810 --> 00:24:41,790
+يا أنا
+
+305
+00:24:41,790 --> 00:24:48,280
+يا أنا حكيتها قبل بشوية أنه ما دامت اللي هي X
+
+306
+00:24:48,280 --> 00:24:53,260
+complete إذا بالـ K-Pair Category Theorem اللي
+
+307
+00:24:53,260 --> 00:24:58,240
+كتبت في آخر النظرية A Knot Contains An Open Ball
+
+308
+00:24:58,240 --> 00:25:02,220
+في واحدة من هنا على الأقل اللي فرّضتها في أول K
+
+309
+00:25:02,220 --> 00:25:05,280
+-Pair Category Theorem الجزء الثاني منها أنه ما 
+
+310
+00:25:05,280 --> 00:25:09,720
+دامت X complete و X مكتوبة على صورة Union لـ Closed
+
+311
+00:25:09,720 --> 00:25:13,790
+Set إذاً في واحدة من هنا مش rare يعني في واحدة من
+
+312
+00:25:13,790 --> 00:25:17,230
+هنا على الأقل a k note contains open ball سميناها
+
+313
+00:25:17,230 --> 00:25:21,130
+إيش اسمها a k note بعد إذنكم say اللي هي الـ open
+
+314
+00:25:21,130 --> 00:25:25,310
+ball هذه بي نوت بسوا بي إكس نوت و R جزئية من مين
+
+315
+00:25:25,310 --> 00:25:28,570
+من a k note اللي هي سميناها كنا a k note وكلها
+
+316
+00:25:28,570 --> 00:25:32,910
+جميعها نوت اللي هي close بتطلع نفسها طيب الآن اطلع
+
+317
+00:25:32,910 --> 00:25:37,850
+على فوق now let x be element in x be R literally
+
+318
+00:25:38,750 --> 00:25:44,830
+and non-zero و let z بتساوي x not زائد gamma x 
+
+319
+00:25:44,830 --> 00:25:52,590
+اللي هي x not اللي حكينا عنها فوق الآن خد gamma 
+
+320
+00:25:52,590 --> 00:25:57,060
+بتساوي R على 2 في جذر الـ X لا تساوي 0 ماشي الحال
+
+321
+00:25:57,060 --> 00:26:00,160
+يعني الجامعة ما بتديش أيها سفر اللي .. اللي أيها
+
+322
+00:26:00,160 --> 00:26:03,000
+سفر اللي هي R على 2 جدر الـ X ما بتش .. ما بتساويش سفر
+
+323
+00:26:03,000 --> 00:26:06,640
+الـ .. الـ .. الـ .. الجامعة أخي سميت هيك جامعة R على
+
+324
+00:26:06,640 --> 00:26:09,420
+2 في جدر الـ X هذه طبعاً R اللي هي الـ .. الـ ..
+
+325
+00:26:09,420 --> 00:26:12,140
+المركز اللي .. اللي .. نصف القطر مش سفر إذن هذا 
+
+326
+00:26:12,140 --> 00:26:14,300
+كله مش سفر إذا الجامعة نفسي صارت إيه أشمل أنها مش
+
+327
+00:26:14,300 --> 00:26:17,820
+سفر عشان بتكسب عليها بعد شوية أخدت Z بتساوي X نور
+
+328
+00:26:17,820 --> 00:26:21,100
+زي الجامعة X ليش هذه؟ أجيت بعد شوية بتشوف عسى
+
+329
+00:26:21,100 --> 00:26:25,460
+استخدامي أن أوصلي أنه نور الـTN 
+
+330
+00:26:26,750 --> 00:26:30,170
+أصغر أو يساوي، إيش بالنسبة للـ Gamma؟ هذي C يعني
+
+331
+00:26:30,170 --> 00:26:38,130
+هذي تنشوفكم احسبلي الآن خد الـ Z minus X naught 
+
+332
+00:26:38,130 --> 00:26:43,090
+طالعها بـ C Gamma X بصير norm of z نقص x0 بيساوي
+
+333
+00:26:43,090 --> 00:26:47,950
+norm of gamma x norm of gamma x اضرب اللي هو اللي
+
+334
+00:26:47,950 --> 00:26:51,670
+هي norm of x في الجامعة هي هذه norm of x مع norm
+
+335
+00:26:51,670 --> 00:26:55,270
+of x بيبقى همين R على اتنين R على اتنين أصغر من
+
+336
+00:26:55,270 --> 00:26:59,030
+مين من R يعني بمعنى آخر z minus x0 أصغر من R صارت
+
+337
+00:26:59,030 --> 00:27:04,510
+z في الـ ballباشي إذا hence z في b note and so z في
+
+338
+00:27:04,510 --> 00:27:09,410
+واحدة من مين من الـ a k not اللي هي لظبط هذه لأن b
+
+339
+00:27:09,410 --> 00:27:13,110
+not جزء من مين من الـ a k not إذا صارت عند الـ z هذه
+
+340
+00:27:13,110 --> 00:27:17,250
+اللي كتبتها بالصورة هذه في الـ a k not then by the
+
+341
+00:27:17,250 --> 00:27:21,130
+definition of a k not هيكون الـ T and z أصغر شهو
+
+342
+00:27:21,130 --> 00:27:26,410
+مين؟ k not هذا الكلام for all and عند الـ X note في
+
+343
+00:27:26,410 --> 00:27:31,850
+B note صبست من A K note إذا ما دام X note هنا إذا
+
+344
+00:27:31,850 --> 00:27:37,250
+هنا ما دام X note هنا إذا بتحقق خاصية أنه TN X note
+
+345
+00:27:37,250 --> 00:27:42,100
+أظهر شاومين اللي هي K note مشاكل مؤهلة تدخل في الـ
+
+346
+00:27:42,100 --> 00:27:45,900
+Knot إذا صانعين دي الـ norm الـ TN X knot برضه أصغر 
+
+347
+00:27:45,900 --> 00:27:50,480
+يساوي مين Knot و هاد الـ TN Z برضه أصغر يساوي مين
+
+348
+00:27:50,480 --> 00:27:58,120
+Knot لأن خلّينا نستخدم تلاتة و الـ X إيش بتساوي Z
+
+349
+00:27:58,120 --> 00:28:04,690
+minus X knot على Gammathen for all and لأن norm of
+
+350
+00:28:04,690 --> 00:28:08,090
+T and X لأنها الـ X كانت arbitrary والـ X note هذه 
+
+351
+00:28:08,090 --> 00:28:11,290
+اللي لجيتها اللي هي الـ bridge اللي ده صار من خلاله
+
+352
+00:28:11,290 --> 00:28:19,290
+بيصير norm of T and X بيساوي اللي هو norm الـ TN 
+
+353
+00:28:19,290 --> 00:28:23,170
+لهذه بنطلع الواحد على جامعة برا بيصير واحد على
+
+354
+00:28:23,170 --> 00:28:28,430
+جامعة لأنها موجبة في TN of Z minus X0 وهذه
+
+355
+00:28:28,430 --> 00:28:31,490
+بالتريان جالين كواليتي أصغر أو يساوي حضرتله هذا 
+
+356
+00:28:31,490 --> 00:28:38,570
+أوجدت TN Z و TN X0 أصغر أو يساوي أنه TN Z زي TN X0
+
+357
+00:28:38,570 --> 00:28:43,470
+هذه أوجدناها قبل بشوية فوق اللي هي أصغر أو يساوي
+
+358
+00:28:43,470 --> 00:28:45,710
+اللي هو 2K0
+
+359
+00:28:48,270 --> 00:28:52,490
+أوجدناها هيها أصغر يساوي كنوت وهذه أصغر يساوي مين؟ 
+
+360
+00:28:52,490 --> 00:28:57,810
+كنوت بدي أعوض مكانها صارت واحد على جامعة TNZ أصغر
+
+361
+00:28:57,810 --> 00:29:01,750
+من كنوت وهذه أصغر من كنوت التنتين أصغر من مين؟ من
+
+362
+00:29:01,750 --> 00:29:06,390
+اتنين كنوت فبصير عبارة عن اللي هو عوضه عن جامعة
+
+363
+00:29:06,390 --> 00:29:10,950
+بقيمتها اللي هي R على اتنين في الـ Normal X بصير
+
+364
+00:29:10,950 --> 00:29:15,490
+اللي هو اتنين Normal X على R لأنها مجلوبها فاهمين؟ 
+
+365
+00:29:15,940 --> 00:29:19,760
+في اتنين كينوت اتنين مع اتنين فبصير عبارة عن كينوت
+
+366
+00:29:19,760 --> 00:29:22,520
+اتنين في اتنين لأ اتنين في اتنين في أربعة بروحانش
+
+367
+00:29:22,520 --> 00:29:26,100
+مبارك اتنين في اتنين أربعة كينوت عالمين على الـ R
+
+368
+00:29:26,100 --> 00:29:35,300
+اللي هي في X يعني بصير عندي TNX TNX
+
+369
+00:29:35,300 --> 00:29:40,900
+أزرع شاوي اللي طلع عندي اتنين في اتنين أربعة على A 
+
+370
+00:29:40,900 --> 00:29:47,050
+أربعة كنوت على R فنور main الـ X خدوا الآن الـ
+
+371
+00:29:47,050 --> 00:29:51,130
+supremum إيش اسمه على هذه للـ Xات اللي مش سفر و
+
+372
+00:29:51,130 --> 00:29:56,510
+خدوا الـ supremum بيطلع هذا norm الـ TN أصغر أو يساوي
+
+373
+00:29:56,510 --> 00:30:02,710
+4k نوت على R وهذا ثابت إذا بغض النظر عن اللي هو
+
+374
+00:30:02,710 --> 00:30:07,550
+الـ TN بيطلع norm الـ TN إلهم كلهم أصغر أو يساوي 4k
+
+375
+00:30:07,550 --> 00:30:14,250
+نوت وهذا يعني T note TN أصغر يساوي C for all N حيث
+
+376
+00:30:14,250 --> 00:30:19,850
+C عبارة عن مقدار ثابت اطلع لفترة يلّا لبعده الآن
+
+377
+00:30:19,850 --> 00:30:25,070
+space of polynomials تطبيق على اللي هو النظرية اللي
+
+378
+00:30:25,070 --> 00:30:30,230
+قبل بشوية إيش 
+
+379
+00:30:30,230 --> 00:30:36,510
+بتقول هذه؟ norm الـ space X of all polynomials
+
+380
+00:30:36,510 --> 00:30:42,910
+ليس كامل تحت النورم التي تسمى بالنورم الـ X بيساوي
+
+381
+00:30:42,910 --> 00:30:47,190
+الماكسيمم Gamma J Alpha J over J where Alpha 0
+
+382
+00:30:47,190 --> 00:30:50,970
+و Alpha 1 و Alpha 2 are the coefficients of X يعني
+
+383
+00:30:50,970 --> 00:30:55,590
+بدنا نشوف كيف نستخدم الإجابة اللي قبل بشوية على 
+
+384
+00:30:55,590 --> 00:31:02,730
+أساس أننا نثبت أن X ليس كامل الـ X إيش ماله؟ مش 
+
+385
+00:31:02,730 --> 00:31:05,170
+complete مين الـ X هذا هو الـ space of all
+
+386
+00:31:05,170 --> 00:31:09,330
+polynomial under this norm under this norm ممكن
+
+387
+00:31:09,330 --> 00:31:14,310
+حكينا عليه قبل هيك بس بطريقة أخرى كان أظن سؤال
+
+388
+00:31:14,310 --> 00:31:19,990
+معاكم ولا لأ سؤال ولا لأ طيب
+
+389
+00:31:19,990 --> 00:31:24,970
+خلينا الآن نستخدم اللي هو النظرية اللي جابله شوية 
+
+390
+00:31:24,970 --> 00:31:27,230
+في إثبات اللي هو
+
+391
+00:31:30,090 --> 00:31:36,090
+النظرية كانت تقول إن لو كان عندك TN من X لعند Y 
+
+392
+00:31:36,090 --> 00:31:45,150
+هذه complete وهذه لأ ومش شرط يعني قصدي و norm TN X 
+
+393
+00:31:45,150 --> 00:31:52,470
+أصغر يساوي CX هذا مع بعض بيعطيني norm TN أصغر
+
+394
+00:31:52,470 --> 00:31:54,050
+يساوي 100 S
+
+395
+00:31:57,120 --> 00:32:03,120
+بدي اللي هي أجيب اللي هو عنده we construct a
+
+396
+00:32:03,120 --> 00:32:06,880
+sequence of bounded linear functionals on مين on X 
+
+397
+00:32:06,880 --> 00:32:10,260
+sequence
+
+398
+00:32:10,260 --> 00:32:16,180
+الـ TN بدي الـ TN يعني هاخدها من الـ polynomial TN
+
+399
+00:32:16,180 --> 00:32:20,900
+أو أفعى اللي بسميها من الـ polynomials أو the space
+
+400
+00:32:20,900 --> 00:32:24,540
+of all polynomials لعند مين الـ K اللي هو Escalar
+
+401
+00:32:24,540 --> 00:32:29,100
+field الآن بدي اللي هو أعملها أن هذه تتحقق لكن
+
+402
+00:32:29,100 --> 00:32:33,240
+هذه إيش مالها؟ لا تتحقق لأن لو كان هذا complete
+
+403
+00:32:33,240 --> 00:32:37,900
+أتوماتيك هذا هتتحقق بما أنه ما اتحققتش إذن وين 
+
+404
+00:32:37,900 --> 00:32:41,740
+هيكون عنده؟ لو P is not complete إذن we construct
+
+405
+00:32:41,740 --> 00:32:44,840
+a sequence of bounded linear functional on X أو 
+
+406
+00:32:44,840 --> 00:32:49,840
+functional on X which satisfies one but not two
+
+407
+00:32:49,840 --> 00:32:53,680
+ماشي الحال let X be a non-zero polynomial of 
+
+408
+00:32:53,680 --> 00:32:57,680
+degree إيش ما قالها NX يعني الـ X بولونوميال درجتها
+
+409
+00:32:57,680 --> 00:33:02,930
+إيش بتساوي NX ماشي الحال يعني بعد الـ NX صفر اللي 
+
+410
+00:33:02,930 --> 00:33:08,030
+هو الـ coefficients ثم X of T بتساوي Alpha T ..
+
+411
+00:33:08,030 --> 00:33:11,890
+Alpha J .. T is J .. J من صفر لمين .. لعند .. من
+
+412
+00:33:11,890 --> 00:33:15,470
+النهاية كتبتها الصورة هذه و أنا بقول شمالها الـ
+
+413
+00:33:15,470 --> 00:33:19,090
+degree اللي هي نكس إذا هتكون الـ Alpha J بتساوي صفر
+
+414
+00:33:19,090 --> 00:33:23,250
+فوق كل الجزر اللي شمالهن اللي أكبر من نكس هذا دي
+
+415
+00:33:23,250 --> 00:33:27,190
+معناته الـ degree اللي هي .. بتساوي نكس الآن let's 
+
+416
+00:33:27,190 --> 00:33:31,540
+of .. هنشوف كيف بدو .. بدو يعرف إذا الآن لأ خليني 
+
+417
+00:33:31,540 --> 00:33:37,760
+أنزل شوية لأن let FN be a sequence of functionals
+
+418
+00:33:37,760 --> 00:33:48,120
+that are defined on X by FN of 0 بيساوي 0 FN of X
+
+419
+00:33:48,120 --> 00:33:51,400
+بيساوى Alpha node زي ده الف واحد زي ده الف اتنين زي
+
+420
+00:33:51,400 --> 00:33:55,780
+ده الف ان مين ماقص واحد الآن
+
+421
+00:33:57,390 --> 00:34:01,610
+عندي وكأني بأخذ اللي هو الـ Coefficients إسلاميين
+
+422
+00:34:01,610 --> 00:34:07,080
+للي عندي هنا عندي مثلا X of T بيساوي Alpha Note
+
+423
+00:34:07,080 --> 00:34:10,640
+زائد Alpha واحد T زائد Alpha اثنين T تربيع زائد
+
+424
+00:34:10,640 --> 00:34:14,080
+Alpha اثنين T تربيع الآخرين ايش بياخذ مجموع ال
+
+425
+00:34:14,080 --> 00:34:16,320
+coefficients FN of X ايش بيساوي مجموع ال
+
+426
+00:34:16,320 --> 00:34:20,120
+coefficients سبعتها it is left to the reader to
+
+427
+00:34:20,120 --> 00:34:24,180
+show that for any fixed N FN ايش معناه is linear
+
+428
+00:34:24,180 --> 00:34:28,720
+FN is linear بتكون بثبتها بثبتها يعني اثباتها اللي 
+
+429
+00:34:28,720 --> 00:34:29,040
+هو
+
+430
+00:34:31,910 --> 00:34:39,290
+برضه سهل يعني إن شاء الله ما بيكونش صعب طيب
+
+431
+00:34:39,290 --> 00:34:46,570
+عندي بتاخدوا اللي هو X اللي هو بتساوي Alpha Node
+
+432
+00:34:46,570 --> 00:34:52,450
+زائد Alpha واحد X زائد Alpha N ناقص واحد مثلا X أس
+
+433
+00:34:52,450 --> 00:34:57,150
+N ناقص واحد الأخرى و ال Xات هذه T
+
+434
+00:35:02,090 --> 00:35:07,350
+Y بنفس الشيء بيساوي مثلا Gamma Node زي Gamma 1
+
+435
+00:35:07,350 --> 00:35:11,170
+plus Gamma n minus 1 plus Gamma n minus 1 plus
+
+436
+00:35:11,170 --> 00:35:11,210
+Gamma n minus 1 plus Gamma n minus 1 plus Gamma n
+
+437
+00:35:11,210 --> 00:35:11,750
+minus 1 plus Gamma n minus 1 plus Gamma n minus 1
+
+438
+00:35:11,750 --> 00:35:13,190
+plus Gamma n minus 1 plus Gamma n minus 1 plus
+
+439
+00:35:13,190 --> 00:35:13,230
+Gamma n minus 1 plus Gamma n minus 1 plus Gamma n
+
+440
+00:35:13,230 --> 00:35:13,310
+plus Gamma n minus 1 plus Gamma n minus 1 plus
+
+441
+00:35:13,310 --> 00:35:13,450
+minus 1 plus Gamma n minus 1 plus Gamma n minus 1
+
+442
+00:35:13,450 --> 00:35:13,550
+plus Gamma n minus 1 plus Gamma n minus 1 plus
+
+443
+00:35:13,550 --> 00:35:14,250
+Gamma n minus 1 plus Gamma n minus 1 plus Gamma n
+
+444
+00:35:14,250 --> 00:35:15,210
+minus 1 plus Gamma n minus 1 plus Gamma n minus 1
+
+445
+00:35:15,210 --> 00:35:15,710
+plus Gamma n minus 1 plus Gamma n minus 1 plus
+
+446
+00:35:15,710 --> 00:35:21,510
+Gamma n minus 1 plus Gamma n minus 1 plus Gamma n
+
+447
+00:35:21,510 --> 00:35:24,450
+minus 1 plus Gamma n
+
+448
+00:35:30,230 --> 00:35:31,390
+للتفصيل
+
+449
+00:35:33,880 --> 00:35:37,820
+حالة خلاص فكينا من أنها Linear لأن نثبت أنها ايه
+
+450
+00:35:37,820 --> 00:35:40,960
+شمالها لأن نصل للـ boundedness أولا الشيء ال
+
+451
+00:35:40,960 --> 00:35:44,460
+absolute value لـ α J الـ coefficients هدول أكيد
+
+452
+00:35:44,460 --> 00:35:48,080
+أصغر أو يساوي الـ maximum اللي هو مين هو الـ norm X
+
+453
+00:35:48,080 --> 00:35:52,240
+مش norm X هو الـ maximum الـ maximum لأ اللي هي ال
+
+454
+00:35:52,240 --> 00:35:55,940
+coefficients اللي عند .. اللي عندي الـ norm X كده
+
+455
+00:35:55,940 --> 00:36:00,300
+عرفنا الـ norm احنا then الـ absolute value لـ FN of
+
+456
+00:36:00,300 --> 00:36:06,620
+X ماله الـ FN of X هيهم FN of X اللي هي عبارة عن ألفا
+
+457
+00:36:06,620 --> 00:36:10,080
+نوت و ألفا واحد و كل واحدة منهم أصغر من مين من Norm
+
+458
+00:36:10,080 --> 00:36:16,640
+الـ X إذا مجموعهم أصغر أو يساوي N في مين في Norm الـ X
+
+459
+00:36:16,860 --> 00:36:23,780
+هذا كل fixed N يعني F1 أصغر أو يساوي Norm X F2
+
+460
+00:36:23,780 --> 00:36:28,720
+أصغر أو يساوي N2 Norm X وهكذا إذا F1 وF2 وF3 كلهم 
+
+461
+00:36:28,720 --> 00:36:32,260
+هم bounded functionals إذا صار عبارة عن sequence
+
+462
+00:36:32,260 --> 00:36:36,380
+of bounded functionals ومش هيك لكل X element in X
+
+463
+00:36:36,380 --> 00:36:39,460
+ده أنا متلزمني هذا بعد شوية خدوا الـ absolute value
+
+464
+00:36:39,460 --> 00:36:44,740
+لـ FN of X الأبسلوت زي الـ αن نوف إكس هي هتكون أصغر
+
+465
+00:36:44,740 --> 00:36:47,300
+أو يساوي N X زائد واحد في الـ maximum للـ alpha
+
+466
+00:36:47,300 --> 00:36:53,760
+j ليش؟ لأنه ال .. ال .. ال .. البعد لهذه أسفار آه
+
+467
+00:36:53,760 --> 00:36:57,980
+وكل واحد اللي هو ايش ماله اللي هو أكيد هدول ايش
+
+468
+00:36:57,980 --> 00:37:02,020
+قمتهن Alpha 0, Alpha 1, Alpha 2, Alpha 3 إلى ..
+
+469
+00:37:02,020 --> 00:37:05,520
+إلى ما .. إلى ما شاء الله أكيد مش هيبقوا الإعداد
+
+470
+00:37:05,520 --> 00:37:09,820
+هن لأنك زاد واحد لأنه بعدها بيصير إنه أسفار فبيصير
+
+471
+00:37:09,820 --> 00:37:12,800
+عنده أصغر أو يساوي اللي هو هذه في الـ coefficients
+
+472
+00:37:12,800 --> 00:37:15,840
+الأولى .. الأولى .. الأولى كله أصغر من الـ maximum
+
+473
+00:37:15,840 --> 00:37:19,320
+فصار مجموعهم أصغر من مين من هذا في ال .. في هذا
+
+474
+00:37:23,670 --> 00:37:29,470
+عيدوا يدمع FN of X هيها ألفا نوت ألفا واحد ألفا
+
+475
+00:37:29,470 --> 00:37:33,310
+اثنين ألفا N هالجهة الـ absolute value لها أصغر أو 
+
+476
+00:37:33,310 --> 00:37:36,130
+يساوي هذه الـ absolute value هذه زي الـ absolute
+
+477
+00:37:36,130 --> 00:37:39,830
+value هذه زي الـ absolute value لهذه الآن هذول
+
+478
+00:37:39,830 --> 00:37:44,270
+أصغر أو يساوي maximum تبحث كل واحدةعداد هنا دول
+
+479
+00:37:44,270 --> 00:37:49,750
+لن يتجاوز بغض النظر عن X لن يتجاوز الـ maximum اللي هو
+
+480
+00:37:49,750 --> 00:37:53,490
+الـ NX زائد واحد اللي هي درجة الـ polynomial زائد
+
+481
+00:37:53,490 --> 00:37:57,330
+واحد لن يتجاوزها فبيصير عند الـ FNX أصغر أو يساوي
+
+482
+00:37:57,330 --> 00:37:59,690
+اللي هو هذا المقدار في هذا اللي هو بعتمد على ال
+
+483
+00:37:59,690 --> 00:38:03,670
+maximum على X أصغر أو يساوي CX since X has و بقى
+
+484
+00:38:03,670 --> 00:38:08,090
+polynomial of degree NX that has NX زائد واحد من
+
+485
+00:38:08,090 --> 00:38:12,780
+الـ coefficients اطلع إلى فوق إذن therefore الـ
+
+486
+00:38:12,780 --> 00:38:15,540
+absolute value of FN of X satisfies one اللي في
+
+487
+00:38:15,540 --> 00:38:19,540
+الآخر الآن أنا بثبت لك أنه لن يحقق مين اللي هو هذه
+
+488
+00:38:19,540 --> 00:38:26,320
+norm لأف N مستحيل يحقق لك أنه أصغر أو يساوي C بل
+
+489
+00:38:26,320 --> 00:38:32,650
+هأثبت لك أنه unbounded شوف خذ الآن finally we show
+
+490
+00:38:32,650 --> 00:38:35,570
+that fn does not satisfy اثنين choose a polynomial
+
+491
+00:38:35,570 --> 00:38:39,030
+x by x of t بالساوي وصنعنا اللي هي T J J من
+
+492
+00:38:39,030 --> 00:38:41,630
+صفر لعند مين لعند N هاي الـ X تبعها اللي 
+
+493
+00:38:41,630 --> 00:38:46,920
+بتاخذ لك اياها اللي بتخرب الدنيا then Norm الـ X بساوي
+
+494
+00:38:46,920 --> 00:38:50,020
+واحدة لأنه الـ maximum اللي هنا دول العوامل كل واحد
+
+495
+00:38:50,020 --> 00:38:52,800
+واحد واحد ده الـ norm هنا ايش بيساوي بيساوي واحد ده
+
+496
+00:38:52,800 --> 00:38:55,420
+الـ norm الـ X بيساوي واحد الـ FN of X في هذه الحالة
+
+497
+00:38:55,420 --> 00:38:59,060
+ايش بيساوي اللي هو واحد زائد واحد زائد واحد ده ايش
+
+498
+00:38:59,060 --> 00:39:04,820
+بيساوي N من المصير اللي بيساوي N N ويساوي N في مين
+
+499
+00:39:04,820 --> 00:39:10,740
+في Norm الـ X وهذا معناه صار عنده الـ FN of X بيساوي
+
+500
+00:39:10,740 --> 00:39:17,310
+N في Norm الـ X إذا Norm FN هيكون هو الـ supremum
+
+501
+00:39:17,310 --> 00:39:21,750
+هيكون أكبر أو يساوي واحدة منهم اللي هي عبارة عن
+
+502
+00:39:21,750 --> 00:39:24,910
+هذا FN of X اللي هي أكبر أو يساوي FN of X على Norm X
+
+503
+00:39:25,520 --> 00:39:29,540
+الـ N في X على Norm الـ X ويساوي N صارت Norm الـ
+
+504
+00:39:29,540 --> 00:39:33,540
+FN أكبر أو يساوي ومياشي يساوي N إذن مستحيل اللي هي 
+
+505
+00:39:33,540 --> 00:39:37,760
+hence the sequence of FN is unbounded and so two is
+
+506
+00:39:37,760 --> 00:39:42,220
+not satisfied they are satisfied then أو therefore
+
+507
+00:39:42,220 --> 00:39:46,800
+by uniform boundedness theorem الـ X is not
+
+508
+00:39:46,800 --> 00:39:49,980
+complete أو اللي هو the space of all such
+
+509
+00:39:49,980 --> 00:39:53,580
+polynomials under this norm is not complete وإلى
+
+510
+00:39:53,580 --> 00:39:54,440
+لقاء آخر
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/yv5MMmcmY8k_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/yv5MMmcmY8k_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..efe6e542973572072dd52139a3e9693851186b05
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/yv5MMmcmY8k_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2205, "start": 5.23, "end": 22.05, "text": "بسم الله الرحمن الرحيم الحمد لله رب العالمين والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى أهله وصحبه أجمعين هذه المحاضرة رقم 31 مساق تحليل اقتراني أو تحليل جالي لطلاب وطالبات الجامعة الإسلامية قسم الرياضيات ال magisterium", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21542, 2304, 3215, 24976, 3224, 12602, 3555, 18863, 45340, 9957, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 8608, 25708, 9673, 2288, 3794, 1211, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 5551, 3224, 43761, 4032, 9381, 5016, 3555, 3224, 5551, 7435, 2304, 3615, 9957, 29538, 9673, 5016, 46958, 25720, 12602, 4587, 2304, 10353, 47524, 995, 4587, 6055, 5016, 20292, 1211, 1975, 38149, 2288, 7649, 1829, 34051, 6055, 5016, 20292, 1211, 10874, 6027, 1829, 5296, 9566, 15040, 3555, 4032, 9566, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 12174, 38251, 2423, 16572, 46958, 1829, 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190.82, "end": 191.08, "word": " is", "probability": 0.76025390625}, {"start": 191.08, "end": 191.68, "word": " complete", "probability": 0.92138671875}, {"start": 191.68, "end": 192.56, "word": " إذا", "probability": 0.9208984375}, {"start": 192.56, "end": 192.78, "word": " كان", "probability": 0.98291015625}, {"start": 192.78, "end": 192.9, "word": " ال", "probability": 0.75390625}, {"start": 192.9, "end": 193.14, "word": " metric", "probability": 0.9619140625}, {"start": 193.14, "end": 193.66, "word": " space", "probability": 0.94873046875}, {"start": 193.66, "end": 194.5, "word": " X", "probability": 0.7822265625}, {"start": 194.5, "end": 194.72, "word": " is", "probability": 0.66162109375}, {"start": 194.72, "end": 195.34, "word": " complete", "probability": 0.8994140625}, {"start": 195.34, "end": 196.18, "word": " then", "probability": 0.474609375}, {"start": 196.18, "end": 196.52, "word": " it", "probability": 0.96044921875}, {"start": 196.52, "end": 196.82, "word": " is", 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"end": 204.26, "word": " major", "probability": 0.88720703125}, {"start": 204.26, "end": 204.6, "word": " في", "probability": 0.92138671875}, {"start": 204.6, "end": 204.98, "word": " itself", "probability": 0.28173828125}], "temperature": 1.0}, {"id": 11, "seek": 22925, "start": 206.43, "end": 229.25, "text": "هنس اوتوماتيك إذا كانت اللي هو a non major in itself if x لتسوى فيه is complete and x بيسوى لينو لل a k و a k is a closed for all k then at least one a k contains a non implicit subset اللي هو الجزء التاني هذا سهل الآن بنقول الآن إذا كانت ال x لتسوى فيه complete", "tokens": [3224, 1863, 3794, 1975, 35473, 20498, 9307, 1829, 4117, 11933, 15730, 25961, 2655, 13672, 1829, 31439, 257, 2107, 2563, 294, 2564, 498, 2031, 5296, 2655, 3794, 2407, 7578, 8978, 3224, 307, 3566, 293, 2031, 4724, 1829, 3794, 2407, 7578, 5296, 9957, 2407, 24976, 257, 350, 4032, 257, 350, 307, 257, 5395, 337, 439, 350, 550, 412, 1935, 472, 257, 350, 8306, 257, 2107, 26947, 25993, 13672, 1829, 31439, 25724, 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للأم واحد closer ماشي نقدر نقدر نلاقي بي واحد ماشي", "tokens": [2304, 33599, 1829, 29538, 5395, 3714, 24793, 1211, 2655, 11296, 1269, 3714, 33599, 1829, 21542, 1211, 11933, 15730, 29538, 1269, 4032, 718, 311, 584, 498, 286, 307, 364, 6707, 293, 1269, 992, 370, 321, 393, 2826, 363, 11933, 1829, 8592, 3714, 6027, 11296, 11933, 15730, 44945, 28543, 2288, 8717, 15040, 38436, 4724, 1829, 36764, 24401, 4478, 2423, 17103, 24976, 10721, 2304, 36764, 24401, 4966, 3714, 33599, 1829, 8717, 28543, 2288, 8717, 28543, 2288, 8717, 15040, 38436, 4724, 1829, 36764, 24401, 3714, 33599, 1829], "avg_logprob": -0.32105655613399686, "compression_ratio": 1.6684491978609626, "no_speech_prob": 3.5762786865234375e-06, "words": [{"start": 392.41, "end": 392.97, "word": "ماشي", "probability": 0.7503255208333334}, {"start": 392.97, "end": 393.75, "word": " هذه", "probability": 0.1973876953125}, {"start": 393.75, "end": 394.23, "word": " closed", "probability": 0.275634765625}, {"start": 394.23, "end": 395.15, 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"probability": 0.9117838541666666}, {"start": 412.35, "end": 412.95, "word": " نقدر", "probability": 0.9454752604166666}, {"start": 412.95, "end": 413.17, "word": " نلاقي", "probability": 0.9684244791666666}, {"start": 413.17, "end": 413.35, "word": " بي", "probability": 0.923828125}, {"start": 413.35, "end": 413.61, "word": " واحد", "probability": 0.995361328125}, {"start": 413.61, "end": 414.57, "word": " ماشي", "probability": 0.8986002604166666}], "temperature": 1.0}, {"id": 20, "seek": 44541, "start": 416.03, "end": 445.41, "text": "and an open ball about it و open ball كمان بيقدر نجي about it خلّينا نسمي بي واحد بساوة بي of بي واحد و إبسلون واحد هذه ال open ball اللي وجناها حوالين ال بي واحد و جواها كده دي مظبوط؟ فاهمين عليها؟ اللي هي subset مي ال knot M واحد closure و أنا بقدر أزغيرها زي ما بدي", "tokens": [474, 364, 1269, 2594, 466, 309, 4032, 1269, 2594, 9122, 2304, 7649, 4724, 1829, 28543, 2288, 8717, 7435, 1829, 466, 309, 16490, 1211, 11703, 1829, 8315, 8717, 38251, 1829, 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"probability": 0.7626953125}, {"start": 418.01, "end": 418.33, "word": " about", "probability": 0.9169921875}, {"start": 418.33, "end": 418.85, "word": " it", "probability": 0.974609375}, {"start": 418.85, "end": 419.27, "word": " و", "probability": 0.2646484375}, {"start": 419.27, "end": 419.51, "word": " open", "probability": 0.3994140625}, {"start": 419.51, "end": 419.77, "word": " ball", "probability": 0.888671875}, {"start": 419.77, "end": 419.99, "word": " كمان", "probability": 0.958984375}, {"start": 419.99, "end": 420.29, "word": " بيقدر", "probability": 0.71136474609375}, {"start": 420.29, "end": 420.49, "word": " نجي", "probability": 0.7197265625}, {"start": 420.49, "end": 420.69, "word": " about", "probability": 0.92431640625}, {"start": 420.69, "end": 421.11, "word": " it", "probability": 0.97802734375}, {"start": 421.11, "end": 421.79, "word": " خلّينا", "probability": 0.7534912109375}, {"start": 421.79, "end": 422.25, "word": " نسمي", "probability": 0.9788411458333334}, {"start": 422.25, "end": 422.53, "word": " بي", "probability": 0.58544921875}, {"start": 422.53, "end": 423.09, "word": " واحد", "probability": 0.979736328125}, {"start": 423.09, "end": 424.63, "word": " بساوة", "probability": 0.734521484375}, {"start": 424.63, "end": 425.69, "word": " بي", "probability": 0.7078857421875}, {"start": 425.69, "end": 425.91, "word": " of", "probability": 0.8359375}, {"start": 425.91, "end": 426.25, "word": " بي", "probability": 0.972900390625}, {"start": 426.25, "end": 426.79, "word": " واحد", "probability": 0.98876953125}, {"start": 426.79, "end": 427.19, "word": " و", "probability": 0.95703125}, {"start": 427.19, "end": 427.61, "word": " إبسلون", "probability": 0.82197265625}, {"start": 427.61, "end": 428.09, "word": " واحد", "probability": 0.985595703125}, {"start": 428.09, "end": 428.77, "word": " هذه", "probability": 0.482421875}, {"start": 428.77, "end": 428.99, "word": " ال", "probability": 0.91064453125}, {"start": 428.99, "end": 429.33, "word": " open", "probability": 0.89111328125}, {"start": 429.33, "end": 429.77, "word": " ball", "probability": 0.8935546875}, {"start": 429.77, "end": 429.97, "word": " اللي", "probability": 0.974853515625}, {"start": 429.97, "end": 430.41, "word": " وجناها", "probability": 0.5834147135416666}, {"start": 430.41, "end": 430.99, "word": " حوالين", "probability": 0.946044921875}, {"start": 430.99, "end": 431.15, "word": " ال", "probability": 0.763671875}, {"start": 431.15, "end": 431.35, "word": " بي", "probability": 0.760009765625}, {"start": 431.35, "end": 431.67, "word": " واحد", "probability": 0.994384765625}, {"start": 431.67, "end": 431.81, "word": " و", "probability": 0.751953125}, {"start": 431.81, "end": 432.19, "word": " جواها", "probability": 0.8390299479166666}, {"start": 432.19, "end": 432.47, "word": " كده", "probability": 0.6885579427083334}, {"start": 432.47, "end": 432.89, "word": " دي", "probability": 0.6341552734375}, {"start": 432.89, "end": 434.19, "word": " مظبوط؟", "probability": 0.78857421875}, {"start": 434.19, "end": 435.03, "word": " فاهمين", "probability": 0.83349609375}, {"start": 435.03, "end": 436.19, "word": " عليها؟", "probability": 0.8601888020833334}, {"start": 436.19, "end": 436.33, "word": " اللي", "probability": 0.9228515625}, {"start": 436.33, "end": 436.57, "word": " هي", "probability": 0.92626953125}, {"start": 436.57, "end": 437.41, "word": " subset", "probability": 0.9169921875}, {"start": 437.41, "end": 438.83, "word": " مي", "probability": 0.52099609375}, {"start": 438.83, "end": 439.51, "word": " ال", "probability": 0.6220703125}, {"start": 439.51, "end": 439.97, "word": " knot", "probability": 0.229248046875}, {"start": 439.97, "end": 440.35, "word": " M", "probability": 0.2493896484375}, {"start": 440.35, "end": 440.87, "word": " واحد", "probability": 0.933837890625}, {"start": 440.87, "end": 441.43, "word": " closure", "probability": 0.84619140625}, {"start": 441.43, "end": 444.03, "word": " و", "probability": 0.66552734375}, {"start": 444.03, "end": 444.17, "word": " أنا", "probability": 0.54345703125}, {"start": 444.17, "end": 444.47, "word": " بقدر", "probability": 0.8224283854166666}, {"start": 444.47, "end": 444.91, "word": " أزغيرها", "probability": 0.760107421875}, {"start": 444.91, "end": 445.01, "word": " زي", "probability": 0.8671875}, {"start": 445.01, "end": 445.09, "word": " ما", "probability": 0.78515625}, {"start": 445.09, "end": 445.41, "word": " بدي", "probability": 0.6544189453125}], "temperature": 1.0}, {"id": 21, "seek": 47487, "start": 445.97, "end": 474.87, "text": "و بقدر أخد الـ Y الواحد أشمالها أصغر من مين؟ من النص واضح هاه؟ طيب الان since M2 is not wordens ما هي زيها M2 is not wordens، rare يعني إذا أكيد الـ M2 closure does not contain a non-empty open set تطلع على فوق برضه الـ M2 closure مابتحتويش open set إذا مش هتحتوي هذه", "tokens": [2407, 4724, 28543, 2288, 5551, 9778, 3215, 2423, 39184, 398, 2423, 14407, 24401, 5551, 8592, 2304, 6027, 11296, 5551, 9381, 17082, 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0.6533203125}, {"start": 446.91, "end": 447.03, "word": " Y", "probability": 0.402099609375}, {"start": 447.03, "end": 447.45, "word": " الواحد", "probability": 0.7158203125}, {"start": 447.45, "end": 448.17, "word": " أشمالها", "probability": 0.9447265625}, {"start": 448.17, "end": 449.07, "word": " أصغر", "probability": 0.977783203125}, {"start": 449.07, "end": 449.27, "word": " من", "probability": 0.99560546875}, {"start": 449.27, "end": 450.19, "word": " مين؟", "probability": 0.6531575520833334}, {"start": 450.19, "end": 450.97, "word": " من", "probability": 0.9775390625}, {"start": 450.97, "end": 451.35, "word": " النص", "probability": 0.844482421875}, {"start": 451.35, "end": 453.27, "word": " واضح", "probability": 0.9064127604166666}, {"start": 453.27, "end": 453.83, "word": " هاه؟", "probability": 0.4708251953125}, {"start": 453.83, "end": 454.07, "word": " طيب", "probability": 0.9111328125}, {"start": 454.07, "end": 455.03, "word": " الان", "probability": 0.5616455078125}, {"start": 455.03, "end": 455.95, "word": " since", "probability": 0.7490234375}, {"start": 455.95, "end": 456.73, "word": " M2", "probability": 0.898681640625}, {"start": 456.73, "end": 457.09, "word": " is", "probability": 0.93408203125}, {"start": 457.09, "end": 457.39, "word": " not", "probability": 0.4716796875}, {"start": 457.39, "end": 457.95, "word": " wordens", "probability": 0.5042724609375}, {"start": 457.95, "end": 458.09, "word": " ما", "probability": 0.38525390625}, {"start": 458.09, "end": 458.21, "word": " هي", "probability": 0.9111328125}, {"start": 458.21, "end": 458.67, "word": " زيها", "probability": 0.99365234375}, {"start": 458.67, "end": 459.57, "word": " M2", "probability": 0.868896484375}, {"start": 459.57, "end": 459.69, "word": " is", "probability": 0.375244140625}, {"start": 459.69, "end": 459.81, "word": " not", "probability": 0.9306640625}, {"start": 459.81, "end": 460.25, "word": " wordens،", "probability": 0.8092447916666666}, {"start": 460.25, "end": 460.59, "word": " rare", "probability": 0.79296875}, {"start": 460.59, "end": 460.95, "word": " يعني", "probability": 0.91748046875}, {"start": 460.95, "end": 461.67, "word": " إذا", "probability": 0.697998046875}, {"start": 461.67, "end": 462.25, "word": " أكيد", "probability": 0.9423828125}, {"start": 462.25, "end": 462.53, "word": " الـ", "probability": 0.773193359375}, {"start": 462.53, "end": 463.03, "word": " M2", "probability": 0.91015625}, {"start": 463.03, "end": 463.55, "word": " closure", "probability": 0.8115234375}, {"start": 463.55, "end": 463.85, "word": " does", "probability": 0.62744140625}, {"start": 463.85, "end": 464.19, "word": " not", "probability": 0.96923828125}, {"start": 464.19, "end": 465.07, "word": " contain", "probability": 0.94677734375}, {"start": 465.07, "end": 466.11, "word": " a", "probability": 0.57177734375}, {"start": 466.11, "end": 466.37, "word": " non", "probability": 0.873046875}, {"start": 466.37, "end": 467.05, "word": "-empty", "probability": 0.7991536458333334}, {"start": 467.05, "end": 467.31, "word": " open", "probability": 0.541015625}, {"start": 467.31, "end": 467.53, "word": " set", "probability": 0.6923828125}, {"start": 467.53, "end": 467.81, "word": " تطلع", "probability": 0.95849609375}, {"start": 467.81, "end": 467.93, "word": " على", "probability": 0.3486328125}, {"start": 467.93, "end": 468.21, "word": " فوق", "probability": 0.978515625}, {"start": 468.21, "end": 469.63, "word": " برضه", "probability": 0.951171875}, {"start": 469.63, "end": 469.97, "word": " الـ", "probability": 0.855224609375}, {"start": 469.97, "end": 470.53, "word": " M2", "probability": 0.953369140625}, {"start": 470.53, "end": 471.25, "word": " closure", "probability": 0.947265625}, {"start": 471.25, "end": 472.73, "word": " مابتحتويش", "probability": 0.867919921875}, {"start": 472.73, "end": 473.17, "word": " open", "probability": 0.93408203125}, {"start": 473.17, "end": 473.55, "word": " set", "probability": 0.9755859375}, {"start": 473.55, "end": 473.99, "word": " إذا", "probability": 0.929443359375}, {"start": 473.99, "end": 474.15, "word": " مش", "probability": 0.85009765625}, {"start": 474.15, "end": 474.63, "word": " هتحتوي", "probability": 0.9534912109375}, {"start": 474.63, "end": 474.87, "word": " هذه", "probability": 0.6396484375}], "temperature": 1.0}, {"id": 22, "seek": 49581, "start": 481.95, "end": 495.81, "text": "الـ M2 is nowhere dense يعني غير موجود يعني بمعنى اخر M2 closure interior بساوي فاي معناته M2 closure does not contain any open any non M2 open set", "tokens": [6027, 39184, 376, 17, 307, 11159, 18011, 37495, 22653, 32771, 13546, 3714, 29245, 23328, 37495, 22653, 4724, 2304, 3615, 1863, 7578, 1975, 34740, 376, 17, 24653, 10636, 4724, 3794, 995, 45865, 6156, 47302, 20449, 8315, 47395, 376, 17, 24653, 775, 406, 5304, 604, 1269, 604, 2107, 376, 17, 1269, 992], "avg_logprob": -0.4019607808075699, "compression_ratio": 1.3146853146853146, "no_speech_prob": 6.377696990966797e-06, "words": [{"start": 481.95000000000005, "end": 482.79, "word": "الـ", "probability": 0.319580078125}, {"start": 482.79, "end": 483.31, "word": " M2", "probability": 0.927978515625}, {"start": 483.31, "end": 483.53, "word": " is", "probability": 0.33251953125}, {"start": 483.53, "end": 483.83, "word": " nowhere", "probability": 0.74169921875}, {"start": 483.83, "end": 484.33, "word": " dense", "probability": 0.96923828125}, {"start": 484.33, "end": 485.47, "word": " يعني", "probability": 0.81396484375}, {"start": 485.47, "end": 485.81, "word": " غير", "probability": 0.36688232421875}, {"start": 485.81, "end": 485.85, "word": " موجود", "probability": 0.6028645833333334}, {"start": 485.85, "end": 486.27, "word": " يعني", "probability": 0.75927734375}, {"start": 486.27, "end": 486.57, "word": " بمعنى", "probability": 0.95205078125}, {"start": 486.57, "end": 486.89, "word": " اخر", "probability": 0.671875}, {"start": 486.89, "end": 487.45, "word": " M2", "probability": 0.887939453125}, {"start": 487.45, "end": 487.93, "word": " closure", "probability": 0.7353515625}, {"start": 487.93, "end": 488.67, "word": " interior", "probability": 0.712890625}, {"start": 488.67, "end": 489.03, "word": " بساوي", "probability": 0.544219970703125}, {"start": 489.03, "end": 489.41, "word": " فاي", "probability": 0.41729736328125}, {"start": 489.41, "end": 490.45, "word": " معناته", "probability": 0.86474609375}, {"start": 490.45, "end": 490.93, "word": " M2", "probability": 0.925537109375}, {"start": 490.93, "end": 491.41, "word": " closure", "probability": 0.8623046875}, {"start": 491.41, "end": 491.65, "word": " does", "probability": 0.56298828125}, {"start": 491.65, "end": 492.03, "word": " not", "probability": 0.95751953125}, {"start": 492.03, "end": 492.69, "word": " contain", "probability": 0.9384765625}, {"start": 492.69, "end": 493.19, "word": " any", "probability": 0.8876953125}, {"start": 493.19, "end": 494.07, "word": " open", "probability": 0.70849609375}, {"start": 494.07, "end": 494.65, "word": " any", "probability": 0.31201171875}, {"start": 494.65, "end": 494.95, "word": " non", "probability": 0.83056640625}, {"start": 494.95, "end": 495.27, "word": " M2", "probability": 0.755859375}, {"start": 495.27, "end": 495.51, "word": " open", "probability": 0.5791015625}, {"start": 495.51, "end": 495.81, "word": " set", "probability": 0.9013671875}], "temperature": 1.0}, {"id": 23, "seek": 52163, "start": 496.43, "end": 521.63, "text": "بالتالي P of P واحد و نص Y واحد ليس مجموعة من ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة", "tokens": [3555, 6027, 2655, 6027, 1829, 430, 295, 430, 36764, 24401, 4032, 8717, 9381, 398, 36764, 24401, 32239, 3794, 3714, 7435, 2304, 2407, 27884, 9154, 3714, 1829, 7649, 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"end": 572.14, "word": " عشان", "probability": 0.9378255208333334}, {"start": 572.14, "end": 572.5, "word": " بيداخل", "probability": 0.61566162109375}, {"start": 572.5, "end": 572.86, "word": " حاجة", "probability": 0.8738606770833334}, {"start": 572.86, "end": 573.36, "word": " convergence", "probability": 0.3232421875}, {"start": 573.36, "end": 573.7, "word": " بس", "probability": 0.940673828125}], "temperature": 1.0}, {"id": 26, "seek": 59115, "start": 574.29, "end": 591.15, "text": "الأن by induction بقدر أكملها لأن احنا بنعرف الام واحد و الام اتنين و الام تلاتة كلهن where و كلهن اللي سوناه على الام واحد و الام اتنين بقدر أسويه على الباقية اذا by induction we obtain a sequence of balls", "tokens": [6027, 33456, 538, 33371, 4724, 28543, 2288, 5551, 24793, 1211, 11296, 5296, 33456, 1975, 5016, 8315, 44945, 3615, 28480, 2423, 10943, 36764, 24401, 4032, 2423, 10943, 1975, 2655, 1863, 9957, 4032, 2423, 10943, 6055, 1211, 9307, 3660, 28242, 3224, 1863, 689, 4032, 28242, 3224, 1863, 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"word": " بنعرف", "probability": 0.8204752604166666}, {"start": 578.17, "end": 578.89, "word": " الام", "probability": 0.5032958984375}, {"start": 578.89, "end": 579.37, "word": " واحد", "probability": 0.950927734375}, {"start": 579.37, "end": 579.77, "word": " و", "probability": 0.43212890625}, {"start": 579.77, "end": 579.95, "word": " الام", "probability": 0.864013671875}, {"start": 579.95, "end": 580.43, "word": " اتنين", "probability": 0.9398193359375}, {"start": 580.43, "end": 580.73, "word": " و", "probability": 0.96875}, {"start": 580.73, "end": 580.91, "word": " الام", "probability": 0.961181640625}, {"start": 580.91, "end": 581.27, "word": " تلاتة", "probability": 0.8734130859375}, {"start": 581.27, "end": 581.73, "word": " كلهن", "probability": 0.5299479166666666}, {"start": 581.73, "end": 582.13, "word": " where", "probability": 0.3125}, {"start": 582.13, "end": 582.95, "word": " و", "probability": 0.6103515625}, {"start": 582.95, "end": 583.31, "word": " كلهن", "probability": 0.9033203125}, {"start": 583.31, "end": 583.45, "word": " اللي", "probability": 0.974853515625}, {"start": 583.45, "end": 583.89, "word": " سوناه", "probability": 0.66741943359375}, {"start": 583.89, "end": 584.03, "word": " على", "probability": 0.802734375}, {"start": 584.03, "end": 584.29, "word": " الام", "probability": 0.982177734375}, {"start": 584.29, "end": 584.57, "word": " واحد", "probability": 0.963134765625}, {"start": 584.57, "end": 584.69, "word": " و", "probability": 0.97314453125}, {"start": 584.69, "end": 584.81, "word": " الام", "probability": 0.953125}, {"start": 584.81, "end": 585.05, "word": " اتنين", "probability": 0.979736328125}, {"start": 585.05, "end": 585.33, "word": " بقدر", "probability": 0.9755859375}, {"start": 585.33, "end": 585.61, "word": " أسويه", "probability": 0.728271484375}, {"start": 585.61, "end": 585.75, "word": " على", "probability": 0.81494140625}, {"start": 585.75, "end": 586.25, "word": " الباقية", "probability": 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اتنين أس minus كه وبحيث انه كل مرة باخد ال بك زاد واحد جزئية من مين من اللي هي اللي جابلها بك نص إبسلون كه وهذه جزئية من مين اللي سميتها بك", "tokens": [3555, 4117, 4724, 3794, 995, 2407, 3660, 4724, 4117, 11933, 3555, 3794, 1211, 11536, 9122, 3224, 16070, 28814, 3555, 3794, 1211, 11536, 9122, 3224, 5551, 9778, 3215, 2655, 11296, 5551, 12610, 36764, 24401, 5551, 9381, 17082, 2288, 9154, 11933, 3555, 3794, 1211, 11536, 16070, 2655, 7649, 1829, 5551, 9381, 17082, 2288, 9154, 8717, 9381, 11296, 16070, 2655, 6027, 2655, 5551, 9381, 17082, 2288, 9154, 8717, 9381, 11296, 4032, 2288, 16758, 3615, 1975, 15730, 5551, 4117, 25708, 11331, 26108, 3660, 11331, 36520, 15844, 11933, 3555, 3794, 1211, 11536, 9122, 3224, 5551, 9381, 17082, 2288, 9154, 3714, 9957, 9154, 1975, 2655, 1863, 9957, 5551, 3794, 3175, 9122, 3224, 4032, 49628, 1829, 12984, 16472, 3224, 28242, 3714, 25720, 4724, 47283, 3215, 2423, 4724, 4117, 30767, 18513, 36764, 24401, 10874, 11622, 19986, 10632, 9154, 3714, 9957, 9154, 13672, 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"probability": 0.73876953125}, {"start": 610.45, "end": 610.89, "word": " واحد", "probability": 0.990966796875}, {"start": 610.89, "end": 611.57, "word": " جزئية", "probability": 0.9306640625}, {"start": 611.57, "end": 611.77, "word": " من", "probability": 0.9921875}, {"start": 611.77, "end": 612.17, "word": " مين", "probability": 0.978515625}, {"start": 612.17, "end": 612.75, "word": " من", "probability": 0.9501953125}, {"start": 612.75, "end": 612.97, "word": " اللي", "probability": 0.969970703125}, {"start": 612.97, "end": 613.27, "word": " هي", "probability": 0.47119140625}, {"start": 613.27, "end": 613.67, "word": " اللي", "probability": 0.960205078125}, {"start": 613.67, "end": 614.31, "word": " جابلها", "probability": 0.8729248046875}, {"start": 614.31, "end": 614.85, "word": " بك", "probability": 0.957275390625}, {"start": 614.85, "end": 615.19, "word": " نص", "probability": 0.975341796875}, {"start": 615.19, "end": 615.57, "word": " إبسلون", "probability": 0.985546875}, {"start": 615.57, "end": 616.07, "word": " كه", "probability": 0.983154296875}, {"start": 616.07, "end": 616.53, "word": " وهذه", "probability": 0.701904296875}, {"start": 616.53, "end": 616.91, "word": " جزئية", "probability": 0.93408203125}, {"start": 616.91, "end": 617.07, "word": " من", "probability": 0.98681640625}, {"start": 617.07, "end": 617.31, "word": " مين", "probability": 0.98388671875}, {"start": 617.31, "end": 617.49, "word": " اللي", "probability": 0.97900390625}, {"start": 617.49, "end": 618.17, "word": " سميتها", "probability": 0.974853515625}, {"start": 618.17, "end": 618.87, "word": " بك", "probability": 0.9775390625}], "temperature": 1.0}, {"id": 28, "seek": 64298, "start": 619.56, "end": 642.98, "text": "الأن و Epsilon K أصغر من مين؟ من 2 to the minus K إذا بيصير عنده الآن المسافة بين أي بي ك و بي ك زائد واحد اللي هو بيكون أصغر من اللي هو كل مرة أصغر من اللي هي ال Epsilon تبعته أصغر من ال Epsilon تبعته إذا كل واحدة من هذول أصغر من 2 to the minus K", "tokens": 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"end": 707.14, "word": " الـ", "probability": 0.860595703125}, {"start": 707.14, "end": 707.56, "word": " Sequence", "probability": 0.786376953125}, {"start": 707.56, "end": 708.0, "word": " هذه", "probability": 0.7392578125}, {"start": 708.0, "end": 709.2, "word": " صارت", "probability": 0.9837239583333334}, {"start": 709.2, "end": 709.58, "word": " Cauchy", "probability": 0.9562174479166666}, {"start": 709.58, "end": 710.28, "word": " Sequence", "probability": 0.972412109375}, {"start": 710.28, "end": 711.04, "word": " في", "probability": 0.89697265625}, {"start": 711.04, "end": 714.28, "word": " الـ", "probability": 0.6793212890625}, {"start": 714.28, "end": 714.52, "word": " Complete", "probability": 0.60546875}, {"start": 714.52, "end": 715.04, "word": " Space", "probability": 0.56640625}, {"start": 715.04, "end": 715.42, "word": " X", "probability": 0.9765625}, {"start": 715.42, "end": 715.74, "word": " إذا", "probability": 0.792236328125}, {"start": 715.74, "end": 716.2, "word": " أكيد", "probability": 0.9169921875}, {"start": 716.2, "end": 716.42, "word": " هذه", "probability": 0.5009765625}, {"start": 716.42, "end": 716.76, "word": " هتكون", "probability": 0.98193359375}, {"start": 716.76, "end": 717.32, "word": " converts", "probability": 0.71630859375}, {"start": 717.32, "end": 718.22, "word": " BK", "probability": 0.91796875}, {"start": 718.22, "end": 718.42, "word": " to", "probability": 0.90966796875}, {"start": 718.42, "end": 718.7, "word": " some", "probability": 0.90283203125}, {"start": 718.7, "end": 719.06, "word": " element", "probability": 0.90087890625}, {"start": 719.06, "end": 719.6, "word": " سميه", "probability": 0.7784423828125}, {"start": 719.6, "end": 720.24, "word": " مين؟", "probability": 0.8230794270833334}, {"start": 720.24, "end": 721.3, "word": " سميه", "probability": 0.969970703125}, {"start": 721.3, "end": 721.52, "word": " B", "probability": 0.85498046875}, {"start": 721.52, "end": 722.14, "word": " والـ", "probability": 0.68798828125}, {"start": 722.14, "end": 722.2, "word": " B", "probability": 0.73828125}, {"start": 722.2, "end": 722.54, "word": " هتكون", "probability": 0.7623697916666666}, {"start": 722.54, "end": 723.22, "word": " وموجودة", "probability": 0.829736328125}, {"start": 723.22, "end": 723.84, "word": " في", "probability": 0.96533203125}, {"start": 723.84, "end": 724.02, "word": " الـ", "probability": 0.733642578125}, {"start": 724.02, "end": 724.24, "word": " X", "probability": 0.92236328125}, {"start": 724.24, "end": 725.1, "word": " تشوف", "probability": 0.8898111979166666}, {"start": 725.1, "end": 725.36, "word": " الآن", "probability": 0.6517333984375}], "temperature": 1.0}, {"id": 33, "seek": 74736, "start": 726.26, "end": 747.36, "text": "إذاً بي وان موجود في ال X الآن اطلع لفوق بدي أوصل لك لإن بي مش في ال X اه ويصير Contradiction شوف كده Also for all M and all M أكبر من M we have ال بي and الأمات الصغيرة", "tokens": [28814, 15730, 14111, 4724, 1829, 4032, 7649, 3714, 29245, 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{"start": 733.52, "end": 733.86, "word": " X", "probability": 0.986328125}, {"start": 733.86, "end": 735.24, "word": " اه", "probability": 0.43109130859375}, {"start": 735.24, "end": 735.54, "word": " ويصير", "probability": 0.68621826171875}, {"start": 735.54, "end": 736.22, "word": " Contradiction", "probability": 0.7574869791666666}, {"start": 736.22, "end": 736.6, "word": " شوف", "probability": 0.659912109375}, {"start": 736.6, "end": 737.34, "word": " كده", "probability": 0.8854166666666666}, {"start": 737.34, "end": 739.28, "word": " Also", "probability": 0.261474609375}, {"start": 739.28, "end": 739.66, "word": " for", "probability": 0.8916015625}, {"start": 739.66, "end": 739.9, "word": " all", "probability": 0.8759765625}, {"start": 739.9, "end": 740.14, "word": " M", "probability": 0.513671875}, {"start": 740.14, "end": 740.42, "word": " and", "probability": 0.939453125}, {"start": 740.42, "end": 740.68, "word": " all", "probability": 0.330078125}, {"start": 740.68, "end": 740.94, "word": " M", "probability": 0.49951171875}, {"start": 740.94, "end": 741.36, "word": " أكبر", "probability": 0.9197591145833334}, {"start": 741.36, "end": 741.54, "word": " من", "probability": 0.962890625}, {"start": 741.54, "end": 741.78, "word": " M", "probability": 0.91796875}, {"start": 741.78, "end": 742.06, "word": " we", "probability": 0.439697265625}, {"start": 742.06, "end": 742.46, "word": " have", "probability": 0.96533203125}, {"start": 742.46, "end": 743.12, "word": " ال", "probability": 0.74609375}, {"start": 743.12, "end": 743.38, "word": " بي", "probability": 0.7073974609375}, {"start": 743.38, "end": 743.76, "word": " and", "probability": 0.8720703125}, {"start": 743.76, "end": 745.76, "word": " الأمات", "probability": 0.66162109375}, {"start": 745.76, "end": 747.36, "word": " الصغيرة", "probability": 0.9695638020833334}], "temperature": 1.0}, {"id": 34, "seek": 76790, "start": 747.88, "end": 767.9, "text": "الـ Bm كل ما كبرت الـ M أشمالها بتصغر الـ B الـ ball مش أنا كل مرة بزغر ال ball فبتصير الـ Bm subset من ال ball اللي بعدها اللي نقطتها مركزها بيبقى BM و نص قطرها نص في EM إذا صارت المسافة بين BM و B أصغر أو يساوي", "tokens": [6027, 39184, 363, 76, 28242, 19446, 9122, 26890, 2655, 2423, 39184, 376, 5551, 8592, 2304, 6027, 11296, 39894, 9381, 17082, 2288, 2423, 39184, 363, 2423, 39184, 2594, 37893, 41850, 28242, 3714, 25720, 4724, 11622, 17082, 2288, 2423, 2594, 6156, 3555, 2655, 9381, 13546, 2423, 39184, 363, 76, 25993, 9154, 2423, 2594, 13672, 1829, 39182, 11296, 13672, 1829, 8717, 47432, 2655, 11296, 3714, 31747, 11622, 11296, 4724, 1829, 3555, 4587, 7578, 15901, 4032, 8717, 9381, 12174, 9566, 2288, 11296, 8717, 9381, 8978, 16237, 11933, 15730, 20328, 9640, 2655, 9673, 3794, 31845, 3660, 49374, 15901, 4032, 363, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865], "avg_logprob": -0.24047619274684362, "compression_ratio": 1.764102564102564, "no_speech_prob": 1.6093254089355469e-06, "words": [{"start": 747.88, "end": 748.32, "word": 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{"start": 751.78, "end": 752.36, "word": " مش", "probability": 0.7109375}, {"start": 752.36, "end": 752.5, "word": " أنا", "probability": 0.5029296875}, {"start": 752.5, "end": 752.66, "word": " كل", "probability": 0.97021484375}, {"start": 752.66, "end": 752.8, "word": " مرة", "probability": 0.97998046875}, {"start": 752.8, "end": 753.22, "word": " بزغر", "probability": 0.855224609375}, {"start": 753.22, "end": 753.32, "word": " ال", "probability": 0.9521484375}, {"start": 753.32, "end": 753.6, "word": " ball", "probability": 0.68505859375}, {"start": 753.6, "end": 754.46, "word": " فبتصير", "probability": 0.87822265625}, {"start": 754.46, "end": 754.64, "word": " الـ", "probability": 0.926025390625}, {"start": 754.64, "end": 755.06, "word": " Bm", "probability": 0.784423828125}, {"start": 755.06, "end": 755.52, "word": " subset", "probability": 0.88818359375}, {"start": 755.52, "end": 755.76, "word": " من", "probability": 0.9912109375}, {"start": 755.76, "end": 755.9, "word": " ال", "probability": 0.97509765625}, {"start": 755.9, "end": 756.08, "word": " ball", "probability": 0.830078125}, {"start": 756.08, "end": 756.24, "word": " اللي", "probability": 0.944580078125}, {"start": 756.24, "end": 756.72, "word": " بعدها", "probability": 0.7239990234375}, {"start": 756.72, "end": 757.54, "word": " اللي", "probability": 0.794189453125}, {"start": 757.54, "end": 758.24, "word": " نقطتها", "probability": 0.916259765625}, {"start": 758.24, "end": 759.14, "word": " مركزها", "probability": 0.73651123046875}, {"start": 759.14, "end": 759.4, "word": " بيبقى", "probability": 0.85244140625}, {"start": 759.4, "end": 759.84, "word": " BM", "probability": 0.406005859375}, {"start": 759.84, "end": 760.3, "word": " و", "probability": 0.9287109375}, {"start": 760.3, "end": 760.52, "word": " نص", "probability": 0.864501953125}, {"start": 760.52, "end": 761.0, "word": " قطرها", "probability": 0.71734619140625}, {"start": 761.0, "end": 761.42, "word": " نص", "probability": 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{"start": 886.84, "end": 886.94, "word": " في", "probability": 0.96923828125}, {"start": 886.94, "end": 887.24, "word": " الام", "probability": 0.94775390625}, {"start": 887.24, "end": 887.42, "word": " أم", "probability": 0.918701171875}, {"start": 887.42, "end": 888.04, "word": " مكلوجر", "probability": 0.49888916015625}], "temperature": 1.0}, {"id": 41, "seek": 91427, "start": 889.49, "end": 914.27, "text": "إذا مش موجودة في الـMM إذا صارت عندي الـB مش موجودة فيها طب ما هي مدام مش موجودة فيهن كلهن إذا مش موجودة في ال union و ال union هو ال X إذا صارت ال B مش موجودة في من؟ في ال X و هذا معناته صار في عندي contradiction لأن ال B من ال X إذا نفس ال X هتصير إذا ما الفرضية الأولى اللي فرضناها مش صحيحة إذا ال X must be non major", "tokens": [28814, 15730, 37893, 3714, 29245, 23328, 3660, 8978, 2423, 39184, 17365, 11933, 15730, 20328, 9640, 2655, 18871, 16254, 2423, 39184, 33, 37893, 3714, 29245, 23328, 3660, 8978, 11296, 23032, 3555, 19446, 39896, 3714, 3215, 10943, 37893, 3714, 29245, 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0.9876708984375}, {"start": 890.61, "end": 890.73, "word": " في", "probability": 0.96044921875}, {"start": 890.73, "end": 891.19, "word": " الـMM", "probability": 0.5278727213541666}, {"start": 891.19, "end": 892.05, "word": " إذا", "probability": 0.843505859375}, {"start": 892.05, "end": 892.51, "word": " صارت", "probability": 0.9435221354166666}, {"start": 892.51, "end": 892.85, "word": " عندي", "probability": 0.63134765625}, {"start": 892.85, "end": 893.17, "word": " الـB", "probability": 0.7361653645833334}, {"start": 893.17, "end": 893.37, "word": " مش", "probability": 0.97900390625}, {"start": 893.37, "end": 893.85, "word": " موجودة", "probability": 0.9862060546875}, {"start": 893.85, "end": 894.27, "word": " فيها", "probability": 0.97900390625}, {"start": 894.27, "end": 895.03, "word": " طب", "probability": 0.848876953125}, {"start": 895.03, "end": 895.11, "word": " ما", "probability": 0.88916015625}, {"start": 895.11, "end": 895.35, "word": " هي", "probability": 0.8134765625}, {"start": 895.35, "end": 895.81, "word": " مدام", "probability": 0.578125}, {"start": 895.81, "end": 895.99, "word": " مش", "probability": 0.97509765625}, {"start": 895.99, "end": 896.41, "word": " موجودة", "probability": 0.986328125}, {"start": 896.41, "end": 896.71, "word": " فيهن", "probability": 0.54248046875}, {"start": 896.71, "end": 897.13, "word": " كلهن", "probability": 0.7645670572916666}, {"start": 897.13, "end": 897.25, "word": " إذا", "probability": 0.83349609375}, {"start": 897.25, "end": 897.41, "word": " مش", "probability": 0.958984375}, {"start": 897.41, "end": 897.75, "word": " موجودة", "probability": 0.990478515625}, {"start": 897.75, "end": 897.83, "word": " في", "probability": 0.9716796875}, {"start": 897.83, "end": 897.93, "word": " ال", "probability": 0.947265625}, {"start": 897.93, "end": 898.23, "word": " union", "probability": 0.53955078125}, {"start": 898.23, "end": 899.11, "word": " و", "probability": 0.44921875}, {"start": 899.11, "end": 899.23, "word": " ال", "probability": 0.85302734375}, {"start": 899.23, "end": 899.47, "word": " union", "probability": 0.95751953125}, {"start": 899.47, "end": 899.71, "word": " هو", "probability": 0.9814453125}, {"start": 899.71, "end": 899.87, "word": " ال", "probability": 0.94921875}, {"start": 899.87, "end": 900.11, "word": " X", "probability": 0.89501953125}, {"start": 900.11, "end": 900.29, "word": " إذا", "probability": 0.9833984375}, {"start": 900.29, "end": 900.65, "word": " صارت", "probability": 0.9873046875}, {"start": 900.65, "end": 900.75, "word": " ال", "probability": 0.98095703125}, {"start": 900.75, "end": 900.85, "word": " B", "probability": 0.6435546875}, {"start": 900.85, "end": 900.99, "word": " مش", "probability": 0.98828125}, {"start": 900.99, "end": 901.33, "word": " موجودة", "probability": 0.9912109375}, {"start": 901.33, "end": 901.47, "word": " في", "probability": 0.97021484375}, {"start": 901.47, "end": 902.01, "word": " من؟", "probability": 0.5701904296875}, {"start": 902.01, "end": 902.31, "word": " في", "probability": 0.90380859375}, {"start": 902.31, "end": 902.41, "word": " ال", "probability": 0.939453125}, {"start": 902.41, "end": 902.69, "word": " X", "probability": 0.98974609375}, {"start": 902.69, "end": 903.31, "word": " و", "probability": 0.54443359375}, {"start": 903.31, "end": 903.59, "word": " هذا", "probability": 0.89990234375}, {"start": 903.59, "end": 904.21, "word": " معناته", "probability": 0.9928385416666666}, {"start": 904.21, "end": 904.85, "word": " صار", "probability": 0.95556640625}, {"start": 904.85, "end": 904.93, "word": " في", "probability": 0.90673828125}, {"start": 904.93, "end": 905.15, "word": " عندي", "probability": 0.626708984375}, {"start": 905.15, "end": 905.69, "word": " contradiction", "probability": 0.890625}, {"start": 905.69, "end": 906.03, "word": " لأن", "probability": 0.825927734375}, {"start": 906.03, "end": 906.15, "word": " ال", "probability": 0.81494140625}, {"start": 906.15, "end": 906.25, "word": " B", "probability": 0.89501953125}, {"start": 906.25, "end": 906.35, "word": " من", "probability": 0.93994140625}, {"start": 906.35, "end": 906.47, "word": " ال", "probability": 0.91357421875}, {"start": 906.47, "end": 906.71, "word": " X", "probability": 0.98779296875}, {"start": 906.71, "end": 907.33, "word": " إذا", "probability": 0.9541015625}, {"start": 907.33, "end": 907.91, "word": " نفس", "probability": 0.89501953125}, {"start": 907.91, "end": 908.11, "word": " ال", "probability": 0.986328125}, {"start": 908.11, "end": 908.33, "word": " X", "probability": 0.98779296875}, {"start": 908.33, "end": 908.83, "word": " هتصير", "probability": 0.833740234375}, {"start": 908.83, "end": 909.05, "word": " إذا", "probability": 0.758056640625}, {"start": 909.05, "end": 909.17, "word": " ما", "probability": 0.7099609375}, {"start": 909.17, "end": 910.15, "word": " الفرضية", "probability": 0.7338053385416666}, {"start": 910.15, "end": 910.43, "word": " الأولى", "probability": 0.98095703125}, {"start": 910.43, "end": 910.51, "word": " اللي", "probability": 0.802490234375}, {"start": 910.51, "end": 910.93, "word": " فرضناها", "probability": 0.9893798828125}, {"start": 910.93, "end": 911.09, "word": " مش", "probability": 0.98583984375}, {"start": 911.09, "end": 911.81, "word": " صحيحة", "probability": 0.9890625}, {"start": 911.81, "end": 912.25, "word": " إذا", "probability": 0.968994140625}, {"start": 912.25, "end": 912.41, "word": " ال", "probability": 0.97265625}, {"start": 912.41, "end": 912.61, "word": " X", "probability": 0.98583984375}, {"start": 912.61, "end": 912.91, "word": " must", "probability": 0.74853515625}, {"start": 912.91, "end": 913.23, "word": " be", "probability": 0.96435546875}, {"start": 913.23, "end": 913.71, "word": " non", "probability": 0.8876953125}, {"start": 913.71, "end": 914.27, "word": " major", "probability": 0.6044921875}], "temperature": 1.0}, {"id": 42, "seek": 94823, "start": 919.43, "end": 948.23, "text": "يلا لبعدها الـ Uniform Boundedness Theorem هي النظرية اللي بنحكي عنها الأساسية التانية و ألطف برهانها من الأولى خلّينا نشوف أيش اللي بتقوله اللي بتقوله النظرية انه Uniform Boundedness Theorem نشوف كيف let TN be a sequence of bounded linear operators", "tokens": [1829, 15040, 5296, 3555, 22488, 11296, 2423, 39184, 1156, 8629, 363, 37706, 1287, 440, 37956, 39896, 28239, 19913, 2288, 10632, 13672, 1829, 44945, 5016, 4117, 1829, 18871, 11296, 16247, 3794, 32277, 10632, 16712, 7649, 10632, 4032, 5551, 1211, 9566, 5172, 4724, 2288, 3224, 7649, 11296, 9154, 16247, 12610, 7578, 16490, 1211, 11703, 9957, 995, 8717, 8592, 38688, 36632, 8592, 13672, 1829, 39894, 39648, 3224, 13672, 1829, 39894, 39648, 3224, 28239, 19913, 2288, 10632, 16472, 3224, 1156, 8629, 363, 37706, 1287, 440, 37956, 8717, 8592, 38688, 9122, 33911, 718, 314, 45, 312, 257, 8310, 295, 37498, 8213, 19077], "avg_logprob": -0.2095025469149862, "compression_ratio": 1.7116279069767442, "no_speech_prob": 2.664327621459961e-05, "words": [{"start": 919.43, "end": 919.71, "word": "يلا", "probability": 0.38079833984375}, {"start": 919.71, "end": 920.35, "word": " لبعدها", "probability": 0.839111328125}, {"start": 920.35, "end": 923.21, "word": " الـ", "probability": 0.680419921875}, {"start": 923.21, "end": 923.55, "word": " Uniform", "probability": 0.7509765625}, {"start": 923.55, "end": 924.15, "word": " Boundedness", "probability": 0.8068033854166666}, {"start": 924.15, "end": 924.39, "word": " Theorem", "probability": 0.6689453125}, {"start": 924.39, "end": 924.55, "word": " هي", "probability": 0.8251953125}, {"start": 924.55, "end": 924.97, "word": " النظرية", "probability": 0.9410400390625}, {"start": 924.97, "end": 925.03, "word": " اللي", "probability": 0.85400390625}, {"start": 925.03, "end": 925.33, "word": " بنحكي", "probability": 0.873291015625}, {"start": 925.33, "end": 925.67, "word": " عنها", "probability": 0.994873046875}, {"start": 925.67, "end": 926.71, "word": " الأساسية", "probability": 0.95068359375}, {"start": 926.71, "end": 927.15, "word": " التانية", "probability": 0.962890625}, {"start": 927.15, "end": 927.37, "word": " و", "probability": 0.467529296875}, {"start": 927.37, "end": 927.85, "word": " ألطف", "probability": 0.7918701171875}, {"start": 927.85, "end": 928.47, "word": " برهانها", "probability": 0.80380859375}, {"start": 928.47, "end": 928.63, "word": " من", "probability": 0.9912109375}, {"start": 928.63, "end": 930.25, "word": " الأولى", "probability": 0.9759114583333334}, {"start": 930.25, "end": 932.41, "word": " خلّينا", "probability": 0.74814453125}, {"start": 932.41, "end": 932.69, "word": " نشوف", "probability": 0.99560546875}, {"start": 932.69, "end": 932.91, "word": " أيش", "probability": 0.640380859375}, {"start": 932.91, "end": 933.03, "word": " اللي", "probability": 0.987060546875}, {"start": 933.03, "end": 933.67, "word": " بتقوله", "probability": 0.9490559895833334}, {"start": 933.67, "end": 935.79, "word": " اللي", "probability": 0.96337890625}, {"start": 935.79, "end": 936.35, "word": " بتقوله", "probability": 0.9910481770833334}, {"start": 936.35, "end": 937.15, "word": " النظرية", "probability": 0.9803466796875}, {"start": 937.15, "end": 939.25, "word": " انه", "probability": 0.649658203125}, {"start": 939.25, "end": 940.79, "word": " Uniform", "probability": 0.665771484375}, {"start": 940.79, "end": 942.05, "word": " Boundedness", "probability": 0.9270833333333334}, {"start": 942.05, "end": 942.37, "word": " Theorem", "probability": 0.927978515625}, {"start": 942.37, "end": 942.69, "word": " نشوف", "probability": 0.7552083333333334}, {"start": 942.69, "end": 942.93, "word": " كيف", "probability": 0.918212890625}, {"start": 942.93, "end": 944.11, "word": " let", "probability": 0.197021484375}, {"start": 944.11, "end": 944.59, "word": " TN", "probability": 0.768310546875}, {"start": 944.59, "end": 944.75, "word": " be", "probability": 0.9072265625}, {"start": 944.75, "end": 944.97, "word": " a", "probability": 0.9443359375}, {"start": 944.97, "end": 945.69, "word": " sequence", "probability": 0.9677734375}, {"start": 945.69, "end": 946.25, "word": " of", "probability": 0.9775390625}, {"start": 946.25, "end": 946.91, "word": " bounded", "probability": 0.91455078125}, {"start": 946.91, "end": 947.67, "word": " linear", "probability": 0.9423828125}, {"start": 947.67, "end": 948.23, "word": " operators", "probability": 0.93310546875}], "temperature": 1.0}, {"id": 43, "seek": 96147, "start": 949.01, "end": 961.47, "text": "TN هي Sequence of Bounded Linear Operators من بنخ X إلى بنخ Y من بنخ X إلى بنخ Y", "tokens": [51, 45, 39896, 46859, 655, 295, 363, 37706, 14670, 289, 12480, 3391, 9154, 44945, 9778, 1783, 30731, 44945, 9778, 398, 9154, 44945, 9778, 1783, 30731, 44945, 9778, 398], "avg_logprob": -0.5096982594194084, "compression_ratio": 1.3164556962025316, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 949.01, "end": 949.49, "word": "TN", "probability": 0.4193115234375}, {"start": 949.49, "end": 949.75, "word": " هي", "probability": 0.080810546875}, {"start": 949.75, "end": 950.33, "word": " Sequence", "probability": 0.7386474609375}, {"start": 950.33, "end": 950.49, "word": " of", "probability": 0.8212890625}, {"start": 950.49, "end": 952.07, "word": " Bounded", "probability": 0.6602783203125}, {"start": 952.07, "end": 952.53, "word": " Linear", "probability": 0.94921875}, {"start": 952.53, "end": 953.09, "word": " Operators", "probability": 0.938232421875}, {"start": 953.09, "end": 953.83, "word": " من", "probability": 0.642578125}, {"start": 953.83, "end": 954.29, "word": " بنخ", "probability": 0.837158203125}, {"start": 954.29, "end": 954.71, "word": " X", "probability": 0.11981201171875}, {"start": 954.71, "end": 956.15, "word": " إلى", "probability": 0.395263671875}, {"start": 956.15, "end": 956.57, "word": " بنخ", "probability": 0.60430908203125}, {"start": 956.57, "end": 957.23, "word": " Y", "probability": 0.98486328125}, {"start": 957.23, "end": 957.85, "word": " من", "probability": 0.548828125}, {"start": 957.85, "end": 959.59, "word": " بنخ", "probability": 0.790283203125}, {"start": 959.59, "end": 960.21, "word": " X", "probability": 0.5634765625}, {"start": 960.21, "end": 960.59, "word": " إلى", "probability": 0.9443359375}, {"start": 960.59, "end": 960.75, "word": " بنخ", "probability": 0.9052734375}, {"start": 960.75, "end": 961.47, "word": " Y", "probability": 0.96923828125}], "temperature": 1.0}, {"id": 44, "seek": 97075, "start": 964.69, "end": 970.75, "text": "Such that norm of TN is bounded for every X element in X", "tokens": [50, 625, 300, 2026, 295, 314, 45, 307, 37498, 337, 633, 1783, 4478, 294, 1783], "avg_logprob": -0.5092773400247097, "compression_ratio": 0.9032258064516129, "no_speech_prob": 8.165836334228516e-06, "words": [{"start": 964.69, "end": 965.09, "word": "Such", "probability": 0.54229736328125}, {"start": 965.09, "end": 965.51, "word": " that", "probability": 0.947265625}, {"start": 965.51, "end": 966.61, "word": " norm", "probability": 0.345947265625}, {"start": 966.61, "end": 966.99, "word": " of", "probability": 0.65673828125}, {"start": 966.99, "end": 967.69, "word": " TN", "probability": 0.599365234375}, {"start": 967.69, "end": 968.93, "word": " is", "probability": 0.77490234375}, {"start": 968.93, "end": 969.29, "word": " bounded", "probability": 0.8251953125}, {"start": 969.29, "end": 969.53, "word": " for", "probability": 0.89208984375}, {"start": 969.53, "end": 969.81, "word": " every", "probability": 0.79150390625}, {"start": 969.81, "end": 970.03, "word": " X", "probability": 0.456787109375}, {"start": 970.03, "end": 970.27, "word": " element", "probability": 0.343994140625}, {"start": 970.27, "end": 970.47, "word": " in", "probability": 0.94384765625}, {"start": 970.47, "end": 970.75, "word": " X", "probability": 0.9951171875}], "temperature": 1.0}, {"id": 45, "seek": 100808, "start": 983.66, "end": 1008.08, "text": "اللي هي لكل X فيه الـ H ياش اللي هي بتجيلها ثابت يعملها bound ثابت يعملها bound يعني بمعنى أخر TNX1 بتجيلها CX1 TNX2 بتجيلها CX2 TNX3 بتجيلها CX3 ماشي الحال هذا اللي هو ياش ماله المُعطَى بيقول لو كانت ال sequence هذه تتمتع بالخاصية هذه بيقول لك الآن", "tokens": [6027, 20292, 39896, 5296, 28820, 1783, 8978, 3224, 2423, 39184, 389, 7251, 33599, 13672, 1829, 39896, 39894, 7435, 26895, 11296, 38637, 16758, 2655, 7251, 25957, 1211, 11296, 5472, 38637, 16758, 2655, 7251, 25957, 1211, 11296, 5472, 37495, 22653, 4724, 2304, 3615, 1863, 7578, 5551, 34740, 314, 45, 55, 16, 39894, 7435, 26895, 11296, 383, 55, 16, 314, 45, 55, 17, 39894, 7435, 26895, 11296, 383, 55, 17, 314, 45, 55, 18, 39894, 7435, 26895, 11296, 383, 55, 18, 3714, 33599, 1829, 21542, 6027, 23758, 13672, 1829, 31439, 7251, 33599, 3714, 6027, 3224, 9673, 10859, 3615, 9566, 6808, 7578, 4724, 1829, 39648, 45164, 25961, 2655, 2423, 8310, 29538, 6055, 39237, 2655, 3615, 20666, 9778, 33546, 10632, 29538, 4724, 1829, 39648, 5296, 4117, 6024, 48506], "avg_logprob": -0.21622983943070134, "compression_ratio": 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"probability": 0.97119140625}, {"start": 1206.89, "end": 1208.83, "word": " فبصير", "probability": 0.7196044921875}, {"start": 1208.83, "end": 1209.01, "word": " مش", "probability": 0.75244140625}, {"start": 1209.01, "end": 1209.31, "word": " هوا", "probability": 0.54931640625}, {"start": 1209.31, "end": 1210.61, "word": " مشاكلكم", "probability": 0.6314697265625}, {"start": 1210.61, "end": 1210.77, "word": " ما", "probability": 0.595703125}, {"start": 1210.77, "end": 1210.85, "word": " انتم", "probability": 0.638427734375}, {"start": 1210.85, "end": 1211.29, "word": " معايا", "probability": 0.9280598958333334}, {"start": 1211.29, "end": 1212.53, "word": " كي", "probability": 0.851806640625}, {"start": 1212.53, "end": 1212.89, "word": " باثبت", "probability": 0.768896484375}, {"start": 1212.89, "end": 1213.01, "word": " ان", "probability": 0.75390625}, {"start": 1213.01, "end": 1213.43, "word": " ال", "probability": 0.1954345703125}, {"start": 1213.43, "end": 1213.53, "word": " a", "probability": 0.8662109375}, {"start": 1213.53, "end": 1213.87, "word": " كي", "probability": 0.64697265625}, {"start": 1213.87, "end": 1214.03, "word": " is", "probability": 0.640625}, {"start": 1214.03, "end": 1214.51, "word": " closed", "probability": 0.87890625}], "temperature": 1.0}, {"id": 54, "seek": 123033, "start": 1215.62, "end": 1230.34, "text": "الـ AK closure بيساوي الـ A كيف بيداخدها؟ بيداخد X في الـ AK closure و أثبتها أن X في 100 في الـ AK لأن العكس صحيح دايما، اه، ماشي بخير، اذا خلينا نشوف الآن", "tokens": [6027, 39184, 24789, 24653, 4724, 1829, 3794, 995, 45865, 2423, 39184, 316, 9122, 33911, 4724, 25708, 47283, 3215, 11296, 22807, 4724, 25708, 47283, 3215, 1783, 8978, 2423, 39184, 24789, 24653, 4032, 5551, 12984, 3555, 2655, 11296, 14739, 1783, 8978, 2319, 8978, 2423, 39184, 24789, 5296, 33456, 18863, 4117, 3794, 20328, 5016, 1829, 5016, 11778, 47302, 15042, 12399, 1975, 3224, 12399, 3714, 33599, 1829, 4724, 9778, 13546, 12399, 1975, 15730, 16490, 20292, 8315, 8717, 8592, 38688, 6024, 48506], "avg_logprob": -0.3721955025043243, "compression_ratio": 1.5617283950617284, "no_speech_prob": 6.0558319091796875e-05, "words": [{"start": 1215.62, "end": 1215.96, "word": "الـ", "probability": 0.5203857421875}, {"start": 1215.96, "end": 1216.14, "word": " AK", "probability": 0.6552734375}, {"start": 1216.14, "end": 1216.6, "word": " closure", "probability": 0.39111328125}, {"start": 1216.6, "end": 1217.02, "word": " بيساوي", "probability": 0.74873046875}, {"start": 1217.02, "end": 1217.18, "word": " الـ", "probability": 0.321533203125}, {"start": 1217.18, "end": 1217.26, "word": " A", "probability": 0.4033203125}, {"start": 1217.26, "end": 1218.98, "word": " كيف", "probability": 0.7314453125}, {"start": 1218.98, "end": 1219.34, "word": " بيداخدها؟", "probability": 0.52490234375}, {"start": 1219.34, "end": 1219.7, "word": " بيداخد", "probability": 0.850341796875}, {"start": 1219.7, "end": 1219.9, "word": " X", "probability": 0.693359375}, {"start": 1219.9, "end": 1220.04, "word": " في", "probability": 0.85302734375}, {"start": 1220.04, "end": 1220.22, "word": " الـ", "probability": 0.69384765625}, {"start": 1220.22, "end": 1220.5, "word": " AK", "probability": 0.92236328125}, {"start": 1220.5, "end": 1221.2, "word": " closure", "probability": 0.52734375}, {"start": 1221.2, "end": 1221.94, "word": " و", "probability": 0.84814453125}, {"start": 1221.94, "end": 1222.38, "word": " أثبتها", "probability": 0.8974609375}, {"start": 1222.38, "end": 1222.52, "word": " أن", "probability": 0.435791015625}, {"start": 1222.52, "end": 1222.8, "word": " X", "probability": 0.97607421875}, {"start": 1222.8, "end": 1222.98, "word": " في", "probability": 0.701171875}, {"start": 1222.98, "end": 1223.16, "word": " 100", "probability": 0.71044921875}, {"start": 1223.16, "end": 1223.32, "word": " في", "probability": 0.96044921875}, {"start": 1223.32, "end": 1223.46, "word": " الـ", "probability": 0.72412109375}, {"start": 1223.46, "end": 1223.72, "word": " AK", "probability": 0.9443359375}, {"start": 1223.72, "end": 1224.54, "word": " لأن", "probability": 0.841796875}, {"start": 1224.54, "end": 1224.86, "word": " العكس", "probability": 0.8351236979166666}, {"start": 1224.86, "end": 1225.42, "word": " صحيح", "probability": 0.9801025390625}, {"start": 1225.42, "end": 1226.14, "word": " دايما،", "probability": 0.67724609375}, {"start": 1226.14, "end": 1226.98, "word": " اه،", "probability": 0.5653076171875}, {"start": 1226.98, "end": 1227.28, "word": " ماشي", "probability": 0.8933919270833334}, {"start": 1227.28, "end": 1227.72, "word": " بخير،", "probability": 0.57781982421875}, {"start": 1227.72, "end": 1228.04, "word": " اذا", "probability": 0.718505859375}, {"start": 1228.04, "end": 1229.42, "word": " خلينا", "probability": 0.7208658854166666}, {"start": 1229.42, "end": 1229.82, "word": " نشوف", "probability": 0.99609375}, {"start": 1229.82, "end": 1230.34, "word": " الآن", "probability": 0.838623046875}], "temperature": 1.0}, {"id": 55, "seek": 125941, "start": 1231.37, "end": 1259.41, "text": "نشوف الآن خدوا x في الـ a k closure إذا حسب تعريف الـ x في ال a k closure بقدر ألاقي sequence xj of elements in a k such that limit الـ xj أيش بساوي بساوي الـ x هذا تعريف الـ x والي موجودة في ال a closure في ال a k closure then for any fixed n we have norm Tn xj هذا الـ xj هذا الـ xj أصغر أو يساوي مين أصغر يساوي k", "tokens": [1863, 8592, 38688, 6024, 48506, 16490, 3215, 14407, 2031, 8978, 2423, 39184, 257, 350, 24653, 11933, 15730, 11331, 35457, 37279, 16572, 5172, 2423, 39184, 2031, 8978, 2423, 257, 350, 24653, 4724, 28543, 2288, 5551, 15040, 38436, 8310, 2031, 73, 295, 4959, 294, 257, 350, 1270, 300, 4948, 2423, 39184, 2031, 73, 36632, 8592, 4724, 3794, 995, 45865, 4724, 3794, 995, 45865, 2423, 39184, 2031, 23758, 37279, 16572, 5172, 2423, 39184, 2031, 16070, 1829, 3714, 29245, 23328, 3660, 8978, 2423, 257, 24653, 8978, 2423, 257, 350, 24653, 550, 337, 604, 6806, 297, 321, 362, 2026, 314, 77, 2031, 73, 23758, 2423, 39184, 2031, 73, 23758, 2423, 39184, 2031, 73, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 3714, 9957, 5551, 9381, 17082, 2288, 7251, 3794, 995, 45865, 350], "avg_logprob": -0.2860949612403101, "compression_ratio": 1.83402489626556, "no_speech_prob": 2.1457672119140625e-06, "words": [{"start": 1231.37, "end": 1231.83, "word": "نشوف", "probability": 0.6640625}, {"start": 1231.83, "end": 1232.23, "word": " الآن", "probability": 0.680419921875}, {"start": 1232.23, "end": 1233.23, "word": " خدوا", "probability": 0.8181966145833334}, {"start": 1233.23, "end": 1233.47, "word": " x", "probability": 0.496826171875}, {"start": 1233.47, "end": 1233.63, "word": " في", "probability": 0.82373046875}, {"start": 1233.63, "end": 1233.75, "word": " الـ", "probability": 0.77978515625}, {"start": 1233.75, "end": 1233.87, "word": " a", "probability": 0.1805419921875}, {"start": 1233.87, "end": 1234.03, "word": " k", "probability": 0.2919921875}, {"start": 1234.03, "end": 1234.45, "word": " closure", "probability": 0.84716796875}, {"start": 1234.45, "end": 1235.39, "word": " إذا", "probability": 0.67041015625}, {"start": 1235.39, "end": 1235.97, "word": " حسب", "probability": 0.974853515625}, {"start": 1235.97, "end": 1236.41, "word": " تعريف", "probability": 0.9890950520833334}, {"start": 1236.41, "end": 1236.59, "word": " الـ", "probability": 0.71630859375}, {"start": 1236.59, "end": 1236.69, "word": " x", "probability": 0.81201171875}, {"start": 1236.69, "end": 1236.81, "word": " في", "probability": 0.9423828125}, {"start": 1236.81, "end": 1236.91, "word": " ال", "probability": 0.8583984375}, {"start": 1236.91, "end": 1237.01, "word": " a", "probability": 0.42431640625}, {"start": 1237.01, "end": 1237.17, "word": " k", "probability": 0.56884765625}, {"start": 1237.17, "end": 1237.65, "word": " closure", "probability": 0.958984375}, {"start": 1237.65, "end": 1238.31, "word": " بقدر", "probability": 0.9417317708333334}, {"start": 1238.31, "end": 1238.51, "word": " ألاقي", "probability": 0.9007161458333334}, {"start": 1238.51, "end": 1238.99, "word": " sequence", "probability": 0.77783203125}, {"start": 1238.99, "end": 1239.53, "word": " xj", "probability": 0.869873046875}, {"start": 1239.53, "end": 1239.93, "word": " of", "probability": 0.9326171875}, {"start": 1239.93, "end": 1240.49, "word": " elements", "probability": 0.8896484375}, {"start": 1240.49, "end": 1240.73, "word": " in", "probability": 0.94482421875}, {"start": 1240.73, "end": 1240.91, "word": " a", "probability": 0.87646484375}, {"start": 1240.91, "end": 1241.15, "word": " k", "probability": 0.6162109375}, {"start": 1241.15, "end": 1241.73, "word": " such", "probability": 0.8125}, {"start": 1241.73, "end": 1242.05, "word": " that", "probability": 0.95166015625}, {"start": 1242.05, "end": 1242.29, "word": " limit", "probability": 0.89599609375}, {"start": 1242.29, "end": 1242.53, "word": " الـ", "probability": 0.6092529296875}, {"start": 1242.53, "end": 1242.85, "word": " xj", 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"probability": 0.98095703125}, {"start": 1246.05, "end": 1246.17, "word": " ال", "probability": 0.8798828125}, {"start": 1246.17, "end": 1246.25, "word": " a", "probability": 0.7119140625}, {"start": 1246.25, "end": 1246.63, "word": " closure", "probability": 0.767578125}, {"start": 1246.63, "end": 1247.53, "word": " في", "probability": 0.8076171875}, {"start": 1247.53, "end": 1247.61, "word": " ال", "probability": 0.9755859375}, {"start": 1247.61, "end": 1247.71, "word": " a", "probability": 0.84765625}, {"start": 1247.71, "end": 1247.81, "word": " k", "probability": 0.95458984375}, {"start": 1247.81, "end": 1248.21, "word": " closure", "probability": 0.95947265625}, {"start": 1248.21, "end": 1249.19, "word": " then", "probability": 0.6025390625}, {"start": 1249.19, "end": 1249.47, "word": " for", "probability": 0.95263671875}, {"start": 1249.47, "end": 1249.65, "word": " any", "probability": 0.86328125}, {"start": 1249.65, "end": 1249.95, "word": " fixed", "probability": 0.93408203125}, {"start": 1249.95, "end": 1250.23, "word": " n", "probability": 0.68603515625}, {"start": 1250.23, "end": 1251.91, "word": " we", "probability": 0.7412109375}, {"start": 1251.91, "end": 1252.33, "word": " have", "probability": 0.9677734375}, {"start": 1252.33, "end": 1252.97, "word": " norm", "probability": 0.92041015625}, {"start": 1252.97, "end": 1253.63, "word": " Tn", "probability": 0.4976806640625}, {"start": 1253.63, "end": 1254.39, "word": " xj", "probability": 0.83154296875}, {"start": 1254.39, "end": 1255.33, "word": " هذا", "probability": 0.60888671875}, {"start": 1255.33, "end": 1255.49, "word": " الـ", "probability": 0.68798828125}, {"start": 1255.49, "end": 1255.73, "word": " xj", "probability": 0.955078125}, {"start": 1255.73, "end": 1255.95, "word": " هذا", "probability": 0.3876953125}, {"start": 1255.95, "end": 1256.57, "word": " الـ", "probability": 0.513916015625}, {"start": 1256.57, "end": 1256.93, "word": " xj", "probability": 0.96923828125}, {"start": 1256.93, "end": 1257.47, "word": " أصغر", "probability": 0.9805908203125}, {"start": 1257.47, "end": 1257.59, "word": " أو", "probability": 0.92822265625}, {"start": 1257.59, "end": 1257.95, "word": " يساوي", "probability": 0.8206787109375}, {"start": 1257.95, "end": 1258.31, "word": " مين", "probability": 0.86572265625}, {"start": 1258.31, "end": 1258.87, "word": " أصغر", "probability": 0.86456298828125}, {"start": 1258.87, "end": 1259.15, "word": " يساوي", "probability": 0.864501953125}, {"start": 1259.15, "end": 1259.41, "word": " k", "probability": 0.51171875}], "temperature": 1.0}, {"id": 56, "seek": 128817, "start": 1260.19, "end": 1288.17, "text": "أه من تعريفها لأن الـ X هو الموجودة في ال .. آسف في الـ XJ هو الموجودة في الـ AK وعلاصر الـ AK إيه شمالها؟ XJ فيها إذا TN XJ أظهر فيها OK ماشي الحال شوف شوية علامة ماعرفش علاقة بال convergence إذا انتبهوا الآن عندي الـ XJ هدولة من وين جاية؟ من الـ AK مدام الـ XJ", "tokens": [10721, 3224, 9154, 37279, 16572, 5172, 11296, 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"word": " اذا", "probability": 0.699462890625}, {"start": 1650.11, "end": 1650.83, "word": " مادام", "probability": 0.5491129557291666}, {"start": 1650.83, "end": 1651.01, "word": " X", "probability": 0.9326171875}, {"start": 1651.01, "end": 1651.33, "word": " note", "probability": 0.7998046875}, {"start": 1651.33, "end": 1651.65, "word": " هنا", "probability": 0.60107421875}, {"start": 1651.65, "end": 1651.85, "word": " اذا", "probability": 0.791259765625}, {"start": 1651.85, "end": 1652.21, "word": " هنا", "probability": 0.91015625}, {"start": 1652.21, "end": 1652.61, "word": " مادام", "probability": 0.86181640625}, {"start": 1652.61, "end": 1652.81, "word": " X", "probability": 0.9736328125}, {"start": 1652.81, "end": 1653.01, "word": " note", "probability": 0.9052734375}, {"start": 1653.01, "end": 1653.29, "word": " هنا", "probability": 0.95458984375}, {"start": 1653.29, "end": 1653.57, "word": " اذا", "probability": 0.885009765625}, {"start": 1653.57, "end": 1654.13, "word": " بتحقق", "probability": 0.8875732421875}, {"start": 1654.13, "end": 1655.11, "word": " خاصية", "probability": 0.9786783854166666}, {"start": 1655.11, "end": 1655.73, "word": " انه", "probability": 0.765380859375}, {"start": 1655.73, "end": 1656.57, "word": " TN", "probability": 0.673583984375}, {"start": 1656.57, "end": 1656.89, "word": " X", "probability": 0.826171875}, {"start": 1656.89, "end": 1657.25, "word": " note", "probability": 0.81103515625}, {"start": 1657.25, "end": 1657.57, "word": " أظهر", "probability": 0.65765380859375}, {"start": 1657.57, "end": 1658.19, "word": " شاومين", "probability": 0.8690185546875}, {"start": 1658.19, "end": 1658.67, "word": " اللي", "probability": 0.833251953125}, {"start": 1658.67, "end": 1658.79, "word": " هي", "probability": 0.787109375}, {"start": 1658.79, "end": 1659.01, "word": " K", "probability": 0.92138671875}, {"start": 1659.01, "end": 1659.31, "word": " note", "probability": 0.7978515625}], "temperature": 1.0}, {"id": 73, "seek": 167990, "start": 1659.96, "end": 1679.9, "text": "مشاكل مؤهلة تدخل في الـ Knot إذا صانعين دي ال norm ال TN X knot برضه أصغر يساوي مين Knot و هاد ال TN Z برضه أصغر يساوي مين Knot لأن خلّينا نستخدم تلاتة و ال X إيش بتساوي Z minus X knot على Gamma", "tokens": [2304, 8592, 995, 28820, 3714, 33604, 3224, 37977, 6055, 3215, 9778, 1211, 8978, 2423, 39184, 591, 2247, 11933, 15730, 20328, 7649, 3615, 9957, 11778, 1829, 2423, 2026, 2423, 314, 45, 1783, 16966, 4724, 43042, 3224, 5551, 9381, 17082, 2288, 7251, 3794, 995, 45865, 3714, 9957, 591, 2247, 4032, 8032, 18513, 2423, 314, 45, 1176, 4724, 43042, 3224, 5551, 9381, 17082, 2288, 7251, 3794, 995, 45865, 3714, 9957, 591, 2247, 5296, 33456, 16490, 1211, 11703, 1829, 8315, 8717, 14851, 9778, 40448, 6055, 1211, 9307, 3660, 4032, 2423, 1783, 11933, 1829, 8592, 39894, 3794, 995, 45865, 1176, 3175, 1783, 16966, 15844, 24723, 1696], "avg_logprob": -0.2561274410462847, "compression_ratio": 1.618279569892473, "no_speech_prob": 1.8537044525146484e-05, "words": [{"start": 1659.96, "end": 1660.34, "word": "مشاكل", "probability": 0.714111328125}, {"start": 1660.34, "end": 1661.4, "word": " مؤهلة", "probability": 0.958251953125}, {"start": 1661.4, "end": 1661.86, "word": " تدخل", "probability": 0.9228515625}, {"start": 1661.86, "end": 1661.96, "word": " في", "probability": 0.91162109375}, {"start": 1661.96, "end": 1662.1, "word": " الـ", "probability": 0.65966796875}, {"start": 1662.1, "end": 1662.56, "word": " Knot", "probability": 0.3572998046875}, {"start": 1662.56, "end": 1663.28, "word": " إذا", "probability": 0.65478515625}, {"start": 1663.28, "end": 1663.68, "word": " صانعين", "probability": 0.71807861328125}, {"start": 1663.68, "end": 1663.84, "word": " دي", "probability": 0.6553955078125}, {"start": 1663.84, "end": 1663.92, "word": " ال", "probability": 0.27001953125}, {"start": 1663.92, "end": 1664.18, "word": " norm", "probability": 0.57763671875}, {"start": 1664.18, "end": 1664.42, "word": " ال", "probability": 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{"start": 1668.86, "end": 1669.06, "word": " Z", "probability": 0.869140625}, {"start": 1669.06, "end": 1669.46, "word": " برضه", "probability": 0.9694010416666666}, {"start": 1669.46, "end": 1669.78, "word": " أصغر", "probability": 0.9781494140625}, {"start": 1669.78, "end": 1670.04, "word": " يساوي", "probability": 0.9840087890625}, {"start": 1670.04, "end": 1670.48, "word": " مين", "probability": 0.972900390625}, {"start": 1670.48, "end": 1671.76, "word": " Knot", "probability": 0.958740234375}, {"start": 1671.76, "end": 1672.26, "word": " لأن", "probability": 0.646728515625}, {"start": 1672.26, "end": 1673.48, "word": " خلّينا", "probability": 0.624853515625}, {"start": 1673.48, "end": 1673.96, "word": " نستخدم", "probability": 0.9952392578125}, {"start": 1673.96, "end": 1674.7, "word": " تلاتة", "probability": 0.9324951171875}, {"start": 1674.7, "end": 1675.36, "word": " و", "probability": 0.67529296875}, {"start": 1675.36, "end": 1675.5, "word": " ال", "probability": 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TN X0 أصغر أو ساوي أنه TN Z زي TN X0 هذه أوجدناها قبل بشوية فوق اللي هي أصغر أو يساوي اللي هو 2K0", "tokens": [1863, 13063, 2304, 2423, 39184, 314, 45, 46740, 24192, 44945, 9566, 1211, 3615, 2423, 14407, 24401, 15844, 10874, 10943, 27884, 4724, 23557, 4724, 1829, 9381, 13546, 36764, 24401, 15844, 10874, 10943, 27884, 5296, 33456, 11296, 3714, 29245, 49401, 8978, 314, 45, 295, 1176, 3175, 1783, 15, 37037, 24192, 20666, 2655, 16572, 7649, 10874, 6027, 9957, 9122, 2407, 6027, 1829, 31371, 5551, 9381, 17082, 2288, 34051, 8608, 995, 45865, 11331, 11242, 43500, 43761, 23758, 34051, 7435, 3215, 2655, 314, 45, 1176, 4032, 314, 45, 1783, 15, 5551, 9381, 17082, 2288, 34051, 8608, 995, 45865, 14739, 3224, 314, 45, 1176, 30767, 1829, 314, 45, 1783, 15, 29538, 34051, 7435, 3215, 8315, 11296, 12174, 36150, 4724, 8592, 2407, 10632, 6156, 30543, 13672, 1829, 39896, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 13672, 1829, 31439, 568, 42, 15], "avg_logprob": -0.22627736617178812, 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"probability": 0.824951171875}, {"start": 1882.97, "end": 1883.27, "word": " هو", "probability": 0.99267578125}, {"start": 1883.27, "end": 1884.01, "word": " النظرية", "probability": 0.947265625}, {"start": 1884.01, "end": 1884.17, "word": " اللي", "probability": 0.98388671875}, {"start": 1884.17, "end": 1884.45, "word": " جابله", "probability": 0.7496744791666666}, {"start": 1884.45, "end": 1884.97, "word": " شوية", "probability": 0.9142252604166666}, {"start": 1884.97, "end": 1885.91, "word": " في", "probability": 0.82373046875}, {"start": 1885.91, "end": 1886.61, "word": " إثبات", "probability": 0.911376953125}, {"start": 1886.61, "end": 1886.91, "word": " اللي", "probability": 0.977294921875}, {"start": 1886.91, "end": 1887.23, "word": " هو", "probability": 0.9951171875}], "temperature": 1.0}, {"id": 83, "seek": 191405, "start": 1890.09, "end": 1914.05, "text": "النظرية كانت تقول إن لو كان عندك TN من X لعند Y هذه complete وهذه لأ ومش شرط يعني قصدي و norm TN X أصغر يساوي CX هذا مع 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"probability": 0.78173828125}, {"start": 1934.72, "end": 1936.18, "word": " TN", "probability": 0.927978515625}, {"start": 1936.18, "end": 1936.78, "word": " أو", "probability": 0.80810546875}, {"start": 1936.78, "end": 1937.1, "word": " أفعى", "probability": 0.6588134765625}, {"start": 1937.1, "end": 1937.16, "word": " اللي", "probability": 0.795166015625}, {"start": 1937.16, "end": 1937.68, "word": " بسميها", "probability": 0.8134765625}], "temperature": 1.0}, {"id": 85, "seek": 196576, "start": 1938.28, "end": 1965.76, "text": "من الـ polynomials أو the space of all polynomials لعند مين الـ K اللي هو Escalar field الآن بدّي اللي هو أعملها أن هذه تتحقق لكن هذه إيش مالها؟ لا تتحقق لأن لو كان هذا complete اتوماتيك هذا هتتحقق بما أنه ما اتحققتش إذن وين هيكون عنده؟ لو P is not complete إذن we construct a sequence of bounded linear functional on X أو functional on X", "tokens": [27842, 2423, 39184, 22560, 12356, 34051, 264, 1901, 295, 439, 22560, 12356, 5296, 3615, 41260, 3714, 9957, 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2389.4, "end": 2389.62, "word": " all", "probability": 0.88720703125}, {"start": 2389.62, "end": 2389.98, "word": " such", "probability": 0.9345703125}, {"start": 2389.98, "end": 2390.72, "word": " polynomials", "probability": 0.838623046875}, {"start": 2390.72, "end": 2391.1, "word": " under", "probability": 0.916015625}, {"start": 2391.1, "end": 2391.4, "word": " this", "probability": 0.953125}, {"start": 2391.4, "end": 2391.76, "word": " norm", "probability": 0.95361328125}, {"start": 2391.76, "end": 2391.94, "word": " is", "probability": 0.96142578125}, {"start": 2391.94, "end": 2392.14, "word": " not", "probability": 0.95263671875}, {"start": 2392.14, "end": 2392.68, "word": " complete", "probability": 0.830078125}, {"start": 2392.68, "end": 2393.58, "word": " وإلى", "probability": 0.8406575520833334}, {"start": 2393.58, "end": 2394.02, "word": " لقاء", "probability": 0.78662109375}, {"start": 2394.02, "end": 2394.44, "word": " آخر", "probability": 0.916015625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2394.581, "duration_after_vad": 2338.4987499999934}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/yv5MMmcmY8k_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/yv5MMmcmY8k_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f3cdf398c6e2a24e2a8d3367fbffbea58671cae8
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/yv5MMmcmY8k_raw.srt
@@ -0,0 +1,2060 @@
+1
+00:00:05,230 --> 00:00:08,170
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,170 --> 00:00:10,790
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,790 --> 00:00:16,990
+أهله وصحبه أجمعين هذه المحاضرة رقم 31 مساق تحليل
+
+4
+00:00:16,990 --> 00:00:19,630
+اقتراني أو تحليل جالي لطلاب وطالبات الجامعة
+
+5
+00:00:19,630 --> 00:00:24,950
+الإسلامية قسم الرياضيات ال magisteriumالان وصلنا
+
+6
+00:00:24,950 --> 00:00:29,890
+لعند اللي هي اربعة سبعة وهي تحت عنوان category
+
+7
+00:00:29,890 --> 00:00:32,930
+theorem and uniform boundedness theorem وهذه
+
+8
+00:00:32,930 --> 00:00:35,610
+النظرية الأساسية الثانية بعد ال handball theorem
+
+9
+00:00:35,610 --> 00:00:40,090
+اللي هي التحليل
+
+10
+00:00:40,090 --> 00:00:46,700
+الداليعشان نصلها بدنا نبرهن الـ Rare Category
+
+11
+00:00:46,700 --> 00:00:51,580
+Theorem وبدنا نعرف بعض التعريفات اللي هي طبولوجية
+
+12
+00:00:51,580 --> 00:00:57,360
+ومن ثم نصلها اللي هي نظريتنا a subset M of a
+
+13
+00:00:57,360 --> 00:01:01,960
+metric space X is said to be واحدة بلان بنسمي الـ
+
+14
+00:01:01,960 --> 00:01:08,030
+M مجموعة جزية من X انها rareor nowhere dense rare
+
+15
+00:01:08,030 --> 00:01:12,250
+أو nowhere dense if الـ M closure إليها has no
+
+16
+00:01:12,250 --> 00:01:16,490
+interior point يعني بمعنى آخر إنه الـ M closure
+
+17
+00:01:16,490 --> 00:01:23,970
+interior بتساوي 5 فهذه الحملة بنسمي الـ M is rare
+
+18
+00:01:23,970 --> 00:01:32,920
+is rare أو nowhere dense طيب الآن بنسمي اللي هوالـ
+
+19
+00:01:32,920 --> 00:01:41,320
+M is major أو of first category in X if M is the
+
+20
+00:01:41,320 --> 00:01:46,180
+union of countably many sets each of which is rare
+
+21
+00:01:46,180 --> 00:01:57,410
+يعني بنسمي ال هوالان ال subset M is major
+
+22
+00:01:57,410 --> 00:02:02,050
+in X إذا كنا نكتب ال M as a union أو countable
+
+23
+00:02:02,050 --> 00:02:06,910
+union of A I مثلا I من عند واحد لعنده اللي هو
+
+24
+00:02:06,910 --> 00:02:11,510
+معناه نهاية countable unionEach of which كل واحدة
+
+25
+00:02:11,510 --> 00:02:15,310
+من هدولة ايش ما لها is rare يعني ايش ما لها كل
+
+26
+00:02:15,310 --> 00:02:18,670
+واحدة من هدول اللي هو ال closure لها interior
+
+27
+00:02:18,670 --> 00:02:22,910
+بيساوي ايش بيساوفها يعني contains no open balls
+
+28
+00:02:23,490 --> 00:02:29,050
+يعني هذه معناته أن الـ M closure contains no open
+
+29
+00:02:29,050 --> 00:02:31,310
+balls لأن لو اختوت open balls معناته الـ M
+
+30
+00:02:31,310 --> 00:02:35,010
+interior يشملها ال closure اللي ال interior بسويش
+
+31
+00:02:35,010 --> 00:02:39,490
+في عجبه طيب إلى ال non-major or of the second
+
+32
+00:02:39,490 --> 00:02:44,070
+category هذه of first category non-major or of the
+
+33
+00:02:44,070 --> 00:02:49,170
+second category in X إذا كانت مش majorأو مش First
+
+34
+00:02:49,170 --> 00:02:52,870
+Category إذا ال Second Category ما هي إلا نفن مين
+
+35
+00:02:52,870 --> 00:02:57,330
+لل First Category حلو تقلت Free Definitions بس حيث
+
+36
+00:02:57,330 --> 00:03:03,460
+يلزمنك أدوات للوصول للي بدناها اطلع لفوقالعنوان
+
+37
+00:03:03,460 --> 00:03:07,220
+الـ Pair Category Theorem ماش بتقول إذا metric
+
+38
+00:03:07,220 --> 00:03:10,820
+space X لات سوى Y is complete إذا ال metric space
+
+39
+00:03:10,820 --> 00:03:15,340
+is complete إذا كان ال metric space X is complete
+
+40
+00:03:15,340 --> 00:03:22,040
+then it is non-major in itself يعني هيكون ال X ال
+
+41
+00:03:22,040 --> 00:03:28,590
+complete space مش major في itselfهنس اوتوماتيك إذا
+
+42
+00:03:28,590 --> 00:03:32,510
+كانت اللي هو a non major in itself if x لتسوى فيه
+
+43
+00:03:32,510 --> 00:03:36,870
+is complete and x بيسوى لينو لل a k و a k is a
+
+44
+00:03:36,870 --> 00:03:41,070
+closed for all k then at least one a k contains a
+
+45
+00:03:41,070 --> 00:03:44,690
+non implicit subset اللي هو الجزء التاني هذا سهل
+
+46
+00:03:44,690 --> 00:03:49,250
+الآن بنقول الآن إذا كانت ال x لتسوى فيه complete
+
+47
+00:03:52,020 --> 00:03:56,240
+ماشي إذا إيه إيش ما هي اللي هتقول non-major مدام
+
+48
+00:03:56,240 --> 00:04:00,900
+non-major إذا اللي هي can't be written as a
+
+49
+00:04:00,900 --> 00:04:05,300
+countable union of rare sets يعني في على الأقل
+
+50
+00:04:05,300 --> 00:04:09,480
+واحدة من هدولة مش rare إيش يعني؟ يعني لو كان عندي
+
+51
+00:04:09,480 --> 00:04:12,840
+يعني خلّيني أقول لو كان عندي ال union للـAK X
+
+52
+00:04:12,840 --> 00:04:15,720
+بيساوي ال union لـAK K من واحد لإنفينيتي وكل واحدة
+
+53
+00:04:15,720 --> 00:04:20,110
+فيه closedإذا أكيد هذا مش rare واحدة من هنا على
+
+54
+00:04:20,110 --> 00:04:22,710
+الأقل مش rare إيش معناته واحدة من هنا مش rare يعني
+
+55
+00:04:22,710 --> 00:04:27,530
+الـ AK closure إلها interior بسويش في يعني بمعنى
+
+56
+00:04:27,530 --> 00:04:32,210
+ال AK closure interior واحدة من هنا على الأقل لا
+
+57
+00:04:32,210 --> 00:04:38,230
+تسويش في بمعنى إنه AK interior لا يساوي في لإنه
+
+58
+00:04:38,230 --> 00:04:41,670
+closed إحنا بنحكي عنه closed يعني بمعنى أخر إنه ال
+
+59
+00:04:41,670 --> 00:04:50,130
+AK contains open set فيهابس هذا اللي هو الجزء هذا
+
+60
+00:04:50,130 --> 00:04:55,030
+لو برهنا اللي فوق هذا الجزء هذا لو برهنا اللي فوق
+
+61
+00:04:55,030 --> 00:05:00,990
+اذا انطلنا برهين مين اللي فوقالان سببوز that the
+
+62
+00:05:00,990 --> 00:05:04,250
+complete metric space X لاتساوه فيه is not major
+
+63
+00:05:04,250 --> 00:05:08,310
+is major اصل الان طولوا رحكم عليها بنفرض انه ايش
+
+64
+00:05:08,310 --> 00:05:13,270
+معنى العكس ان X لاتساوه فيه is major in itself ايش
+
+65
+00:05:13,270 --> 00:05:19,230
+معنى major then X بتساوه ال union خليني عشان نكتب
+
+66
+00:05:19,230 --> 00:05:24,410
+هنا نرخص ما بنحصل عليه عشان نشوف كيف بنحصل على ال
+
+67
+00:05:24,410 --> 00:05:28,250
+contradiction الان
+
+68
+00:05:29,160 --> 00:05:32,860
+ثم X بيساوي ال union لـMK كام من واحد إلى مناهية
+
+69
+00:05:32,860 --> 00:05:36,740
+with each MK إزاي إيش؟ إيش rare؟ حيكون كل واحدة من
+
+70
+00:05:36,740 --> 00:05:41,960
+هنا إشمالها rare in X إذا بمعنى آخر الان M closure
+
+71
+00:05:41,960 --> 00:05:49,320
+واحد interior إشماله بيساوي 5 الآن واحدة واحدة
+
+72
+00:05:49,320 --> 00:05:53,900
+that means ان M1 closure does not contain a non
+
+73
+00:05:53,900 --> 00:05:59,690
+-empty open sets مافيش فيها non-empty open setsBut
+
+74
+00:05:59,690 --> 00:06:04,630
+X does But X إيش؟ Does إذا X نفسها نحنا open set
+
+75
+00:06:04,630 --> 00:06:09,350
+إذا بتحتوي في داخلها عليا شمالها على open sets for
+
+76
+00:06:09,350 --> 00:06:14,410
+example X itself وممكن غيرها So that أم واحد
+
+77
+00:06:14,410 --> 00:06:19,980
+closure مش هي ال X أكيد أكيدلأن هذي rare وهذه مش
+
+78
+00:06:19,980 --> 00:06:24,580
+rare hence اللي هو ال complement لل M1 closure
+
+79
+00:06:24,580 --> 00:06:29,280
+اللي بيساوي X minus M1 closure فيها نقاط لا تساوي
+
+80
+00:06:29,280 --> 00:06:35,450
+5 في نفس الوقت openماشي هذه closed مكملتها open
+
+81
+00:06:35,450 --> 00:06:39,090
+ماشي الحل إذا هذه open و let's say if I is an
+
+82
+00:06:39,090 --> 00:06:44,830
+empty and open set so we can choose B إيش مالها
+
+83
+00:06:44,830 --> 00:06:49,970
+إذا بنقدر نلاقي بي واحد element ال complement للأم
+
+84
+00:06:49,970 --> 00:06:56,450
+واحد closer ماشي نقدر نقدر نلاقي بي واحد ماشيand
+
+85
+00:06:56,450 --> 00:07:00,490
+an open ball about it و open ball كمان بيقدر نجي
+
+86
+00:07:00,490 --> 00:07:07,190
+about it خلّينا نسمي بي واحد بساوة بي of بي واحد و
+
+87
+00:07:07,190 --> 00:07:11,150
+إبسلون واحد هذه ال open ball اللي وجناها حوالين ال
+
+88
+00:07:11,150 --> 00:07:16,330
+بي واحد و جواها كده دي مظبوط؟ فاهمين عليها؟ اللي
+
+89
+00:07:16,330 --> 00:07:24,470
+هي subset مي ال knot M واحد closure و أنا بقدر
+
+90
+00:07:24,470 --> 00:07:28,170
+أزغيرها زي ما بديو بقدر أخد الـ Y الواحد أشمالها
+
+91
+00:07:28,170 --> 00:07:36,730
+أصغر من مين؟ من النص واضح هاه؟ طيب الان since M2
+
+92
+00:07:36,730 --> 00:07:40,590
+is not wordens ما هي زيها M2 is not wordens، rare
+
+93
+00:07:40,590 --> 00:07:46,110
+يعني إذا أكيد الـ M2 closure does not contain a
+
+94
+00:07:46,110 --> 00:07:50,530
+non-empty open set تطلع على فوق برضه الـ M2
+
+95
+00:07:50,530 --> 00:07:54,870
+closure مابتحتويش open set إذا مش هتحتوي هذه
+
+96
+00:08:01,950 --> 00:08:06,570
+الـ M2 is nowhere dense يعني غير موجود يعني بمعنى
+
+97
+00:08:06,570 --> 00:08:10,930
+اخر M2 closure interior بساوي فاي معناته M2
+
+98
+00:08:10,930 --> 00:08:15,510
+closure does not contain any open any non M2 open
+
+99
+00:08:15,510 --> 00:08:23,010
+setبالتالي P of P واحد و نص Y واحد ليس مجموعة من
+
+100
+00:08:23,010 --> 00:08:25,010
+ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان
+
+101
+00:08:25,010 --> 00:08:26,530
+M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2
+
+102
+00:08:26,530 --> 00:08:30,210
+مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2
+
+103
+00:08:30,210 --> 00:08:32,910
+مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2
+
+104
+00:08:32,910 --> 00:08:33,350
+مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2
+
+105
+00:08:33,350 --> 00:08:35,030
+مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2
+
+106
+00:08:35,030 --> 00:08:41,630
+مجموعة ميان M2
+
+107
+00:08:41,630 --> 00:08:45,770
+مجموعةSo we can choose B2 من مين من التقاطع إذا
+
+108
+00:08:45,770 --> 00:08:50,730
+بقدر ألاقي B2 من الموجودة B2 element in M2 closure
+
+109
+00:08:50,730 --> 00:08:57,850
+complement تقاطع اللي هو B of B1 و نص إبسلون واحد
+
+110
+00:08:57,850 --> 00:09:06,610
+طيب and an open ball about it أكيد مدام هدولة open
+
+111
+00:09:07,460 --> 00:09:10,940
+و بي اتنين فيهم إذا بقدر لاجي open ball حوالين هذه
+
+112
+00:09:10,940 --> 00:09:17,620
+جوات هذه إذا سميها بي اتنين بي بي اتنين و ابسلون
+
+113
+00:09:17,620 --> 00:09:20,940
+اتنين subset من مين من M اتنين ال closure ال
+
+114
+00:09:20,940 --> 00:09:24,800
+complement لها تقاطع بي واحد بي بي واحد و نص
+
+115
+00:09:24,800 --> 00:09:28,900
+ابسلون و اختار للأبسلون اتنين أصغر من مين من نص
+
+116
+00:09:28,900 --> 00:09:31,900
+ابسلون واحد طبعا نص ابسلون واحد ربع ابسلون واحد
+
+117
+00:09:31,900 --> 00:09:36,010
+عشان بيداخل حاجة convergence بسالأن by induction
+
+118
+00:09:36,010 --> 00:09:40,430
+بقدر أكملها لأن احنا بنعرف الام واحد و الام اتنين
+
+119
+00:09:40,430 --> 00:09:44,290
+و الام تلاتة كلهن where و كلهن اللي سوناه على الام
+
+120
+00:09:44,290 --> 00:09:47,670
+واحد و الام اتنين بقدر أسويه على الباقية اذا by
+
+121
+00:09:47,670 --> 00:09:54,230
+induction we obtain a sequence of ballsبك بساوة بك
+
+122
+00:09:54,230 --> 00:09:58,410
+إبسلون كه والإبسلون كه أخدتها أول واحد أصغر من
+
+123
+00:09:58,410 --> 00:10:01,550
+إبسلون والتاني أصغر من نصها والتالت أصغر من نصها
+
+124
+00:10:01,550 --> 00:10:04,970
+ورابع اذا أكيد حاجة حصل على إبسلون كه أصغر من مين
+
+125
+00:10:04,970 --> 00:10:10,150
+من اتنين أس minus كه وبحيث انه كل مرة باخد ال بك
+
+126
+00:10:10,150 --> 00:10:15,190
+زاد واحد جزئية من مين من اللي هي اللي جابلها بك نص
+
+127
+00:10:15,190 --> 00:10:20,100
+إبسلون كه وهذه جزئية من مين اللي سميتها بكالأن و
+
+128
+00:10:20,100 --> 00:10:25,520
+Epsilon K أصغر من مين؟ من 2 to the minus K إذا
+
+129
+00:10:25,520 --> 00:10:29,960
+بيصير عنده الآن المسافة بين أي بي ك و بي ك زائد
+
+130
+00:10:29,960 --> 00:10:37,260
+واحد اللي هو بيكون أصغر من اللي هو كل مرة أصغر من
+
+131
+00:10:37,260 --> 00:10:39,700
+اللي هي ال Epsilon تبعته أصغر من ال Epsilon تبعته
+
+132
+00:10:39,700 --> 00:10:44,120
+إذا كل واحدة من هذول أصغر من 2 to the minus Kالان
+
+133
+00:10:44,120 --> 00:10:47,720
+بين bk و bk زد واحد أصغر من two تقريبا minus k ال
+
+134
+00:10:47,720 --> 00:10:50,480
+summation اللي من k من واحد إلى نهاية أصغر شهو مين
+
+135
+00:10:50,480 --> 00:10:53,920
+ال summation من سفر إلى مين إلى مانا نهاية صار
+
+136
+00:10:53,920 --> 00:10:57,560
+عندي أنا sequence من ال bees بي واحد و بي اتنين و
+
+137
+00:10:57,560 --> 00:11:02,600
+بي تلاتة و بي أربعة إلى أخره كل مرة اللي هو بديب
+
+138
+00:11:02,600 --> 00:11:05,480
+أكتر و بيصير كله موجودات في آخر واحدة موجودة فيهم
+
+139
+00:11:05,920 --> 00:11:10,200
+الأنفة بيصير ND اللي هو المسافات بينهم مجموح كل
+
+140
+00:11:10,200 --> 00:11:14,640
+واحدة أصغر من 2 إلى الأولى بين B1 وB2 أصغر من 2
+
+141
+00:11:14,640 --> 00:11:20,460
+إلى minus 1 بين B2 وB3 من 2 إلى minus 2 بين B4 وB5
+
+142
+00:11:20,460 --> 00:11:24,340
+إلى أخره إذا صماش اللي هنا أصغر من الصماش الى 2
+
+143
+00:11:24,340 --> 00:11:27,930
+إلى minus Kالأن هذا convergence إذا قطعا هذا
+
+144
+00:11:27,930 --> 00:11:32,310
+إشماله convergence صار إذا عندي sequence of
+
+145
+00:11:32,310 --> 00:11:36,150
+elements BK كوشي sequence in the complete metric
+
+146
+00:11:36,150 --> 00:11:40,760
+space Xوالـ Cauchy Sequence أكيد هتكون إيه اشمالها
+
+147
+00:11:40,760 --> 00:11:45,820
+So it converts C limit BK إيش بيساوي B element in
+
+148
+00:11:45,820 --> 00:11:50,280
+X يعني الآن الـ Sequence هذه صارت Cauchy Sequence
+
+149
+00:11:50,280 --> 00:11:54,280
+في الـ
+
+150
+00:11:54,280 --> 00:11:58,420
+Complete Space X إذا أكيد هذه هتكون converts BK to
+
+151
+00:11:58,420 --> 00:12:03,220
+some element سميه مين؟ سميه B والـ B هتكون وموجودة
+
+152
+00:12:03,220 --> 00:12:09,280
+في الـ X تشوف الآنإذاً بي وان موجود في ال X الآن
+
+153
+00:12:09,280 --> 00:12:15,540
+اطلع لفوق بدي أوصل لك لإن بي مش في ال X اه ويصير
+
+154
+00:12:15,540 --> 00:12:20,940
+Contradiction شوف كده Also for all M and all M
+
+155
+00:12:20,940 --> 00:12:28,780
+أكبر من M we have ال بي and الأمات الصغيرةالـ Bm
+
+156
+00:12:28,780 --> 00:12:32,360
+كل ما كبرت الـ M أشمالها بتصغر الـ B الـ ball مش
+
+157
+00:12:32,360 --> 00:12:35,900
+أنا كل مرة بزغر ال ball فبتصير الـ Bm subset من ال
+
+158
+00:12:35,900 --> 00:12:40,520
+ball اللي بعدها اللي نقطتها مركزها بيبقى BM و نص
+
+159
+00:12:40,520 --> 00:12:47,380
+قطرها نص في EM إذا صارت المسافة بين BM و B أصغر أو
+
+160
+00:12:47,380 --> 00:12:56,900
+يساويBM و BN و BM و B و المسافة بين BM و BN أصغر
+
+161
+00:12:56,900 --> 00:12:59,620
+من مين من نفس N لأن هذه جزئية من مين من التانية
+
+162
+00:12:59,620 --> 00:13:03,280
+اللي هنا فادي فبصير عنده اللي هو المسافة أصغر من
+
+163
+00:13:03,280 --> 00:13:08,050
+مين من أكيد من الصغيرة من الكبيرةمش الـ N هذه BM
+
+164
+00:13:08,050 --> 00:13:13,390
+BM موجودة هنا و BM أصلا موجودة هنا لذا صارت ال BM
+
+165
+00:13:13,390 --> 00:13:17,330
+و ال BM فاد على الأقل ماشي و المسافة بين أي نقطين
+
+166
+00:13:17,330 --> 00:13:21,210
+فيه أصغر من مين من نص EM لذا صار عندي هذه المسافة
+
+167
+00:13:21,210 --> 00:13:27,890
+أصغر من نص EM و هذه زائد D BN OB لأن هذه صارتأصغر
+
+168
+00:13:27,890 --> 00:13:31,090
+أو يساوي هذا المقدار و أنا ماخد ال M أكبر من M
+
+169
+00:13:31,090 --> 00:13:34,130
+بطير ال M إلى ما لنهايه زي ما بده و ال M بتلغى
+
+170
+00:13:34,130 --> 00:13:38,130
+بيعدى زي ما هي إذا as M goes to infinity اللي هم
+
+171
+00:13:38,130 --> 00:13:44,650
+بيصير عندي المسافة بين ال B M و ال B هذي بتروح
+
+172
+00:13:44,650 --> 00:13:49,190
+للصفرلأن as n goes to infinity بيشهر بجد سير بسير
+
+173
+00:13:49,190 --> 00:13:54,170
+فيه بيه هاد ال bm و ال b بتروح لمين للصفر فاهمين
+
+174
+00:13:54,170 --> 00:13:58,130
+اللي بحكيه؟ الان هاد بتظل عند as n goes to
+
+175
+00:13:58,130 --> 00:14:01,690
+infinity ال distance بين ال bm و ال b أصغر من نص
+
+176
+00:14:01,690 --> 00:14:05,570
+ال EM لأن هاد راح لمين للصفر الان هذا إيش معناته
+
+177
+00:14:05,570 --> 00:14:09,570
+أن المسافة بين ال bm و ال b أصغر من نص ال EM؟
+
+178
+00:14:09,910 --> 00:14:14,790
+معناته أن الـ B موجودة في الـ BM لأن المسافة بين
+
+179
+00:14:14,790 --> 00:14:19,030
+الـ BM و الـ B أصغر من نص EM هذه المركز وهذا نص
+
+180
+00:14:19,030 --> 00:14:22,850
+القطر إذن في الـ Bolt بيتهم إذا صارت الـ B موجودة
+
+181
+00:14:22,850 --> 00:14:28,810
+في الـ BM for all M إذا وعندي الـ BM جزئية من مين؟
+
+182
+00:14:28,810 --> 00:14:32,350
+من الـ complement في التركيبة كنت أخد الـ BM جزئية
+
+183
+00:14:32,350 --> 00:14:38,300
+من مين؟هي rare جزء من هذه then B is not element in
+
+184
+00:14:38,300 --> 00:14:44,640
+main in اللي هو جزئية من وين من مكملتها إذا أكيد
+
+185
+00:14:44,640 --> 00:14:47,420
+مش موجودة في الام أم إذا مش موجودة في الام أم
+
+186
+00:14:47,420 --> 00:14:53,370
+مكلوجرإذا مش موجودة في الـMM إذا صارت عندي الـB مش
+
+187
+00:14:53,370 --> 00:14:57,250
+موجودة فيها طب ما هي مدام مش موجودة فيهن كلهن إذا
+
+188
+00:14:57,250 --> 00:15:00,650
+مش موجودة في ال union و ال union هو ال X إذا صارت
+
+189
+00:15:00,650 --> 00:15:04,930
+ال B مش موجودة في من؟ في ال X و هذا معناته صار في
+
+190
+00:15:04,930 --> 00:15:08,330
+عندي contradiction لأن ال B من ال X إذا نفس ال X
+
+191
+00:15:08,330 --> 00:15:11,810
+هتصير إذا ما الفرضية الأولى اللي فرضناها مش صحيحة
+
+192
+00:15:11,810 --> 00:15:14,270
+إذا ال X must be non major
+
+193
+00:15:19,430 --> 00:15:24,550
+يلا لبعدها الـ Uniform Boundedness Theorem هي
+
+194
+00:15:24,550 --> 00:15:27,850
+النظرية اللي بنحكي عنها الأساسية التانية و ألطف
+
+195
+00:15:27,850 --> 00:15:35,790
+برهانها من الأولى خلّينا نشوف أيش اللي بتقوله اللي
+
+196
+00:15:35,790 --> 00:15:42,370
+بتقوله النظرية انه Uniform Boundedness Theorem
+
+197
+00:15:42,370 --> 00:15:47,670
+نشوف كيف let TN be a sequence of bounded linear
+
+198
+00:15:47,670 --> 00:15:52,530
+operatorsTN هي Sequence of Bounded Linear
+
+199
+00:15:52,530 --> 00:16:01,470
+Operators من بنخ X إلى بنخ Y من بنخ X إلى بنخ Y
+
+200
+00:16:04,690 --> 00:16:10,030
+Such that norm of TN is bounded for every X
+
+201
+00:16:10,030 --> 00:16:10,750
+element in X
+
+202
+00:16:23,660 --> 00:16:29,020
+اللي هي لكل X فيه الـ H ياش اللي هي بتجيلها ثابت
+
+203
+00:16:29,020 --> 00:16:33,660
+يعملها bound ثابت يعملها bound يعني بمعنى أخر TNX1
+
+204
+00:16:33,660 --> 00:16:40,080
+بتجيلها CX1 TNX2 بتجيلها CX2 TNX3 بتجيلها CX3 ماشي
+
+205
+00:16:40,080 --> 00:16:44,020
+الحال هذا اللي هو ياش ماله المُعطَى بيقول لو كانت
+
+206
+00:16:44,020 --> 00:16:48,080
+ال sequence هذه تتمتع بالخاصية هذه بيقول لك الآن
+
+207
+00:16:48,770 --> 00:16:53,750
+بما انه هذه sequence of bounded اللي هي بالشكل هذا
+
+208
+00:16:53,750 --> 00:16:58,650
+وكانت من بنخ space ل Y اللي هو normed space انا
+
+209
+00:16:58,650 --> 00:17:03,230
+بضمنك ..الان قوة النظرية بقولك انا بضمنك ان ال
+
+210
+00:17:03,230 --> 00:17:06,070
+sequence هذا يكون ال boundedness uniform يعني لا
+
+211
+00:17:06,070 --> 00:17:09,190
+يعتمد على مين؟ على ال X عشان هي اسمها uniform
+
+212
+00:17:09,190 --> 00:17:12,280
+boundedness theoremuniform boundedness هذا يعني
+
+213
+00:17:12,280 --> 00:17:15,660
+بمعنى أخر بقدر ألاقي C بتنفع لكل شي يعني نورم ال
+
+214
+00:17:15,660 --> 00:17:20,900
+TN أصغر أو ساوي C لكل اللي هي ال Xات بغض النظر
+
+215
+00:17:20,900 --> 00:17:24,700
+يعني بل بقولك نورم ال TN نفسه أصغر أو ساوي مين؟
+
+216
+00:17:24,700 --> 00:17:29,480
+أصغر أو ساوي C لأنه لما نلاقي نورم ال TN X أصغر أو
+
+217
+00:17:29,480 --> 00:17:32,740
+ساوي C في نورم ال X خلاص على نورم ال X بطلع نورم
+
+218
+00:17:32,740 --> 00:17:38,280
+ال TN أصغر أو ساوي مين؟ some constant Cنأتي الآن
+
+219
+00:17:38,280 --> 00:17:48,640
+لنثبت هذا اللي هو اتنين اكيد
+
+220
+00:17:48,640 --> 00:17:51,720
+بستخدم الكتاب البركاتو كوريو تيريم و لا ليش اصلا
+
+221
+00:17:51,720 --> 00:17:59,880
+نثبتها and x is complete مظبوط؟ اه طيب for every k
+
+222
+00:17:59,880 --> 00:18:04,010
+element لانخلّيني أحضر بس سؤال برهان Let A K
+
+223
+00:18:04,010 --> 00:18:08,450
+subset من X أشهى A K be the set of all X such that
+
+224
+00:18:08,450 --> 00:18:12,750
+T N X أصغر شهو K for all N يعني بمعنى أخر خلّيني
+
+225
+00:18:12,750 --> 00:18:20,650
+أنفسر أكتر أنه لو أخدنا A 1 هي عبارة عن كل الإكسات
+
+226
+00:18:20,650 --> 00:18:29,730
+such that T 1 X أصغر أو آسف T N Xأصغر أو سوى واحد
+
+227
+00:18:29,730 --> 00:18:35,530
+لكل N element in R A2
+
+228
+00:18:35,530 --> 00:18:43,430
+بساوية اللي هو كل ال X such that TNX أصغر أو سوى
+
+229
+00:18:43,430 --> 00:18:50,090
+اتنين لكل N element in R AK in general هي عبارة عن
+
+230
+00:18:50,090 --> 00:18:55,470
+كل ال X such that TNXأصغر أو يساوي اللي هو الـ K
+
+231
+00:18:55,470 --> 00:19:04,910
+for every N element in N ماشي الحل ال
+
+232
+00:19:04,910 --> 00:19:08,790
+TNX اللي أصغر أو يساوي واحد أكيد هيكون إيه شماله
+
+233
+00:19:08,790 --> 00:19:13,270
+أصغر أو يساوي اتنين يعني اللي لو خدنا element 10
+
+234
+00:19:13,270 --> 00:19:19,810
+هلاجيه automatic element 10 صح؟فبصير عندى ال .. ال
+
+235
+00:19:19,810 --> 00:19:21,610
+.. ال .. لو أخدنا .. يعني عندنا بصير تانية الـ X
+
+236
+00:19:21,610 --> 00:19:24,130
+أصغر أصغر شويه واحد معناته أصغر شويه اتنين معناته
+
+237
+00:19:24,130 --> 00:19:28,030
+احد يعني ا واحد جزء من اتنين جزء من اتنين طيب
+
+238
+00:19:28,030 --> 00:19:34,430
+مظبوط الحاجة تقولها طيب شوفوا لان بس عشان أتعرف
+
+239
+00:19:34,430 --> 00:19:38,210
+عليها هنا to show that a k is closed ده انت بتقول
+
+240
+00:19:38,210 --> 00:19:40,590
+انه a k مثلا كل واحدة فيه نقش معناها closed set
+
+241
+00:19:40,590 --> 00:19:47,870
+خدوا X في مين في ال a closure اه a k closurethen
+
+242
+00:19:47,870 --> 00:19:51,890
+there exists a sequence xj بدأ اثبت لكم بلق ال
+
+243
+00:19:51,890 --> 00:19:54,410
+sequence xj في ال a كي ا convert the mean لل x
+
+244
+00:19:54,410 --> 00:19:59,030
+بيكون خلصنا صح؟ then there is a sequence xj of
+
+245
+00:19:59,030 --> 00:20:04,010
+elements لأ اسف لان اثبتت اللي هي ال x في ال a كي
+
+246
+00:20:04,010 --> 00:20:09,310
+اخدت في ال a كلوجة بدأ اثبتها في ال a فبصير مش هوا
+
+247
+00:20:09,310 --> 00:20:14,030
+مشاكلكم ما انتم معايا كي باثبت ان ال a كي is
+
+248
+00:20:14,030 --> 00:20:19,340
+closedالـ AK closure بيساوي الـ A كيف بيداخدها؟
+
+249
+00:20:19,340 --> 00:20:23,320
+بيداخد X في الـ AK closure و أثبتها أن X في 100 في
+
+250
+00:20:23,320 --> 00:20:28,040
+الـ AK لأن العكس صحيح دايما، اه، ماشي بخير، اذا
+
+251
+00:20:28,040 --> 00:20:34,450
+خلينا نشوف الآننشوف الآن خدوا x في الـ a k closure
+
+252
+00:20:34,450 --> 00:20:38,510
+إذا حسب تعريف الـ x في ال a k closure بقدر ألاقي
+
+253
+00:20:38,510 --> 00:20:42,530
+sequence xj of elements in a k such that limit الـ
+
+254
+00:20:42,530 --> 00:20:45,610
+xj أيش بساوي بساوي الـ x هذا تعريف الـ x والي
+
+255
+00:20:45,610 --> 00:20:49,470
+موجودة في ال a closure في ال a k closure then for
+
+256
+00:20:49,470 --> 00:20:56,570
+any fixed n we have norm Tn xj هذا الـ xj هذا الـ
+
+257
+00:20:56,570 --> 00:21:01,670
+xj أصغر أو يساوي مين أصغر يساوي kأه من تعريفها لأن
+
+258
+00:21:01,670 --> 00:21:04,990
+الـ X هو الموجودة في ال .. آسف في الـ XJ هو
+
+259
+00:21:04,990 --> 00:21:11,570
+الموجودة في الـ AK وعلاصر الـ AK إيه شمالها؟ XJ
+
+260
+00:21:11,570 --> 00:21:18,090
+فيها إذا TN XJ أظهر فيها OK ماشي الحال شوف شوية
+
+261
+00:21:18,090 --> 00:21:20,050
+علامة ماعرفش علاقة بال convergence إذا انتبهوا
+
+262
+00:21:20,050 --> 00:21:27,370
+الآن عندي الـ XJ هدولة من وين جاية؟ من الـ AK مدام
+
+263
+00:21:27,370 --> 00:21:33,660
+الـ XJفي الـ AK إذا انتحقق شروطها ايش شروطها ان
+
+264
+00:21:33,660 --> 00:21:39,760
+يكون TN هذي ال XJ أصغر يساوي مين؟ أصغر يساوي K صح؟
+
+265
+00:21:39,760 --> 00:21:44,700
+لكل N هذا الكلام طيب إذا صار عندي TN XJ أصغر يساوي
+
+266
+00:21:44,700 --> 00:21:48,880
+Kلأن by the continuity of TN كل واحدة ما هي
+
+267
+00:21:48,880 --> 00:21:52,720
+bounded linear bounded then continuous and the
+
+268
+00:21:52,720 --> 00:21:55,480
+continuity of norm ويهب يعني ما نقدر ندخل ال limit
+
+269
+00:21:55,480 --> 00:22:00,520
+وين؟ جوا norm و جوا mean ال TN فبصير عنده اللي هو
+
+270
+00:22:00,520 --> 00:22:05,100
+limit دخل جوا ودخل على ال TN ودخل جوا الآن فبصير
+
+271
+00:22:05,100 --> 00:22:09,200
+عنده TN limit XJ و limit XJ ايش بيساوي؟ بيصير X
+
+272
+00:22:09,200 --> 00:22:13,940
+إذا صار عنده norm TN X أصغر أو شوه مين؟ أصغر أو
+
+273
+00:22:13,940 --> 00:22:18,190
+شوه كامما معناته هذا؟ مدام الـ TN X أصغر أو يساوي
+
+274
+00:22:18,190 --> 00:22:23,050
+K هذا أحلها أن تكون دوا الـ A K إذا صار عند ال X
+
+275
+00:22:23,050 --> 00:22:29,030
+في الـ A K معناته صارت A K is closed لأنه
+
+276
+00:22:29,030 --> 00:22:33,430
+حسب الكلام اللي حكيته قبل شوية طيب اللي بعده for
+
+277
+00:22:33,430 --> 00:22:38,690
+every X element in X there exists CX such that
+
+278
+00:22:38,690 --> 00:22:43,830
+norm TN X أصغر أو يساوي CX for all N هذا مقطع مقطع
+
+279
+00:22:43,830 --> 00:22:49,720
+الـ Nهلقن then for each x element in x belongs to
+
+280
+00:22:49,720 --> 00:22:54,420
+some a k لإن احنا مسترضين ان ال X ايش بتساوي احنا
+
+281
+00:22:54,420 --> 00:23:02,200
+ال X انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+282
+00:23:02,200 --> 00:23:02,240
+انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+283
+00:23:02,240 --> 00:23:02,920
+انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+284
+00:23:02,920 --> 00:23:05,620
+انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+285
+00:23:05,620 --> 00:23:09,280
+انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+286
+00:23:09,280 --> 00:23:09,320
+انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+287
+00:23:09,320 --> 00:23:09,320
+انزل انزل
+
+288
+00:23:22,360 --> 00:23:26,480
+ماشي الحال احنا ماشي الحال هذا أثبتنا
+
+289
+00:23:29,810 --> 00:23:34,050
+الان I X element in X belongs to مين؟ to some A K
+
+290
+00:23:34,050 --> 00:23:37,270
+من مين؟ من اللي عرفناها لأنه في الأخر هيطلع اللي
+
+291
+00:23:37,270 --> 00:23:41,990
+هو T أن X الها أصغر أو شاوى some number الواحد،
+
+292
+00:23:41,990 --> 00:23:43,890
+التاني، التلاتي، ماكانش من الواحد، من التاني، من
+
+293
+00:23:43,890 --> 00:23:46,790
+البعد، من التلاتي، من البعد وكذا وكأن ال X يعضرها
+
+294
+00:23:46,790 --> 00:23:51,280
+عن union مين؟ ونقدر نكتبها union لل A Kإذا صار
+
+295
+00:23:51,280 --> 00:23:55,180
+عندى الان X بelongs to some A K Hence X can be
+
+296
+00:23:55,180 --> 00:23:58,080
+written as ال union لمن؟ لل A K كمان واحدة عند من؟
+
+297
+00:23:58,080 --> 00:24:02,520
+لما أنت منها نهاية وكل واحدة منهم اشمالها اللى هو
+
+298
+00:24:02,520 --> 00:24:08,660
+عبارة عن اللى هو closed كمان مرة يا جماعة الآن أي
+
+299
+00:24:08,660 --> 00:24:16,790
+X في ال X لو حسبنا لها T عن Xالـ T and X لأن T and
+
+300
+00:24:16,790 --> 00:24:24,370
+X هتكون الـ X يانا يانا يانا يانا يانا يانا يانا
+
+301
+00:24:24,370 --> 00:24:26,430
+يانا يانا يانا يانا يانا يانا يانا يانا يانا يانا
+
+302
+00:24:26,430 --> 00:24:27,550
+يانا يانا يانا يانا يانا يانا يانا يانا يانا يانا
+
+303
+00:24:27,550 --> 00:24:28,130
+يانا يانا يانا يانا يانا يانا يانا يانا يانا يانا
+
+304
+00:24:28,130 --> 00:24:28,130
+يانا يانا يانا يانا يانا يانا يانا يانا يانا يانا
+
+305
+00:24:28,130 --> 00:24:28,130
+يانا يانا يانا يانا يانا يانا يانا يانا يانا يانا
+
+306
+00:24:28,130 --> 00:24:34,810
+يانا يانا يانا يانا يانا يانا يانا يانا يانا يانا
+
+307
+00:24:34,810 --> 00:24:41,790
+يانا
+
+308
+00:24:41,790 --> 00:24:48,280
+يانا يحكيتها قبل بشوية أنه ما دامت اللي هي X
+
+309
+00:24:48,280 --> 00:24:53,260
+complete إذا بالـ K-Pair Category Theorem اللي
+
+310
+00:24:53,260 --> 00:24:58,240
+كتبت في آخر النظرية A Knot Contains An Open Ball
+
+311
+00:24:58,240 --> 00:25:02,220
+في واحدة من هنا على الأقل اللي فرهنتها في أول K
+
+312
+00:25:02,220 --> 00:25:05,280
+-Pair Category Theorem الجزء الثاني منها أنه ما
+
+313
+00:25:05,280 --> 00:25:09,720
+دامت X complete و X مكتوبة على صورة Union لClosed
+
+314
+00:25:09,720 --> 00:25:13,790
+Setإذاً في واحدة من هنا مش rare يعني في واحدة من
+
+315
+00:25:13,790 --> 00:25:17,230
+هنا على الأقل a k note contains open ball سمناها
+
+316
+00:25:17,230 --> 00:25:21,130
+إيش اسمها a k note بعد أذنكم say اللي هي ال open
+
+317
+00:25:21,130 --> 00:25:25,310
+ball هذه بي نوت بسوا بي إكس نوت و R جزئية من مين
+
+318
+00:25:25,310 --> 00:25:28,570
+من a k note اللي هي سمناها كنا a k note و كلها
+
+319
+00:25:28,570 --> 00:25:32,910
+جميعها نوت اللي هي close بتطلع نفسها طيب الان اطلع
+
+320
+00:25:32,910 --> 00:25:37,850
+على فوق now let x be element in x be R literally
+
+321
+00:25:38,750 --> 00:25:44,830
+and non-zero و let z بتساوي x not زائد gamma x
+
+322
+00:25:44,830 --> 00:25:52,590
+اللي هي x not اللي حكينا عنها فوق الآن خد gamma
+
+323
+00:25:52,590 --> 00:25:57,060
+بتساوي R على 2 في جذر ال X لاتساوي 0ماشي الحال
+
+324
+00:25:57,060 --> 00:26:00,160
+يعني الجامعة مابتديش إيها سفر اللي .. اللي إيها
+
+325
+00:26:00,160 --> 00:26:03,000
+سفر اللي هي R على 2 جدر ال X مابتش .. مابتسويش سفر
+
+326
+00:26:03,000 --> 00:26:06,640
+ال .. ال .. ال .. الجامعة أخي سميت هيك جامعة R على
+
+327
+00:26:06,640 --> 00:26:09,420
+2 في جدر ال X هذه طبعاً R اللي هي ال .. ال ..
+
+328
+00:26:09,420 --> 00:26:12,140
+المركز اللي .. اللي .. النصف القطر مش سفر إذن هذا
+
+329
+00:26:12,140 --> 00:26:14,300
+كله مش سفر إذا الجامعة نفسي صارت أيه أشمل أنها مش
+
+330
+00:26:14,300 --> 00:26:17,820
+سفر عشان بتكسب عليها بعد شوية أخدت Z بتسوي X نور
+
+331
+00:26:17,820 --> 00:26:21,100
+زي الجامعة X ليش هذه؟ أجيت بعد شوية بتشوف عسى
+
+332
+00:26:21,100 --> 00:26:25,460
+استخدامي أن توصلي أنه نور الـTN
+
+333
+00:26:26,750 --> 00:26:30,170
+أصغر أو ساوي، ايش بالنسبة للـ Gamma؟ هذي C يعني
+
+334
+00:26:30,170 --> 00:26:38,130
+هذي تنشيوفكم احسبلي الآن خد الـ Z minus X naught
+
+335
+00:26:38,130 --> 00:26:43,090
+طالعها بـ C Gamma Xبصير norm of z نقص x0 بيسوي
+
+336
+00:26:43,090 --> 00:26:47,950
+norm of gamma x norm of gamma x اضرب اللي هو اللي
+
+337
+00:26:47,950 --> 00:26:51,670
+هي norm of x في الجامعة هي هذه norm of x مع norm
+
+338
+00:26:51,670 --> 00:26:55,270
+of x بيبقى همين R على اتنين R على اتنين اصغر من
+
+339
+00:26:55,270 --> 00:26:59,030
+مين من R يعني بمعنى اخر z minus x0 اصغر من R صارت
+
+340
+00:26:59,030 --> 00:27:04,510
+z في ال ballباشي إذا hence z في b note and so z في
+
+341
+00:27:04,510 --> 00:27:09,410
+واحدة من مين من ال a k not اللي هي لظبط هذه لأن b
+
+342
+00:27:09,410 --> 00:27:13,110
+not جزء من مين من ال a k not إذا صارت عند ال z هذه
+
+343
+00:27:13,110 --> 00:27:17,250
+اللي كتبته بالصورة هذه في ال a k not then by the
+
+344
+00:27:17,250 --> 00:27:21,130
+definition of a k not هيكون ال T and z أصغر شهو
+
+345
+00:27:21,130 --> 00:27:26,410
+مين؟ k notهذا الكلام for all and عند ال X note في
+
+346
+00:27:26,410 --> 00:27:31,850
+B note صبست من A K note اذا مادام X note هنا اذا
+
+347
+00:27:31,850 --> 00:27:37,250
+هنا مادام X note هنا اذا بتحقق خاصية انه TN X note
+
+348
+00:27:37,250 --> 00:27:42,100
+أظهر شاومين اللي هي K noteمشاكل مؤهلة تدخل في الـ
+
+349
+00:27:42,100 --> 00:27:45,900
+Knot إذا صانعين دي ال norm ال TN X knot برضه أصغر
+
+350
+00:27:45,900 --> 00:27:50,480
+يساوي مين Knot و هاد ال TN Z برضه أصغر يساوي مين
+
+351
+00:27:50,480 --> 00:27:58,120
+Knot لأن خلّينا نستخدم تلاتة و ال X إيش بتساوي Z
+
+352
+00:27:58,120 --> 00:28:04,690
+minus X knot على Gammathen for all and لأن norm of
+
+353
+00:28:04,690 --> 00:28:08,090
+T and X لأنها ال X كانت arbitrary وال X note هذه
+
+354
+00:28:08,090 --> 00:28:11,290
+اللي لجيتها اللي هي ال bridge اللي ده صار من خلاله
+
+355
+00:28:11,290 --> 00:28:19,290
+بيصير norm of T and X بساوي اللي هونورم الـ TN
+
+356
+00:28:19,290 --> 00:28:23,170
+لهذه بنطلع الواحد على جامعة برا بيصير واحد على
+
+357
+00:28:23,170 --> 00:28:28,430
+جامعة لأنها موجبة في TN of Z minus X0 وهذه
+
+358
+00:28:28,430 --> 00:28:31,490
+بالتريان جالين كواليتي أصغر أو ساوي حضرتله هذا
+
+359
+00:28:31,490 --> 00:28:38,570
+أوجدت TN Z و TN X0 أصغر أو ساوي أنه TN Z زي TN X0
+
+360
+00:28:38,570 --> 00:28:43,470
+هذه أوجدناها قبل بشوية فوق اللي هي أصغر أو يساوي
+
+361
+00:28:43,470 --> 00:28:45,710
+اللي هو 2K0
+
+362
+00:28:48,270 --> 00:28:52,490
+أوجدناها هيها أصغر يساوي كنوت وهذه أصغر يساوي مين؟
+
+363
+00:28:52,490 --> 00:28:57,810
+كنوت بدي أعوض مكانها صارت واحد على جامعة TNZ أصغر
+
+364
+00:28:57,810 --> 00:29:01,750
+من كنوت وهذه أصغر من كنوت التنتين أصغر من مين؟ من
+
+365
+00:29:01,750 --> 00:29:06,390
+اتنين كنوت فبصير عبارة عن اللي هو عوضه عن جامعة
+
+366
+00:29:06,390 --> 00:29:10,950
+بقيمتها اللي هي R على اتنين في ال Normal X بصير
+
+367
+00:29:10,950 --> 00:29:15,490
+اللي هو اتنين Normal X على R لأنها مجلوبها فاهمين؟
+
+368
+00:29:15,940 --> 00:29:19,760
+فى اتنين كينوت اتنين مع اتنين فبصير عبارة عن كينوت
+
+369
+00:29:19,760 --> 00:29:22,520
+اتنين فى اتنين لأ اتنين فى اتنين فى اربع بروحانش
+
+370
+00:29:22,520 --> 00:29:26,100
+مبارك اتنين فى اتنين اربع كينوت عالمين على ال R
+
+371
+00:29:26,100 --> 00:29:35,300
+اللى هى في X يعني بصير عندى TNX TNX
+
+372
+00:29:35,300 --> 00:29:40,900
+أزرع شاوي اللى طلع عندى اتنين فى اتنين أربعة على A
+
+373
+00:29:40,900 --> 00:29:47,050
+أربعةكنوت على R فنور main ال X خدوا الأن ال
+
+374
+00:29:47,050 --> 00:29:51,130
+supremum ايه اسمه على هذه لل Xات اللي مش سفر و
+
+375
+00:29:51,130 --> 00:29:56,510
+خدوا ال supremumبطلع هذا norm الـ TN أصغر أو يساوي
+
+376
+00:29:56,510 --> 00:30:02,710
+4k نوت على R وهذا ثابت إذا بغض النظر عن اللي هو
+
+377
+00:30:02,710 --> 00:30:07,550
+الـ TN بطلع نورم الـ TN إلهم كلهم أصغر أو يساوي 4k
+
+378
+00:30:07,550 --> 00:30:14,250
+نوت وهذا يعني T note TN أصغر يساوي C for all N حيث
+
+379
+00:30:14,250 --> 00:30:19,850
+C عبارة عن مقدار ثابت اطلع لفترة يلّا لبعده الان
+
+380
+00:30:19,850 --> 00:30:25,070
+space of polynomialsتطبيق على اللي هو النظرية اللي
+
+381
+00:30:25,070 --> 00:30:30,230
+قبل بشوية إيش
+
+382
+00:30:30,230 --> 00:30:36,510
+بتقول هذه؟النورم الـ space X of all polynomials
+
+383
+00:30:36,510 --> 00:30:42,910
+ليس كامل تحت النورم التي تسمى بالنورم الـ X بيساوي
+
+384
+00:30:42,910 --> 00:30:47,190
+الماكسيمم Gamma J Alpha J over J where Alpha 0
+
+385
+00:30:47,190 --> 00:30:50,970
+وAlpha 1 وAlpha 2 are the coefficients of X يعني
+
+386
+00:30:50,970 --> 00:30:55,590
+بدنا نشوف كيف نستخدم الإجابة اللي قبل بشوية على
+
+387
+00:30:55,590 --> 00:31:02,730
+أساس أننا نثبت أن X ليس كاملالـ X إيش ماله؟ مش
+
+388
+00:31:02,730 --> 00:31:05,170
+complete مين الـ X هذا هو الـ space of all
+
+389
+00:31:05,170 --> 00:31:09,330
+polynomial under this norm under this norm ممكن
+
+390
+00:31:09,330 --> 00:31:14,310
+حكينا عليه قبل هيك بس بطريقة أخرى كان أظن سؤال
+
+391
+00:31:14,310 --> 00:31:19,990
+معاكم و لا لأ سؤال و لا لأ طيب
+
+392
+00:31:19,990 --> 00:31:24,970
+خلينا الأن نستخدم اللي هو النظرية اللي جابله شوية
+
+393
+00:31:24,970 --> 00:31:27,230
+في إثبات اللي هو
+
+394
+00:31:30,090 --> 00:31:36,090
+النظرية كانت تقول إن لو كان عندك TN من X لعند Y
+
+395
+00:31:36,090 --> 00:31:45,150
+هذه complete وهذه لأ ومش شرط يعني قصدي و norm TN X
+
+396
+00:31:45,150 --> 00:31:52,470
+أصغر يساوي CX هذا مع بعض بيعطيني norm TN أصغر
+
+397
+00:31:52,470 --> 00:31:54,050
+يساوي 100 S
+
+398
+00:31:57,120 --> 00:32:03,120
+بدي اللي هي أجيب اللي هو عنده we construct a
+
+399
+00:32:03,120 --> 00:32:06,880
+sequence of bounded linear functionals on مين on X
+
+400
+00:32:06,880 --> 00:32:10,260
+sequence
+
+401
+00:32:10,260 --> 00:32:16,180
+الـ TN بدي الـ TN يعني هاخدها من ال polynomial TN
+
+402
+00:32:16,180 --> 00:32:20,900
+أو أفعى اللي بسميهامن الـ polynomials أو the space
+
+403
+00:32:20,900 --> 00:32:24,540
+of all polynomials لعند مين الـ K اللي هو Escalar
+
+404
+00:32:24,540 --> 00:32:29,100
+field الآن بدّي اللي هو أعملها أن هذه تتحقق لكن
+
+405
+00:32:29,100 --> 00:32:33,240
+هذه إيش مالها؟ لا تتحقق لأن لو كان هذا complete
+
+406
+00:32:33,240 --> 00:32:37,900
+اتوماتيك هذا هتتحقق بما أنه ما اتحققتش إذن وين
+
+407
+00:32:37,900 --> 00:32:41,740
+هيكون عنده؟ لو P is not complete إذن we construct
+
+408
+00:32:41,740 --> 00:32:44,840
+a sequence of bounded linear functional on X أو
+
+409
+00:32:44,840 --> 00:32:49,840
+functional on Xwhich satisfies one but not two
+
+410
+00:32:49,840 --> 00:32:53,680
+ماشي الحال let X be a non-zero polynomial of
+
+411
+00:32:53,680 --> 00:32:57,680
+degree إيش ما قالها NX يعني ال X بولونوميال درجتها
+
+412
+00:32:57,680 --> 00:33:02,930
+إيش بتساوي NX ماشي الحال يعني بعد ال NX أصفراللي
+
+413
+00:33:02,930 --> 00:33:08,030
+هو الـ coefficients ثم X of T بتساوي Alpha T ..
+
+414
+00:33:08,030 --> 00:33:11,890
+Alpha J .. T is J .. J من صفر لمين .. لعند .. من
+
+415
+00:33:11,890 --> 00:33:15,470
+النهاية كتبتها الصورة هذه و أنا بقول أشمالها ال
+
+416
+00:33:15,470 --> 00:33:19,090
+degree اللي هي نكس إذا هتكون ال Alpha J بتساوي صفر
+
+417
+00:33:19,090 --> 00:33:23,250
+فوق كل الجزر اللي أشمالهن اللي أكبر من نكس هذا دي
+
+418
+00:33:23,250 --> 00:33:27,190
+معناته ال degree اللي هي .. بتساوي نكس الان let's
+
+419
+00:33:27,190 --> 00:33:31,540
+of .. هنشوف كيف بدو .. بدو يعرفإذا الأن لأ خلّيني
+
+420
+00:33:31,540 --> 00:33:37,760
+أنزل شوية لأن let FN be a sequence of functionals
+
+421
+00:33:37,760 --> 00:33:48,120
+that are defined on X by FN of 0 بساوي 0 FN of X
+
+422
+00:33:48,120 --> 00:33:51,400
+بساوي Alpha node زي ده الف واحد زي ده الف اتنين زي
+
+423
+00:33:51,400 --> 00:33:55,780
+ده الف انمين ماقص واحد الآن
+
+424
+00:33:57,390 --> 00:34:01,610
+عندي وكأني باخد اللي هو الـ Coefficient إسلاميين
+
+425
+00:34:01,610 --> 00:34:07,080
+للي عندي هانعندي مثلا X of T بيساوي Alpha Note
+
+426
+00:34:07,080 --> 00:34:10,640
+زايد Alpha واحد T زايد Alpha اتنين T تربية زايد
+
+427
+00:34:10,640 --> 00:34:14,080
+Alpha اتنين T تربية الاخرين ايش بياخد مجموع ال
+
+428
+00:34:14,080 --> 00:34:16,320
+coefficients FN of X ايش بيساوي مجموع ال
+
+429
+00:34:16,320 --> 00:34:20,120
+coefficients سبعتها it is left to the reader to
+
+430
+00:34:20,120 --> 00:34:24,180
+show that for any fixed N FN ايش معناه is linear
+
+431
+00:34:24,180 --> 00:34:28,720
+FN is linear بتكون بثبتها بثبتها يعني اثباتها اللي
+
+432
+00:34:28,720 --> 00:34:29,040
+هو
+
+433
+00:34:31,910 --> 00:34:39,290
+برضه قمر يعني ان شاء الله مابكونش صعب طيب
+
+434
+00:34:39,290 --> 00:34:46,570
+عندي بتاخدوا اللي هو X اللي هو بتسوي Alpha node
+
+435
+00:34:46,570 --> 00:34:52,450
+زائد Alpha واحد X زائد Alpha N ناقص واحد مثلا X أس
+
+436
+00:34:52,450 --> 00:34:57,150
+N ناقص واحد الاخري وش ال Xات هاذ T
+
+437
+00:35:02,090 --> 00:35:07,350
+Y بنفس الأشي بيساوي مثلا Gamma node زي Gamma 1
+
+438
+00:35:07,350 --> 00:35:11,170
+plus Gamma n minus 1 plus Gamma n minus 1 plus
+
+439
+00:35:11,170 --> 00:35:11,210
+Gamma n minus 1 plus Gamma n minus 1 plus Gamma n
+
+440
+00:35:11,210 --> 00:35:11,750
+minus 1 plus Gamma n minus 1 plus Gamma n minus 1
+
+441
+00:35:11,750 --> 00:35:13,190
+plus Gamma n minus 1 plus Gamma n minus 1 plus
+
+442
+00:35:13,190 --> 00:35:13,230
+Gamma n minus 1 plus Gamma n minus 1 plus Gamma n
+
+443
+00:35:13,230 --> 00:35:13,230
+minus 1 plus Gamma n minus 1 plus Gamma n minus 1
+
+444
+00:35:13,230 --> 00:35:13,310
+plus Gamma n minus 1 plus Gamma n minus 1 plus
+
+445
+00:35:13,310 --> 00:35:13,310
+Gamma n minus 1 plus Gamma n minus 1 plus Gamma n
+
+446
+00:35:13,310 --> 00:35:13,450
+minus 1 plus Gamma n minus 1 plus Gamma n minus 1
+
+447
+00:35:13,450 --> 00:35:13,550
+plus Gamma n minus 1 plus Gamma n minus 1 plus
+
+448
+00:35:13,550 --> 00:35:14,250
+Gamma n minus 1 plus Gamma n minus 1 plus Gamma n
+
+449
+00:35:14,250 --> 00:35:15,210
+minus 1 plus Gamma n minus 1 plus Gamma n minus 1
+
+450
+00:35:15,210 --> 00:35:15,710
+plus Gamma n minus 1 plus Gamma n minus 1 plus
+
+451
+00:35:15,710 --> 00:35:21,510
+Gamma n minus 1 plus Gamma n minus 1 plus Gamma n
+
+452
+00:35:21,510 --> 00:35:24,450
+minus 1 plus Gamma n
+
+453
+00:35:30,230 --> 00:35:31,390
+للتفصيل
+
+454
+00:35:33,880 --> 00:35:37,820
+حالان خلاص فكّينا من أنها Linear لأن نثبت أنها إيه
+
+455
+00:35:37,820 --> 00:35:40,960
+شمالها لإن نصل للboundedness أولا الشيء ال
+
+456
+00:35:40,960 --> 00:35:44,460
+absolute value لـ α J ال coefficients هدولة أكيد
+
+457
+00:35:44,460 --> 00:35:48,080
+أصغر أو أشهر هو ال maximum اللي هو مين هو normal X
+
+458
+00:35:48,080 --> 00:35:52,240
+مش normal X هو ال maximum ال maximum لأ اللي هي ال
+
+459
+00:35:52,240 --> 00:35:55,940
+coefficients اللي عند .. اللي عندي normal X كده
+
+460
+00:35:55,940 --> 00:36:00,300
+عرفنا ال norm احنا then ال absolute value لأفقن of
+
+461
+00:36:00,300 --> 00:36:06,620
+Xماله ال FN of X هيهم FN of X اللي هي عبارة عن ألف
+
+462
+00:36:06,620 --> 00:36:10,080
+نوت و ألف واحد و كل واحدة منهم أصغر من مين من نورم
+
+463
+00:36:10,080 --> 00:36:16,640
+ال X إذا مجموحين أصغر يساوي N في مين في نورم ال F
+
+464
+00:36:16,860 --> 00:36:23,780
+هذا كل fixed N يعني F1 أصغر من ساوي Normal X F2
+
+465
+00:36:23,780 --> 00:36:28,720
+أصغر من N2 Normal X وهكذا إذا F1 وF2 وF3 كله نجمان
+
+466
+00:36:28,720 --> 00:36:32,260
+هم bounded functionals إذا صار عبارة عن sequence
+
+467
+00:36:32,260 --> 00:36:36,380
+of bounded functionals ومش هيك لكل X element in X
+
+468
+00:36:36,380 --> 00:36:39,460
+ده أنا متلزمني هذا بعد شوية خدوا ال absolute value
+
+469
+00:36:39,460 --> 00:36:44,740
+ل FN of Xالأبسلوت زي الـ αن نوف إكس هي هتكون أصغر
+
+470
+00:36:44,740 --> 00:36:47,300
+أو ساوية أن إكس زائد واحد في ال maximum للـ alpha
+
+471
+00:36:47,300 --> 00:36:53,760
+jليش؟ لأنه ال .. ال .. ال .. البعد لهذه أسفار أه
+
+472
+00:36:53,760 --> 00:36:57,980
+وكل واحد اللي هو إيش ماله اللي هو أكيد هدولة إيش
+
+473
+00:36:57,980 --> 00:37:02,020
+قمتهن Alpha 0, Alpha 1, Alpha 2, Alpha 3 إلى ..
+
+474
+00:37:02,020 --> 00:37:05,520
+إلى ما .. إلى ما شاء الله أكيد مش هيبقوا الإتعداد
+
+475
+00:37:05,520 --> 00:37:09,820
+هن لأنك زاد واحد لأنه بعدها بيصير إنه أسفار فبيصير
+
+476
+00:37:09,820 --> 00:37:12,800
+عنده أصغر أو ساوي اللي هو هذه في ال coefficients
+
+477
+00:37:12,800 --> 00:37:15,840
+الأولة .. الأولة .. الأولة كله أصغر من ال maximum
+
+478
+00:37:15,840 --> 00:37:19,320
+فصار مقدموح أن أصغر من مين من هذا في ال .. في هذا
+
+479
+00:37:23,670 --> 00:37:29,470
+عيدوا يدمع أف أن أو في X هيها ألف نوت ألف واحد ألف
+
+480
+00:37:29,470 --> 00:37:33,310
+اتنين ألف أن هال جهة ال absolute value لها أصغر أو
+
+481
+00:37:33,310 --> 00:37:36,130
+شاوري هذه ال absolute value هذه زي ال absolute
+
+482
+00:37:36,130 --> 00:37:39,830
+value هذه زي ال absolute value لهذه الآن هذولة
+
+483
+00:37:39,830 --> 00:37:44,270
+أصغر أو شاوري maximum تبحن كل واحدةعداد هنا دولة
+
+484
+00:37:44,270 --> 00:37:49,750
+لن يتجاوز بغض النظر عن X لن يتجاوز ال main اللي هو
+
+485
+00:37:49,750 --> 00:37:53,490
+ال NX زائد واحد اللي هي درجة ال polynomial زائد
+
+486
+00:37:53,490 --> 00:37:57,330
+واحد لن يتجاوزها فبصير عند ال FNX أصغر أو ساوي
+
+487
+00:37:57,330 --> 00:37:59,690
+اللي هو هذا المقدار في هذا اللي هو بعتمد على ال
+
+488
+00:37:59,690 --> 00:38:03,670
+main على X أصغر أو ساوي CX since X has و بقى
+
+489
+00:38:03,670 --> 00:38:08,090
+polynomial of degree NX that has NX زائد واحد من
+
+490
+00:38:08,090 --> 00:38:12,780
+ال coefficients اطلع إلى فوقإذن therefore ال
+
+491
+00:38:12,780 --> 00:38:15,540
+absolute value of N of X satisfies one اللي في
+
+492
+00:38:15,540 --> 00:38:19,540
+الآخر الآن أنا بتثبتلك أنه لن يحقق مين اللي هو هذه
+
+493
+00:38:19,540 --> 00:38:26,320
+norm لأف N مستحيل يحققلك أنه أصغر أو سوى C بل
+
+494
+00:38:26,320 --> 00:38:32,650
+هأثبتلك أنه unbounded شوفخد الآن finally we show
+
+495
+00:38:32,650 --> 00:38:35,570
+that fn does not satisfy اتنين choose a polynomial
+
+496
+00:38:35,570 --> 00:38:39,030
+x by x of t بالساوية وصميش اللي التي جيه جيه من
+
+497
+00:38:39,030 --> 00:38:41,630
+سفر لعند مين لعند ان هاي ال X تبعتين اللي
+
+498
+00:38:41,630 --> 00:38:46,920
+بتاخدلكيها اللي بتخرب الدنيا then norm ال Xبساوة
+
+499
+00:38:46,920 --> 00:38:50,020
+واحدة انه ال maximum اللي هنا دول العوامل كل واحد
+
+500
+00:38:50,020 --> 00:38:52,800
+واحد واحد ده النورم هنا ايش بساوة بساوة واحدة ده
+
+501
+00:38:52,800 --> 00:38:55,420
+النورم ال X بساوة واحدة ال FN of X في هذه الحالة
+
+502
+00:38:55,420 --> 00:38:59,060
+ايش بساوة اللي هو واحد زاد واحد زاد واحد ده ايش
+
+503
+00:38:59,060 --> 00:39:04,820
+بساوة N من المصير اللي بساوة نهن ويساوة N في مين
+
+504
+00:39:04,820 --> 00:39:10,740
+في نورم ال X وهذا معناته صار عنده ال FN of X بساوة
+
+505
+00:39:10,740 --> 00:39:17,310
+N في نورم ال Xإذا Normal FN هيكون هو الـ supremum
+
+506
+00:39:17,310 --> 00:39:21,750
+هيكون أكبر أو يساوي واحدة منهم اللي هي عبارة عن
+
+507
+00:39:21,750 --> 00:39:24,910
+هذا FN of X اللي هي أكبر يساوي FN of X ع Normal X
+
+508
+00:39:25,520 --> 00:39:29,540
+الـ N في X على نورم الـ X و يسوى N صارت نورم الـ
+
+509
+00:39:29,540 --> 00:39:33,540
+FN أكبر ويسوى ومياشي سوى N إذن مستحيل اللي هي
+
+510
+00:39:33,540 --> 00:39:37,760
+hence the sequence of N is unbounded and so two is
+
+511
+00:39:37,760 --> 00:39:42,220
+not satisfied they are satisfied then أو therefore
+
+512
+00:39:42,220 --> 00:39:46,800
+by uniform boundedness theorem ال X is not
+
+513
+00:39:46,800 --> 00:39:49,980
+complete أو اللي هو the space of all such
+
+514
+00:39:49,980 --> 00:39:53,580
+polynomials under this norm is not complete وإلى
+
+515
+00:39:53,580 --> 00:39:54,440
+لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/zFznbPjt0NA_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/zFznbPjt0NA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..ebf32760669dc56ed07c52d5b20e3033e19f373b
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/zFznbPjt0NA_raw.json
@@ -0,0 +1 @@
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يعني absolutely convergent مين ال absolutely convergent هاد؟ لأنه بدون absolute value أو بدون نهار مين بتطلع ال summation X to the JJ من صفر إلى مين إلى ما لليها يعني اللي في الواقع هي هاد إذا صارت هاد عبارة عن أشمالها converges absolutely", "tokens": [28814, 15730, 341, 1355, 300, 2139, 28811, 295, 1783, 5551, 8592, 2304, 6027, 11296, 9652, 2880, 3122, 37495, 22653, 13672, 1829, 10874, 14407, 20328, 9640, 2655, 8032, 18513, 9652, 2880, 37495, 22653, 3122, 9652, 6930, 3714, 9957, 2423, 3122, 9652, 6930, 8032, 18513, 22807, 5296, 33456, 3224, 47525, 11536, 8236, 2158, 34051, 47525, 11536, 8717, 3224, 9640, 3714, 9957, 39894, 9566, 1211, 3615, 2423, 28811, 1783, 281, 264, 21386, 9154, 20328, 5172, 2288, 30731, 3714, 9957, 30731, 19446, 5296, 20292, 11296, 37495, 22653, 13672, 1829, 8978, 2423, 14407, 4587, 3615, 39896, 8032, 18513, 11933, 15730, 20328, 9640, 2655, 8032, 18513, 6225, 3555, 9640, 3660, 18871, 5551, 8592, 2304, 6027, 11296, 9652, 2880, 3122], "avg_logprob": 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"probability": 0.513671875}, {"start": 999.77, "end": 1000.15, "word": " summation", "probability": 0.91455078125}, {"start": 1000.15, "end": 1000.47, "word": " X", "probability": 0.81689453125}, {"start": 1000.47, "end": 1000.63, "word": " to", "probability": 0.54931640625}, {"start": 1000.63, "end": 1000.75, "word": " the", "probability": 0.86328125}, {"start": 1000.75, "end": 1000.93, "word": " JJ", "probability": 0.269287109375}, {"start": 1000.93, "end": 1001.19, "word": " من", "probability": 0.97265625}, {"start": 1001.19, "end": 1001.43, "word": " صفر", "probability": 0.7413736979166666}, {"start": 1001.43, "end": 1001.57, "word": " إلى", "probability": 0.9130859375}, {"start": 1001.57, "end": 1001.81, "word": " مين", "probability": 0.8349609375}, {"start": 1001.81, "end": 1002.03, "word": " إلى", "probability": 0.93359375}, {"start": 1002.03, "end": 1002.17, "word": " ما", "probability": 0.314453125}, {"start": 1002.17, "end": 1002.53, "word": " لليها", "probability": 0.4895833333333333}, {"start": 1002.53, "end": 1002.67, "word": " يعني", "probability": 0.5916748046875}, {"start": 1002.67, "end": 1003.05, "word": " اللي", "probability": 0.90185546875}, {"start": 1003.05, "end": 1003.15, "word": " في", "probability": 0.94580078125}, {"start": 1003.15, "end": 1003.49, "word": " الواقع", "probability": 0.8675537109375}, {"start": 1003.49, "end": 1003.65, "word": " هي", "probability": 0.8408203125}, {"start": 1003.65, "end": 1004.03, "word": " هاد", "probability": 0.81982421875}, {"start": 1004.03, "end": 1004.87, "word": " إذا", "probability": 0.80859375}, {"start": 1004.87, "end": 1005.27, "word": " صارت", "probability": 0.96142578125}, {"start": 1005.27, "end": 1005.49, "word": " هاد", "probability": 0.955810546875}, {"start": 1005.49, "end": 1005.87, "word": " عبارة", "probability": 0.996826171875}, {"start": 1005.87, "end": 1006.01, "word": " عن", "probability": 0.96240234375}, {"start": 1006.01, "end": 1006.65, "word": " أشمالها", "probability": 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{"start": 1340.14, "end": 1342.16, "word": " الـ", "probability": 0.718017578125}, {"start": 1342.16, "end": 1342.7, "word": " Rovix", "probability": 0.5589599609375}, {"start": 1342.7, "end": 1342.92, "word": " هو", "probability": 0.966796875}, {"start": 1342.92, "end": 1343.48, "word": " المنطلق", "probability": 0.9201171875}, {"start": 1343.48, "end": 1343.94, "word": " برا", "probability": 0.725830078125}, {"start": 1343.94, "end": 1344.66, "word": " هو", "probability": 0.375732421875}, {"start": 1344.66, "end": 1345.4, "word": " اللي", "probability": 0.880615234375}, {"start": 1345.4, "end": 1345.64, "word": " هو", "probability": 0.95263671875}, {"start": 1345.64, "end": 1347.18, "word": " unbounded", "probability": 0.9010416666666666}, {"start": 1347.18, "end": 1347.96, "word": " و", "probability": 0.97021484375}, {"start": 1347.96, "end": 1348.28, "word": " open", "probability": 0.8720703125}, {"start": 1348.28, "end": 1348.66, "word": " set", "probability": 0.74267578125}, {"start": 1348.66, "end": 1351.68, "word": " فانجسمت", "probability": 0.82109375}, {"start": 1351.68, "end": 1352.0, "word": " اللي", "probability": 0.942138671875}, {"start": 1352.0, "end": 1352.44, "word": " هي", "probability": 0.84619140625}, {"start": 1352.44, "end": 1352.76, "word": " ال", "probability": 0.86767578125}, {"start": 1352.76, "end": 1353.14, "word": " complex", "probability": 0.65380859375}, {"start": 1353.14, "end": 1353.66, "word": " plane", "probability": 0.2138671875}, {"start": 1353.66, "end": 1354.3, "word": " إلى", "probability": 0.904296875}, {"start": 1354.3, "end": 1354.8, "word": " جزئين", "probability": 0.8792724609375}, {"start": 1354.8, "end": 1355.1, "word": " جزء", "probability": 0.9353841145833334}, {"start": 1355.1, "end": 1355.26, "word": " اللي", "probability": 0.945068359375}, {"start": 1355.26, "end": 1355.4, "word": " هو", "probability": 0.95556640625}, {"start": 1355.4, "end": 1355.64, "word": " sigma", "probability": 0.2421875}, {"start": 1355.64, "end": 1355.98, "word": " rovix", "probability": 0.6650390625}, {"start": 1355.98, "end": 1356.12, "word": " اللي", "probability": 0.93212890625}, {"start": 1356.12, "end": 1356.24, "word": " هي", "probability": 0.77392578125}, {"start": 1356.24, "end": 1356.58, "word": " عناصر", "probability": 0.9827473958333334}, {"start": 1356.58, "end": 1356.9, "word": " الطرف", "probability": 0.3878173828125}, {"start": 1356.9, "end": 1357.04, "word": " اللي", "probability": 0.9501953125}, {"start": 1357.04, "end": 1357.24, "word": " هي", "probability": 0.92041015625}, {"start": 1357.24, "end": 1357.9, "word": " closed", "probability": 0.85888671875}, {"start": 1357.9, "end": 1358.04, "word": " و", "probability": 0.98388671875}, {"start": 1358.04, "end": 1358.36, "word": " bounded", "probability": 0.93408203125}, {"start": 1358.36, "end": 1359.3, "word": " و", "probability": 0.830078125}, {"start": 1359.3, "end": 1359.6, "word": " اللي", "probability": 0.974365234375}, {"start": 1359.6, "end": 1359.74, "word": " هو", "probability": 0.9501953125}, {"start": 1359.74, "end": 1359.92, "word": " اللي", "probability": 0.94287109375}, {"start": 1359.92, "end": 1360.26, "word": " فوق", "probability": 0.976318359375}, {"start": 1360.26, "end": 1360.54, "word": " اللي", "probability": 0.98974609375}, {"start": 1360.54, "end": 1360.8, "word": " هي", "probability": 0.90087890625}, {"start": 1360.8, "end": 1361.36, "word": " open", "probability": 0.9287109375}, {"start": 1361.36, "end": 1361.72, "word": " set", "probability": 0.93115234375}, {"start": 1361.72, "end": 1361.88, "word": " و", "probability": 0.98974609375}, {"start": 1361.88, "end": 1362.46, "word": " unbounded", "probability": 0.95458984375}, {"start": 1362.46, "end": 1362.7, "word": " set", "probability": 0.97509765625}], "temperature": 1.0}, {"id": 61, "seek": 136827, "start": 1364.53, "end": 1368.27, "text": "وبارك الله فيكم والسلام عليكم ورحمة الله وبركاته", "tokens": [37746, 9640, 4117, 21984, 8978, 24793, 16070, 3794, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224], "avg_logprob": -0.12366832860491493, "compression_ratio": 1.2361111111111112, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1364.53, "end": 1365.17, "word": "وبارك", "probability": 0.8307291666666666}, {"start": 1365.17, "end": 1365.31, "word": " الله", "probability": 0.9677734375}, {"start": 1365.31, "end": 1365.75, "word": " فيكم", "probability": 0.967529296875}, {"start": 1365.75, "end": 1366.41, "word": " والسلام", "probability": 0.7676595052083334}, {"start": 1366.41, "end": 1366.95, "word": " عليكم", "probability": 0.95458984375}, {"start": 1366.95, "end": 1367.37, "word": " ورحمة", "probability": 0.93408203125}, {"start": 1367.37, "end": 1367.51, "word": " الله", "probability": 0.9658203125}, {"start": 1367.51, "end": 1368.27, "word": " وبركاته", "probability": 0.94248046875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1368.769875, "duration_after_vad": 1344.758749999998}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/4xIBSxYcbs0.srt b/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/4xIBSxYcbs0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..642aedbf86731e52fd672cddd160ad5e953c9096
--- /dev/null
+++ b/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/4xIBSxYcbs0.srt
@@ -0,0 +1,1643 @@
+1
+00:00:04,940 --> 00:00:07,820
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:07,820 --> 00:00:11,800
+وبركاته اليوم هنبدأ Chapter جديد اللي هو ال-Plan
+
+3
+00:00:11,800 --> 00:00:14,260
+motion of rigid bodies forces and acceleration
+
+4
+00:00:14,260 --> 00:00:19,440
+يعني الحركة المستوية للأجسام الصلبة هندرس علاقة
+
+5
+00:00:19,440 --> 00:00:25,760
+القوة المؤثرة مع الجسم مع حركة الجسم الموضوعات
+
+6
+00:00:25,760 --> 00:00:29,940
+اللي هنغطيها في هذا ال-Chapter هي equations of
+
+7
+00:00:29,940 --> 00:00:33,000
+motion of a rigid body اللي هي معادلة الحركة للجسم 
+
+8
+00:00:33,000 --> 00:00:37,700
+الصلب الزخم ال-Angular momentum of a rigid body in a
+
+9
+00:00:37,700 --> 00:00:41,980
+plane motion الزخم الزاوي لجسم صلب في حالة
+
+10
+00:00:41,980 --> 00:00:46,520
+المستوى رقم تلاتة اللي هي constraint plane motion
+
+11
+00:00:46,520 --> 00:00:50,800
+اللي هي الحركة المستوية المقيدة هندرس نوعين اللي
+
+12
+00:00:50,800 --> 00:00:53,640
+هي non-centroidal rotation يعني بيكون الجسم يدور
+
+13
+00:00:53,640 --> 00:00:58,040
+حول نقطة ليست واقعة على مركز ثقلَه الحالة الثانية
+
+14
+00:00:58,040 --> 00:01:01,240
+اللي هي الحركة التدحرجية rolling motion
+
+15
+00:01:04,870 --> 00:01:07,470
+هنبدأ في الموضوع الأول اللي هي equations of motion
+
+16
+00:01:07,470 --> 00:01:16,230
+for a rigid body أنا في عندي هنا إن بين جسم ماثر
+
+17
+00:01:16,230 --> 00:01:23,930
+أيه القوة F1, F2, F3, F4 نتيجة القوة المؤثرة على
+
+18
+00:01:23,930 --> 00:01:29,010
+الجسم الجسم هيتحرك وهصير لَه rotation هصير لَه حركة
+
+19
+00:01:29,010 --> 00:01:33,790
+وهصير rotation يعني عندي forces بتعطيني آش
+
+20
+00:01:34,820 --> 00:01:39,980
+translational motion and rotational motion طبقا
+
+21
+00:01:39,980 --> 00:01:43,760
+طبعا في عندي two frame of reference في عندي fixed
+
+22
+00:01:43,760 --> 00:01:52,420
+frame of reference X capital Y capital Z capital
+
+23
+00:01:52,420 --> 00:01:58,920
+وفي عندي frame of reference أنا حاطّه بالمركز استقل
+
+24
+00:01:58,920 --> 00:02:09,400
+X prime Y prime وZ prime طبعا
+
+25
+00:02:09,400 --> 00:02:15,860
+طبقا لنيوتن Second اللي هو هكون summation لل
+
+26
+00:02:15,860 --> 00:02:24,160
+forces بيستوي M في A مجموعة القوة المؤثرة كـ vector
+
+27
+00:02:24,160 --> 00:02:29,280
+equation بيستوي حصل ضرب الكتلة في ال-Acceleration
+
+28
+00:02:29,280 --> 00:02:36,320
+على فرض إن كتلة الجسم بتظل ثابتة مش متغيرة هذا الجزء
+
+29
+00:02:36,320 --> 00:02:42,860
+الأول من المعادلة الجزء الثاني مجموع القوة حول
+
+30
+00:02:42,860 --> 00:02:52,120
+مركز استقل بالساوية HG Dot مجموع العزوم حول
+
+31
+00:02:52,120 --> 00:02:56,840
+مركز استقل GE بالساوية معدل التغير في الزخم 
+
+32
+00:02:56,840 --> 00:03:02,820
+الزاوي معدل التغير في الزخم الزاوي هدول هي
+
+33
+00:03:02,820 --> 00:03:08,460
+المعادلتين هما المعدلتين اللي بحكموا حركة الأجسام
+
+34
+00:03:08,460 --> 00:03:13,900
+الصلبة اللي بيكون فيها تتحرك حركة انتقالية زائد
+
+35
+00:03:13,900 --> 00:03:19,280
+حركة دورانية في
+
+36
+00:03:19,280 --> 00:03:25,200
+حالة حركة الأجسام الصلبة في المستوى أنا مش هخش في
+
+37
+00:03:25,200 --> 00:03:32,060
+الاشتقاقات ال-Derivation ساعتها ال-HGO اللي هي زخم
+
+38
+00:03:32,060 --> 00:03:36,240
+الزاوي حول مركز الثقل أو معدل الزخم الزاوي
+
+39
+00:03:36,240 --> 00:03:42,820
+حول مركز الثقل بيستوي I في Alpha ال-Alpha هي
+
+40
+00:03:42,820 --> 00:03:49,540
+Angular Acceleration للجسم والـ I هي Moment of
+
+41
+00:03:49,540 --> 00:03:55,780
+Inertia للجسم حول مركز ثقله ممكن تدرس الجسم
+
+42
+00:03:55,780 --> 00:04:00,580
+حول مركز ثقله يعني في الحالة هذي هتكون حول الـ
+
+43
+00:04:00,580 --> 00:04:05,760
+Z الـ IZ أنا ببين دي هين جسم Symmetrical about the 
+
+44
+00:04:05,760 --> 00:04:09,960
+plane يعني above the plane is mirror image of the
+
+45
+00:04:09,960 --> 00:04:14,700
+below the plane طبعا هذه النتائج اللي هي HG Dot
+
+46
+00:04:14,700 --> 00:04:19,470
+بالساوية I في Alpha بتكون صحيحة فقط في حالة كان
+
+47
+00:04:19,470 --> 00:04:25,010
+الجسم متماثل حول المستوى تحت الدراسة Otherwise
+
+48
+00:04:25,010 --> 00:04:29,470
+يعني إذا كان الجسم شكله مش متماثل حول المستوى
+
+49
+00:04:29,470 --> 00:04:33,350
+XY plane هذه ال-Results أو النتيجة هذه مش صحيحة
+
+50
+00:04:33,350 --> 00:04:36,770
+يعني هذه ال-Results ال-HG dot بسوء I في Alpha
+
+51
+00:04:36,770 --> 00:04:41,530
+بتكون صحيحة في حالة إنه كان الجسم شكله متماثل
+
+52
+00:04:41,530 --> 00:04:47,410
+حول الـ XY plane يعني شكله Above المستوى عبارة عن
+
+53
+00:04:47,410 --> 00:04:57,870
+مراية أو mirror image لشكله تحت المستوى الآن
+
+54
+00:04:57,870 --> 00:05:00,690
+في حالة الحركة المستوية
+
+55
+00:05:04,000 --> 00:05:07,940
+في حالة الحركة المستوية عند جسم مبين جسم 2D body
+
+56
+00:05:07,940 --> 00:05:11,880
+that is symmetrical with respect to the plane
+
+57
+00:05:11,880 --> 00:05:18,140
+مأثرة القوة F1, F2, F3, F4 نتيجة هذه القوة هيكون
+
+58
+00:05:18,140 --> 00:05:21,900
+في انتقال يعني في عند هصير Motion هيكون في inertia
+
+59
+00:05:21,900 --> 00:05:26,880
+force MA وفي عند ريتشن انيرشيا I في Alpha يعني هذه
+
+60
+00:05:26,880 --> 00:05:31,930
+جزئية لـ Translation هجزئية الـ Rotation يعني الـ
+
+61
+00:05:31,930 --> 00:05:38,130
+Total Motion اللي مكونين جزء انتقالي وجزء دوراني
+
+62
+00:05:38,130 --> 00:05:47,050
+طيب
+
+63
+00:05:47,050 --> 00:05:48,590
+ممكن
+
+64
+00:05:50,510 --> 00:05:53,430
+يعني أعبر أعمل free body diagram عند هذه ال-Forces
+
+65
+00:05:53,430 --> 00:05:58,070
+F1, F2, F3, F4 هتعطيني ال-Motion اللي هي M في A
+
+66
+00:05:58,070 --> 00:06:03,890
+وعندي إيش I في Alpha أو أحول مسألة .. مسألة
+
+67
+00:06:03,890 --> 00:06:07,910
+aesthetics .. مسألة استاتيكية هذه ال-Forces F1,
+
+68
+00:06:07,990 --> 00:06:12,070
+F2, F3, F4 واخد ال-Inertia forces اللي هي ال-
+
+69
+00:06:12,070 --> 00:06:15,800
+Inertia force ده ال-Translation minus MA والـ
+
+70
+00:06:15,800 --> 00:06:20,820
+Inertia ال-Rotation Inertia للـ I Alpha هتكون minus
+
+71
+00:06:20,820 --> 00:06:26,720
+I Alpha فبيصير عندي ال-Forces هي F1 وF2 وF3 وF4
+
+72
+00:06:26,720 --> 00:06:31,300
+و minus MA و minus I Alpha بالحالة هتبتساوى Zero
+
+73
+00:06:31,300 --> 00:06:36,580
+هنشوف
+
+74
+00:06:36,580 --> 00:06:43,900
+مثال مثال
+
+75
+00:06:45,420 --> 00:06:50,320
+نقرأ المثال نلخصه وبعدين نبدأ نعمل Analysis at a
+
+76
+00:06:50,320 --> 00:06:54,100
+forward speed of 30 feet per second the track
+
+77
+00:06:54,100 --> 00:06:57,040
+brakes were applied causing wheels to stop
+
+78
+00:06:57,040 --> 00:07:02,960
+rotating عندي سيارة لما كانت ماشية بسرعة تلاتين
+
+79
+00:07:02,960 --> 00:07:06,920
+قدم في الثانية يعني السرعة الابتدائية إلها كانت V0
+
+80
+00:07:06,920 --> 00:07:09,940
+بالساوية
+
+81
+00:07:09,940 --> 00:07:16,000
+تلاتين قدم على الثانية لما كان سورة تبدأ تلاتين قدم
+
+82
+00:07:16,000 --> 00:07:20,320
+على الثانية السائق استخدم الكوابح تغطى ال-Brakes
+
+83
+00:07:20,320 --> 00:07:28,780
+لما تغطى ال-Brakes العجلات هتبطل تدور تتمتع الحركة
+
+84
+00:07:28,780 --> 00:07:33,880
+وهتصير إيش السيارة تنزلق إلى الأمام It has
+
+85
+00:07:33,880 --> 00:07:37,000
+observed that the truck is skidded to a stop in
+
+86
+00:07:37,000 --> 00:07:42,840
+twenty feet لوحظ أن السيارة وصلت لحالة الوقوف في
+
+87
+00:07:42,840 --> 00:07:50,000
+مسافة مقدارها عشرين قدم يعني كانت عندي Delta X لحد
+
+88
+00:07:50,000 --> 00:07:57,320
+الوقوف بيستوي عشرين قدم والسرعة النهائية كانت صفر
+
+89
+00:07:57,320 --> 00:08:00,880
+المطلوب
+
+90
+00:08:02,590 --> 00:08:07,430
+Determine the magnitude of the normal reaction and
+
+91
+00:08:07,430 --> 00:08:11,450
+friction force at each wheel as the track is
+
+92
+00:08:11,450 --> 00:08:20,750
+skidded to a stop أوجد قيمة رد الفعل العمودي لكل
+
+93
+00:08:20,750 --> 00:08:26,750
+عجلة عند العجلات A وعند العجلات B والـ Friction
+
+94
+00:08:26,750 --> 00:08:32,330
+Force عند كل Wheel Friction Force عند كل Wheel
+
+95
+00:08:37,490 --> 00:08:40,930
+طيب في الأول خلينا نحسب ال-Acceleration الـ
+
+96
+00:08:40,930 --> 00:08:44,490
+Acceleration للسيارة السيارة بدأت في سرعة ابتدائية
+
+97
+00:08:44,490 --> 00:08:48,690
+تلاتين قدم على الثانية وتم استخدام الكوابح وتوقفت
+
+98
+00:08:48,690 --> 00:08:52,390
+خلال مسافة مقدارها عشرين قدم لحد ما وصلت سرعتها صفر
+
+99
+00:08:52,390 --> 00:09:03,190
+ممكن أحكي V تربيع بيستوي V نود تربيع زائد اتنين A
+
+100
+00:09:03,190 --> 00:09:04,950
+في Delta X
+
+101
+00:09:07,910 --> 00:09:16,750
+الـ V النهائية صفر والـ V الابتدائية تلاتين تربيع زائد
+
+102
+00:09:16,750 --> 00:09:26,510
+اتنين A ال-Delta X اللي هي عشرين معناته الـ A هتكون
+
+103
+00:09:26,510 --> 00:09:32,710
+ساوي تسعمية على اربعين تسعمية على اربعين آه كم
+
+104
+00:09:32,710 --> 00:09:34,570
+تطلع يعني
+
+105
+00:09:36,870 --> 00:09:41,610
+تسعمية على اربعين يعني تسعين على أربعة تسعين على
+
+106
+00:09:41,610 --> 00:09:45,590
+اتنين خمسة اربعين اتنين وعشرين minus اتنين و
+
+107
+00:09:45,590 --> 00:09:58,170
+عشرين ونص قدم على الثانية تربيع هاد
+
+108
+00:09:58,170 --> 00:10:01,870
+الـ Explanation الآن
+
+109
+00:10:01,870 --> 00:10:06,940
+هعمل free width diagram للسيارة أشوف إيش القوة
+
+110
+00:10:06,940 --> 00:10:14,440
+المؤثرة عليها السيارة بيأثر عليها وزنها
+
+111
+00:10:14,440 --> 00:10:19,280
+الوزن
+
+112
+00:10:19,280 --> 00:10:23,140
+هذا
+
+113
+00:10:23,140 --> 00:10:24,140
+مركز ثقلها
+
+114
+00:10:26,890 --> 00:10:38,510
+هذه العجلات A والعجلات B في رد الفعل عند A NA رد
+
+115
+00:10:38,510 --> 00:10:45,510
+الفعل العمودي ورد الفعل N
+
+116
+00:10:45,510 --> 00:10:49,830
+B وفي
+
+117
+00:10:49,830 --> 00:10:53,290
+الاحتكاك عند A
+
+118
+00:11:00,490 --> 00:11:16,110
+اللي هي هكون الـ Mu K أو خاني أسميها FA و
+
+119
+00:11:16,110 --> 00:11:23,470
+FB F
+
+120
+00:11:23,470 --> 00:11:25,410
+A وFB
+
+121
+00:11:28,210 --> 00:11:32,350
+الآن معناته الجسم واقع تحت تأثير ووزنه رد الفعل
+
+122
+00:11:32,350 --> 00:11:36,950
+العمودي عند A وعند B والـ Friction Force عند A و
+
+123
+00:11:36,950 --> 00:11:40,570
+الـ Friction Force عند B نتيجة هذه القوة الجسم
+
+124
+00:11:40,570 --> 00:11:54,190
+هيمتحرك بـ Acceleration اللي هي 22.5 ام
+
+125
+00:11:54,190 --> 00:12:06,710
+في A هذا مركز ثقلها هذه A وهذه B هل في Rotation
+
+126
+00:12:06,710 --> 00:12:09,850
+للسيارة؟ لأ طبعا السيارة ما حصل فيها Rotation
+
+127
+00:12:09,850 --> 00:12:14,530
+دلتها ماشية على خط مستقيم لأن عشان يكون Free Body
+
+128
+00:12:14,530 --> 00:12:21,950
+Diagram كامل الأركان لازم أحط أعرف اللي هو محاور
+
+129
+00:12:21,950 --> 00:12:24,330
+إحداثيات محاور إحداثيات خلينا نحكي هي
+
+130
+00:12:28,880 --> 00:12:47,020
+الـ X هي الـ Y لأن
+
+131
+00:12:47,020 --> 00:12:51,400
+عشان أوجد رد الفعل عند A وعند B بدي اخذ الـ
+
+132
+00:12:51,400 --> 00:12:56,700
+Moment حول A أو الـ Moment حول B يعني لو حكيت
+
+133
+00:12:56,700 --> 00:13:05,220
+الـ Moment Summation للـ MA بدي
+
+134
+00:13:05,220 --> 00:13:14,060
+أعتبر هذا الاتجاه الـ Clockwise هو الموجب هتكون
+
+135
+00:13:14,060 --> 00:13:21,840
+سواء M أو A Effective نأخذ
+
+136
+00:13:21,840 --> 00:13:28,980
+الجهة الشمالية الجهة الشمالية بدي اخذ الـ Moment حول
+
+137
+00:13:28,980 --> 00:13:34,100
+A طبعا الـ FA بتعملش Moment والـ NA بتعملش Moment
+
+138
+00:13:34,100 --> 00:13:36,600
+والـ FB بتعملش Moment الوحيد اللي بيعمل Moment
+
+139
+00:13:36,600 --> 00:13:40,500
+اللي هي الوزن والـ Normal Force عند B يعني هيكون
+
+140
+00:13:40,500 --> 00:13:45,540
+عندي هذه المسافة بتعطيني خمس أقدام وهذه السبعة
+
+141
+00:13:45,540 --> 00:13:52,660
+أقدام و هذه المسافة أربعة قدم
+
+142
+00:14:20,520 --> 00:14:24,360
+طيب أنا هاخد الموضوع حوالين A على الجهة دي طبعا ال
+
+143
+00:14:24,360 --> 00:14:28,560
+N A والـ F A بيعملوش عزم و الـ FB بيعملوش عزم
+
+144
+00:14:28,560 --> 00:14:32,840
+الواحد بيعمل عزم اللي هي W هيكون عندي خمسة في W
+
+145
+00:14:32,840 --> 00:14:38,100
+خمسة في الوزن W
+
+146
+00:14:40,990 --> 00:14:46,690
+لأن الـ clockwise موجب ناقص
+
+147
+00:14:46,690 --> 00:14:54,950
+NB في خمسة زي سبعة ناقص اثنا عشر NB
+
+148
+00:14:54,950 --> 00:15:03,110
+هذا على الجهة الشمالية بتساوي العزم للـ MA حوالين A
+
+149
+00:15:06,120 --> 00:15:10,580
+بتعمل counter clockwise moment حوالين a هتكون
+
+150
+00:15:10,580 --> 00:15:14,880
+minus أربعة 
+
+151
+00:15:14,880 --> 00:15:17,980
+M
+
+152
+00:15:17,980 --> 00:15:23,980
+في A يعني
+
+153
+00:15:23,980 --> 00:15:31,060
+ضربت الطرفين بـ minus أو
+
+154
+00:15:31,060 --> 00:15:34,060
+منها باطل بطل عنده
+
+155
+00:15:45,740 --> 00:15:51,820
+بيطلع عندي الآن بي
+
+156
+00:15:51,820 --> 00:15:59,320
+أنا هجيب هذه على اليمين وهذه على الشمال بالسواء
+
+157
+00:15:59,320 --> 00:16:06,360
+خمسة W زائد أربعة M A
+
+158
+00:16:17,380 --> 00:16:25,920
+على اثنا عشر بتساوي
+
+159
+00:16:25,920 --> 00:16:32,140
+خمسة W زائد
+
+160
+00:16:32,140 --> 00:16:43,560
+أربعة الأمر اللي هي W على G اللي هي الـ gravity في
+
+161
+00:16:43,560 --> 00:16:52,290
+ال acceleration اثنين و عشرين و نص على اثنا عشر يعني
+
+162
+00:16:52,290 --> 00:16:59,690
+حدث سيئوي عندي خمسة
+
+163
+00:16:59,690 --> 00:17:07,750
+زائد أربعة في اثنين و عشرين و نص تسعين على جيل هي
+
+164
+00:17:07,750 --> 00:17:13,630
+اثنين و ثلاثين و اثنين من عشرة على اثنا عشر
+
+165
+00:17:16,040 --> 00:17:26,760
+في W هتكون
+
+166
+00:17:26,760 --> 00:17:34,320
+تسعين تقسيم زائد
+
+167
+00:17:34,320 --> 00:17:43,380
+خمسة تقسيم اثنا عشر تطلع بين ستة خمسة W
+
+168
+00:17:50,420 --> 00:17:56,800
+1.65W الآن هاخد summation of forces بالاتجاه الـ Y
+
+169
+00:17:56,800 --> 00:18:02,400
+direction summation of forces بالاتجاه الـ Y هي
+
+170
+00:18:02,400 --> 00:18:07,040
+الاتجاه الموجب واضح السيارة حركتها بالاتجاه الـ X
+
+171
+00:18:07,040 --> 00:18:14,660
+هتكون تساوي إيه؟ صفر هيكون
+
+172
+00:18:14,660 --> 00:18:16,880
+دي minus W
+
+173
+00:18:23,250 --> 00:18:28,710
+زائد N A زائد
+
+174
+00:18:28,710 --> 00:18:43,790
+N B يعني هتكون إندي N A بيساوي W minus N B يعني
+
+175
+00:18:43,790 --> 00:18:46,450
+هيكون W
+
+176
+00:18:49,770 --> 00:18:57,290
+-0.65w يعني نحسبه 0.35w
+
+177
+00:18:57,290 --> 00:19:01,090
+طبعا
+
+178
+00:19:01,090 --> 00:19:04,610
+هذا هو هذا الـ normal reaction a و b لكل عجلتين
+
+179
+00:19:04,610 --> 00:19:08,070
+يعني العجل الواحدة هقسم على اثنين يعني for each
+
+180
+00:19:08,070 --> 00:19:13,870
+wheel هيكون الـ NB 0.65w على اثنين والـ NA for each
+
+181
+00:19:13,870 --> 00:19:16,930
+wheel هيكون 0.35w على اثنين
+
+182
+00:19:27,780 --> 00:19:33,980
+طبعا الـ friction force الـ F A هتكون ساوي ميو كيه
+
+183
+00:19:33,980 --> 00:19:41,520
+معامل احتكاك ديناميكي في N A الـ ميو كيه اللي هي
+
+184
+00:19:41,520 --> 00:19:51,760
+عند نفترض أنها معروفة هتكون point 65 W point 35
+
+185
+00:19:51,760 --> 00:19:55,680
+point
+
+186
+00:19:57,470 --> 00:20:07,450
+ثلاثة خمسة W ميو كي والـ FB بيساوي ميو كي في إن
+
+187
+00:20:07,450 --> 00:20:18,190
+بي يعني هتساوي point ستة خمسة W ميو كي طبعا هذه ال
+
+188
+00:20:18,190 --> 00:20:24,550
+forces pair two wheels معناته ال
+
+189
+00:20:24,550 --> 00:20:42,750
+forcespair wheel لكل عجلة are given as follows ال
+
+190
+00:20:42,750 --> 00:20:51,990
+N A لـ one wheel هتكون point ستة خمسة W على
+
+191
+00:20:51,990 --> 00:21:00,030
+اثنين يعني هتكون point ثلاثة اثنين خمسة W والـ N A for
+
+192
+00:21:00,030 --> 00:21:07,570
+each wheel الـ N D for each wheel هتكون point ثلاثة 
+
+193
+00:21:07,570 --> 00:21:15,650
+خمسة W على اثنين يعني هتكون point واحد سبعة خمسة W
+
+194
+00:21:15,650 --> 00:21:22,800
+ونفس الشيء الـ friction force F A per wheelهيكون
+
+195
+00:21:22,800 --> 00:21:34,200
+الساوي point واحد سبعة خمسة W UK والـ FAB pair
+
+196
+00:21:34,200 --> 00:21:42,780
+wheel هيكون point ثلاثة اثنين خمسة W UK
+
+197
+00:21:51,470 --> 00:21:52,790
+نحّل كمان مثال
+
+198
+00:22:24,280 --> 00:22:33,080
+حالة ثالثة يعني زي
+
+199
+00:22:33,080 --> 00:22:40,020
+ما أنتم شايفين فاندي plate ممسوك
+
+200
+00:22:40,020 --> 00:22:49,640
+بـ link AE عن نقطة A و link DF وممسوك بحبل أو خيط
+
+201
+00:22:49,640 --> 00:22:58,420
+إندي هاي AE F
+
+202
+00:22:58,420 --> 00:23:10,840
+D B C H ومعطين
+
+203
+00:23:10,840 --> 00:23:17,690
+ال dimensions بتاعته خمسمائة ملي اثمائة ملي والزاوية
+
+204
+00:23:17,690 --> 00:23:21,170
+في اللحظة احنا شايفينها زاوية الـ link a أو ae
+
+205
+00:23:21,170 --> 00:23:25,370
+ثلاثين درجة والـ link fd ثلاثين درجة معناته ال
+
+206
+00:23:25,370 --> 00:23:33,610
+link ae موازية للـ link df the
+
+207
+00:23:33,610 --> 00:23:37,830
+thin plate of mass eight kilogram is held in place
+
+208
+00:23:37,830 --> 00:23:41,750
+as shown ال plate اللي هو وزنه ثمانية kilogram ال
+
+209
+00:23:41,750 --> 00:23:42,090
+mass
+
+210
+00:23:46,270 --> 00:23:52,970
+مستوى ثمانية كيلو جرام ممسوك
+
+211
+00:23:52,970 --> 00:23:55,330
+في الوضع اللي احنا شايفينه من خلال الحبل BH
+
+212
+00:23:55,330 --> 00:24:00,250
+Neglecting
+
+213
+00:24:00,250 --> 00:24:07,110
+mass of links إذا تم اهمال وزن اللينكات AE و FD
+
+214
+00:24:08,190 --> 00:24:11,310
+determined immediately after the wire has been cut
+
+215
+00:24:11,310 --> 00:24:14,890
+أوجد مباشرة بعد قطع الحبل إذا قطع الحبل لن يبدأ ال
+
+216
+00:24:14,890 --> 00:24:19,630
+plate يتحرك ال acceleration of the plate العجلة لل
+
+217
+00:24:19,630 --> 00:24:23,930
+plate نحسب
+
+218
+00:24:23,930 --> 00:24:28,590
+العجلة لل plate أولا
+
+219
+00:24:28,590 --> 00:24:32,310
+خليني أحدد نوع الحركة لل plate مباشرة بعد قطع
+
+220
+00:24:32,310 --> 00:24:36,770
+الحبل هل حركته انتقالية؟
+
+221
+00:24:37,510 --> 00:24:46,430
+ولا دورانية ولا الاثنين انتقال مع دوران الآن مجرد
+
+222
+00:24:46,430 --> 00:24:52,050
+ما يصير قطع للحبل هنا الدراع أو الـ link EA هيدور
+
+223
+00:24:52,050 --> 00:24:54,470
+حوالين A هذا هأعمل له دائرة
+
+224
+00:24:57,540 --> 00:25:03,160
+والـ link FD هأعمل له دائرة H موازية معناته المسار
+
+225
+00:25:03,160 --> 00:25:09,880
+هذا هو نقطة A لأن نقطة A نقطة واقعة على ال plate ونقطة
+
+226
+00:25:09,880 --> 00:25:16,560
+D نقطة ثانية واقعة على ال plate المسار الدائرة
+
+227
+00:25:16,560 --> 00:25:22,880
+عند A موازي لمسار الدائرة عند D معناته
+
+228
+00:25:24,180 --> 00:25:27,580
+عندي two particles على الجسم بتحركوا على مسارين
+
+229
+00:25:27,580 --> 00:25:32,740
+متوازيين بنية الجسم في حالة انتقال نحكي immediately
+
+230
+00:25:32,740 --> 00:25:41,320
+after
+
+231
+00:25:41,320 --> 00:25:49,280
+wire is cut سنتبع
+
+232
+00:25:49,280 --> 00:25:52,360
+we trace two points we trace
+
+233
+00:25:54,930 --> 00:26:01,550
+two points أو two particles on
+
+234
+00:26:01,550 --> 00:26:07,590
+the plate خليني
+
+235
+00:26:07,590 --> 00:26:20,350
+أحكي الـ say اللي هم particle a و particle d الآن
+
+236
+00:26:20,350 --> 00:26:22,890
+الـ particle a
+
+237
+00:26:27,940 --> 00:26:38,020
+أو follows الـ circular path بمشي على follows ال
+
+238
+00:26:38,020 --> 00:26:41,980
+circular path
+
+239
+00:26:41,980 --> 00:26:53,480
+وبرضه الـ particle d follows برضه
+
+240
+00:26:53,480 --> 00:26:54,340
+الـ circular path
+
+241
+00:26:58,560 --> 00:27:09,940
+لاحظوا أنه path followed by a المسار by
+
+242
+00:27:09,940 --> 00:27:18,700
+a is parallel to
+
+243
+00:27:18,700 --> 00:27:23,820
+path followed
+
+244
+00:27:23,820 --> 00:27:26,960
+by
+
+245
+00:27:28,030 --> 00:27:34,870
+D معناته الجسم is in a pure translation معناته ال
+
+246
+00:27:34,870 --> 00:27:39,310
+plate is
+
+247
+00:27:39,310 --> 00:27:44,670
+in a pure translation
+
+248
+00:27:54,230 --> 00:27:56,910
+معناته if it is in pure translation معناته ال
+
+249
+00:27:56,910 --> 00:28:00,830
+acceleration of all points on the plate لهم نفس ال
+
+250
+00:28:00,830 --> 00:28:03,430
+acceleration من ناحية القيم من ناحية التجاه
+
+251
+00:28:03,430 --> 00:28:10,050
+معناته all particles on
+
+252
+00:28:10,050 --> 00:28:19,610
+a plate have the same acceleration
+
+253
+00:28:23,020 --> 00:28:29,940
+معناته هذا معناته أن A هتكون تساوي D هتكون
+
+254
+00:28:29,940 --> 00:28:41,740
+تساوي G G اللي هو المركز استقل
+
+255
+00:28:41,740 --> 00:28:47,860
+لأن
+
+256
+00:28:47,860 --> 00:28:53,110
+مباشرة بعد قطعة الحبل لسه ما فيش الوصول على الجسم يعني
+
+257
+00:28:53,110 --> 00:28:56,670
+هيكون ما زي ما فيش له سرعة ما يعني ما فيش له angular
+
+258
+00:28:56,670 --> 00:29:00,990
+velocity عندي
+
+259
+00:29:00,990 --> 00:29:09,590
+نقطة velocity va مباشرة بعد قطر الحبل بيساوي صفر و
+
+260
+00:29:09,590 --> 00:29:15,750
+بتساوي برضه vd معناته
+
+261
+00:29:15,750 --> 00:29:18,330
+الـ acceleration لـ a
+
+262
+00:29:22,900 --> 00:29:33,120
+هتكون مماس للمسار يعني هتكون عمودية هتكون
+
+263
+00:29:33,120 --> 00:29:42,020
+عمودية على الـ .. اللي هو EA هذه
+
+264
+00:29:42,020 --> 00:29:50,820
+AA وهذه
+
+265
+00:29:50,820 --> 00:29:51,180
+AD
+
+266
+00:29:59,080 --> 00:30:07,520
+معناته a a كـ vector بيساوي a d كـ vector بيساوي a g
+
+267
+00:30:07,520 --> 00:30:14,020
+كـ vector بيساوي .. خلينا نسميها a بيساوي a كقيمة و
+
+268
+00:30:14,020 --> 00:30:17,560
+بتعمل زاوية ثلاثين مع الرأس زاوية
+
+269
+00:30:27,040 --> 00:30:34,260
+ثلاثين درجة مع الرأس يعني كل
+
+270
+00:30:34,260 --> 00:30:37,280
+الشغل هذا عشان نعرف اتجاه الـ acceleration بتاعة G
+
+271
+00:30:37,280 --> 00:30:44,080
+لأن
+
+272
+00:30:44,080 --> 00:30:48,100
+خلينا نعمل free body diagram للـ plate free body
+
+273
+00:30:48,100 --> 00:30:49,980
+diagram للـ plate
+
+274
+00:31:01,750 --> 00:31:14,230
+عندي هذه المقطعة A D C B E F هذه زاوية ثلاثين
+
+275
+00:31:14,230 --> 00:31:22,490
+درجة وهذه ثلاثين درجة هذه A B
+
+276
+00:31:24,520 --> 00:31:36,960
+C D F دي A القوة
+
+277
+00:31:36,960 --> 00:31:40,700
+اللي بتأثر لو أخذت بس الـ plate لحاله هيأثر وزنه
+
+278
+00:31:40,700 --> 00:31:49,140
+لتحت اللي 
+
+279
+00:31:49,140 --> 00:31:57,890
+هو M في G وهي أثر الـ forces اللي جاية من الـ link ال
+
+280
+00:31:57,890 --> 00:32:07,810
+link بتحاول تشد بهذا الاتجاه عندها تكون خلينا 
+
+281
+00:32:07,810 --> 00:32:11,790
+نسميها fa احنا نفرض أن الـ link is a two force 
+
+282
+00:32:11,790 --> 00:32:13,510
+member
+
+283
+00:32:30,230 --> 00:32:33,310
+عالأغلب هذه هتكون tension هين هكون compression
+
+284
+00:32:33,310 --> 00:32:36,530
+بتوقع تكون compression خليني أفرضها compression
+
+285
+00:32:36,530 --> 00:32:42,290
+حتى لو فرضتها tension إذا الفرضية خاطئة تطلع
+
+286
+00:32:42,290 --> 00:32:45,490
+الإشارة إيش سالي بس أنا واضح انها هتكون
+
+287
+00:32:45,490 --> 00:32:56,310
+compression force هذه FD هذه
+
+288
+00:32:56,310 --> 00:32:59,430
+الـ force بتأثر على الـ plate
+
+289
+00:33:16,610 --> 00:33:23,450
+هذا مركز اتقال هيكون
+
+290
+00:33:23,450 --> 00:33:27,550
+له acceleration اللي هي A تعمل تلاتين درجة مع
+
+291
+00:33:27,550 --> 00:33:41,310
+الرأس هذه
+
+292
+00:33:41,310 --> 00:33:56,440
+M في A تعمل تلاتين درجة مع الرأس هذه
+
+293
+00:33:56,440 --> 00:34:07,180
+جي مركز استقل جي وهذه جي
+
+294
+00:34:07,180 --> 00:34:10,580
+الآن
+
+295
+00:34:10,580 --> 00:34:13,820
+أنا عندي free body diagram متكامل
+
+296
+00:34:15,390 --> 00:34:21,230
+بس في شيء ناقص بدي أحط محاور إحداثيات الـ X و الـ Y
+
+297
+00:34:21,230 --> 00:34:26,610
+هاي
+
+298
+00:34:26,610 --> 00:34:32,050
+الـ X و هاي الـ Y عشان أعرف المرجعيات لكل شيء هيك
+
+299
+00:34:32,050 --> 00:34:32,630
+مرجعية
+
+300
+00:35:05,960 --> 00:35:10,720
+طيب احنا حكينا الجسم is in pure translation in
+
+301
+00:35:10,720 --> 00:35:14,080
+pure translation يعني ما فيش له alpha فيه له
+
+302
+00:35:14,080 --> 00:35:18,900
+acceleration صح اتجاهها مائل لأنه مركز ثقل هياخد
+
+303
+00:35:18,900 --> 00:35:22,840
+حركته مسار دائري مسار دائري موازن المسار عند a
+
+304
+00:35:22,840 --> 00:35:28,340
+موازن المسار عند d معناته عندنا two D problem
+
+305
+00:35:28,340 --> 00:35:32,130
+معناته هيكون عندي تلت معادلات اللي هي summation of
+
+306
+00:35:32,130 --> 00:35:35,230
+force تجاه الـ X و summation of force تجاه الـ Y و
+
+307
+00:35:35,230 --> 00:35:40,630
+summation للمoment طيب
+
+308
+00:35:40,630 --> 00:35:44,970
+لو
+
+309
+00:35:44,970 --> 00:35:48,490
+أخدت summation of force .. summation moment حوالين
+
+310
+00:35:48,490 --> 00:35:54,590
+D summation للمoment
+
+311
+00:35:54,590 --> 00:35:56,170
+حوالين
+
+312
+00:35:57,930 --> 00:36:06,510
+D واعتبرت بعكس عقارب الساعة هو الموجب حيث هو MD
+
+313
+00:36:06,510 --> 00:36:15,810
+effective لأن أنا مش 
+
+314
+00:36:15,810 --> 00:36:20,450
+ماخد حوالين G ماخد حوالين نقطة D بختلف الأشياء لأن
+
+315
+00:36:20,450 --> 00:36:21,290
+حوالين D
+
+316
+00:36:34,640 --> 00:36:39,240
+هتكون الـ MG هتكون
+
+317
+00:36:39,240 --> 00:36:46,580
+بالـ minus minus MG في 250 هذه المسافة هتكون 250
+
+318
+00:36:46,580 --> 00:36:53,580
+ملي يعني ربع متر هتكون minus point
+
+319
+00:36:53,580 --> 00:36:58,460
+2 5 الـ MG
+
+320
+00:37:04,830 --> 00:37:08,870
+لأن عن D معناته الـ F دي مش هتعمل moment الـ F A
+
+321
+00:37:08,870 --> 00:37:13,250
+هكونها مركبتين مركبة
+
+322
+00:37:13,250 --> 00:37:22,710
+أفقية مركبة رأسية المركبة
+
+323
+00:37:22,710 --> 00:37:25,150
+الرأسية بتمر في النقطة دي مش هتعمل moment معناته
+
+324
+00:37:25,150 --> 00:37:27,450
+الـ moment المركبة الأفقية اللي هي هتعمل moment
+
+325
+00:37:27,450 --> 00:37:37,070
+معناته هتكون عندي F هتكون زائد F A هذه المسافة 2 من 10
+
+326
+00:37:37,070 --> 00:37:40,590
+زائد
+
+327
+00:37:40,590 --> 00:37:51,030
+2 من 10 في FA cosine التلاتين هذا على الجهة
+
+328
+00:37:51,030 --> 00:38:01,970
+الشمال حيث ساوى عند MA هيكون لها مركبة أفقية
+
+329
+00:38:04,470 --> 00:38:09,770
+و اللي هي مركبة إيش مركبة رأسية مركبة أفقية
+
+330
+00:38:09,770 --> 00:38:15,870
+هتكون المركبة الرأسية بتعمل moment باتجاهها 
+
+331
+00:38:15,870 --> 00:38:22,670
+عكسها هتكون minus MA minus
+
+332
+00:38:22,670 --> 00:38:29,310
+MA cosine التلاتين في 
+
+333
+00:38:29,310 --> 00:38:38,550
+2 من 5 و المركبة الأفقية بعكس عقارب الساعة
+
+334
+00:38:38,550 --> 00:38:43,870
+زائد MA
+
+335
+00:38:43,870 --> 00:38:53,310
+sin 30 في المسافة هذه اللي هي هتكون نصف الـ 2 من 10 اللي
+
+336
+00:38:53,310 --> 00:38:54,570
+هي 100 في point 1
+
+337
+00:39:06,430 --> 00:39:15,110
+يعني خلينا نبسط عند
+
+338
+00:39:15,110 --> 00:39:23,330
+هنا ربع في cosine التلاتين في 
+
+339
+00:39:23,330 --> 00:39:31,550
+الـ MA عندي اللي هي التمانية هيكون عندي ناقص point 2
+
+340
+00:39:31,550 --> 00:39:40,390
+خمسة في 8 في 9 point 8 0 6 زائد
+
+341
+00:39:40,390 --> 00:39:45,950
+point 2 في cosine التلاتين اللي هي point
+
+342
+00:39:45,950 --> 00:39:56,380
+8 6 6 في FA بتساوي minus 8 الـ cosine 
+
+343
+00:39:56,380 --> 00:40:04,240
+التلاتين اللي هي 8 6 6 في ربع في a
+
+344
+00:40:04,240 --> 00:40:07,260
+زائد
+
+345
+00:40:07,260 --> 00:40:11,380
+8 
+
+346
+00:40:11,380 --> 00:40:19,760
+في الـ sine التلاتين نصف في 10 كله مضروب في a في
+
+347
+00:40:19,760 --> 00:40:19,940
+a
+
+348
+00:40:25,930 --> 00:40:27,330
+مش عارف
+
+349
+00:41:02,800 --> 00:41:10,900
+هييطلع واحد minus واحد point 3 3 2 1 
+
+350
+00:41:10,900 --> 00:41:28,480
+point 3 3 2 في a زائد زائد
+
+351
+00:41:28,480 --> 00:41:29,920
+point 1 7 2
+
+352
+00:41:35,530 --> 00:41:41,710
+FA بتساوي أنا خليت المتغيرات على الجهة والثابت على
+
+353
+00:41:41,710 --> 00:41:46,750
+الجهة سابونت
+
+354
+00:41:46,750 --> 00:41:53,670
+2 5 في 8 بتسعة point 8 0 6 
+
+355
+00:41:53,670 --> 00:41:59,070
+9 8 point 6 1 2 9 8 point 6
+
+356
+00:41:59,070 --> 00:42:02,810
+1 2 هذا معادلة إيه؟ 1
+
+357
+00:42:11,520 --> 00:42:16,240
+هذه معادلة معادلة
+
+358
+00:42:16,240 --> 00:42:21,240
+ثانية ممكن نحكي summation of forces بتجاه الـ X
+
+359
+00:42:21,240 --> 00:42:24,620
+بالساوية صفر و summation of force بتجاه الـ Y
+
+360
+00:42:24,620 --> 00:42:26,400
+بالساوية صفر
+
+361
+00:42:44,910 --> 00:42:48,790
+أنا ممكن خليني أحلها بطريقة ثانية خلي هذه
+
+362
+00:42:48,790 --> 00:42:53,530
+المعادلة خليها لأن عشان أوجد الـ acceleration أنا 
+
+363
+00:42:53,530 --> 00:42:59,230
+بفكر أعرف محاور إحداثيات مائلة بزاوية تلاتين درجة
+
+364
+00:42:59,230 --> 00:43:10,910
+يعني أحط محاور إحداثيات محاور
+
+365
+00:43:10,910 --> 00:43:13,350
+إحداثيات x prime
+
+366
+00:43:17,740 --> 00:43:24,640
+Y' ومايل بالشكل هذا تلاتين درجة ليش
+
+367
+00:43:24,640 --> 00:43:30,940
+المحاور هذه الـ X' Y' الـ Y' عمودي على الـ F A و
+
+368
+00:43:30,940 --> 00:43:36,420
+عمودي على الـ F D باخد summation of forces باتجاه
+
+369
+00:43:36,420 --> 00:43:41,240
+الـ Y' summation لل forces
+
+370
+00:43:44,350 --> 00:43:54,750
+باتجاه الـ y prime اللي هي اتجاهها هتساوي لاحظوا
+
+371
+00:43:54,750 --> 00:43:58,750
+هذا مش كلها component ولا هاد الـ component الآن
+
+372
+00:43:58,750 --> 00:44:06,050
+هاي الـ x هاي المحاور هاي
+
+373
+00:44:06,050 --> 00:44:11,570
+الـ x prime وهاي 
+
+374
+00:44:11,570 --> 00:44:12,270
+الـ y prime
+
+375
+00:44:16,900 --> 00:44:21,200
+هذا هتكون تلاتين
+
+376
+00:44:21,200 --> 00:44:31,460
+درجة هتكون معناته minus mg بالساوية m a y prime
+
+377
+00:44:31,460 --> 00:44:45,420
+يعني هتكون minus mg كوساين تلاتين هتساوي 
+
+378
+00:44:50,180 --> 00:44:58,860
+minus MA مباشرة هتساوي minus MA
+
+379
+00:44:58,860 --> 00:45:04,660
+معناته A هتساوي 
+
+380
+00:45:04,660 --> 00:45:07,760
+A
+
+381
+00:45:07,760 --> 00:45:14,860
+هتساوي G cosine التلاتين
+
+382
+00:45:16,520 --> 00:45:21,540
+تحسبها مباشرة يعني هذه خطوة اختصرت كثير الحل عندي
+
+383
+00:45:21,540 --> 00:45:29,600
+تطلع 
+
+384
+00:45:29,600 --> 00:45:37,320
+8 point 4 9 2 8 point
+
+385
+00:45:37,320 --> 00:45:43,540
+4 9 2 meter per second square بعوض
+
+386
+00:45:43,540 --> 00:45:54,110
+بواحد from one بحسب FA بتساوي
+
+387
+00:45:54,110 --> 00:46:00,910
+اللي هي 9 8 point 6 1 2 ناقص 1 
+
+388
+00:46:00,910 --> 00:46:06,190
+point 3 3 2 في 8 point 4 
+
+389
+00:46:06,190 --> 00:46:22,740
+9 2 كله على point 1 7 2 هيطلع 9 
+
+390
+00:46:22,740 --> 00:46:31,180
+8 point 6 1 2 ناقص 1 point 3 3 2
+
+391
+00:46:31,180 --> 00:46:46,550
+في 8 point 4 9 2 يساوي تقسيم point 1 7 2 بيطلع 4 
+
+392
+00:46:46,550 --> 00:46:53,610
+8 point 2 6 4 8 نيوتن
+
+393
+00:46:53,610 --> 00:46:57,830
+6 نيوتن هذا الـ F A
+
+394
+00:47:06,850 --> 00:47:10,390
+عشان أوجد الـ FD باخد summation force باتجاه الـ X'
+
+395
+00:47:10,750 --> 00:47:23,190
+summation لل forces باتجاه الـ X' هيها بالساوية M A
+
+396
+00:47:23,190 --> 00:47:30,230
+X' يعني هتكون عندنا FD
+
+397
+00:47:34,400 --> 00:47:40,820
+minus FA minus 
+
+398
+00:47:40,820 --> 00:47:59,680
+FA زائد MG sin 30 زائد MG sin 30 درجة هتساوي صفر فيش 
+
+399
+00:47:59,680 --> 00:48:10,270
+في الـ x prime يساوي صفر يعني FD حسبه و FA اللي هي
+
+400
+00:48:10,270 --> 00:48:15,070
+8 و 48 point 
+
+401
+00:48:15,070 --> 00:48:23,910
+2 6 minus M اللي هي 8 في G اللي هي 9
+
+402
+00:48:23,910 --> 00:48:29,330
+point 8 0 6 في sin التلاتين اللي هي نصف
+
+403
+00:48:51,800 --> 00:48:56,760
+هتساوي تطلع 9 point 0 3 6
+
+404
+00:49:01,290 --> 00:49:07,910
+N مع أن فرضيتنا أن FD compression صحيحة يعني
+
+405
+00:49:07,910 --> 00:49:14,090
+طلعت الإجابة موجبة لو
+
+406
+00:49:14,090 --> 00:49:19,750
+استخدمت المحاور الـ X Y العادية هيصير المسألة أكثر
+
+407
+00:49:19,750 --> 00:49:25,430
+تعقيدا .. المسألة هتصير أكثر تعقيدا باستخدام محاور
+
+408
+00:49:25,430 --> 00:49:29,410
+ميلة x prime و y prime حلت الإشكال بسرعة كبيرة جدا
+
+409
+00:49:29,410 --> 00:49:36,750
+طيب
+
+410
+00:49:36,750 --> 00:49:42,810
+المحاضرة الجاي بنكمل .. بنحل مجموعة ثانية من 
+
+411
+00:49:42,810 --> 00:49:45,910
+الأمثلة وبعدين بنخش على موضوع جديد أعطيكم العفو 
diff --git a/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/6yU9Y-KY0Bs_postprocess.srt b/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/6yU9Y-KY0Bs_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b267222b815e36e170952e8ec26b441b606d239f
--- /dev/null
+++ b/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/6yU9Y-KY0Bs_postprocess.srt
@@ -0,0 +1,1612 @@
+1
+00:00:05,380 --> 00:00:08,800
+طب بسم الله الرحمن الرحيم بداية منرحب فيكوا طبعا
+
+2
+00:00:08,800 --> 00:00:12,860
+احنا هنعيد اللي حكيناه للمحاضرة الفاتتة لإن في بعض
+
+3
+00:00:12,860 --> 00:00:17,140
+الطلاب أجوا له أول مرة هنبدأ في عرض ال course
+
+4
+00:00:17,140 --> 00:00:22,960
+outline أو خطة المساق طبعا ال course اسمه dynamics
+
+5
+00:00:22,960 --> 00:00:27,360
+هو ال course الأول في الهندسة الميكانيكية بعد
+
+6
+00:00:27,360 --> 00:00:31,570
+course الاستاتيكاالهدف من ال course أو نوصف ال
+
+7
+00:00:31,570 --> 00:00:34,650
+course بغطي اللي هي Mechanica Newton اللي هي
+
+8
+00:00:34,650 --> 00:00:39,850
+mechanics of Newton هتشمل ال course دراسة اللي هي
+
+9
+00:00:39,850 --> 00:00:44,510
+kinematics of particles and rigid bodies و برضه
+
+10
+00:00:44,510 --> 00:00:47,310
+kinetics of particles and rigid bodies لما بحكي
+
+11
+00:00:47,310 --> 00:00:53,110
+kinematics بحكي عن دراسة الحركة للأجسام دراسة
+
+12
+00:00:53,110 --> 00:00:59,080
+الحركة للأجسام اللي هي بتتعلق بالإزاحةو السرعة و
+
+13
+00:00:59,080 --> 00:01:03,860
+ال acceleration مع الزمن بدون التطرق للمؤثر
+
+14
+00:01:03,860 --> 00:01:08,120
+الخارجي اللي هو القوة اللي خلت الجسم يتحرك ال
+
+15
+00:01:08,120 --> 00:01:14,080
+kinetics انا بقربط بين الحركة و المؤثر يعني بربط
+
+16
+00:01:14,080 --> 00:01:20,080
+بين ال forces و ال motion طبعا هنستخدم العديد من
+
+17
+00:01:20,080 --> 00:01:27,160
+الطرقفي تحليلنا لدراسة الأجسام المتحركة هنستخدم ال
+
+18
+00:01:27,160 --> 00:01:30,560
+Newton's law هنستخدم ال principle of impulse and
+
+19
+00:01:30,560 --> 00:01:34,720
+momentum هنستخدم ال principle of work and energy
+
+20
+00:01:34,720 --> 00:01:41,020
+برضه هندرس التصادمات خلال هذا ال courseال course
+
+21
+00:01:41,020 --> 00:01:45,680
+هيكون نشتغل فيه على مستويين مستوى ال particle
+
+22
+00:01:45,680 --> 00:01:51,060
+level و مستوى ال rigid body level هيكون فيه تلاتة
+
+23
+00:01:51,060 --> 00:01:54,460
+chapters على ال particle dynamics و تلاتة chapters
+
+24
+00:01:54,460 --> 00:01:58,320
+على ال rigid body dynamics في نهاية ال course
+
+25
+00:01:58,320 --> 00:02:04,110
+المفروض الطالب يكون قادر على نمذجمسألة او مشكلة
+
+26
+00:02:04,110 --> 00:02:08,430
+دينامكية او لدراسة حركة الجسم لازم يكون قادر ان
+
+27
+00:02:08,430 --> 00:02:11,950
+يرسم free body diagram يعمل معادلة الحركة
+
+28
+00:02:11,950 --> 00:02:17,090
+equations of motion يعمل kinematic analysis سواء
+
+29
+00:02:17,090 --> 00:02:28,470
+كان ب 2D او ب 3D الكتاب
+
+30
+00:02:30,710 --> 00:02:34,330
+الكتاب يعني هو من أشهر الكتب المستخدمة في المجال
+
+31
+00:02:34,330 --> 00:02:38,970
+اللي هو المؤلف بتاعه B.Ferdinand & Johnson اسمه
+
+32
+00:02:38,970 --> 00:02:42,890
+vector mechanics for engineers dynamics النسخة
+
+33
+00:02:42,890 --> 00:02:47,770
+الأطماش الناشر macro hill وانا مابعطيكوا ال ISBN
+
+34
+00:02:47,770 --> 00:02:53,070
+number الموضوعات اللي هيتم تغطيتها في ال course
+
+35
+00:02:53,070 --> 00:02:58,770
+chapter واحد هي kinematics of particlesاللي هي
+
+36
+00:02:58,770 --> 00:03:04,450
+دراسة هندسة الحركة للجسيمات اللي هي الحركة على خط
+
+37
+00:03:04,450 --> 00:03:08,530
+مستقيم و الحركة على منحنيات ال chapter التاني اللي
+
+38
+00:03:08,530 --> 00:03:14,170
+هي kinetics of particles حربط بين ال motion و
+
+39
+00:03:14,170 --> 00:03:18,270
+المؤثر ال forces من خلال نيوتنز second law اللي F
+
+40
+00:03:18,270 --> 00:03:22,410
+بصوة M في A بشكل أساسي ال chapter التالت kinetics
+
+41
+00:03:22,410 --> 00:03:28,730
+of particles برضه حربط المؤثرمع ال motion بس
+
+42
+00:03:28,730 --> 00:03:31,730
+باستخدام طريقة اللي هي ال energy and momentum
+
+43
+00:03:31,730 --> 00:03:37,470
+methods chapter 4 اللي هي system of particles هدرس
+
+44
+00:03:37,470 --> 00:03:42,370
+مجموعة من ال particles تتحرك مع بعض وبشكل منفصل
+
+45
+00:03:42,370 --> 00:03:49,830
+chapter 4 انا هخطي بشكل يعني built in او مخفي من
+
+46
+00:03:49,830 --> 00:03:55,240
+خلال chapter 5 و6 و7الجزء التاني اللي هو chapter
+
+47
+00:03:55,240 --> 00:03:58,320
+خمسة و ستة و سبعة اللي هي dynamics of rigid bodies
+
+48
+00:03:58,320 --> 00:04:02,040
+اللي هي ديناميكا الأجسام الجاسية هيكون عندك أولا
+
+49
+00:04:02,040 --> 00:04:07,860
+ال kinematics of rigid bodies بعدين plan motion of
+
+50
+00:04:07,860 --> 00:04:11,160
+rigid bodies forces and acceleration plan motion
+
+51
+00:04:11,160 --> 00:04:13,500
+of rigid bodies energy and momentum method
+
+52
+00:04:16,700 --> 00:04:20,420
+chapter تمانية هنستخدم ال complex number analysis
+
+53
+00:04:20,420 --> 00:04:24,780
+عشان ندرس ال kinematics ل .. لل .. لل ..
+
+54
+00:04:24,780 --> 00:04:28,620
+للميكانيزم و ال rigid bodies طبعا هذا ال course
+
+55
+00:04:28,620 --> 00:04:32,660
+اختياري optional اذا ضال معانا وقت هنغطيه او
+
+56
+00:04:32,660 --> 00:04:36,260
+الشابتر هذا اذا ما اجربناش نغطيه هنغطيه في ال
+
+57
+00:04:36,260 --> 00:04:37,960
+course اللي بعد اللي هو theory of machines
+
+58
+00:04:43,010 --> 00:04:48,950
+الآن تقييم الطالب باتجاه تحقيق أهداف المصادق هيكون
+
+59
+00:04:48,950 --> 00:04:57,170
+من خلال واجبات أسبوعية CAD problems midterms هيكون
+
+60
+00:04:57,170 --> 00:05:01,650
+كل chapter عليه امتحان مدته ساعة يعني هيكون عندنا
+
+61
+00:05:01,650 --> 00:05:07,130
+من أربع لست امتحانات حلغي في آخر الفصل أقل اقل
+
+62
+00:05:07,130 --> 00:05:13,960
+درجة حلغيها عن كل طالب هيكون the final examهيكون
+
+63
+00:05:13,960 --> 00:05:19,160
+design projects إذا تطلب الأمر طبعا كل امتحانات
+
+64
+00:05:19,160 --> 00:05:24,320
+هتكون في الفصل و هتكون نظام كتاب مغلق يعني closed
+
+65
+00:05:24,320 --> 00:05:27,780
+book في
+
+66
+00:05:27,780 --> 00:05:32,400
+بعض الأحيان هطلوا منك الواجبات تستخدموا software
+
+67
+00:05:32,400 --> 00:05:37,040
+زي ال office ال MS word و ال MS Excel طبعا هذا
+
+68
+00:05:37,040 --> 00:05:41,610
+تبقى للحاجة مش دايماال late assignments الواجبات
+
+69
+00:05:41,610 --> 00:05:46,770
+اللي بتتأخر عن تقديمها مش هتقبل الانتحان النهائي
+
+70
+00:05:46,770 --> 00:05:48,970
+هيكون شامل لكل المادة
+
+71
+00:05:52,650 --> 00:05:57,590
+فيه هنستخدم برامج عشانك بنصحي انكوا تجيبوا معاكوا
+
+72
+00:05:57,590 --> 00:06:01,010
+إذا حد معاه laptop اجيب ال laptop و ينزل برامج
+
+73
+00:06:01,010 --> 00:06:04,750
+التالية اللي هي Adams ال SolidWorks Mathematica
+
+74
+00:06:04,750 --> 00:06:09,250
+MathLab و Microsoft Office هنستخدم كتير ال
+
+75
+00:06:09,250 --> 00:06:14,870
+SolidWorks و Adamsو Mathematica Math Lab يعني
+
+76
+00:06:14,870 --> 00:06:17,150
+أنتوا أخدتوا course Math Lab و أنتوا أحرار ممكن
+
+77
+00:06:17,150 --> 00:06:20,030
+تستخدموا Math Lab أو تستخدموا Mathematica بس هذه
+
+78
+00:06:20,030 --> 00:06:24,590
+البرامج ابدوا نزلوها و ابدوا اتعرف عليها و حسنوا
+
+79
+00:06:24,590 --> 00:06:29,430
+قدراتكوا فيها الساعات
+
+80
+00:06:29,430 --> 00:06:32,570
+المكتبية تاتية حكونا أن السبت هو أربع من تمانية
+
+81
+00:06:32,570 --> 00:06:37,110
+لعشرة و اتنين من تسعة لعشرة يوم الأحد من تمانية
+
+82
+00:06:37,110 --> 00:06:37,790
+لتسعة و نص
+
+83
+00:06:42,030 --> 00:06:48,730
+سياسة الدرجات طبعا عند الحضور و أنك تجيب ال laptop
+
+84
+00:06:48,730 --> 00:06:52,630
+عليه خمسة في المية طبعا تعريف الحضور أو بدي احكي
+
+85
+00:06:52,630 --> 00:06:57,330
+تعريف الغياب اكتر دقة تعريف الغياب انك اتغيب عن
+
+86
+00:06:57,330 --> 00:07:02,370
+المحاضرة او انك تتأخر سواء اتأخرت دقيقة او نص ساعة
+
+87
+00:07:02,370 --> 00:07:07,570
+نفس الشيء طبعا هسمحلك تدخل تحضر المحاضرة بس هترصد
+
+88
+00:07:07,570 --> 00:07:09,230
+انك غايب اذا كنت متأخر
+
+89
+00:07:12,830 --> 00:07:19,210
+جزء من المساق جزء
+
+90
+00:07:19,210 --> 00:07:24,630
+من المساق اللي احنا فيه اربع كفايات كفايات فنية
+
+91
+00:07:24,630 --> 00:07:30,650
+كفايات منهجية كفايات شخصية و كفايات اجتماعية من
+
+92
+00:07:30,650 --> 00:07:33,390
+ضمن الكفايات الشخصية انك تلتزم بالوقت انك تكون
+
+93
+00:07:33,390 --> 00:07:36,050
+منضبط فانك حضبطها بشكل هذا
+
+94
+00:07:41,110 --> 00:07:43,630
+في عندي طبعا في نهاية كل chapter عندى امتحان هكون
+
+95
+00:07:43,630 --> 00:07:47,950
+عندى اربع على ست امتحانات وحلغ اقل امتحان اقل درجة
+
+96
+00:07:47,950 --> 00:07:51,950
+من الامتحانات الخامسة او الستة هكون عندى CAD
+
+97
+00:07:51,950 --> 00:07:54,710
+problems and projects وعندى final exam عليها خمس
+
+98
+00:07:54,710 --> 00:08:03,350
+تلاتين في المية ال total بيكون مية في المية في
+
+99
+00:08:03,350 --> 00:08:07,700
+سياسات عامة في ال courseطبعا ال .. ال .. الغش و
+
+100
+00:08:07,700 --> 00:08:11,220
+انك تنسخه من .. او اي طالب ينسخ من زميله هذا مرفوض
+
+101
+00:08:11,220 --> 00:08:16,260
+بشكل قطعي لأنه في النهاية شغله غير أخلاقية انك
+
+102
+00:08:16,260 --> 00:08:20,840
+تاخد شغل غيرك و تنسبه اليك طبعا هذا بمنحنا الحق
+
+103
+00:08:20,840 --> 00:08:26,960
+انه احطلك علامة راسب في المساق اذا انت غشيت
+
+104
+00:08:29,760 --> 00:08:32,460
+الان انا عامل اربع على ست امتحانات، معناته بما
+
+105
+00:08:32,460 --> 00:08:34,760
+احنا مش هيكون عندنا امتحانات تعويضية، مش هيكون
+
+106
+00:08:34,760 --> 00:08:37,340
+عندنا امتحانات make up exams، يعني اصلا عندك ظرف
+
+107
+00:08:37,340 --> 00:08:42,620
+خلال فترة الأربع شهور، انا حالغي في الآخر امتحان،
+
+108
+00:08:42,620 --> 00:08:46,500
+يعني اعمل لكل طالب امتحان عشان الظروف الخاصة، ممكن
+
+109
+00:08:46,500 --> 00:08:50,880
+تكون ظروف مرضية، ظروف نفسية أو ظروف عائلية
+
+110
+00:08:53,400 --> 00:08:57,060
+إذا حد ماتتخاطب معاه ممكن يبعتلي على ال email طبعا
+
+111
+00:08:57,060 --> 00:09:00,540
+ما تتوقعوش أن أرد عليكم بشكل فوري يعني اعطوا نفسكم
+
+112
+00:09:00,540 --> 00:09:09,400
+يومين لتلاتة عشان أرد على ال email الآن
+
+113
+00:09:09,400 --> 00:09:15,700
+إذا طالب غاب نتيجة ضرف معينطبعا هو مسئول عن كل
+
+114
+00:09:15,700 --> 00:09:20,840
+كلمة تنذكر او تقال في خلال المحاضرة هو مسئول انه
+
+115
+00:09:20,840 --> 00:09:25,040
+يراجع المحاضرة يعني مسئولية ابتقى عليه بشكل كامل
+
+116
+00:09:25,040 --> 00:09:28,400
+اذا غاب المحاضرة كل ما ذكر المحاضرة هو مسئول عنها
+
+117
+00:09:28,400 --> 00:09:33,160
+طيب في اي سؤال او استفسار يعني نبدأ الشبتر الأول
+
+118
+00:09:33,160 --> 00:09:39,460
+نبدأ
+
+119
+00:09:39,460 --> 00:09:40,140
+الشبتر الأول يعني
+
+120
+00:09:54,020 --> 00:09:57,220
+طب هنبدأ بال chapter لو هو chapter 11 في الكتاب
+
+121
+00:09:57,220 --> 00:10:03,980
+اللي هو kinematics of particles طبعا
+
+122
+00:10:03,980 --> 00:10:08,820
+v average هتكون تستوى اللي
+
+123
+00:10:08,820 --> 00:10:15,820
+هو delta x على delta t if without السرعة اللحظية
+
+124
+00:10:15,820 --> 00:10:21,860
+باخد ال limit صح ال instantaneous velocity v تستوى
+
+125
+00:10:21,860 --> 00:10:30,330
+ال limitdelta x ع delta t as delta t approaches
+
+126
+00:10:30,330 --> 00:10:37,430
+zero يعني هيكون سوى dx by dt يعني الصراع اللحظية
+
+127
+00:10:37,430 --> 00:10:44,630
+هي ال differential لإزاحة بالنسبة للزمن طبعا
+
+128
+00:10:44,630 --> 00:10:50,210
+الصراع ممكن تكون موجبة إذا بالاتجاه الموجب لمحور
+
+129
+00:10:50,210 --> 00:10:50,970
+الإحداثيات
+
+130
+00:10:53,530 --> 00:10:59,710
+ممكن تكون سالبة يعني لو انا اتحركت لو حكيت انا هاي
+
+131
+00:10:59,710 --> 00:11:04,010
+الموجة ورايا ال X موجة ورايا و اتحركت بهذا الاتجاه
+
+132
+00:11:04,010 --> 00:11:11,550
+الصورة هتكون موجبة لو كنت هنا و رجعت رجوع اتجاه
+
+133
+00:11:11,550 --> 00:11:16,190
+الصورة بتاعتهلورا سالب معناته إذا بتحرك باتجاه ال
+
+134
+00:11:16,190 --> 00:11:20,230
+positive x axis بتكون السرعة موجبة إذا بتحرك
+
+135
+00:11:20,230 --> 00:11:29,290
+باتجاه ال negative x axis بتكون السرعة سالبة هنا
+
+136
+00:11:29,290 --> 00:11:32,910
+بحكي على ال difference يعني أنا مشيت مثلا ال
+
+137
+00:11:32,910 --> 00:11:39,790
+particle ماشي مسافة متر في خلال مثلا فترة زمنية
+
+138
+00:11:39,790 --> 00:11:41,470
+عشر عشر ثوانية
+
+139
+00:11:44,410 --> 00:11:47,910
+السرعة المتوسطة طبعا خلال الفترة هذه مش بضرورة
+
+140
+00:11:47,910 --> 00:11:53,750
+تكون السرعة ثابتة و تكون متغيرة فالسرعة المتوسطة
+
+141
+00:11:53,750 --> 00:12:00,590
+هتكون الفرق اللي هو واحد متر اللي V average على
+
+142
+00:12:00,590 --> 00:12:05,910
+عشر ثوانة هتكون point one meter per second يعني
+
+143
+00:12:05,910 --> 00:12:09,610
+خلال الفترة هذه السرعة المتوسطة قد تكون سرعة أقل
+
+144
+00:12:09,610 --> 00:12:16,910
+او اعلى من القيمة الوسطىو ده ال X و ده ال P ال
+
+145
+00:12:16,910 --> 00:12:20,610
+differential لان انا بزغر ال time of increment ال
+
+146
+00:12:20,610 --> 00:12:22,770
+time of increment it approaches zero يعني انا باخد
+
+147
+00:12:22,770 --> 00:12:34,110
+بشكل لحظة بشكل لحظي عشانك بيصير differential ال
+
+148
+00:12:34,110 --> 00:12:41,550
+acceleration بتمثل التغير في السرعة بالنسبة لزمان
+
+149
+00:12:41,550 --> 00:12:44,250
+عندي جسم
+
+150
+00:12:48,150 --> 00:12:58,350
+الـ Time T كانت
+
+151
+00:12:58,350 --> 00:13:04,290
+السرعة له V الـ
+
+152
+00:13:04,290 --> 00:13:11,470
+Time T زاد Delta T يعني بعد Delta T زمن صارت
+
+153
+00:13:11,470 --> 00:13:16,570
+السرعة V زاد Delta V طب يكون ال Delta V تكون
+
+154
+00:13:17,650 --> 00:13:22,810
+بالزيادة او نقصان معناته ال average acceleration A
+
+155
+00:13:22,810 --> 00:13:30,830
+average هتكون سوى V ذائد Delta V السرعة النهائية
+
+156
+00:13:30,830 --> 00:13:40,010
+minus V على T ذائد Delta T minus T يعني هتسوى
+
+157
+00:13:40,010 --> 00:13:44,490
+Delta V على Delta T
+
+158
+00:13:46,690 --> 00:13:51,150
+إذا باخد ال limit بحسب
+
+159
+00:13:51,150 --> 00:13:59,190
+ال A اللحظية هتكون limit delta V ع delta T as
+
+160
+00:13:59,190 --> 00:14:09,970
+delta T approaches 0 يستوى DV by DT لأن
+
+161
+00:14:09,970 --> 00:14:12,790
+لا يعني إن أنا ماشي في الاتجاه هذا اتجاه ال
+
+162
+00:14:12,790 --> 00:14:18,170
+positive Xإن ال acceleration موجبة ممكن تكون موجبة
+
+163
+00:14:18,170 --> 00:14:22,470
+وممكن تكون سالبة ولأن أنا ماشي بهذا الاتجاه
+
+164
+00:14:22,470 --> 00:14:26,730
+الاتجاه المعاكس إن ال acceleration تكون سالبة ممكن
+
+165
+00:14:26,730 --> 00:14:31,450
+تكون موجبة وممكن تكون سالبة الآن ناخد حالات مختلفة
+
+166
+00:14:31,450 --> 00:14:39,390
+لو أخدت الحالة الأولى اتطلع على طول السهم هاي
+
+167
+00:14:39,390 --> 00:14:48,660
+V و V Prime مين أكبر؟V' أكبر من V معناته وانا طبعا
+
+168
+00:14:48,660 --> 00:14:52,460
+الجسم ماشي باتجاه ال positive x axis معناته إذا V'
+
+169
+00:14:52,720 --> 00:14:58,160
+أكبر من V معناته الجسم بتسارع سرعته بتزيد معناته
+
+170
+00:14:58,160 --> 00:15:01,200
+ال acceleration هتكون أيش موجبة معناته هنا ال
+
+171
+00:15:01,200 --> 00:15:05,640
+acceleration هتكون أكبر من 0 موجبة ناخد الحالة
+
+172
+00:15:05,640 --> 00:15:15,990
+التانية عندي هاي V و هاي V' مين أكبر V' ولا VV
+
+173
+00:15:15,990 --> 00:15:23,290
+معناته السرعة بتقل، معناته انا ماشي بهذا الاتجاه،
+
+174
+00:15:23,290 --> 00:15:29,890
+بديت مثلا بسرعة معينة وكل ما لها سرعة بتقل، معناته
+
+175
+00:15:29,890 --> 00:15:34,750
+فيه تناقص في السرعة، تناقص في السرعة معناته اتجاه
+
+176
+00:15:34,750 --> 00:15:38,660
+الـ X ليش؟ هكون باتجاه المعاكسيعني انا الحالة هذه
+
+177
+00:15:38,660 --> 00:15:44,060
+انا ماشي في ال positive x axis لكن سرعتي موجبة وال
+
+178
+00:15:44,060 --> 00:15:51,160
+acceleration بالسالب لأن الجسم بيمشي بسرعة تناقصية
+
+179
+00:15:51,160 --> 00:15:54,900
+او بتناقص حالة
+
+180
+00:15:54,900 --> 00:16:03,880
+تالتة عندي جسم ماشي بال negative x axis هذه V وهذه
+
+181
+00:16:03,880 --> 00:16:07,530
+V primeلأنه ماشي في الـ negative x-axis بهذا
+
+182
+00:16:07,530 --> 00:16:14,050
+الاتجاه السرعة V أكبر من V' يعني بهذا الاتجاه
+
+183
+00:16:14,050 --> 00:16:18,350
+السرعة بتتنقص بهذا الاتجاه صح؟ معناه ال
+
+184
+00:16:18,350 --> 00:16:21,730
+acceleration هتكون معاكسة في الحال هذا هتكون ال
+
+185
+00:16:21,730 --> 00:16:24,690
+acceleration إيش مالها؟ موجبة، موجبة، ما يعني أن
+
+186
+00:16:24,690 --> 00:16:28,250
+الجسم بتتحرك باتجاه ال negative x-axis الحالة
+
+187
+00:16:28,250 --> 00:16:34,540
+الرابعة بدأ ال particle من النقطة هذهماشي بسرعة V
+
+188
+00:16:34,540 --> 00:16:40,340
+و السرعة النهائية V' لأن أنا بدأت سرعة معينة من
+
+189
+00:16:40,340 --> 00:16:45,700
+هنا و بدأت متسارعة معناته انا بتسارع بهذا الاتجاه
+
+190
+00:16:45,700 --> 00:16:49,800
+معناته ال acceleration موجبة او هذه اتجاه ال
+
+191
+00:16:49,800 --> 00:16:54,000
+acceleration بالنسبة لل XX ايش هتكون negative
+
+192
+00:16:54,000 --> 00:17:00,600
+معناته ال velocity اتجاه الحركة بحدي اتجاه السرعة
+
+193
+00:17:01,760 --> 00:17:05,300
+لكن اتجاه الحركة مش بالضروري يكون متوافق مع اتجاه
+
+194
+00:17:05,300 --> 00:17:22,500
+ال acceleration خلّيني
+
+195
+00:17:22,500 --> 00:17:29,910
+أخد particle بتحرك على خط مستقيمطب قلنا المعادلة
+
+196
+00:17:29,910 --> 00:17:35,830
+هذه X أسواس تتاربية ناقص ت كيب الان ال X تتغير
+
+197
+00:17:35,830 --> 00:17:41,170
+المعادلة من الدرجة التالتة ممكن
+
+198
+00:17:41,170 --> 00:17:44,290
+قد يفهم ان الجسم متحركش على خط مستقيم لان المعادلة
+
+199
+00:17:44,290 --> 00:17:48,010
+مش من الدرجة الأولى مش بالضرورة انا ممكن امشي
+
+200
+00:17:48,010 --> 00:17:54,610
+بسرعة امشي باتجاه ال X X بسرعة منتظرة مظلوط ممكن
+
+201
+00:17:55,620 --> 00:17:58,900
+الزيد السرعة أنا ماشي على خط مستقيم في الآخر ممكن
+
+202
+00:17:58,900 --> 00:18:05,860
+ازيد بشكل linear ممكن ازيد بشكل non-linear فهذه
+
+203
+00:18:05,860 --> 00:18:12,860
+بتعبر عن التغير في قيمة ال position ماعيش زمن ما
+
+204
+00:18:12,860 --> 00:18:16,080
+بتعبر ان هو اللي هو بتحرك على خط مستقيم او غير خط
+
+205
+00:18:16,080 --> 00:18:19,980
+مستقيم بس هو في الحالة هذي بتحرك على خط مستقيم طبق
+
+206
+00:18:19,980 --> 00:18:29,360
+المعادل هذه عند X بالساوية 6T تربيعناقص تتكيب لو
+
+207
+00:18:29,360 --> 00:18:39,720
+بدى احسب السرعة اللحظية مش تقة ال V ساوى DX by DT
+
+208
+00:18:39,720 --> 00:18:49,860
+هتساوى اتناشر T ناقص تلاتة T تربع طيب ال
+
+209
+00:18:49,860 --> 00:18:52,800
+acceleration DV
+
+210
+00:19:02,380 --> 00:19:10,000
+عشان امثل ال a و ال v و ال x graphically مع الزمن
+
+211
+00:19:10,000 --> 00:19:16,000
+انا هعمل تلت منحنيات واحد لل acceleration واحد لل
+
+212
+00:19:16,000 --> 00:19:18,740
+velocity واحد لل displacement
+
+213
+00:19:22,010 --> 00:19:28,310
+وحدتها متر هنا V وحدتها متر كل ثانية هنا
+
+214
+00:19:28,310 --> 00:19:34,430
+acceleration وحدتها متر لكل ثانية تربيع انا هعمل
+
+215
+00:19:34,430 --> 00:19:42,210
+جدول T
+
+216
+00:19:42,210 --> 00:19:47,510
+عندي
+
+217
+00:19:47,510 --> 00:19:49,050
+هنا ال X
+
+218
+00:19:52,270 --> 00:19:58,150
+و ال V و
+
+219
+00:19:58,150 --> 00:20:04,730
+ال acceleration لو عوضت عن T طبعا دائما نقطة سهلة
+
+220
+00:20:04,730 --> 00:20:13,290
+سفر عوضت عن T سفر اللي بدات الحركة هتكون ال X سفر
+
+221
+00:20:13,290 --> 00:20:17,830
+و ال V سفر
+
+222
+00:20:19,320 --> 00:20:28,640
+و ال acceleration ايش اتناش هنجيه
+
+223
+00:20:28,640 --> 00:20:36,980
+لها شوية شوية الان ال a هي ال slope للسرعة يعني
+
+224
+00:20:36,980 --> 00:20:43,300
+لما تكون ال v maximum a is the slope
+
+225
+00:20:46,180 --> 00:20:58,960
+of V معناته when V is maximum or minimum بتكون ال
+
+226
+00:20:58,960 --> 00:21:09,680
+acceleration شمالها Zero مظبوط يعني A بتساوي Zero
+
+227
+00:21:09,680 --> 00:21:17,940
+when اتناش ماقصتتي بتساوي Zeroيعني ال A equal zero
+
+228
+00:21:17,940 --> 00:21:27,160
+when T ساوى two second يعني انا بالزمن احط عند
+
+229
+00:21:27,160 --> 00:21:31,600
+اتنين second واحسب
+
+230
+00:21:31,600 --> 00:21:38,880
+ال A هتكون اياش؟ Zero طيب
+
+231
+00:21:38,880 --> 00:21:48,170
+نحسب Vهتكون ال V هتكون اتناش في اتنين اربع و عشرين
+
+232
+00:21:48,170 --> 00:21:56,110
+ناقص اتناش اتناش وال
+
+233
+00:21:56,110 --> 00:22:04,630
+X ستة في اربعة اربع و عشرين ناقص تمانية ستة عشر
+
+234
+00:22:12,400 --> 00:22:17,800
+بنفس المنطقة V is
+
+235
+00:22:17,800 --> 00:22:23,660
+the slope of
+
+236
+00:22:23,660 --> 00:22:30,040
+X يعني
+
+237
+00:22:30,040 --> 00:22:39,020
+X is maximum or minimum when
+
+238
+00:22:42,670 --> 00:22:49,190
+V بستوى Zero صح؟ المعنى هو خلينا نشوف V متى بستوى
+
+239
+00:22:49,190 --> 00:22:55,570
+Zero اعوض عن V بستوى Zero يعني Zero هيكون ساوى ستة
+
+240
+00:22:55,570 --> 00:23:03,930
+T تربيع ناقص T تكيب اتناشر
+
+241
+00:23:03,930 --> 00:23:09,270
+T ناقص
+
+242
+00:23:09,270 --> 00:23:19,000
+تلاتةT تربيع هاخد تلاتة T على المشترك هيكون
+
+243
+00:23:19,000 --> 00:23:30,320
+عندي أربعة ماقص T معناته V بالزيرو V بالزيرو when
+
+244
+00:23:30,320 --> 00:23:41,230
+T بالساوة سفر or T بالساوية أربعة secondأنا سنفر
+
+245
+00:23:41,230 --> 00:23:47,430
+already غطناها لأن
+
+246
+00:23:47,430 --> 00:23:51,870
+عندي ال T أربعة second نشوف
+
+247
+00:23:51,870 --> 00:24:02,210
+في ال X ستة في ستاش ستة وتسعين ناقص أربعة ستين نين
+
+248
+00:24:02,210 --> 00:24:07,550
+و تلاتين ال
+
+249
+00:24:07,550 --> 00:24:14,900
+V اتناشف أربعةتمانية و اربعين اربعين زيروا احنا
+
+250
+00:24:14,900 --> 00:24:21,600
+حكينا زيروا already زيروا ال A هتكون اتناش ناقص
+
+251
+00:24:21,600 --> 00:24:24,600
+ستة في اربعة سالب اتناش
+
+252
+00:24:37,220 --> 00:24:45,540
+طيب احنا اخر اشي نشوف بقتش X بالساوة صفر X بالساوة
+
+253
+00:24:45,540 --> 00:24:49,300
+صفر وين
+
+254
+00:24:49,300 --> 00:24:59,980
+ستة تلتربيع ناقص T تكيب بالساوة صفر لو أخدت تتربيع
+
+255
+00:24:59,980 --> 00:25:12,590
+مشترك هكون عندي ستة ناقص Tيعني تساوى سفر معناته x
+
+256
+00:25:12,590 --> 00:25:24,350
+بالساوية سفر when t بالساوية سفر or x بالساوية ..
+
+257
+00:25:24,350 --> 00:25:31,630
+ال t بالساوية ستة
+
+258
+00:25:31,630 --> 00:25:33,470
+معناته هنحط هنا
+
+259
+00:25:39,180 --> 00:25:47,340
+T6 X0 V12×6
+
+260
+00:25:47,340 --> 00:25:52,480
+72-108
+
+261
+00:25:52,480 --> 00:26:01,260
+-36 12
+
+262
+00:26:01,260 --> 00:26:05,420
+-36-24
+
+263
+00:26:11,520 --> 00:26:18,440
+معناته انا مش محتاج اعوض قيم بشكل عشوائي الان
+
+264
+00:26:18,440 --> 00:26:23,760
+هابدأ ارسم المنحنيات هابدأ بال acceleration لان
+
+265
+00:26:23,760 --> 00:26:28,140
+درجتها اقل درجة مظبوط هي ال linear احنا حكينا ال
+
+266
+00:26:28,140 --> 00:26:33,480
+acceleration ال time بالساوة سفر بالساوة ايش اتناش
+
+267
+00:26:33,480 --> 00:26:41,810
+هعندي نقطة هنا اتناش و ال time equal toبساوي السفر
+
+268
+00:26:41,810 --> 00:26:48,770
+والتغير بتاعها خطه مع أنها تخلط بكافية نقطتين حمص
+
+269
+00:26:48,770 --> 00:26:58,710
+وصوم خط مستقيم انا احكي ان انا عند اتنين اربع ستة
+
+270
+00:26:58,710 --> 00:27:07,410
+عند الاربعة سالب اتناش وعند
+
+271
+00:27:07,410 --> 00:27:14,010
+الستة سالب اربع وعشرينهذا بالنسبة لل .. لل
+
+272
+00:27:14,010 --> 00:27:18,390
+acceleration بالنسبة
+
+273
+00:27:18,390 --> 00:27:24,450
+لل velocity عند
+
+274
+00:27:24,450 --> 00:27:28,710
+.. عند نقطة ال T equal zero ها هي و عند نقطة عند
+
+275
+00:27:40,680 --> 00:27:44,880
+T بيساوي اتنين
+
+276
+00:27:44,880 --> 00:27:50,480
+اتماش و الاكسراش اشمالها سفر طلع هنا اكسراش قيمتها
+
+277
+00:27:50,480 --> 00:27:54,860
+سفر
+
+278
+00:27:54,860 --> 00:28:00,520
+معناته هتكون ال velocity هتكون maximum اللي هي
+
+279
+00:28:00,520 --> 00:28:04,300
+هتكون اتماش يعني عندي هين وعندي اتنين هين هتكون
+
+280
+00:28:04,300 --> 00:28:14,130
+اتماش الآن ال V بيساوي سفرعند أربع لكن عند أربع
+
+281
+00:28:14,130 --> 00:28:20,010
+بيستوى سفر أربع
+
+282
+00:28:20,010 --> 00:28:28,230
+هو عند ستة ستة و تلاتين واضح
+
+283
+00:28:28,230 --> 00:28:30,710
+ان هذا maximum يعني انت حيجي ال curve حيجي بالشكل
+
+284
+00:28:30,710 --> 00:28:38,530
+هذا نجي
+
+285
+00:28:38,530 --> 00:28:39,210
+لل displacement
+
+286
+00:28:43,220 --> 00:28:47,460
+نجي لـ displacement ال displacement أول شي بتساوي
+
+287
+00:28:47,460 --> 00:28:51,020
+صفر عند
+
+288
+00:28:51,020 --> 00:28:54,900
+T بيساوي صفر وعند T بيساوي ستة يعني عند هذه نقطة
+
+289
+00:28:54,900 --> 00:28:59,140
+وهذه
+
+290
+00:28:59,140 --> 00:29:08,910
+نقطة الان لما كانت ال acceleration بيساوي صفرالـ A
+
+291
+00:29:08,910 --> 00:29:23,830
+نرجع نحكي يعني الـ A بساوة DV by DX بساوة D² X by
+
+292
+00:29:23,830 --> 00:29:28,430
+DT معناته
+
+293
+00:29:28,430 --> 00:29:33,990
+الـ X ليش؟ هي المشتقة التانية ده displacement صح؟
+
+294
+00:29:33,990 --> 00:29:38,030
+لما تكون المشتقة التانية صفر
+
+295
+00:29:43,370 --> 00:29:48,690
+اللي بتكون ال velocity maximum وقيمة ال X هذه
+
+296
+00:29:48,690 --> 00:29:53,650
+بتكون تعبر عن inflection point نقطة انقلاب أنا
+
+297
+00:29:53,650 --> 00:29:59,270
+عندي هين ال V صفر وهين صفر معناته عندي هين هتكون
+
+298
+00:29:59,270 --> 00:30:02,030
+يا minimum يا maximum وهين يا minimum يا maximum
+
+299
+00:30:02,030 --> 00:30:07,430
+يعني انا عندي هين كمان اللي
+
+300
+00:30:07,430 --> 00:30:09,030
+هي عند 4 second اللي هي 32
+
+301
+00:30:13,440 --> 00:30:18,660
+هو عند سفر سفر وفي بينهم ال acceleration بتكون
+
+302
+00:30:18,660 --> 00:30:25,760
+ساوي إيه؟ سفر inflection
+
+303
+00:30:25,760 --> 00:30:28,680
+دايما ال inflection point رياضيا بيصير نقطة تحول
+
+304
+00:30:28,680 --> 00:30:31,840
+نقطة تحول بين minimum و maximum أو maximum و
+
+305
+00:30:31,840 --> 00:30:34,220
+minimum إذا عندي minimum level و maximum level
+
+306
+00:30:34,220 --> 00:30:37,440
+لايمكن أنتقل smoothly من ال minimum ل ال maximum
+
+307
+00:30:37,440 --> 00:30:40,120
+بدون to inflict يعني
+
+308
+00:30:42,770 --> 00:30:44,530
+أو زي هيك أو
+
+309
+00:30:46,830 --> 00:30:49,570
+لازم يصير عندي inflection physically لازم يصير
+
+310
+00:30:49,570 --> 00:30:51,770
+عندي inflection هذا هو ال definition .. ال
+
+311
+00:30:51,770 --> 00:30:54,770
+definition بتاع ال inflection point إذا عندك two
+
+312
+00:30:54,770 --> 00:30:57,970
+levels maximum level و minimum level و بدها تنتقل
+
+313
+00:30:57,970 --> 00:31:00,650
+من ال maximum إلى ال minimum أو بدها تنتقل بالعكس
+
+314
+00:31:00,650 --> 00:31:04,650
+من ال minimum إلى ال maximum you cannot move from
+
+315
+00:31:04,650 --> 00:31:07,130
+minimum to maximum or maximum to minimum to
+
+316
+00:31:07,130 --> 00:31:10,850
+minimum without inflection ايش عن inflection؟ ال
+
+317
+00:31:10,850 --> 00:31:13,330
+slope مثلا اللي كان هنا .. هنا ال slope هنا بزيد
+
+318
+00:31:13,330 --> 00:31:22,720
+بعدين بصلmaximum point بعدين ايش بيبدأ ياشي قل هاي
+
+319
+00:31:22,720 --> 00:31:30,600
+معناه inflict inflict او العكس فهذه تمثل
+
+320
+00:31:30,600 --> 00:31:34,280
+inflection point اللي هي عند X 16 معناه تصل عند
+
+321
+00:31:34,280 --> 00:31:38,640
+هاي نقطة تنتين انا عارف هذه minimum لان ال value
+
+322
+00:31:38,640 --> 00:31:42,820
+is zero وعارف هذه maximum لان ال value is zero
+
+323
+00:31:42,820 --> 00:31:50,070
+وهذه inflection point وهذهzero و ال equation is
+
+324
+00:31:50,070 --> 00:31:54,250
+non linear equation معدلة غير خطية مع أنها تحسير
+
+325
+00:31:54,250 --> 00:32:05,530
+ال curve بالشكل هذا أنا
+
+326
+00:32:05,530 --> 00:32:11,690
+مش محتاج اعوض بالشكل عشوائي بدي اعوض بشكل ذكي عشان
+
+327
+00:32:11,690 --> 00:32:16,590
+ارسم امثل graphically الحركةيعني انا اعتمدت على ان
+
+328
+00:32:16,590 --> 00:32:18,670
+انا عندي .. في عندي .. اعتمدت على فكرة ال minimum
+
+329
+00:32:18,670 --> 00:32:23,210
+و ال maximum و اعتمدت على فكرة reflection و دايما
+
+330
+00:32:23,210 --> 00:32:30,270
+ببدأ من نقطة ال zero في
+
+331
+00:32:30,270 --> 00:32:31,070
+اي سؤال؟
+
+332
+00:32:51,480 --> 00:32:55,840
+طيب لان هشوف determination of motion of a particle
+
+333
+00:32:55,840 --> 00:33:00,060
+how to define motion of a particle اندي تلاتة
+
+334
+00:33:00,060 --> 00:33:03,580
+classes من ال motion في تلت أنواع من الحركة ممكن
+
+335
+00:33:03,580 --> 00:33:08,780
+ان اعرفهم اول نوع الحركة ال acceleration بتكون
+
+336
+00:33:08,780 --> 00:33:11,740
+دالة مع الزمن acceleration is a function of time
+
+337
+00:33:11,740 --> 00:33:18,220
+ال a بكون عرفها كيف تتغير مع الزمن الحالة التانية
+
+338
+00:33:19,030 --> 00:33:21,470
+الـ acceleration is a function of position أنا
+
+339
+00:33:21,470 --> 00:33:25,670
+عارف كيف ال acceleration تتغير مع الموقع الحالة
+
+340
+00:33:25,670 --> 00:33:28,450
+التالتة ال acceleration is a function of the
+
+341
+00:33:28,450 --> 00:33:30,870
+velocity of the particle يعني أنا ماعرف كيف تتغير
+
+342
+00:33:30,870 --> 00:33:36,350
+مع سرعة الجسم تحت الدراسة هندرس التلت حالات بشكل
+
+343
+00:33:36,350 --> 00:33:39,910
+منفرد هندرس الحالة الأولى ال acceleration is a
+
+344
+00:33:39,910 --> 00:33:41,170
+function of time
+
+345
+00:33:54,110 --> 00:33:59,110
+الـ acceleration is a function of time a is a
+
+346
+00:33:59,110 --> 00:34:04,770
+function of time بتساوي ال acceleration مش ساوي dv
+
+347
+00:34:04,770 --> 00:34:10,590
+by dt يعني
+
+348
+00:34:10,590 --> 00:34:22,990
+dv هتساوي f of t dt لو عملت integralمن time zero
+
+349
+00:34:22,990 --> 00:34:28,790
+to any time t ومن v node to any velocity as a
+
+350
+00:34:28,790 --> 00:34:36,350
+function of time هذه تكاملتها سهل هيكون v of t
+
+351
+00:34:36,350 --> 00:34:42,050
+minus v node بالساوية تكامل انا مش عارف ال f of t
+
+352
+00:34:42,050 --> 00:34:50,980
+هذا بشكل عام تكامل من zero ل t ل f of tDT يعني ال
+
+353
+00:34:50,980 --> 00:34:59,260
+V of T هتساوي V node زائد تكامل من صفر ل T لل F of
+
+354
+00:34:59,260 --> 00:35:07,680
+T DT ال
+
+355
+00:35:07,680 --> 00:35:15,060
+V ايش بتساوي DXY DT
+
+356
+00:35:19,570 --> 00:35:31,050
+معناته DX هتكون V of T DT لأن V is already defined
+
+357
+00:35:31,050 --> 00:35:36,190
+as a function of T فممكن نعمل integral from 0 to T
+
+358
+00:35:36,190 --> 00:35:44,530
+وهي من X node ل X of T معناته هتسيب عندي X of T
+
+359
+00:35:44,530 --> 00:35:51,500
+minus X nodeX0 دي اللي هي موقع الجسم في البداية بس
+
+360
+00:35:51,500 --> 00:36:03,120
+هو تكامل Zero ل T ل V of T DT طيب
+
+361
+00:36:03,120 --> 00:36:09,120
+انا حكيتلك حسب ال function ال acceleration انا
+
+362
+00:36:09,120 --> 00:36:13,500
+بكون عارف ال function of T بعوضه هنا بعمل تكامل
+
+363
+00:36:14,290 --> 00:36:17,230
+فبصير بعد ذلك الصرع عندي معروفة هاد بيصير معروفة
+
+364
+00:36:17,230 --> 00:36:20,470
+function of T بعوض بعمل integration هاد بشكل أهم
+
+365
+00:36:20,470 --> 00:36:24,710
+الحالة
+
+366
+00:36:24,710 --> 00:36:31,490
+التانية العجلة is عبارة عن دالة مع الموقع is a
+
+367
+00:36:31,490 --> 00:36:34,910
+function of position يعني ال A is a function of X
+
+368
+00:36:34,910 --> 00:36:43,680
+ال A هاد الحالة الأولىالحالة التانية a function of
+
+369
+00:36:43,680 --> 00:36:50,520
+x ال a ايش يساوي دي V by دي T انا عملت بشكل متعمل
+
+370
+00:36:50,520 --> 00:36:58,100
+زي هيك دي V by دي T لو ضربت البس تب DX على DX DX
+
+371
+00:36:58,100 --> 00:37:05,000
+by دي T ايش هي V V معناته ال a هتكون تساوي اللي هو
+
+372
+00:37:05,000 --> 00:37:15,070
+V DVعلى dx بالثوير اللي
+
+373
+00:37:15,070 --> 00:37:25,410
+هي f of x مظهور معناه ال friend vdv بيصير
+
+374
+00:37:25,410 --> 00:37:37,640
+f of x dx لو أعمل تكوين هنا من x nodeل X وهنا من V
+
+375
+00:37:37,640 --> 00:37:41,200
+نود طبعا ال V في الحالة هذه هتطلع function of X
+
+376
+00:37:41,200 --> 00:37:51,740
+برضه ل V of X هسيني V تربيع على اتنين of X minus V
+
+377
+00:37:51,740 --> 00:38:00,440
+نود تربيع على اتنين يصير تكامل من X نود ل X ل F of
+
+378
+00:38:00,440 --> 00:38:02,200
+X DX
+
+379
+00:38:06,310 --> 00:38:15,890
+يعني انا حاسس ان عندي V تربيع of X بالساوية V ند
+
+380
+00:38:15,890 --> 00:38:26,230
+تربيع زائد اتنين تكامل من X ند ل X ل F of X DX
+
+381
+00:38:26,230 --> 00:38:29,310
+طبعا
+
+382
+00:38:29,310 --> 00:38:33,330
+انا في الأول بكون عارف كيف بتتغير ال acceleration
+
+383
+00:38:33,330 --> 00:38:34,790
+مع الموقع مع X
+
+384
+00:38:38,930 --> 00:38:45,130
+الحالة التالتة ال
+
+385
+00:38:45,130 --> 00:38:49,930
+acceleration is a function of velocity
+
+386
+00:38:49,930 --> 00:38:58,730
+الحالة التالتة ال acceleration is a
+
+387
+00:38:58,730 --> 00:39:04,910
+function of velocity ال acceleration مستوى ايش؟ dv
+
+388
+00:39:04,910 --> 00:39:11,990
+by dtأزود بعمل انا فصل للمتغيرات separation of
+
+389
+00:39:11,990 --> 00:39:21,950
+variables صح حاسيب عندي DV على F of V او
+
+390
+00:39:21,950 --> 00:39:30,090
+خلنا نحكي اللي هو حاسيب عندي دي
+
+391
+00:39:30,090 --> 00:39:45,190
+تي دي تي في ال F of Vبسوى DV صح يعني DT بسوى DV
+
+392
+00:39:45,190 --> 00:39:54,010
+على F of V اللي هو عامل تكامل هنا من
+
+393
+00:39:54,010 --> 00:40:03,210
+V node ل V وهي من صفر ل T هصير
+
+394
+00:40:03,210 --> 00:40:05,190
+عنده T
+
+395
+00:40:07,610 --> 00:40:21,650
+بساوة تكامل DV على F of V من V node ل V او ممكن
+
+396
+00:40:21,650 --> 00:40:33,530
+اعمل اشي تاني احكي ان A بساوة F of V بساوة
+
+397
+00:40:35,580 --> 00:40:48,180
+v dv by dx يعني انا حاسس ان ال dx بيساوي v dv على
+
+398
+00:40:48,180 --> 00:40:58,880
+f of v بدي اعمل تكامل من v node ل v و من x node ل
+
+399
+00:40:58,880 --> 00:41:08,870
+x يعني انا هكون عندى x of vminus X node سوى تكامل
+
+400
+00:41:08,870 --> 00:41:28,910
+V DV على F of V من V node ل V في أي سؤال المحاضرة
+
+401
+00:41:28,910 --> 00:41:32,550
+الجاية بين هال examples اقرأوا ال chapter عشان
+
+402
+00:41:32,550 --> 00:41:39,380
+تكونوا جاهزينو هنغطي طبعا اللي هو هندرس الحالات
+
+403
+00:41:39,380 --> 00:41:43,520
+الخاصة من الحركة والحركة المرتبطة
+
diff --git a/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/K6cPRSlFTWM_raw.srt b/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/K6cPRSlFTWM_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5ac6ba3e41121f439794537c4f588a39450f643a
--- /dev/null
+++ b/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/K6cPRSlFTWM_raw.srt
@@ -0,0 +1,2844 @@
+1
+00:00:04,910 --> 00:00:09,790
+طيب اليوم هنكمل chapter تلتاش اللي هو ال kinetics
+
+2
+00:00:09,790 --> 00:00:15,370
+of particles methods of work and energy و methods
+
+3
+00:00:15,370 --> 00:00:19,070
+of impulse and momentum بس لما نبدأ هنحل أسلة
+
+4
+00:00:19,070 --> 00:00:24,050
+الامتحان التاني اللي كان قبل شوية هنبدأ في السؤال
+
+5
+00:00:24,050 --> 00:00:31,960
+الأول السؤال الأول a twenty kilogram packageis at
+
+6
+00:00:31,960 --> 00:00:36,480
+rest on an incline when a force P is applied to it
+
+7
+00:00:36,480 --> 00:00:42,800
+كان عندى جسم كتلة و عشرين كيلو جرام يعني ال mass
+
+8
+00:00:42,800 --> 00:00:48,220
+عشرين
+
+9
+00:00:48,220 --> 00:00:54,020
+كيلو جرامأثرنا عليه force P طبعا الجسم موجود على
+
+10
+00:00:54,020 --> 00:00:58,820
+مستوى مائل بزاوية عشرين درجة مع القفقة أثرنا عليه
+
+11
+00:00:58,820 --> 00:01:03,100
+force P بتميل على القفقة بزاوية تلاتين درجة
+
+12
+00:01:03,100 --> 00:01:10,040
+determine the magnitude of P احسب قيمة P يعني
+
+13
+00:01:10,040 --> 00:01:10,780
+هنحسب P
+
+14
+00:01:15,900 --> 00:01:18,640
+if ten seconds is required for the package to
+
+15
+00:01:18,640 --> 00:01:23,980
+travel five meters up the incline اذا كان أثارة
+
+16
+00:01:23,980 --> 00:01:29,220
+ال force P هيأخد وقت عشر ثواني عشان تمشي ال
+
+17
+00:01:29,220 --> 00:01:34,460
+package مسافة خمس متر لأعلى طبعا بدءا من السكون
+
+18
+00:01:34,460 --> 00:01:41,460
+يعني الصرافة الدائية بدأت بي نوت بالثورة زيرو و ال
+
+19
+00:01:41,460 --> 00:01:47,600
+time عشرة secondوالمسافة دعوني أعرف عندي هذا هو ال
+
+20
+00:01:47,600 --> 00:01:52,800
+X هذا
+
+21
+00:01:52,800 --> 00:01:58,180
+هو ال X هذا
+
+22
+00:01:58,180 --> 00:02:04,920
+ال Y و Delta X بالساوية خمسة
+
+23
+00:02:04,920 --> 00:02:12,100
+متر معناته
+
+24
+00:02:12,100 --> 00:02:18,790
+إذا عرفت أن الصورة الأبتدائيةوالمسافة و الزمن ممكن
+
+25
+00:02:18,790 --> 00:02:23,570
+نحصل بيهاش تسارع ال acceleration هكون ال delta X
+
+26
+00:02:23,570 --> 00:02:36,390
+بيساو V node T زائد نص AT تربيع Delta X عندي خمسة
+
+27
+00:02:36,390 --> 00:02:47,950
+V node صفر زائد نص في Aفي عشرة تربيع يعني ايه
+
+28
+00:02:47,950 --> 00:02:55,670
+هتطلع واحد
+
+29
+00:02:55,670 --> 00:03:02,350
+عشرة متر على ثانية تربيع عشان اجد P لازم اعمل free
+
+30
+00:03:02,350 --> 00:03:13,150
+body diagram هي الجسم P موجود
+
+31
+00:03:13,150 --> 00:03:14,190
+على منحدر
+
+32
+00:03:16,630 --> 00:03:22,970
+بميل بزاوية عشرين درجة وفي
+
+33
+00:03:22,970 --> 00:03:30,210
+ال force P طبعا
+
+34
+00:03:30,210 --> 00:03:34,990
+هذه ال force P هتكون مع الماية الخمسين
+
+35
+00:03:48,440 --> 00:04:00,480
+هذه عشرين وهذه ايش تلاتين مع معي ال ايش خمسين بأثر
+
+36
+00:04:00,480 --> 00:04:05,060
+عند الوزن اللي تحت MG
+
+37
+00:04:05,060 --> 00:04:11,180
+ورد الفعل لأعلى N
+
+38
+00:04:12,500 --> 00:04:19,800
+وهو ماشي لأعلى الاحتجاز هيكون من العكس ميو
+
+39
+00:04:19,800 --> 00:04:25,400
+ك في
+
+40
+00:04:25,400 --> 00:04:27,520
+ان حيث ساوي
+
+41
+00:04:45,870 --> 00:04:58,270
+م في a هذا ال x هذا ال y هيك رسمنا free pedagram
+
+42
+00:04:58,270 --> 00:05:03,550
+كامل في
+
+43
+00:05:03,550 --> 00:05:08,030
+اتجاه ال y بتحرك الجسم معناته summation force في
+
+44
+00:05:08,030 --> 00:05:11,290
+اتجاه ال y بيستوى سفر summation forces
+
+45
+00:05:16,930 --> 00:05:31,030
+باتجاه ال Y بيساوي صفر وهي الاتجاه الموجب هيكون
+
+46
+00:05:31,030 --> 00:05:43,710
+عندي N minus MG cosine العشرين minus
+
+47
+00:05:43,710 --> 00:05:44,210
+P
+
+48
+00:05:46,760 --> 00:05:52,280
+SIN الخمسين بساوة
+
+49
+00:05:52,280 --> 00:06:02,400
+سفر مظبوط
+
+50
+00:06:02,400 --> 00:06:11,740
+زي هيك عندي N minus MG cosine العشرين minus
+
+51
+00:06:11,740 --> 00:06:15,500
+P SIN الخمسين بساوة سفر معناته ال N
+
+52
+00:06:18,720 --> 00:06:32,860
+هتكون تساوي Mg Cos 20 زائد P Sin 50 هذا بمعنى رقم
+
+53
+00:06:32,860 --> 00:06:39,120
+واحد بعد احنا ناخد summation force بتجاه ال X
+
+54
+00:06:48,860 --> 00:06:55,140
+هتكون تساوي M في A تجاه
+
+55
+00:06:55,140 --> 00:07:06,660
+ال X عندي هيكون طبعا P Cos P Cos الخمسين Minus
+
+56
+00:07:06,660 --> 00:07:15,280
+MG Sin العشرين
+
+57
+00:07:33,050 --> 00:07:41,130
+من واحد سنعود عن قيمة N من واحد
+
+58
+00:07:49,700 --> 00:07:55,380
+بنعوض substitute about
+
+59
+00:07:55,380 --> 00:07:58,420
+n
+
+60
+00:07:58,420 --> 00:08:03,240
+حسينا
+
+61
+00:08:03,240 --> 00:08:13,840
+ان دي T cosine الخمسين درجة هاي
+
+62
+00:08:13,840 --> 00:08:14,620
+ال N minus
+
+63
+00:08:17,680 --> 00:08:29,640
+ميو .. مينوس مجي صين العشرين مينوس ميو ك في
+
+64
+00:08:29,640 --> 00:08:43,760
+N اللي هي مجي كوسين العشرين زاد P صين الخمسين
+
+65
+00:08:49,220 --> 00:08:56,940
+هتساوي M في A هرتب ال terms هاخد ال P مع ال P هسيب
+
+66
+00:08:56,940 --> 00:09:00,780
+ال P في
+
+67
+00:09:00,780 --> 00:09:11,500
+Cos الخمسين هذا ال term الأولاني minus Mu K
+
+68
+00:09:15,890 --> 00:09:22,050
+يعني خلاص ال term هذا و ال term هذا هتساوي M A
+
+69
+00:09:22,050 --> 00:09:25,130
+زائد
+
+70
+00:09:25,130 --> 00:09:28,370
+هذا
+
+71
+00:09:28,370 --> 00:09:35,070
+هتيجي ع اليمين هصير M G هذا
+
+72
+00:09:35,070 --> 00:09:39,490
+ال term مع
+
+73
+00:09:39,490 --> 00:09:40,150
+هذا ال term
+
+74
+00:09:43,470 --> 00:09:53,650
+زاد mg في sin 20 زاد
+
+75
+00:09:53,650 --> 00:10:00,030
+mu k cos
+
+76
+00:10:00,030 --> 00:10:11,350
+20 مظبوط زي هيك يعني نعوض الأرقام هيكون ال P في
+
+77
+00:10:11,350 --> 00:10:19,760
+cosineالخمسين ناقص تلاتة من عشرة sign الخمسين
+
+78
+00:10:19,760 --> 00:10:30,140
+بتستوى لأم عندي أكم عشرين في point one زاد عشرين
+
+79
+00:10:30,140 --> 00:10:40,650
+في تسعة point تمانية سفر ستة في signالعشرين زائد
+
+80
+00:10:40,650 --> 00:10:48,870
+تلاتة من عشرة في كوصين العشرين
+
+81
+00:10:48,870 --> 00:10:58,410
+ومنها بقى احسب ال P كم طلعت معاكم؟ ايش الأرقام
+
+82
+00:10:58,410 --> 00:11:04,590
+طلعتوها؟ عشان كل صح بعد ال 50 عملنا تلقى كلهاماشاء
+
+83
+00:11:04,590 --> 00:11:15,870
+الله عليكم طيب
+
+84
+00:11:15,870 --> 00:11:19,870
+خلّيني أرجع لل .. طيب هذا السؤال الأول في حد أنقله
+
+85
+00:11:19,870 --> 00:11:27,150
+أي استفسار؟ طيب
+
+86
+00:11:27,150 --> 00:11:28,810
+هنحل السؤال التاني
+
+87
+00:12:02,030 --> 00:12:07,430
+انشوف السؤال التاني احنا
+
+88
+00:12:07,430 --> 00:12:14,070
+حاكينا خطوات العمل الكامل، جمع بيانات، تحليلها، خط
+
+89
+00:12:14,070 --> 00:12:20,730
+خطة، نفذ، تفحص، اتأكد شغلك صح، بتوثق، طبعا انت
+
+90
+00:12:20,730 --> 00:12:24,390
+بتوثق عملية مستمر يعني، ممكن من بدايات، بعدين
+
+91
+00:12:24,390 --> 00:12:28,110
+بتطور من حان التعامل اللي اتعلم عندك، يعني تعمل
+
+92
+00:12:28,110 --> 00:12:31,960
+reflection او انأكاس للي اتعلمته في المثل هذهطيب
+
+93
+00:12:31,960 --> 00:12:35,840
+هنقرر المثل عشان نجمع علومات a three pound collar
+
+94
+00:12:35,840 --> 00:12:48,500
+هذا ال collar وزن تلاتة pound slide
+
+95
+00:12:48,500 --> 00:12:53,440
+on a horizontal rod ممكن تنزلق على ال rod هذا طبعا
+
+96
+00:12:53,440 --> 00:12:58,560
+ال rod هذا بيدور في المستوى الأفقي محور دورانه اش
+
+97
+00:12:58,560 --> 00:13:04,150
+رأسي هيكونis free to rotate about a vertical shaft
+
+98
+00:13:04,150 --> 00:13:08,110
+the collar is initially held at A by a cord
+
+99
+00:13:08,110 --> 00:13:11,050
+attached to the shaft في البداية كان ال collar
+
+100
+00:13:11,050 --> 00:13:16,630
+مربوطة بخيط بمركز الدوران في البداية ماعدت في
+
+101
+00:13:16,630 --> 00:13:19,970
+البداية ماكان ليهاش سرعة بهذا الاتجاه ال radial
+
+102
+00:13:19,970 --> 00:13:25,650
+direction ماكان فيه تسرع هناك؟ لأ فيه بس انا خليني
+
+103
+00:13:25,650 --> 00:13:30,230
+اركز واحدة واحدة ال VR في البداية ايش يستوي VR
+
+104
+00:13:30,230 --> 00:13:30,590
+node
+
+105
+00:13:33,950 --> 00:13:39,010
+بس هو سفر لان مافيش اللي هتحرك بهذه الاتجاه a
+
+106
+00:13:39,010 --> 00:13:42,110
+spring of constant two pounds per foot is attached
+
+107
+00:13:42,110 --> 00:13:50,250
+to the collar عند زمبرك ماسك ال collar من جهة
+
+108
+00:13:50,250 --> 00:13:54,430
+ومثبت من الطرف التاني بالعمود الدوران ماطين ال K
+
+109
+00:13:54,430 --> 00:14:02,590
+تبعته ال K اتنين pound لكل قدم
+
+110
+00:14:09,760 --> 00:14:13,120
+and is undeformed when the collar is at A لما كان
+
+111
+00:14:13,120 --> 00:14:18,300
+عند A ماكانش فيه أي شد زمبراكي في الوضع اللي اللي
+
+112
+00:14:18,300 --> 00:14:24,300
+اللي هو الارتخاء يعني ماكان فيه أي شد يعني مافيش
+
+113
+00:14:24,300 --> 00:14:30,240
+عليه أي force في عند A ال
+
+114
+00:14:30,240 --> 00:14:36,200
+node ال free length تبعه ال undeformed length ست
+
+115
+00:14:36,200 --> 00:14:49,080
+انش يعني أكم قدمنص نص قدم قسمت
+
+116
+00:14:49,080 --> 00:14:56,100
+على اتناش ال inch شحتتين و القدم شحتة واحدة طيب
+
+117
+00:14:56,100 --> 00:14:58,980
+as the rod rotates at the rate theta dot بستوى
+
+118
+00:14:58,980 --> 00:15:04,160
+ستاشر radians per second بدور بسرعة الزاوية العمود
+
+119
+00:15:04,160 --> 00:15:15,560
+theta dotبستوى ستاشر رديان per second بستوى ايش؟
+
+120
+00:15:15,560 --> 00:15:25,020
+constant يعني ابتديت أدوّل دوتش الساوية؟ zero the
+
+121
+00:15:25,020 --> 00:15:31,200
+cord is cut فجأة عملنا قطع على الخيط طبعا طرد
+
+122
+00:15:31,200 --> 00:15:39,860
+المركزي هيطرد لبرا وال spring هيحاول يجرّه يرجعand
+
+123
+00:15:39,860 --> 00:15:42,580
+the collar moves out along the rod بدت تتحرك ال
+
+124
+00:15:42,580 --> 00:15:46,920
+collar و هو يدور على ال rod لبرا neglecting
+
+125
+00:15:46,920 --> 00:15:48,520
+friction and the mass of the rod
+
+126
+00:15:48,520 --> 00:15:58,260
+فششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششششش
+
+127
+00:16:09,350 --> 00:16:13,710
+Determine احسب the radial and transverse
+
+128
+00:16:13,710 --> 00:16:17,150
+components of the acceleration of the collar at A
+
+129
+00:16:38,460 --> 00:16:41,340
+طيب في الأول خلّيني اعرف ايش معادلة ال AR ايش
+
+130
+00:16:41,340 --> 00:16:47,920
+معادلة ال AR AR بالساوية
+
+131
+00:16:47,920 --> 00:16:56,120
+R double dot minus theta dot تربيع و A theta ايش
+
+132
+00:16:56,120 --> 00:16:56,540
+الساوية
+
+133
+00:17:15,210 --> 00:17:19,870
+مش هذا الموضوع أنا انا مثلا عايش على ايه ال theta؟
+
+134
+00:17:19,870 --> 00:17:21,790
+عايش ال ايه ال theta؟ ايوة
+
+135
+00:17:27,130 --> 00:17:34,290
+أيوة زائد زائد هك
+
+136
+00:17:34,290 --> 00:17:40,050
+متأكدين؟ ماشي طيب
+
+137
+00:17:40,050 --> 00:17:49,150
+الآن لما انا هاطلع عليه من أعلى يعني ده هحكي take
+
+138
+00:17:49,150 --> 00:17:56,190
+a top view of
+
+139
+00:17:58,290 --> 00:18:07,290
+the free body diagram من ال top view هيكون عنده
+
+140
+00:18:07,290 --> 00:18:15,210
+هاي
+
+141
+00:18:15,210 --> 00:18:19,010
+ال rod وهاي
+
+142
+00:18:19,010 --> 00:18:26,150
+ال collar وهذا
+
+143
+00:18:26,150 --> 00:18:36,400
+محورمحور الدوران او هذا محور الدوران زي هيك هذه
+
+144
+00:18:36,400 --> 00:18:44,500
+المسافة R هذا
+
+145
+00:18:44,500 --> 00:18:50,920
+بشكل عام طبعا لما نلف هيبدأ يطلع لبرا في البداية
+
+146
+00:18:50,920 --> 00:18:57,580
+كان هنا هو صح؟ يعني
+
+147
+00:18:57,580 --> 00:19:10,360
+هذهاللي هي نص قدم معناه
+
+148
+00:19:10,360 --> 00:19:13,420
+الـ deflection في الزنبارك ايش حساه عند اي لحظة
+
+149
+00:19:13,420 --> 00:19:20,160
+الـ deflection دلتا
+
+150
+00:19:20,160 --> 00:19:29,530
+هكون R ناقص نص اللي هو ال deflection في زنباركهو
+
+151
+00:19:29,530 --> 00:19:34,730
+صار على بعد R بس هاي الـ deflection ها دي ايش؟ ها
+
+152
+00:19:34,730 --> 00:19:44,050
+دي Delta Delta سواء R minus نص طيب هعمل free body
+
+153
+00:19:44,050 --> 00:19:49,910
+لل color هاي ال color من ال top of U برضه
+
+154
+00:19:53,700 --> 00:19:59,800
+هيكون فيه وزن ورد فعل عمودي، هاي مش شايفين احنا،
+
+155
+00:19:59,800 --> 00:20:05,800
+مظهور؟ وفيه هو .. هو هيطلع زي هيك، معناه ان
+
+156
+00:20:05,800 --> 00:20:11,680
+الزبارك هحاول يجربه هذا الاتجاه، هاد؟ F spring
+
+157
+00:20:11,680 --> 00:20:19,040
+وفيه رد فعل من العمود من الرد على إيش؟ على ال
+
+158
+00:20:19,040 --> 00:20:22,880
+color، هسميه F ثدر، حيث ساوي
+
+159
+00:20:28,430 --> 00:20:44,450
+هي M A R و M A θ هى فيه
+
+160
+00:20:44,450 --> 00:20:47,810
+اتجاهين فيه فيه اتجاه هذا وفيه اتجاه الرأس اللى
+
+161
+00:20:47,810 --> 00:20:51,110
+احنا مش شايفينه فيه الوزن بيهدى تهدى التجاه وفيه
+
+162
+00:20:51,110 --> 00:20:56,580
+كمان رد فعل معاكس له مش حاب يدونىيعني في التجاه ..
+
+163
+00:20:56,580 --> 00:21:01,220
+يعني هيكون عندى force هي الوزن وفي رد فعلا بيعدلوا
+
+164
+00:21:01,220 --> 00:21:04,280
+بعض مهم مافيش حركة بعدها للاتجاه اللي أنا عاملها
+
+165
+00:21:04,280 --> 00:21:08,920
+شكل cross هنا خلنا
+
+166
+00:21:08,920 --> 00:21:13,400
+نحكي هذا X و
+
+167
+00:21:13,400 --> 00:21:18,140
+هذا ايش؟ Y هيكون
+
+168
+00:21:18,140 --> 00:21:18,700
+عندى summation
+
+169
+00:21:21,300 --> 00:21:31,580
+لل fx هتكون max وبدى اعتبر هذا f لاتجاه الموجب
+
+170
+00:21:31,580 --> 00:21:45,060
+يعني هكون لدي f spring هتساوي mar طيب
+
+171
+00:21:45,060 --> 00:21:47,260
+ال spring force مش هتكون ال spring force
+
+172
+00:21:52,150 --> 00:21:59,630
+اللي هي deflection في ال K K في Delta هتكون تستوى
+
+173
+00:21:59,630 --> 00:22:14,650
+ال K عنده اتنين ال Delta في R ناقص نص يعني
+
+174
+00:22:14,650 --> 00:22:25,940
+هتكون عنده ال Fs Fs اتنين في Rنقص نص بتساوي ال M
+
+175
+00:22:25,940 --> 00:22:31,720
+عندي تلاتة على
+
+176
+00:22:31,720 --> 00:22:43,300
+اتنين و تلاتين و اتنين من عشرة في AR R double dot
+
+177
+00:22:43,300 --> 00:22:49,200
+minus R theta dot تربيع
+
+178
+00:22:52,780 --> 00:22:56,120
+معناته فاكرين example حلته زيه بالظبط ال example
+
+179
+00:22:56,120 --> 00:23:05,180
+نفس المثال هكون ال R double dot minus R تتا دوت و
+
+180
+00:23:05,180 --> 00:23:13,920
+احنا حكيناها كم؟ في ستاش تربيع هتكون تساوي اتنين و
+
+181
+00:23:13,920 --> 00:23:16,500
+تلاتين و اتنين من عشرة في اتنين
+
+182
+00:23:22,680 --> 00:23:34,440
+ع التلاتة في R ماقص نص طيب
+
+183
+00:23:34,440 --> 00:23:38,680
+عندي
+
+184
+00:23:38,680 --> 00:23:44,780
+ال .. ال .. ال .. ال VR عبارة عن أيه؟ عبارة عن ال
+
+185
+00:23:44,780 --> 00:23:48,940
+.. او ال V ال V بشكل عام في ريد الكون بيستوعب
+
+186
+00:23:48,940 --> 00:23:56,150
+إليها VRفى اتجاه ال E R زائد V ثيتا فى اتجاه ال E
+
+187
+00:23:56,150 --> 00:24:03,330
+ثيتا يعنى R Dot زائد
+
+188
+00:24:03,330 --> 00:24:13,230
+R ثيتا Dot E Theta معناته ال V R مش الساوى R Dot
+
+189
+00:24:13,230 --> 00:24:29,940
+معناته هاتكون الساوى D By D Tلـ VR حتساوى
+
+190
+00:24:29,940 --> 00:24:38,020
+16×16 مائتين و ستة و خمسين R جيبت هذا على جهة
+
+191
+00:24:38,020 --> 00:24:41,960
+التانية زاد احسبولها دي اتنين و تلاتين في اتنين و
+
+192
+00:24:41,960 --> 00:24:44,320
+عشرة في اتنين ع تلاتة ضبوة في R
+
+193
+00:25:04,030 --> 00:25:11,450
+زاد 21 R
+
+194
+00:25:11,450 --> 00:25:24,970
+ناقص عند 32 point 2 على 3 أكم تطلع؟ عشرة ما هو نصف
+
+195
+00:25:24,970 --> 00:25:28,230
+في اتنين بتروح عشرة
+
+196
+00:25:33,190 --> 00:25:38,910
+الان هذه ممكن انا اجي احكي هذه حضورها في DR على DR
+
+197
+00:25:38,910 --> 00:25:46,250
+بيأثر عنده فهذه هتصير DVR
+
+198
+00:25:46,250 --> 00:25:56,330
+على DR هذه في DR على DT DR
+
+199
+00:25:56,330 --> 00:26:06,410
+بقى DT اللي هي VRهتكون 256 زي 41 هيكون وح ستة سبعة
+
+200
+00:26:06,410 --> 00:26:15,070
+اتنين وخمسة اتنين
+
+201
+00:26:15,070 --> 00:26:23,410
+وخمسة سبعة اتنين ارق ماقص عشرة point سبعة تلاتة
+
+202
+00:26:23,410 --> 00:26:26,610
+يعني هتصفي عندي هنا
+
+203
+00:26:31,750 --> 00:26:46,650
+vr dvr by dr بتساوي 277.46r minus 10.73 لان بعمل
+
+204
+00:26:46,650 --> 00:26:54,190
+separation of variables بستخدام دي vr dvr
+
+205
+00:26:54,190 --> 00:26:59,830
+بتساوي 277
+
+206
+00:26:59,830 --> 00:27:08,230
+.46.46R-10.73DR
+
+207
+00:27:08,230 --> 00:27:18,470
+واضح عندها VR و هي عندي R بعمل تكامل من VR node ل
+
+208
+00:27:18,470 --> 00:27:22,650
+VR وهذه
+
+209
+00:27:22,650 --> 00:27:31,700
+التكامل من R node ل R و R node عندنا أكم كانتنص
+
+210
+00:27:31,700 --> 00:27:39,220
+قدم حسير
+
+211
+00:27:39,220 --> 00:27:44,220
+عنده نص
+
+212
+00:27:44,220 --> 00:27:48,240
+في
+
+213
+00:27:48,240 --> 00:27:56,580
+VR تربيع minus VR node تربيع بالساوية التكامل هذه
+
+214
+00:27:59,870 --> 00:28:06,670
+متين و سبعة سبعين على اتنين واحد تلاتة تمانية سبعة
+
+215
+00:28:06,670 --> 00:28:16,650
+تلاتة مظبوط R تربيع ناقص عشرة point سبعة تلاتة R
+
+216
+00:28:16,650 --> 00:28:23,290
+وهذا هعمل تكامل بين R not اللي هي نص من نص ل R
+
+217
+00:28:30,280 --> 00:28:39,260
+يعني ال VR مدى كم تساوي؟ هذه .. هذه سفر يعني هتصير
+
+218
+00:28:39,260 --> 00:28:44,220
+عند ال VR تربيع
+
+219
+00:28:44,220 --> 00:28:53,000
+هتساوي ميتين و سبعة و سبعين point أربعة ستة R
+
+220
+00:28:53,000 --> 00:28:57,300
+تربيع في في
+
+221
+00:28:57,300 --> 00:28:59,820
+R تربيع
+
+222
+00:29:01,750 --> 00:29:06,350
+R تربية ناقص
+
+223
+00:29:06,350 --> 00:29:14,430
+64412
+
+224
+00:29:14,430 --> 00:29:20,970
+R ناقص
+
+225
+00:29:20,970 --> 00:29:27,370
+277
+
+226
+00:29:27,370 --> 00:29:37,920
+.46 في نصتربيع ناقص واحد و عشرين بونت اربعة ستة في
+
+227
+00:29:37,920 --> 00:29:41,520
+نصف يعني
+
+228
+00:29:41,520 --> 00:29:46,480
+VR تربيع
+
+229
+00:29:46,480 --> 00:29:52,200
+ايش هتساوي هتكون
+
+230
+00:29:52,200 --> 00:29:58,980
+ميتين و سبعة و سبعينبنت اربع ستة ار تربية ناقص
+
+231
+00:29:58,980 --> 00:30:05,640
+واحد عشرين بنت اربع ستة ار ناقص ستة واربعين minus
+
+232
+00:30:05,640 --> 00:30:10,060
+واحد تلاتة خمسة
+
+233
+00:30:23,610 --> 00:30:32,850
+يعني ال VR هتكون تحت الجدرق بنفعش
+
+234
+00:30:32,850 --> 00:30:39,250
+for any location لازم أحسب هذا ال VR عبارة عن R
+
+235
+00:30:39,250 --> 00:30:46,930
+dot هذه تساوي VR
+
+236
+00:30:49,620 --> 00:30:54,920
+أو .. او هذا .. او هذا يستوى R dot هذا ماشي هذا
+
+237
+00:30:54,920 --> 00:31:09,620
+يستوى R dot اللي هي DR by DT مش
+
+238
+00:31:09,620 --> 00:31:17,780
+هلزم من ال R هعمل تكامل هصير عنده DR على
+
+239
+00:31:22,400 --> 00:31:41,040
+277.46r-21.46r-46.14 كله تحت الجدرس أس
+
+240
+00:31:41,040 --> 00:31:44,420
+نص بالساوية
+
+241
+00:31:47,870 --> 00:31:59,670
+DT بعمل تكامل من صفر ل T و هذه من نصف
+
+242
+00:31:59,670 --> 00:32:05,130
+ل R هذه
+
+243
+00:32:05,130 --> 00:32:07,970
+بتحسب منها ايش ال R as a function of time بتحسب ال
+
+244
+00:32:07,970 --> 00:32:12,290
+R as a function of time هذا مش مطلوبة لأنه انا
+
+245
+00:32:12,290 --> 00:32:17,280
+عارف ال R عند ايه عارف ال Rعند ايه؟ انا بلزمني ر
+
+246
+00:32:17,280 --> 00:32:35,460
+double dot انا عارف دي ار با دي تي هنكمل دي
+
+247
+00:32:35,460 --> 00:32:44,660
+ار با دي تي عندي دي ار با دي تي ايش بتساوي؟
+
+248
+00:32:49,230 --> 00:33:08,510
+277.46R تربيع ناقص 21.46R ناقص 46.14 كله نص يعني ر
+
+249
+00:33:08,510 --> 00:33:12,270
+دبل دوت ماهو مش
+
+250
+00:33:12,270 --> 00:33:22,030
+تقط هذا صح هتكون نصفى 27.46r
+
+251
+00:33:22,030 --> 00:33:35,430
+-21.46r-46.14-1.5 فاشتقاق ايش اللى جوا اشتقاق اللى
+
+252
+00:33:35,430 --> 00:33:46,890
+جوا هيكون 92.27142715225
+
+253
+00:33:48,580 --> 00:33:57,380
+R ناقص واحد عشرين point أربعة ستة هذا الـR double
+
+254
+00:33:57,380 --> 00:34:10,880
+dot الـR double dot الآن at A يكون
+
+255
+00:34:10,880 --> 00:34:15,520
+عند الـR ايش يستوى عند A؟ نص
+
+256
+00:34:17,620 --> 00:34:23,900
+أنا هلزمني ايش؟ هلزمني ال R و ال theta dot أنا
+
+257
+00:34:23,900 --> 00:34:27,600
+بعرفها و بدي ال R double dot هيكون عند ال R double
+
+258
+00:34:27,600 --> 00:34:33,200
+dot هنعوض خمسة
+
+259
+00:34:33,200 --> 00:34:40,360
+خمسة أربعة point تسعة اتنين في نص لأقل واحد عشرين
+
+260
+00:34:40,360 --> 00:34:45,840
+point أربعة ستة على اتنين
+
+261
+00:34:48,270 --> 00:34:56,370
+في 277.46 في نص تربيه ناقص واحد عشرين point اربعة
+
+262
+00:34:56,370 --> 00:35:03,070
+ستة في نص ناقص ستة واربعين point اربعتاش كلو ايش
+
+263
+00:35:03,070 --> 00:35:09,710
+قصد نص تحسبوها حسبنا الارض باللط يعني حسبنا هذه و
+
+264
+00:35:09,710 --> 00:35:14,450
+هذه و هذه بعدين بحسب ايش ال AR
+
+265
+00:35:17,560 --> 00:35:23,220
+هي نص في اللحظة هذه ال R نض نص و R في اللحظة هذه
+
+266
+00:35:23,220 --> 00:35:27,800
+ال time zero هي انا R احد الاحتمالات يعني السفر هي
+
+267
+00:35:27,800 --> 00:35:32,500
+احد الاحتمالات نعم سفر و طلع مش سفر وين المحور
+
+268
+00:35:32,500 --> 00:35:37,300
+عندك وين المرجع المرجع محور الدوران يعني هاي
+
+269
+00:35:37,300 --> 00:35:43,260
+المرجع بتاعي ال R تتغير المركز اسمله ثابت ولا
+
+270
+00:35:43,260 --> 00:35:44,540
+متغير ثابت
+
+271
+00:35:47,650 --> 00:35:54,110
+معناته بحسب ال AR هتكون تستوى ال R double dot اللي
+
+272
+00:35:54,110 --> 00:36:00,230
+أنا حسبتها minus R theta dot تربيع ال R double dot
+
+273
+00:36:00,230 --> 00:36:03,530
+هي اللي حسبتها وال R اللي هي نص و ال theta dot
+
+274
+00:36:03,530 --> 00:36:10,310
+اللي هي ستاش حسبة ال AR طيب
+
+275
+00:36:10,310 --> 00:36:16,010
+ال A theta ال
+
+276
+00:36:16,010 --> 00:36:23,870
+A thetaبتساوي اتنين ار دوت ثتا دوت زائد ار ثتا
+
+277
+00:36:23,870 --> 00:36:34,570
+دابل دوت ثتا دابل دوت زيرو والار
+
+278
+00:36:34,570 --> 00:36:40,810
+بالساوية نص والار دوت اللي هي هادي اللي بالساوية
+
+279
+00:36:40,810 --> 00:36:49,140
+بالتان وسبعة وسبعينpoint اربعة ستة في نص تربيع
+
+280
+00:36:49,140 --> 00:36:57,900
+ناقص واحد وعشرين point اربعة ستة في نص ناقص ستة
+
+281
+00:36:57,900 --> 00:37:05,280
+واربعين point اربعتاش اص نص حسبنا الأرض ومن هنا
+
+282
+00:37:05,280 --> 00:37:10,860
+حسبنا ايه؟ احسبها
+
+283
+00:37:10,860 --> 00:37:22,580
+خلاص سالمبحاول يجرها لإنه طيب هذا المطلوب كان إيش؟
+
+284
+00:37:22,580 --> 00:37:27,980
+المطلوب الأول المطلوب
+
+285
+00:37:27,980 --> 00:37:38,160
+التاني be أمسح هذا the acceleration بده
+
+286
+00:37:38,160 --> 00:37:43,530
+the accelerationof the color relative to the rod
+
+287
+00:37:43,530 --> 00:37:48,210
+at A ال
+
+288
+00:37:48,210 --> 00:37:52,370
+acceleration of the color بالنسبة للرد هتكون اللي
+
+289
+00:37:52,370 --> 00:37:57,610
+هي A
+
+290
+00:37:57,610 --> 00:38:08,090
+ال color بالنسبة للرد هتكون R double dot R double
+
+291
+00:38:08,090 --> 00:38:08,410
+dot
+
+292
+00:38:11,150 --> 00:38:17,670
+وR double dot already حسبناها مطلوب see the
+
+293
+00:38:17,670 --> 00:38:21,330
+transverse component of the velocity of the collar
+
+294
+00:38:21,330 --> 00:38:28,950
+at B عند B بده
+
+295
+00:38:28,950 --> 00:38:37,930
+V theta V theta شو يساوي V
+
+296
+00:38:37,930 --> 00:38:38,670
+theta شو يساوي
+
+297
+00:38:41,510 --> 00:38:48,650
+theta dot عند PR في الساوية تمنتاشر
+
+298
+00:38:48,650 --> 00:38:54,730
+انش يعني واحد و نص قدم يعني هتكون واحد و نص في
+
+299
+00:38:54,730 --> 00:39:02,070
+theta dot اللي هي إيش ستاشت هتكون أربع و عشرين قدم
+
+300
+00:39:02,070 --> 00:39:09,090
+على الثانية في
+
+301
+00:39:09,090 --> 00:39:18,350
+أي سؤال؟طيب السؤال الأول والتالت سهلين
+
+302
+00:39:18,350 --> 00:39:24,310
+مباشرين التاني هذا بدواش شغل بس حلت أخوه example
+
+303
+00:39:24,310 --> 00:39:31,010
+في المحاضرة مظبوط؟
+
+304
+00:39:31,010 --> 00:39:36,370
+ارجعوا للمحاضرة ارجعوا للمحاضرة وشوفوا حالكم ان
+
+305
+00:39:36,370 --> 00:39:40,090
+انا شرحته او ما شرحتهورجعوا على الكتاب المثال وجده
+
+306
+00:39:40,090 --> 00:39:47,470
+في الكتاب وانحل في المحاضرة هذا
+
+307
+00:39:47,470 --> 00:39:56,890
+حكون فيه شغل كتير حكون علامة أكتر عليه خلّيني
+
+308
+00:39:56,890 --> 00:40:01,350
+أرجع للسؤال التالت the two blocks shown في عنده
+
+309
+00:40:01,350 --> 00:40:08,650
+بلوكين بلوك A و بلوك B الكتلة A تلاتين kilogramM A
+
+310
+00:40:08,650 --> 00:40:12,290
+تلاتين
+
+311
+00:40:12,290 --> 00:40:19,130
+كيلو جرام و M B خمس
+
+312
+00:40:19,130 --> 00:40:23,250
+و عشرين كيلو جرام طيب
+
+313
+00:40:23,250 --> 00:40:27,530
+are originally at rest كانوا في البداية في حالة
+
+314
+00:40:27,530 --> 00:40:33,170
+سكون neglecting neglecting the masses of the polis
+
+315
+00:40:33,170 --> 00:40:38,860
+اذا تم اهمال كتل البكراتand the effect of friction
+
+316
+00:40:38,860 --> 00:40:43,520
+in the poles and between block A and the
+
+317
+00:40:43,520 --> 00:40:46,000
+horizontal series التم احتمال الاحتكاك عند ال
+
+318
+00:40:46,000 --> 00:40:51,580
+poles و بين A و المستوى الأفقي to determine the
+
+319
+00:40:51,580 --> 00:40:54,340
+acceleration of each block بدو ال acceleration لكل
+
+320
+00:40:54,340 --> 00:41:00,160
+block بدو AA و AB بدو AA و
+
+321
+00:41:00,160 --> 00:41:10,280
+AB و بدو ال tension في الحبلالحركة هذه مرتبطة
+
+322
+00:41:10,280 --> 00:41:14,840
+constraint motion في الأول لازم أعرف محاول
+
+323
+00:41:14,840 --> 00:41:23,820
+احداثيات صح يعني لو حكيت أنا هذا هو ال
+
+324
+00:41:23,820 --> 00:41:32,740
+x-axis وهذا
+
+325
+00:41:32,740 --> 00:41:35,780
+ال y-axis هذا حيكون
+
+326
+00:41:41,190 --> 00:41:46,450
+هذا XA وهذا
+
+327
+00:41:46,450 --> 00:41:56,350
+YB
+
+328
+00:41:56,350 --> 00:41:59,870
+طبعا
+
+329
+00:41:59,870 --> 00:42:08,150
+سلطة تعملوها الشفوية هتكون هي تلاتة XA زي تلاتة YB
+
+330
+00:42:08,150 --> 00:42:19,080
+هتساوي constantفي داعي نفصلها الواحد
+
+331
+00:42:19,080 --> 00:42:27,940
+الاتنين التلاتة الاربعة الواحد
+
+332
+00:42:27,940 --> 00:42:35,480
+زاد الاتنين زاد التلاتة زاد الاربعة هتكون الساوية
+
+333
+00:42:35,480 --> 00:42:36,080
+ثابت
+
+334
+00:42:40,140 --> 00:42:48,880
+الـ L واحد XA زائد YB
+
+335
+00:42:48,880 --> 00:43:00,100
+زائد YB زائد YB بيساوي constant يعني XA زائد تلاتة
+
+336
+00:43:00,100 --> 00:43:11,390
+YB بيساوي constant حشطق هكون VAزائد تلاتة VB
+
+337
+00:43:11,390 --> 00:43:27,490
+بالساوية سفر وبرضه AA زائد تلاتة AB بالساويهاش سفر
+
+338
+00:43:27,490 --> 00:43:34,570
+يعني لو ال .. ال .. اذا ال A ماشي باتجاه ال
+
+339
+00:43:34,570 --> 00:43:39,890
+negative x axisالـ B هيمشي في اتجاه الـ positive y
+
+340
+00:43:39,890 --> 00:43:44,150
+-axis لأن عندي هى هى اذا هى ده negative عشان
+
+341
+00:43:44,150 --> 00:43:51,470
+اسفرهم هذا لازم يكون positive مظبوط؟
+
+342
+00:43:51,470 --> 00:43:57,070
+طيب لعشان to find acceleration of each block هعمل
+
+343
+00:43:57,070 --> 00:44:02,830
+free path diagram ل A و free path diagram ل B ل A
+
+344
+00:44:09,000 --> 00:44:18,880
+طبعا هيأثر وزنه لتحت MG وفيه normal force وفيه شد
+
+345
+00:44:18,880 --> 00:44:25,140
+في الحبل T هيساوي
+
+346
+00:44:25,140 --> 00:44:33,920
+هيتحرك
+
+347
+00:44:33,920 --> 00:44:51,800
+اكيد في هذا الاتجاه هذه MAهذا سيكون MA A A وهذا
+
+348
+00:44:51,800 --> 00:44:57,900
+اعتبر الموجب هذا الاتجاه الموجب
+
+349
+00:44:57,900 --> 00:45:02,600
+طيب
+
+350
+00:45:02,600 --> 00:45:08,050
+مع انها ستكون summation of forcesباتجاه ال X
+
+351
+00:45:08,050 --> 00:45:16,190
+بيستوى M A X هيكون
+
+352
+00:45:16,190 --> 00:45:23,070
+دي T M A A A هاي واحد
+
+353
+00:45:35,570 --> 00:45:40,610
+فى وزنه لتحت م
+
+354
+00:45:40,610 --> 00:45:54,390
+بي جي وفى عنده تي تي تي تلتة تى حيث ساوى
+
+355
+00:46:06,720 --> 00:46:11,100
+هيمشي لتحت MB
+
+356
+00:46:11,100 --> 00:46:22,960
+AB وهي اتجاه ال Y الموجب summation
+
+357
+00:46:22,960 --> 00:46:31,300
+لل F على ال B سواء MB AB
+
+358
+00:46:34,140 --> 00:46:41,700
+الفرز على B يعني هكون عندي MBG-3T
+
+359
+00:46:41,700 --> 00:46:49,120
+MBAB
+
+360
+00:46:49,120 --> 00:46:53,560
+هد
+
+361
+00:46:53,560 --> 00:47:02,460
+معادلة 2 هضرب معادلة 1 ثلاثة هكون عندي ثلاثة T
+
+362
+00:47:04,690 --> 00:47:18,590
+بتساوى تلاتة M A A A و أجمع M
+
+363
+00:47:18,590 --> 00:47:26,210
+B G بساوى
+
+364
+00:47:26,210 --> 00:47:32,530
+M B A B زائد
+
+365
+00:47:37,580 --> 00:47:50,440
+الان التلاتة او ال a a ايش بتساوي هتقمتها
+
+366
+00:47:50,440 --> 00:47:56,100
+ليش الشوف
+
+367
+00:47:56,100 --> 00:48:01,900
+مش زي السمع انا مش اللي شايفه هى شايف هى اتجاه انا
+
+368
+00:48:01,900 --> 00:48:06,820
+معبّر عن اتجاه الحقيقي مظبوط يعني هدى شوف و هدى
+
+369
+00:48:06,820 --> 00:48:07,180
+سمع
+
+370
+00:48:10,990 --> 00:48:15,390
+يعني انا .. انا قيمة صح لما انا .. انا عملت حسابي
+
+371
+00:48:15,390 --> 00:48:18,490
+اذا هذا ماشي في ال negative xx اللي هناك ماشي لهذه
+
+372
+00:48:18,490 --> 00:48:21,890
+التجاهة هذا هينزل لتحت المعنى التجاهات عندي هنا صح
+
+373
+00:48:21,890 --> 00:48:26,110
+اللي بيحكمني للاتجاهات اللي على الرسم اللي هتبعوض
+
+374
+00:48:26,110 --> 00:48:36,990
+عن القيم هيكون عندي اللي هي a a زائد تلاتة m a
+
+375
+00:48:41,270 --> 00:48:50,570
+فى تلاتة a b واضح
+
+376
+00:48:50,570 --> 00:48:55,770
+انا
+
+377
+00:48:55,770 --> 00:49:05,070
+بحكيلك هى a ماشي هيك وحطلك لتجاه صح راسمه معناه بى
+
+378
+00:49:05,070 --> 00:49:09,730
+نزل لتحت و بى نزل لتحت هل انا ادعيت بى ماشي العكس
+
+379
+00:49:11,890 --> 00:49:15,590
+أنا اللي شايفه الاتجاهات هنا صح ولا غلط صح خلاص
+
+380
+00:49:15,590 --> 00:49:25,490
+خلصنا بحط قيم بحط قيم العلاقة هذه بتبينلي
+
+381
+00:49:25,490 --> 00:49:29,870
+الاتجاهات بالنسبة للمحاول اللي أنا حاططها يعني إذا
+
+382
+00:49:29,870 --> 00:49:33,330
+هذا ماشي أنا هاي ال X axis و هاي ال Y axis إذا
+
+383
+00:49:33,330 --> 00:49:38,530
+ماشي A بال negative X axis هذا هينزل لتحت اتجاه ال
+
+384
+00:49:38,530 --> 00:49:43,210
+positive Y axisمظبوط؟ و انا حضرتلك لتجاه صح هنا
+
+385
+00:49:43,210 --> 00:49:52,050
+العلاقة صحيحة ماناتون بعوض هنا عن القيمة هتكون
+
+386
+00:49:52,050 --> 00:50:00,510
+ضيق بس طيب وينها؟
+
+387
+00:50:00,510 --> 00:50:03,330
+هيها ال .. ال MBG هيها انا بعوض عن تجاهها هي
+
+388
+00:50:03,330 --> 00:50:09,850
+تجاهها صح خلاص بالظبط خلصت منها ماناتون هيكون عندي
+
+389
+00:50:13,630 --> 00:50:20,610
+Mb اللي هي كم؟ خمسة و عشرين في تسعة point تمانية
+
+390
+00:50:20,610 --> 00:50:32,390
+سفر ستة بالساوية AB في Mb اللي هي خمسة و عشرين زي
+
+391
+00:50:32,390 --> 00:50:43,130
+التسعة في MA اللي هي أياش تلاتين و منها بحسبالـ A
+
+392
+00:50:43,130 --> 00:50:50,030
+B احسبوها
+
+393
+00:50:50,030 --> 00:50:53,830
+خمس و عشرين على ميتين و خمس و تسعين في تسع بون
+
+394
+00:50:53,830 --> 00:51:00,190
+تمانس و ستة بالظبط
+
+395
+00:51:00,190 --> 00:51:05,410
+لانه انا خلاص حسمت الجدل و حكيت هاي التجاه ال A A
+
+396
+00:51:05,410 --> 00:51:09,690
+و هاي التجاه ال A B يعني
+
+397
+00:51:09,690 --> 00:51:20,250
+.. نعمpoint تمانية تلاتة meter per second square
+
+398
+00:51:20,250 --> 00:51:30,450
+معناته a a طبعا a b هي لتحت هيك انا حاطط سهم a a
+
+399
+00:51:30,450 --> 00:51:39,710
+بالساوية تسعة تمانية متلاتة اربع عشرينmeter per
+
+400
+00:51:39,710 --> 00:51:45,870
+second squared وهذه اتجاهها بمعنى انه ممكن احسب ال
+
+401
+00:51:45,870 --> 00:51:49,970
+T بيساوي
+
+402
+00:51:49,970 --> 00:51:59,710
+MA AA بتساوي تلاتين في اتنين point اربعة تسعة
+
+403
+00:51:59,710 --> 00:52:08,420
+لأنها هيكون ال D تسعة بتلاتة في سبعة و عشرينتلاتة
+
+404
+00:52:08,420 --> 00:52:13,040
+بتسعة بسبعة عشرين، تلاتة باربعة باربعتاش، تلاتة
+
+405
+00:52:13,040 --> 00:52:19,740
+باتنين بسبعة نيوتن،
+
+406
+00:52:19,740 --> 00:52:26,460
+هزبوت؟
+
+407
+00:52:26,460 --> 00:52:30,280
+في
+
+408
+00:52:30,280 --> 00:52:35,200
+tension في كل حاجة تكون في الحبل اللي هتطار؟
+
+409
+00:52:37,780 --> 00:52:41,420
+كل tension اللي أعلى يعني هو في عندي tension هنا و
+
+410
+00:52:41,420 --> 00:52:44,060
+tension في هذه و ال tension في هذه اللي أخدت ال
+
+411
+00:52:44,060 --> 00:52:49,140
+free body diagram لل .. لل .. للبكرة وزنها مهمل
+
+412
+00:52:49,140 --> 00:52:56,000
+فبطلع هذا زي هذا بستوي هذا بس
+
+413
+00:52:56,000 --> 00:53:01,340
+هو حقيقة مية في المية لأ بستويهوش لإن فيها وزن و
+
+414
+00:53:01,340 --> 00:53:04,120
+acceleration ال potential energy
+
+415
+00:53:09,470 --> 00:53:13,310
+ال potential energy يعني بتحكي عن طاقة محتملة طاقة
+
+416
+00:53:13,310 --> 00:53:20,690
+محتملة يعني مثلا البنزين في potential chemical
+
+417
+00:53:20,690 --> 00:53:26,770
+energy لو عملت اعطيته شعلة بنزين اش هسير فيه هيولع
+
+418
+00:53:26,770 --> 00:53:32,450
+هيحول اتحول من طاقة كيميائيةلطاقة حرارية لان عملية
+
+419
+00:53:32,450 --> 00:53:34,670
+الاشتعالات لو سويتها في ال cylinder بتاعة ال
+
+420
+00:53:34,670 --> 00:53:39,390
+engine هحول الطاقة الحرارية او حولت كيميا لحرارة
+
+421
+00:53:39,390 --> 00:53:45,530
+وبعد الحرارة حولتلها ياش لحركة لان البنزين طول ما
+
+422
+00:53:45,530 --> 00:53:52,950
+هو مش همولع في potential it has an energy عشان
+
+423
+00:53:52,950 --> 00:53:59,430
+استفيد منها بدي اعملها ياش ignition اشعالففي
+
+424
+00:53:59,430 --> 00:54:03,010
+chemical potential energy عندي خزان مثلا على جبل
+
+425
+00:54:03,010 --> 00:54:13,690
+وهي جبل وهي واد وهنا فيه خزان و الخزان فيه ميه و
+
+426
+00:54:13,690 --> 00:54:24,590
+في حنفية هنا الخزان
+
+427
+00:54:24,590 --> 00:54:33,400
+فيه ميهو بالنسبة للواد في عندي potential في عندي
+
+428
+00:54:33,400 --> 00:54:36,140
+طاقة ماعرف ايش اسمها لو انا عايز استخدمها موجودة،
+
+429
+00:54:36,140 --> 00:54:43,120
+مظبوط؟ يعني لو فتحت الحنفية هنا و حطيتلي توربينة و
+
+430
+00:54:43,120 --> 00:54:47,600
+الميه نزلت هتحركها،
+
+431
+00:54:47,600 --> 00:54:50,920
+معناته ال potential اللي جوه هنا الطاقة المقتزنة
+
+432
+00:54:51,570 --> 00:54:56,570
+لما سمحت لها تتدفق ال energy can flow صح؟ لما سمحت
+
+433
+00:54:56,570 --> 00:55:02,170
+تتدفق حولتها لشكل تاني من أشكال الطاقة اللي في
+
+434
+00:55:02,170 --> 00:55:08,230
+الحالة دي حركة لو حطيت عليها تربينة هحول الحركة
+
+435
+00:55:08,230 --> 00:55:16,330
+لياش لكهربا لو أخدت كهربا و أشبكت عليها حمل حراري
+
+436
+00:55:16,330 --> 00:55:23,420
+هحول كهربالحرارة فلو شبكت على غسالة هكون عندى
+
+437
+00:55:23,420 --> 00:55:31,580
+تسخين عندى حرارة و .. و حركة لو اعطيتك .. حولتها
+
+438
+00:55:31,580 --> 00:55:39,600
+من AC ل DC و كان عندى قطبين قطبين
+
+439
+00:55:39,600 --> 00:55:46,280
+موجب و سالب و
+
+440
+00:55:46,280 --> 00:55:47,220
+في عندها المحلول
+
+441
+00:55:49,770 --> 00:55:55,030
+هيصير عملية إيه؟ طلاء كهر يعني أنا في مجال ألعب في
+
+442
+00:55:55,030 --> 00:56:03,030
+الطاقة زي ما بدى بس طول الطاقة ما هي مش مستهلكة
+
+443
+00:56:03,030 --> 00:56:12,370
+جامدة مخزونة عنده بسميها potential energy لما
+
+444
+00:56:12,370 --> 00:56:17,390
+أستخدمها أنا هستخدمها فترة زمنية يعني ال energy is
+
+445
+00:56:17,390 --> 00:56:25,340
+usedover time بتتحول ل power يديه سرعة استهلاك ال
+
+446
+00:56:25,340 --> 00:56:31,620
+how fast I'm using this energy بيعبر
+
+447
+00:56:31,620 --> 00:56:37,520
+how powerful is the load يعني ال load حراري خمس
+
+448
+00:56:37,520 --> 00:56:41,920
+تلاف واط معناته انا باسحب بستهلك خمس تلاف جول في
+
+449
+00:56:41,920 --> 00:56:46,300
+التانية and load مية واط معناته انا بسحب فقط من ال
+
+450
+00:56:46,300 --> 00:56:53,380
+systemميت جول في الثانية عشان هيك مثلا إذا أنا
+
+451
+00:56:53,380 --> 00:56:57,580
+عندي ال load خمس تلاف واط مانفعش أحط سيليكرافية
+
+452
+00:56:57,580 --> 00:57:04,720
+كتير متحملش هيسخن لإن ال resistance بتاعته تتناسب
+
+453
+00:57:04,720 --> 00:57:08,380
+.. تناسب عكس مع القطر هتزيد ال resistance بقى
+
+454
+00:57:08,380 --> 00:57:12,580
+هيسخن مش هجيدا لشيء الأساس أنا أتفرق أنه مصورة ميه
+
+455
+00:57:14,860 --> 00:57:20,360
+هتنفجر مصورة فالان
+
+456
+00:57:20,360 --> 00:57:24,380
+الوزن اذا بيكون على ارتفاع اللي انا حاكيه هنا ال
+
+457
+00:57:24,380 --> 00:57:27,980
+work due to weight اذا ال weight اتغير اتحرك من
+
+458
+00:57:27,980 --> 00:57:34,040
+position one ل position two كان wy1 minus wy2 واضح
+
+459
+00:57:34,040 --> 00:57:39,560
+ان الشغل due to weight بيعتمد فقط على ال initial و
+
+460
+00:57:39,560 --> 00:57:47,570
+ال final position معناتهعند ال position هذا بحكي
+
+461
+00:57:47,570 --> 00:57:51,730
+في potential energy طاقة وضع نتيجة موكة الجسم في
+
+462
+00:57:51,730 --> 00:57:57,090
+طاقة قمتها VG بالساوية
+
+463
+00:57:57,090 --> 00:58:03,850
+W في Y انا
+
+464
+00:58:03,850 --> 00:58:11,480
+هنا عامله break حاطط رجلي لو شتلي break هينزلففي
+
+465
+00:58:11,480 --> 00:58:14,680
+potential energy بس انا المناحة بطريقة ما انه
+
+466
+00:58:14,680 --> 00:58:20,260
+يستفاد منها لأن الأنظمة بشكل عام بغض النظر هل هو
+
+467
+00:58:20,260 --> 00:58:26,360
+كان نظام ميكانيكي او حراري اي نظام بيفضل يروح لوضع
+
+468
+00:58:26,360 --> 00:58:29,360
+الاستقرار انتوا ليش بيصيروا تفاعلات كيميائية
+
+469
+00:58:29,360 --> 00:58:34,860
+أساسا؟ عشان استقر هو بيصير تفاعل كولانه حالة غير
+
+470
+00:58:34,860 --> 00:58:38,790
+مستقرة، مظبوط؟حالات الاستقرار ممكن .. يعني انا
+
+471
+00:58:38,790 --> 00:58:43,370
+ممكن ببساطة ان لو حطيت .. انا عندي كان اشي زيك ..
+
+472
+00:58:43,370 --> 00:58:48,590
+حطيت كورهان و جاي بالظبط بموازن 100% لو حطيت اي
+
+473
+00:58:48,590 --> 00:58:55,990
+انكشة يمين او شمال هتنزل هذه ال condition بسميها
+
+474
+00:58:55,990 --> 00:59:02,910
+stable ولا non-stable؟ non-stablenon-stable لأن أي
+
+475
+00:59:02,910 --> 00:59:07,770
+انحراف بسيط عن وضع الاتزان بتبعد كتير عن وضع الأصل
+
+476
+00:59:07,770 --> 00:59:16,710
+حضرها نازلة وضع تاني عند هاي كورة سواء حركتها يمين
+
+477
+00:59:16,710 --> 00:59:22,910
+أو شمال حضرها راح هجاية لحد ما تثبت في النص هذه
+
+478
+00:59:22,910 --> 00:59:28,510
+non-stable هذه
+
+479
+00:59:28,510 --> 00:59:30,510
+stable
+
+480
+00:59:32,150 --> 00:59:36,290
+حالة تالتة لو
+
+481
+00:59:36,290 --> 00:59:43,570
+حركتها يمين هتتصير هنا لو حركتها شمال هتكون ايش
+
+482
+00:59:43,570 --> 00:59:49,130
+هتظل هنا في الموضوع الجديد مانع تقولها هي stable
+
+483
+00:59:49,130 --> 00:59:56,370
+ولا non-stable neutral في النص روح يبتروح تعالى
+
+484
+00:59:56,370 --> 01:00:00,410
+بتيجي بس يعني
+
+485
+01:00:00,410 --> 01:00:10,340
+مصطلح ايشامعة بتعرفش عن امعة ال neutral يعني
+
+486
+01:00:10,340 --> 01:00:14,920
+ال
+
+487
+01:00:14,920 --> 01:00:25,760
+neutral ففي
+
+488
+01:00:25,760 --> 01:00:34,050
+الحياة الأمور بيصير في كل شي بتفضل وضعلاستقرار
+
+489
+01:00:34,050 --> 01:00:42,770
+حالة الغضب تمثل حالة عدم استقرار بتريح بتغسل وجهك
+
+490
+01:00:42,770 --> 01:00:49,730
+تصل لحالة الاستقرار واحد اتجه واحد غضبان واحد
+
+491
+01:00:49,730 --> 01:00:56,490
+استفز بالزيادة ايش بيرفع حالة عدم الاستقرار فبدوا
+
+492
+01:00:56,490 --> 01:01:03,150
+حد يمطصه يعني لازم فيه تفاعل بالاتجاهإنه يعمل
+
+493
+01:01:03,150 --> 01:01:10,650
+توازن بين حالة الغضب و حالة عدم الغضب طيب معناته
+
+494
+01:01:10,650 --> 01:01:15,890
+الوزن له potential energy due to its position
+
+495
+01:01:15,890 --> 01:01:19,710
+نتيجة موقعه معناته ال work due to weight from
+
+496
+01:01:19,710 --> 01:01:26,980
+position one to two يو واحد لاتنين للوزنهيكون v
+
+497
+01:01:26,980 --> 01:01:30,260
+due to gravity واحد minus v due to gravity اتنين
+
+498
+01:01:30,260 --> 01:01:33,580
+طبعا هذه v مش سرعة potential energy السرعة دايما
+
+499
+01:01:33,580 --> 01:01:46,600
+نكتبها بالشكل هذا واضح هذه v capital لو
+
+500
+01:01:46,600 --> 01:01:50,680
+كان ال system تحت اثير الوزن فقط احنا حكينا ال
+
+501
+01:01:50,680 --> 01:01:56,740
+principle of work energy T واحدزاد U1 ل2 بيساوي T2
+
+502
+01:01:56,740 --> 01:02:07,280
+يعني T1 زاد VG1 minus VG2 بيساوي T2 معناه T1 زاد
+
+503
+01:02:07,280 --> 01:02:13,080
+VG1 ساوية T2 زاد VG2
+
+504
+01:02:26,920 --> 01:02:29,960
+في الحالة اللي بحكي ال taught أو ال mechanical
+
+505
+01:02:29,960 --> 01:02:36,920
+energy is conserved لأن ال T1 زي V1 بستوى T2 زي V2
+
+506
+01:02:36,920 --> 01:02:42,540
+بستوى T3 زي V3 يعني إذا كان له kinetic energy من
+
+507
+01:02:42,540 --> 01:02:47,800
+دافع لأعلى هيطلع لأرتفاع معين لحد ما تصفراللي صار
+
+508
+01:02:47,800 --> 01:02:51,880
+انه تحول الطاقة تحركته من طاقة حركة لطاقة إيش وضع
+
+509
+01:02:51,880 --> 01:02:55,800
+لو كان ارتفاعي و نزل لتحت كل طاقة وضع تحولت ليش
+
+510
+01:02:55,800 --> 01:03:02,120
+لحركة بس تتغير شكل أو نوع الطاقة تكون وضع بيصير
+
+511
+01:03:02,120 --> 01:03:06,980
+حركة أو حركة بيصير وضع في الحالة اللي بحكي عندي
+
+512
+01:03:06,980 --> 01:03:11,620
+conservation of
+
+513
+01:03:11,620 --> 01:03:15,300
+mechanical
+
+514
+01:03:15,300 --> 01:03:15,800
+energy
+
+515
+01:03:21,710 --> 01:03:28,670
+يعني ال forces اللي الشغل تبعها بيتمد على ال
+
+516
+01:03:28,670 --> 01:03:31,150
+initial و ال final position بسميها conservative
+
+517
+01:03:31,150 --> 01:03:34,470
+forces و بسميها conservative forces لإن ال
+
+518
+01:03:34,470 --> 01:03:37,570
+mechanical energy due to these forces ال total
+
+519
+01:03:37,570 --> 01:03:39,770
+mechanical energy اللي هي كيناتك ذات potential
+
+520
+01:03:39,770 --> 01:03:43,710
+تتغيرش ثابتة عشان ذلك بسميها conservative
+
+521
+01:03:52,610 --> 01:03:59,470
+for a space vehicle مركبة في الفضاء بتدور حوالين
+
+522
+01:03:59,470 --> 01:04:05,090
+الأرض مثلا بتكون الأرض دايما بتشدها بقوة جدب قوة
+
+523
+01:04:05,090 --> 01:04:09,190
+الجدب هذه بتأثر بتجاه مركز الأرض و احنا حاكينا ال
+
+524
+01:04:09,190 --> 01:04:12,290
+work due to gravitational force on space vehicles
+
+525
+01:04:12,290 --> 01:04:16,150
+بُعطى بالعلاقة هذه U1 و U2 بستوى G capital M
+
+526
+01:04:16,150 --> 01:04:18,550
+capital M small على R2 minus G capital M capital M
+
+527
+01:04:18,550 --> 01:04:24,780
+small على R1معناته ال V due to gravitational force
+
+528
+01:04:24,780 --> 01:04:30,660
+هتكون اللي هي minus GM capital M small على R
+
+529
+01:04:30,660 --> 01:04:36,920
+لاحظوا في ال .. في ال .. ال U واحد اتنين في حالة
+
+530
+01:04:36,920 --> 01:04:40,060
+ال gravitational force لاحظوا هنا اتنين وهنا واحد
+
+531
+01:04:42,850 --> 01:04:49,670
+2-1، لاحظوا بزنها ديك، 1-2، عشان حكيت ال VG
+
+532
+01:04:49,670 --> 01:04:56,370
+بتاعتها دي بيستوى W في Y، هذي معناته إذا ال VG
+
+533
+01:04:56,370 --> 01:05:00,250
+بتاعتها تكون minus، GM، واضح ليه صارت minus و
+
+534
+01:05:00,250 --> 01:05:03,610
+plus؟
+
+535
+01:05:03,610 --> 01:05:07,790
+بالنسبة ل spring forceأحنا حاكي ان ال work due to
+
+536
+01:05:07,790 --> 01:05:11,370
+spring force يستوي نص كيكس واحد تربيع minus نص
+
+537
+01:05:11,370 --> 01:05:15,390
+كيكس اتنين تربيع واضح ان ال work due to spring
+
+538
+01:05:15,390 --> 01:05:17,990
+force بيتمد على ال initial position و ال final
+
+539
+01:05:17,990 --> 01:05:19,810
+position معناه تبردر spring force is a
+
+540
+01:05:19,810 --> 01:05:21,890
+conservative force
+
+541
+01:05:23,860 --> 01:05:26,880
+ال potential energy due to the elasticity of the
+
+542
+01:05:26,880 --> 01:05:31,840
+spring is given by نص K X تربيع ال X هي ال
+
+543
+01:05:31,840 --> 01:05:36,340
+deflection from undeformed position للspring يعني
+
+544
+01:05:36,340 --> 01:05:40,280
+how much I deform the spring هي ال X ال delta يعني
+
+545
+01:05:40,280 --> 01:05:43,400
+و ال U 1 اتنين بيسوا V elastic واحد minus V
+
+546
+01:05:43,400 --> 01:05:44,640
+elastic اتنين
+
+547
+01:05:57,780 --> 01:06:01,900
+زي ما حكينا when work of a force is independent of
+
+548
+01:06:01,900 --> 01:06:05,420
+the path followed by its point of application
+
+549
+01:06:05,420 --> 01:06:12,520
+حيكون عنده ال work done from position one to
+
+550
+01:06:12,520 --> 01:06:17,780
+position two due to this force depends on the
+
+551
+01:06:17,780 --> 01:06:21,760
+initial position and final position بعتمدش على
+
+552
+01:06:21,760 --> 01:06:26,890
+المصار بتاع الجسم في الحالة هذي بتحكيال force is
+
+553
+01:06:26,890 --> 01:06:30,690
+conservative و ال mechanical energy is conserved
+
+554
+01:06:30,690 --> 01:06:33,550
+يعني ال mechanical energy بيبقى ثابتة ال bc بتتحول
+
+555
+01:06:33,550 --> 01:06:37,910
+من شكل لآخر بس ال friction forces are conservative
+
+556
+01:06:37,910 --> 01:06:45,810
+ولا non conservative forces؟ ليش؟
+
+557
+01:06:45,810 --> 01:06:51,150
+طيب إيش أنا بتعتمد على المسار؟ بالظبط بفقد يعني
+
+558
+01:06:51,150 --> 01:06:56,880
+أنا بدى أروح من النقطة هذهمن هنا لحد الباب لو روحت
+
+559
+01:06:56,880 --> 01:07:00,080
+مباشر الجزء من طالتها هتروح friction مع الأرض
+
+560
+01:07:00,080 --> 01:07:04,480
+مقاومة هوا لكن لو لفيت ضليت ألف ألف رايح أمين
+
+561
+01:07:04,480 --> 01:07:06,980
+أشمال أمين أشمال أشمال و لحد ماوصلت هناك هفقد حتة
+
+562
+01:07:06,980 --> 01:07:14,080
+عب أكتر معناته I lose some of my energy معناته ال
+
+563
+01:07:14,080 --> 01:07:19,740
+mechanical energy في الحالة هذه not conserved لكن
+
+564
+01:07:19,740 --> 01:07:23,300
+ال total energy is conserved يعني
+
+565
+01:07:28,090 --> 01:07:36,910
+T1 V1 T2 V2 Losses
+
+566
+01:07:36,910 --> 01:07:41,530
+فوائد صح؟ اذا مافيش Losses يعني ال forces كانت
+
+567
+01:07:41,530 --> 01:07:46,490
+conservative هيكون T1 V1 T2 V2 او ممكن زي ما هو
+
+568
+01:07:46,490 --> 01:07:51,590
+عبارة عن كتاب بحكي T1 V1
+
+569
+01:07:51,590 --> 01:07:58,080
+زاد ال workdue to non conservative forces او ال ..
+
+570
+01:07:58,080 --> 01:08:00,520
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+571
+01:08:00,520 --> 01:08:00,640
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+572
+01:08:00,640 --> 01:08:02,060
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+573
+01:08:02,060 --> 01:08:02,480
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+574
+01:08:02,480 --> 01:08:05,040
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+575
+01:08:05,040 --> 01:08:05,040
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+576
+01:08:05,040 --> 01:08:05,040
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+577
+01:08:05,040 --> 01:08:05,140
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+578
+01:08:05,140 --> 01:08:05,140
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+579
+01:08:05,140 --> 01:08:12,760
+.. ال .. ال .. ال ..
+
+580
+01:08:12,760 --> 01:08:12,760
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+581
+01:08:12,760 --> 01:08:12,760
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+582
+01:08:12,760 --> 01:08:12,780
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+583
+01:08:12,780 --> 01:08:16,660
+.. ال ..
+
+584
+01:08:22,700 --> 01:08:26,680
+انا بحب اعبر عنها بالشكل هذا T1 زي T1 او T2 زي T2
+
+585
+01:08:26,680 --> 01:08:28,980
+زي T2 زي T2 زي T2 زي T2 زي T2 زي T2 زي T2 زي T2 زي
+
+586
+01:08:28,980 --> 01:08:34,480
+T2 زي T2 زي T1 زي T1 زي T1 زي T1 زي T1 زي T1 زي T1
+
+587
+01:08:34,480 --> 01:08:37,200
+زي T1 زي T1 زي T1 زي T1 زي T1 زي T1 زي T1 زي T1 زي
+
+588
+01:08:37,200 --> 01:08:37,580
+T1 زي T1 زي T1 زي T1 زي T1 زي T1 زي T1 زي T1 زي T1
+
+589
+01:08:37,580 --> 01:08:37,580
+زي T1 زي T1 زي T1 زي T1 زي T1 زي T1 زي T1 زي T1 زي
+
+590
+01:08:37,580 --> 01:08:47,480
+T1 زي T1 زي T1 زي T1 زي T1 زي T1
+
+591
+01:08:47,480 --> 01:08:53,470
+زي T1يعني سواء due to conservative forces أو non
+
+592
+01:08:53,470 --> 01:08:56,790
+conservative forces طبعا ال non conservative
+
+593
+01:08:56,790 --> 01:09:01,370
+forces في معظم الأحوال بتتحول الطاقة المفقودة على
+
+594
+01:09:01,370 --> 01:09:08,870
+شكل حرارة، مظبوط؟
+
+595
+01:09:08,870 --> 01:09:13,670
+إذا
+
+596
+01:09:13,670 --> 01:09:19,070
+كان الجسم تحت أثير central conservative forceيعني
+
+597
+01:09:19,070 --> 01:09:22,830
+في حالة ساتلات بدور حوالين الكورة الأرضية بيكون
+
+598
+01:09:22,830 --> 01:09:27,350
+تحت أثير جذب الأرض جذب الأرض بيأثر باتجاه مركز
+
+599
+01:09:27,350 --> 01:09:32,790
+الكورة الأرضية معناته ال moment of linear momentum
+
+600
+01:09:32,790 --> 01:09:35,330
+هيكون zero في الحال اللي حالي عنده بيكون عنده
+
+601
+01:09:35,330 --> 01:09:40,850
+conservation لحاجتين لل angular ال angular
+
+602
+01:09:40,850 --> 01:09:46,490
+momentum و ال mechanical energyبيكون conservation
+
+603
+01:09:46,490 --> 01:09:51,530
+إذا كان الجسم تحت أثير conservative central force
+
+604
+01:09:51,530 --> 01:09:54,610
+بيكون conservation of angular momentum أو
+
+605
+01:09:54,610 --> 01:10:00,750
+conservation of mechanical energy طيب نحل المثال
+
+606
+01:10:00,750 --> 01:10:08,370
+.. هنحل
+
+607
+01:10:08,370 --> 01:10:09,610
+المثال هذا و ننهي
+
+608
+01:10:16,050 --> 01:10:19,130
+a twenty pound collar slides without friction
+
+609
+01:10:19,130 --> 01:10:27,650
+along a vertical rod as shown في عندي جسم بنزلق
+
+610
+01:10:27,650 --> 01:10:38,010
+على ال رد هذا الجسم هذا وزنه عشرين pound و بساوي
+
+611
+01:10:38,010 --> 01:10:43,370
+عشرين pound هو بيحكيلي في عندي there is no
+
+612
+01:10:43,370 --> 01:10:49,640
+frictionفيش احتكاك يعني no friction لازم يانقياش
+
+613
+01:10:49,640 --> 01:10:52,540
+اجمع معلومات في الأول اتعودوا زي هيك امشوا
+
+614
+01:10:52,540 --> 01:11:03,780
+systematic no friction ال
+
+615
+01:11:03,780 --> 01:11:07,280
+spring attached to the collar has an undeflected
+
+616
+01:11:07,280 --> 01:11:10,260
+length of four inch الآن في مشبوك مع ال collar
+
+617
+01:11:10,260 --> 01:11:11,980
+زمبرك
+
+618
+01:11:13,580 --> 01:11:16,300
+الـ undeflected length له أربع إنش يعني المعنى هو
+
+619
+01:11:16,300 --> 01:11:20,560
+في الوضعية الأولى مشدود أربع إنش مظبوط لأن هذه
+
+620
+01:11:20,560 --> 01:11:24,980
+مسافة تمانية إنش ال undeflected length أربع إنش
+
+621
+01:11:24,980 --> 01:11:30,720
+يعني نسمي ال node بالساوية
+
+622
+01:11:30,720 --> 01:11:38,260
+أربعة إنش وإله
+
+623
+01:11:38,260 --> 01:11:39,540
+k تبعته
+
+624
+01:11:42,400 --> 01:11:52,340
+بالساوية تلاتة pound لكل إنش if
+
+625
+01:11:52,340 --> 01:11:55,660
+the caller is released from rest من ال position
+
+626
+01:11:55,660 --> 01:12:04,440
+واحد تم إطلاقها من السكون يعني V واحد بالساوية
+
+627
+01:12:04,440 --> 01:12:04,940
+سفر
+
+628
+01:12:07,600 --> 01:12:10,800
+determine its velocity after it has moved six
+
+629
+01:12:10,800 --> 01:12:15,060
+inches to position two لأن position two مشيت ستة
+
+630
+01:12:15,060 --> 01:12:25,440
+انش بده ال V عند .. بده V2 لأن
+
+631
+01:12:25,440 --> 01:12:28,180
+فيش كل ال force بتأثر، لأن أنا في وضع ال vertical
+
+632
+01:12:28,180 --> 01:12:33,680
+كل ال force بتأثر، إيش ال force بتأثر؟
+
+633
+01:12:33,680 --> 01:12:38,340
+يعني عند ال springوالوزن فقط من بأثره ال force
+
+634
+01:12:38,340 --> 01:12:42,260
+بتأثر معناته لو انا حكيت معناته في عيندي all
+
+635
+01:12:42,260 --> 01:12:47,860
+forces are
+
+636
+01:12:47,860 --> 01:12:52,980
+conservative مازال
+
+637
+01:12:52,980 --> 01:12:55,900
+all forces are conservative معناته ممكن استخدم ال
+
+638
+01:12:55,900 --> 01:13:00,880
+conservation و mechanical energy احكي T واحد زاد V
+
+639
+01:13:00,880 --> 01:13:10,210
+واحد سوى T اتنينزاد V2 طيب T1 ايش الساوية سفر و T2
+
+640
+01:13:10,210 --> 01:13:26,810
+نص M V2 تربيع يعني نص W على G V2 تربيع طيب
+
+641
+01:13:26,810 --> 01:13:33,450
+انا لازم اعمل ايش مرجع بدون مرجع ماعرفش اشتغلعى
+
+642
+01:13:33,450 --> 01:13:40,270
+المرجع تبعه ممكن اعمل تحت بيصير يعنى هذا
+
+643
+01:13:40,270 --> 01:13:46,550
+reference معناته
+
+644
+01:13:46,550 --> 01:13:57,510
+ال V1 بيصبح V1 due to gravity زي V1 due الاساسي
+
+645
+01:13:57,510 --> 01:14:05,710
+بتاعة ال spring هدش متساوىdue to gravity أنا جاي
+
+646
+01:14:05,710 --> 01:14:12,930
+على ال reference zero زائد طلعت ال spring هتكون نص
+
+647
+01:14:12,930 --> 01:14:24,170
+K X واحد تربيع طيب X واحد إيش يستوي؟ X واحد يستوي
+
+648
+01:14:24,170 --> 01:14:31,110
+تمانية ناقص أربعة يعني أربعة إنش يعني هتكون هذه نص
+
+649
+01:14:34,240 --> 01:14:41,480
+في تلاتة في أربعة تربيع يعني ستاشع تانية تمانية
+
+650
+01:14:41,480 --> 01:14:50,280
+أربعة و عشرين أربعة و عشرين pound انش طيب
+
+651
+01:14:50,280 --> 01:14:58,820
+V2 ايش تساوي V2 due to gravity زي V2 due to
+
+652
+01:14:58,820 --> 01:14:59,280
+elasticity
+
+653
+01:15:03,360 --> 01:15:06,740
+هي واحد ال energy اللى متأثر على الجسم من منطقة
+
+654
+01:15:06,740 --> 01:15:15,160
+واحدة بسبب ال gravity و النابط و النابط بالظبط ال
+
+655
+01:15:15,160 --> 01:15:20,500
+gravity أنا جاي على ال reference سفر ال zombarak
+
+656
+01:15:20,500 --> 01:15:25,420
+مشدود أربع انش لإن هو ال undeflected linked له
+
+657
+01:15:25,420 --> 01:15:30,740
+أربعة هيكون تمانية ناقص أربعة أربعة ففي potential
+
+658
+01:15:30,740 --> 01:15:36,090
+energy due to spring forceV2 مش هتساوي الآن الوزن
+
+659
+01:15:36,090 --> 01:15:45,870
+جاي تحت المرجع هتكون minus minus W Y2
+
+660
+01:15:45,870 --> 01:16:00,110
+زائد نص K X2 تربيع طيب X2 هتكون طول الوطر هذا ناقص
+
+661
+01:16:00,110 --> 01:16:02,950
+أربعة هتكون X2
+
+662
+01:16:08,080 --> 01:16:15,580
+هتكون جزر التربيع ل تمانية تربيع زي ستة تربيع ناقص
+
+663
+01:16:15,580 --> 01:16:19,780
+أربعة صح؟ يعني هتكون تستوى اللي هيدي ستة تمانية
+
+664
+01:16:19,780 --> 01:16:30,820
+عشرة صح؟ هتكون عشرة ناقص أربعة ستة انش هتكون
+
+665
+01:16:30,820 --> 01:16:40,930
+minus الوزن عندي عشرين و Y2 اللي هيستة زائد نص ال
+
+666
+01:16:40,930 --> 01:16:48,890
+K تلاتة في ستة تربيع يعني هيكون ناقص مية و عشرين
+
+667
+01:16:48,890 --> 01:17:05,910
+زائد ال K أكملنا أننا تلاتة أربعة
+
+668
+01:17:07,950 --> 01:17:16,430
+يعني عندى .. يعني .. ستة و تلاتين في تلاتة اربعة
+
+669
+01:17:16,430 --> 01:17:20,730
+و خمسين بس
+
+670
+01:17:20,730 --> 01:17:25,870
+في خطأ كبير اتكبناه
+
+671
+01:17:25,870 --> 01:17:31,590
+انتبهوا ال G .. ال G وحدتها بال foot per second و
+
+672
+01:17:31,590 --> 01:17:37,720
+احنا في عيننا انش موجود كله بده حولهمعناته عندي X1
+
+673
+01:17:37,720 --> 01:17:45,900
+أربع انش يعني أربع .. بانا عارف .. أنت عندك هنا ..
+
+674
+01:17:45,900 --> 01:17:49,880
+أنت عندك هنا بدأ تكون consistent في كل وحدات عندي
+
+675
+01:17:49,880 --> 01:17:59,660
+هيكون X1 يعني هيكون أربع على اتناش يعني تلت قدم و
+
+676
+01:17:59,660 --> 01:18:05,000
+X2 سواء ستة على اتناش مص قدم
+
+677
+01:18:07,740 --> 01:18:16,040
+معناته V elastic واحد هتكون تساوي نص
+
+678
+01:18:16,040 --> 01:18:19,440
+ك
+
+679
+01:18:19,440 --> 01:18:26,740
+.. ك عبارة عن أكم هتكون تلاتة في اتناش هتكون ستة و
+
+680
+01:18:26,740 --> 01:18:33,260
+تلاتين pound على القدم ك بتساوي ستة و تلاتين pound
+
+681
+01:18:33,260 --> 01:18:43,800
+على القدم هتسينا عندي نصفي نص في ستة و تلاتين في X
+
+682
+01:18:43,800 --> 01:18:57,540
+واحد تلت تربيع يعني هكون اتنين pound قدم هنا هتكون
+
+683
+01:18:57,540 --> 01:19:04,260
+عند الوزن هنا هتكون minus عشرين في ستة على اتناش
+
+684
+01:19:04,260 --> 01:19:06,180
+هتكون
+
+685
+01:19:08,200 --> 01:19:19,440
+ناقص عشرين في النص كام؟ ناقص عشرة زائد ستة
+
+686
+01:19:19,440 --> 01:19:23,480
+و تلاتين في
+
+687
+01:19:23,480 --> 01:19:31,480
+نص تربيع يعني عندنا ناقص عشرة زائد ستة و تلاتين
+
+688
+01:19:31,480 --> 01:19:41,520
+على أربعة تسعة زي أربعة و نصهتكون سالب خمسة و نص
+
+689
+01:19:41,520 --> 01:19:51,100
+pound bear pound foot طيب
+
+690
+01:19:51,100 --> 01:19:59,080
+هنعوض T واحد اللي هي سفر زاد V واحد
+
+691
+01:20:03,740 --> 01:20:10,460
+بواحد اللي عملناها اللي هي اتنين بتساوي
+
+692
+01:20:10,460 --> 01:20:19,500
+T2 اللي هي نص في عشرين على اتنين و تلاتين point 2
+
+693
+01:20:19,500 --> 01:20:32,240
+في V2 تربيع زائد V2 اللي هي ناقص خمسة و نص و منها
+
+694
+01:20:32,240 --> 01:20:32,760
+بحسب
+
+695
+01:20:35,960 --> 01:20:47,180
+V2 هتكون خمسة و نص زي اتنين سبعة و نص في اتنين في
+
+696
+01:20:47,180 --> 01:20:56,020
+اتنين و تلاتين و اتنين من عشرة على عشرين يعني
+
+697
+01:20:56,020 --> 01:21:00,860
+على الخمسة فيها الأربعة على الخمسة فيها التلاتة
+
+698
+01:21:00,860 --> 01:21:06,910
+على اتنين اتنينعلى اتنين ستاش point one تطلع ستاش
+
+699
+01:21:06,910 --> 01:21:14,930
+point واحد متر تربيع per second تربيع يعني V2
+
+700
+01:21:14,930 --> 01:21:20,190
+هتكون تساوي اربع point سفر سفر something foot per
+
+701
+01:21:20,190 --> 01:21:24,590
+second
+
+702
+01:21:24,590 --> 01:21:29,670
+انتبهوا
+
+703
+01:21:29,670 --> 01:21:33,670
+ليش اذا اخطأنا في اللحظات اللي بيصيرلأن هنا عندي
+
+704
+01:21:33,670 --> 01:21:37,410
+وحدات يعني يا بحول هذه أو بحول ال .. ال .. ال in
+
+705
+01:21:37,410 --> 01:21:47,350
+chat لازم يكون المرجع الوحدات نفس الشيء طيب لانفحص
+
+706
+01:21:47,350 --> 01:21:56,110
+الأرقام ورايا 4 point 4 point 9 1 4 point 9 1 غلط
+
+707
+01:21:56,110 --> 01:22:00,330
+غلط ال doctor بتطلع يزي .. نه .. من جدر ال 16
+
+708
+01:22:00,330 --> 01:22:01,250
+بتطلع 4 point 01
+
+709
+01:22:04,840 --> 01:22:13,440
+على الحسبة اللي عملناها كم بيطلع 16.1 440 44012
+
+710
+01:22:13,440 --> 01:22:19,100
+بالظبط هيك صح على الحاجة نراجع الأرقام نشوف إذا في
+
+711
+01:22:19,100 --> 01:22:26,260
+خطأ عدله في أي سؤال؟
+
diff --git a/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/UYygS5l5Ctk_postprocess.srt b/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/UYygS5l5Ctk_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bb395426f789e52066508ffbb944d6a287f24889
--- /dev/null
+++ b/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/UYygS5l5Ctk_postprocess.srt
@@ -0,0 +1,1804 @@
+1
+00:00:04,930 --> 00:00:07,850
+السلام عليكم و رحمة الله اليوم هنبدأ المحاضرة
+
+2
+00:00:07,850 --> 00:00:16,490
+هنكمل chapter 12 حلينا مجموعة من الأمثلة هنكمل
+
+3
+00:00:16,490 --> 00:00:20,410
+المثال
+
+4
+00:00:20,410 --> 00:00:21,090
+12-6
+
+5
+00:00:26,290 --> 00:00:30,030
+determine the rated speed of a highway curve of
+
+6
+00:00:30,030 --> 00:00:35,050
+radius rho equal four hundred feet banked through
+
+7
+00:00:35,050 --> 00:00:39,150
+an angle of eighteen degrees بده ال rated speed
+
+8
+00:00:39,150 --> 00:00:45,130
+طبعا هذا الشارع مائل بيلف بهذا الاتجاه معناته
+
+9
+00:00:45,130 --> 00:00:54,690
+حيكون مركز الشارع طبعا
+
+10
+00:00:54,690 --> 00:01:00,690
+هذا هذا مقطعالشارع مائل بتاع لما تلف على دوران
+
+11
+00:01:00,690 --> 00:01:05,550
+لازم يكون فيه ميلان فهذا مقطع فهذا مركز الدوران
+
+12
+00:01:05,550 --> 00:01:13,230
+بتاع السيارة الآن ايش ال rate of speed ال rate of
+
+13
+00:01:13,230 --> 00:01:20,590
+speed لشارع مائل هي السرعة اللي عندها بيكونش في
+
+14
+00:01:20,590 --> 00:01:22,890
+احتكاك جانبي يعني مافيش احتكاك بهذا الاتجاه ولا
+
+15
+00:01:22,890 --> 00:01:27,860
+هذا الاتجاهال rate of speed of a banked highway هي
+
+16
+00:01:27,860 --> 00:01:31,600
+ال speed at which there is no side way friction
+
+17
+00:01:31,600 --> 00:01:37,760
+هنا أنا كاتب ال definition هنا هي speed at which a
+
+18
+00:01:37,760 --> 00:01:41,080
+car should travel if no lateral friction force is
+
+19
+00:01:41,080 --> 00:01:45,600
+to be exerted at its wheels او the speed at which
+
+20
+00:01:45,600 --> 00:01:49,200
+no lateral friction on the wheels يعني مافيش
+
+21
+00:01:49,200 --> 00:01:53,250
+احتكاك بهذا الاتجاه هذه ال rate of speedإذا السرعة
+
+22
+00:01:53,250 --> 00:01:59,210
+زادت عن ال rate of speed هتحاول تطرد لبرا يكون فيه
+
+23
+00:01:59,210 --> 00:02:03,350
+friction لتحت إذا قلت عن السرعة المحددة هتحاول
+
+24
+00:02:03,350 --> 00:02:19,370
+يصير انزلاق بهذا الاتجاه طيب معطين ال radius رو بس
+
+25
+00:02:19,370 --> 00:02:20,370
+400 قدم
+
+26
+00:02:23,660 --> 00:02:30,300
+والزاوية θية 18 عشان نحسب ال rate of speed بدي
+
+27
+00:02:30,300 --> 00:02:35,960
+اعمل free pedo diagram للسيارة هذه
+
+28
+00:02:35,960 --> 00:02:41,700
+السيارة هذه
+
+29
+00:02:41,700 --> 00:02:48,480
+الزاوية 18 درجة ايش القوة اللي بتأثر على السيارة
+
+30
+00:02:48,480 --> 00:02:49,340
+الوزن اللي أسفل
+
+31
+00:02:55,650 --> 00:03:03,330
+و normal force انا
+
+32
+00:03:03,330 --> 00:03:09,430
+حاكي انا at rated speed مافيش عندى كل friction حيث
+
+33
+00:03:09,430 --> 00:03:09,770
+ساوي
+
+34
+00:03:23,930 --> 00:03:31,010
+هيكون عندى M A Normal وفي
+
+35
+00:03:31,010 --> 00:03:36,330
+M A Tendential لجوه عندهين
+
+36
+00:03:36,330 --> 00:03:44,630
+M A Tendential لجوه اللي
+
+37
+00:03:44,630 --> 00:03:49,970
+اعتبرت هذه ال X و
+
+38
+00:03:49,970 --> 00:03:50,710
+هذه ال Y
+
+39
+00:04:06,050 --> 00:04:13,850
+لأ طبعا هو بيلف بيهك الاتجاه بيكون باتجاه المركز
+
+40
+00:04:13,850 --> 00:04:18,090
+المركز مش جاي لتحت انا ماخد section ال section بقى
+
+41
+00:04:18,090 --> 00:04:23,230
+عن دائرة هو ميل صاح بيلف زي .. هو هز بيصرف بيلف
+
+42
+00:04:23,230 --> 00:04:26,550
+فال
+
+43
+00:04:26,550 --> 00:04:32,690
+section بيكون إيهاشدائرة، دائرة high اتجاهها هنا
+
+44
+00:04:32,690 --> 00:04:41,630
+at the rated speed عندي
+
+45
+00:04:41,630 --> 00:04:47,190
+no lateral friction
+
+46
+00:04:47,190 --> 00:04:50,430
+عشان
+
+47
+00:04:50,430 --> 00:04:51,690
+هيك مظهر عشان ال friction هنا
+
+48
+00:04:58,940 --> 00:05:02,940
+حناخذ summation of force باتجاه ال X و summation
+
+49
+00:05:02,940 --> 00:05:07,940
+of force باتجاه ال Y ممكن نبدأ من ال X أسهلنا صح؟
+
+50
+00:05:07,940 --> 00:05:13,400
+نبدأ من ال Y summation of Y هل السيارة تتحرك بهذه
+
+51
+00:05:13,400 --> 00:05:20,960
+الاتجاه؟ بالساوي إيش؟ سفر؟
+
+52
+00:05:20,960 --> 00:05:25,700
+حد ساوي حد
+
+53
+00:05:25,700 --> 00:05:26,480
+زاوية؟
+
+54
+00:05:29,870 --> 00:05:34,130
+طمنتاش خلّيني أسميها theta يعني في الآخر هكون N
+
+55
+00:05:34,130 --> 00:05:45,550
+cosine theta minus W يعني
+
+56
+00:05:45,550 --> 00:05:52,750
+N هتسوى W ع cosine theta
+
+57
+00:06:07,570 --> 00:06:13,150
+بتجاه ال X summation
+
+58
+00:06:13,150 --> 00:06:23,830
+لل forces باتجاه ال X هعتبر هذا موجب بالسوء M Ax
+
+59
+00:06:23,830 --> 00:06:27,410
+هكون
+
+60
+00:06:27,410 --> 00:06:28,810
+دي unsigned theta
+
+61
+00:06:33,840 --> 00:06:42,500
+بتساوي M A Normal صح M A Normal المعادلة اللي هيدي
+
+62
+00:06:42,500 --> 00:06:55,100
+عندي N بتساوي M G على Cos Theta في Sin Theta
+
+63
+00:06:55,100 --> 00:07:02,780
+هتساوي M و A Normal عبارة عن V Square على Rho V
+
+64
+00:07:02,780 --> 00:07:10,330
+Squareعلى رو ال
+
+65
+00:07:10,330 --> 00:07:18,070
+M هتلتغى من هنا بصف
+
+66
+00:07:18,070 --> 00:07:34,150
+عندى V تربية او V هتساوي جزر التربية ل رو G tan θ
+
+67
+00:07:37,510 --> 00:07:46,030
+يعني هتساوي الجزر التربيعي الرمعة نيها أربعة مية و
+
+68
+00:07:46,030 --> 00:07:50,370
+G تنين و تلاتين و اتنين و عشرة قدم على الثانية و
+
+69
+00:07:50,370 --> 00:07:58,270
+θاش تمانتاش حسبوا ليها اربعة
+
+70
+00:07:58,270 --> 00:08:02,210
+و ستين قدم
+
+71
+00:08:02,210 --> 00:08:05,330
+على الثانية
+
+72
+00:08:11,570 --> 00:08:18,050
+يعني عند الصراع هادى بالظبط بيكونش فيه احتكاك بهذا
+
+73
+00:08:18,050 --> 00:08:25,510
+الاتجاه مافي عنده literal friction طيب لو
+
+74
+00:08:25,510 --> 00:08:35,510
+بدى اضيفها السؤال احكي find minimum
+
+75
+00:08:35,510 --> 00:08:38,750
+and
+
+76
+00:08:38,750 --> 00:08:40,890
+maximum
+
+77
+00:08:43,620 --> 00:08:52,500
+speeds او خليني اجزء المثل مرتين find find
+
+78
+00:08:52,500 --> 00:08:55,880
+maximum
+
+79
+00:08:55,880 --> 00:09:06,200
+speed of car ايش
+
+80
+00:09:06,200 --> 00:09:08,720
+اللي بيحدد ال maximum speed للسيارة، بيحدد السرعة
+
+81
+00:09:08,720 --> 00:09:09,760
+القصوى للسيارة؟
+
+82
+00:09:13,210 --> 00:09:16,590
+البحدد لما السرعة زيدة لحد معين تبدأ السيارة
+
+83
+00:09:16,590 --> 00:09:23,170
+بتحاول تنزلق طبعا
+
+84
+00:09:23,170 --> 00:09:30,730
+في مقام ليهاش الاحتكاك لحد ما يصير قوة الطرد لبرا
+
+85
+00:09:30,730 --> 00:09:35,050
+تتغلب على احتكاك في اللحظة ده انا بصل ال maximum
+
+86
+00:09:35,050 --> 00:09:40,270
+speed يعني لو رسمت ال free body diagram تاني نفس
+
+87
+00:09:40,270 --> 00:09:41,010
+ال free body ده
+
+88
+00:09:47,060 --> 00:09:51,180
+عندي هاي الوزن و
+
+89
+00:09:51,180 --> 00:09:54,520
+و
+
+90
+00:09:54,520 --> 00:10:04,200
+هذه n عند
+
+91
+00:10:04,200 --> 00:10:10,120
+ال micro speed هتحاول تصير طرد لبرا المعنى انه
+
+92
+00:10:10,120 --> 00:10:16,700
+الاحتكاك حاسس كل أياش لتحتهتحاول تطلع لبره هقومها
+
+93
+00:10:16,700 --> 00:10:20,420
+يعني الموش هتكون بعيدة للاتجاه المناطق هيكون عندها
+
+94
+00:10:20,420 --> 00:10:24,640
+اللي
+
+95
+00:10:24,640 --> 00:10:35,480
+هي ميو ميو في ان ميو
+
+96
+00:10:35,480 --> 00:10:41,100
+أس ولا ميو كيه ميو أس ميو أس هي ما نزلقتش لسه
+
+97
+00:10:57,590 --> 00:11:04,330
+هتساوي عندي M A normal و في M A tendential عمودي
+
+98
+00:11:04,330 --> 00:11:10,350
+على الصفحة عندي هاي ال X و هاي ال Y
+
+99
+00:11:26,270 --> 00:11:31,250
+هاخد summation لل forces باتجاه ال Y و بتجاه ال X
+
+100
+00:11:31,250 --> 00:11:40,330
+هل
+
+101
+00:11:40,330 --> 00:11:46,710
+ستتحرك باتجاه ال Y؟ مش هتطلع تنجلش هال زي هيك بهذا
+
+102
+00:11:46,710 --> 00:11:55,830
+الاتجاه يعني عندي X انا هلف X على Y هتكون Z لجوه
+
+103
+00:11:56,870 --> 00:12:03,470
+فتنجلش component بهذا الاتجاه اتجاه الـ z هتكون
+
+104
+00:12:03,470 --> 00:12:07,690
+هنا zero هكون
+
+105
+00:12:07,690 --> 00:12:28,280
+دي N cos θ minus mus N sin θما زال N و Mu S N
+
+106
+00:12:28,280 --> 00:12:31,140
+متعمدين على بعض، إذا واحدة كوصينت N هتكون Sin
+
+107
+00:12:31,140 --> 00:12:41,640
+minus Mu S N Sin Theta minus W يعني هتكون عندي N
+
+108
+00:12:41,640 --> 00:12:53,820
+بتساوي W على Cos Theta minus Mu S
+
+109
+00:12:56,370 --> 00:13:02,230
+Sin θ هاي
+
+110
+00:13:02,230 --> 00:13:06,790
+واحد في
+
+111
+00:13:06,790 --> 00:13:13,510
+اتجاه ال X summation لل forces باتجاه ال X بتساوي
+
+112
+00:13:13,510 --> 00:13:15,730
+M Ax
+
+113
+00:13:24,680 --> 00:13:30,860
+هيكون عندي n sin
+
+114
+00:13:30,860 --> 00:13:36,420
+θ زائد
+
+115
+00:13:36,420 --> 00:13:46,140
+mu s n cos θ بساوة
+
+116
+00:13:46,140 --> 00:13:46,860
+m a normal
+
+117
+00:13:56,860 --> 00:14:04,260
+هاخد N على مشترك بـ C land N في sin θ زاد Mu S
+
+118
+00:14:04,260 --> 00:14:18,460
+cosine θ بالساوية M في V تربية على رو طبعا V
+
+119
+00:14:18,460 --> 00:14:19,780
+التربية هنا هتكون V maximum
+
+120
+00:14:29,890 --> 00:14:36,590
+هنعوض عن N حسينا ان ال N عبارة عن ايش هتكون اندي
+
+121
+00:14:36,590 --> 00:14:41,850
+MG في
+
+122
+00:14:41,850 --> 00:15:00,240
+sin θ بزاد mus cos θ على cos θ minus musسين ثيتا
+
+123
+00:15:00,240 --> 00:15:03,700
+هتساوي
+
+124
+00:15:03,700 --> 00:15:16,080
+M V Square Max على رو ال
+
+125
+00:15:16,080 --> 00:15:24,420
+M cancels out لو أقسم هنا في الطرف هذا البست على
+
+126
+00:15:24,420 --> 00:15:30,880
+كسين ثيتاوالمقام على cosine θ بيأثر علي؟ ما بيأثر
+
+127
+00:15:30,880 --> 00:15:37,240
+لما تحسيها عندي هنا tan θ زائد
+
+128
+00:15:37,240 --> 00:15:41,240
+mus على
+
+129
+00:15:41,240 --> 00:15:51,820
+واحد minus mus tan θ بالساوية
+
+130
+00:15:54,690 --> 00:16:04,010
+في جيه طبعا في
+
+131
+00:16:04,010 --> 00:16:15,190
+جيه في رو تعطيني V max تربع معناه
+
+132
+00:16:15,190 --> 00:16:20,950
+V maximum هتكون
+
+133
+00:16:20,950 --> 00:16:22,310
+ساوى جزر التربع يعني
+
+134
+00:16:27,150 --> 00:16:36,210
+لأ رو في جي في
+
+135
+00:16:36,210 --> 00:16:40,550
+tan theta زاد
+
+136
+00:16:40,550 --> 00:16:53,670
+mus على واحد minus mus tan theta هذه
+
+137
+00:16:53,670 --> 00:16:54,890
+ال maximum speed
+
+138
+00:16:57,780 --> 00:17:01,760
+اللي ممكن السيارة تمشيها بدون ما تنزلك السيارة
+
+139
+00:17:01,760 --> 00:17:17,280
+الأعلى اللي انا ممكن احط سؤال تاني find find
+
+140
+00:17:17,280 --> 00:17:21,900
+minimum
+
+141
+00:17:21,900 --> 00:17:34,150
+speed of carsuch that the
+
+142
+00:17:34,150 --> 00:17:51,770
+car will not skid ستنزلق downward لتحت هعمل
+
+143
+00:17:51,770 --> 00:17:57,310
+ال proof دقيقة ال potential إذا حكون في skidding
+
+144
+00:17:57,310 --> 00:18:05,010
+بهذا الاتجاههيكون في احتكارات لاقيهاش لأعلى اذا
+
+145
+00:18:05,010 --> 00:18:12,150
+كنت عند ال US في N على فكرة تطلع نفس المعادلة هذه
+
+146
+00:18:12,150 --> 00:18:17,070
+بستاح بستاح 10 plus يعني عكس الشرطة دي خلينا نشوف
+
+147
+00:18:17,070 --> 00:18:25,530
+هاخد صماش ال forces باتجاه ال Y ساوة
+
+148
+00:18:25,530 --> 00:18:27,770
+سفر بتساوي
+
+149
+00:18:30,600 --> 00:18:41,480
+N cos θ minus ميو أس زائد زائد
+
+150
+00:18:41,480 --> 00:18:45,300
+N
+
+151
+00:18:45,300 --> 00:18:55,660
+في cos θ زائد ميو أس N sin θ minus W اللي هي MG
+
+152
+00:18:55,660 --> 00:19:18,270
+صح؟ يعني هتكون Nبتساوي Mg على Cos θ زائد Mu S sin
+
+153
+00:19:18,270 --> 00:19:22,450
+θ باتجاه
+
+154
+00:19:22,450 --> 00:19:36,150
+ال Y summation Fx بهذا الاتجاه حزب مفي ax يعني
+
+155
+00:19:36,150 --> 00:19:42,110
+اتجاه ال x هيكون عند mew minus
+
+156
+00:19:42,110 --> 00:19:47,350
+n sin
+
+157
+00:19:47,350 --> 00:19:54,970
+theta مظبوط موجب
+
+158
+00:19:54,970 --> 00:20:00,950
+n sin theta n sin theta
+
+159
+00:20:03,930 --> 00:20:18,770
+مينوس ميو أس ميو أس ميو
+
+160
+00:20:18,770 --> 00:20:30,250
+أس ميو أس
+
+161
+00:20:30,250 --> 00:20:32,410
+ميو أس ميو أس ميو أس ميو أس ميو أس ميو أس ميو أس
+
+162
+00:20:32,410 --> 00:20:38,840
+ميو أس ميو أس ميو أس ميو أس ميو أس مفى sin θ minus
+
+163
+00:20:38,840 --> 00:20:54,320
+µs cos θ بسوء M V minimum square على ρ هنعوض
+
+164
+00:20:54,320 --> 00:20:59,960
+عن N اللى هي بقى عالى Mg فى
+
+165
+00:20:59,960 --> 00:21:09,100
+sin θ minus µscos θ على
+
+166
+00:21:09,100 --> 00:21:14,600
+cos
+
+167
+00:21:14,600 --> 00:21:18,880
+θ زائد
+
+168
+00:21:18,880 --> 00:21:30,740
+mu s sin θ بيستوى M V square minimum على ρ نقسم
+
+169
+00:21:30,740 --> 00:21:35,470
+الطرف يه على ال M بتروح ال Mأقصد البسطى على كوسين
+
+170
+00:21:35,470 --> 00:21:44,430
+والمقام على كوسين بصفة عند V minimum بالسواء
+
+171
+00:21:44,430 --> 00:21:55,190
+جزر التربيعي لروفجي في tan
+
+172
+00:21:55,190 --> 00:21:58,850
+θ minus
+
+173
+00:21:58,850 --> 00:22:02,610
+ميو
+
+174
+00:22:05,500 --> 00:22:18,300
+S على واحد زاد ميو S tan
+
+175
+00:22:18,300 --> 00:22:24,920
+θ نفس الشكل المعادلة نفس الشكل عندين tan θ هين tan
+
+176
+00:22:24,920 --> 00:22:30,970
+θعندي هنا ميو أس وعندي ميو أس وعندي ميو أس وعندي
+
+177
+00:22:30,970 --> 00:22:31,250
+ميو أس وعندي ميو أس وعندي ميو أس وعندي ميو أس
+
+178
+00:22:31,250 --> 00:22:31,330
+وعندي ميو أس وعندي ميو أس وعندي ميو أس وعندي ميو
+
+179
+00:22:31,330 --> 00:22:31,550
+أس وعندي ميو أس وعندي ميو أس وعندي ميو أس وعندي
+
+180
+00:22:31,550 --> 00:22:32,310
+ميو أس وعندي ميو أس وعندي ميو أس وعندي ميو أس
+
+181
+00:22:32,310 --> 00:22:37,350
+وعندي ميو أس وعندي ميو أس وعندي ميو أس وعندي ميو
+
+182
+00:22:37,350 --> 00:22:48,980
+أس وعندي ميو أس وعندي ميو أس وعندي ميو أهنا عندي
+
+183
+00:22:48,980 --> 00:22:54,080
+plus يعني المقام بيكبر بقى نقطة ال V minimum بتصغر
+
+184
+00:22:54,080 --> 00:22:58,640
+فهتمثل ايه؟ ال V minimum هذا جزء من ال check او ال
+
+185
+00:22:58,640 --> 00:23:07,060
+control على الحل تبعي ان الاشي يكون منطقي في
+
+186
+00:23:07,060 --> 00:23:07,740
+اي سؤال؟
+
+187
+00:23:33,650 --> 00:23:36,870
+هذا بناء على .. بناء على المعادلات هذا بيحطه
+
+188
+00:23:36,870 --> 00:23:45,510
+الصراعات القصوى والصراعات الدنيا على خطوط المداخل
+
+189
+00:23:45,510 --> 00:23:53,530
+ال highway الخط السريع طبعا
+
+190
+00:23:53,530 --> 00:24:01,720
+إذا كانت ال V maximum مية بيخليهاش ميةخلّى تسعين،
+
+191
+00:24:01,720 --> 00:24:10,380
+خمس تسعين بيكون في عنده هامش أمان طيب
+
+192
+00:24:10,380 --> 00:24:13,760
+نكمل
+
+193
+00:24:13,760 --> 00:24:20,800
+هنحكي على العزم الزاوي
+
+194
+00:24:20,800 --> 00:24:25,120
+اللي هو the angular momentum في عندي جسم، في عندي
+
+195
+00:24:25,120 --> 00:24:36,270
+محاولة أثيات X, Y, Zوفي جسم ماشي على منحنة طبعا
+
+196
+00:24:36,270 --> 00:24:42,330
+الصرعة تاعته هتكون مماسة للمصار دايما وبالتالي
+
+197
+00:24:42,330 --> 00:24:47,090
+العزم او .. او .. او كمية التحرك او زخم الخط برضه
+
+198
+00:24:47,090 --> 00:24:55,160
+هيكون مماسلأنه الزخم الخط يبقى عن كتلة في السرعة
+
+199
+00:24:55,160 --> 00:25:00,680
+الكتلة كمية غير متجهة والسرعة كمية متجهة معناته ال
+
+200
+00:25:00,680 --> 00:25:06,180
+MV is also tangent لمصار الحركة الآن في اللحظة
+
+201
+00:25:06,180 --> 00:25:12,590
+اللي احنا شايفينها الجسم موقعه عن مركز الهدوثياتاه
+
+202
+00:25:12,590 --> 00:25:16,750
+اللي انا اذا عندي انا مثلا لو اي اشي بلف انا عندي
+
+203
+00:25:16,750 --> 00:25:24,190
+ماسك اشي او عندي دراع ويله محور وفي
+
+204
+00:25:24,190 --> 00:25:31,270
+اجراء شخص بيجري في هذا الاتجاه على بعد مثلا تلاتة
+
+205
+00:25:31,270 --> 00:25:37,130
+متر وشخص تاني بيجري باتجاه نفس السرعة ونفس الكتلة
+
+206
+00:25:37,130 --> 00:25:43,880
+بالاتجاه المعاكس بس على بعد متر تقريباالان هيجري
+
+207
+00:25:43,880 --> 00:25:47,720
+.. هيجري .. هيجري و يدفع هيكون فيله ال MV بتاعته
+
+208
+00:25:47,720 --> 00:25:52,960
+تعمل عزم المعاكس هعمل عزم عشان يصل لمرحلة الإيقاف
+
+209
+00:25:52,960 --> 00:25:59,120
+لازم عزم الشخص اللي من جهه هذه يكون تلت أضعاف
+
+210
+00:25:59,120 --> 00:26:02,320
+العزم اللي جا من هنا لأن هو عنده الإدراع أحيان
+
+211
+00:26:02,320 --> 00:26:07,440
+أصغر اللي على جهه هذه الإدراع بتاعه أطول وبالتالي
+
+212
+00:26:07,440 --> 00:26:16,190
+هذا ما يسمى بعزمالزخم الخطي او الزخم الزاوي الزخم
+
+213
+00:26:16,190 --> 00:26:23,230
+الزاوي بيكون حاصل ضرب الموقع
+
+214
+00:26:23,230 --> 00:26:30,250
+الجسم في الزخم الخطي R cross MV طبعا ويرمز له
+
+215
+00:26:30,250 --> 00:26:37,310
+بالرمز HO ال HO بيكون عمودي على المستوى المكون من
+
+216
+00:26:37,310 --> 00:26:39,490
+R و MV لأن هذا cross product
+
+217
+00:26:45,950 --> 00:26:54,470
+قيمة الزخم الزاوية HO هتكون R قيمة ال position
+
+218
+00:26:54,470 --> 00:27:03,610
+vector في ال MV في sin الزاوية بينهم sin Phi هذه
+
+219
+00:27:03,610 --> 00:27:04,470
+الزاوية بينهم
+
+220
+00:27:08,570 --> 00:27:14,690
+فعلياً بيتمثل مساحة بيتمثل مساحة متوازة أطلع إذا
+
+221
+00:27:14,690 --> 00:27:23,350
+عندي هاي متوازة أطلع أنا خدته لحاله هذا R و هذا
+
+222
+00:27:23,350 --> 00:27:30,950
+ضلع MV و هذا الزاوية إيش فاي متوازة أطلع
+
+223
+00:27:39,760 --> 00:27:44,640
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+المُثَلَث الواحد هكون القاعدة .. نُص القاعدة في
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+227
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+الأضلاع اللى هى RMV Sin Phi ال H O عموديه على
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+228
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+المستوى المكون من position vector R و ال MV يعني
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+229
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+239
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+240
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+245
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+248
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+عشانك
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+250
+00:30:43,320 --> 00:30:51,030
+ثتا Dot بيصير MR تربيع ثتا Dotممكن نستخدم المحددات
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+251
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+طالما انه .. انه MV is a vector و R is a vector
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+252
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+253
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+254
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+Z component و هذه مركبات الزخم الخط باتجاه ال X
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+255
+00:31:12,230 --> 00:31:14,730
+MVX MVY و MVZ
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+256
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+257
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+258
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+261
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+فهذه V V ك vector cross MV
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+262
+00:32:23,010 --> 00:32:29,750
+zr cross m a a ك vector اللي مركب تجاه ال radial
+
+263
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+264
+00:32:32,650 --> 00:32:38,270
+استخدمت ال polar coordinates الان v cross v أشو
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+265
+00:32:38,270 --> 00:32:44,570
+تساوي صفر لأن الخط بيكون كأنه ال vectors متلاسقين
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+266
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+271
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+272
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+
+273
+00:33:37,570 --> 00:33:44,670
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+
+274
+00:33:44,670 --> 00:33:50,010
+هو معدل التغير في الذخم الخطي احنا سابقا حكينا
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+275
+00:33:50,010 --> 00:33:51,890
+summation of forces
+
+276
+00:33:57,110 --> 00:34:05,970
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+
+277
+00:34:05,970 --> 00:34:10,210
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+
+278
+00:34:10,210 --> 00:34:16,390
+التاني لل particles مكوّن من شقين أول شق summation
+
+279
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+
+280
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+moment
+
+281
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+282
+00:34:35,940 --> 00:34:40,960
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+
+283
+00:34:40,960 --> 00:34:45,040
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+
+284
+00:34:45,040 --> 00:34:49,200
+of moments حوالين O سواء معدل التغير الزخم الزاوي
+
+285
+00:34:49,200 --> 00:34:50,740
+حوالين نقطة O
+
+286
+00:35:01,310 --> 00:35:06,610
+high particle ماشي على المصار هذا في اللحظة هذه
+
+287
+00:35:06,610 --> 00:35:16,310
+انا في عندي high v و high mv نحكي
+
+288
+00:35:16,310 --> 00:35:18,970
+ان ال cross product عبارة عن مساحة متوازن أضلاع
+
+289
+00:35:18,970 --> 00:35:22,550
+المكون لل two vectors هدول جايين two vectors
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+290
+00:35:22,550 --> 00:35:29,220
+منطبقين على بعض ايش مساحتهم متساوي؟ صفرو بعدين
+
+291
+00:35:29,220 --> 00:35:31,980
+بيحكي لك sin phi لو بدي أحكي أنا بس مش physics
+
+292
+00:35:31,980 --> 00:35:35,140
+أحكي رياضيات هتكون ال vector الأول في ال vector ..
+
+293
+00:35:35,140 --> 00:35:37,160
+قيمة ال vector الأول في ال vector التاني في ال sin
+
+294
+00:35:37,160 --> 00:35:38,820
+الزوابينهم و الزوابينهم صفر
+
+295
+00:35:58,680 --> 00:36:02,140
+يعني ممكن احكي المعنى تاني ان انا هاي الزخم بتاعي
+
+296
+00:36:02,140 --> 00:36:05,600
+بهذا الاتجاه اذا همشي في نفس الاتجاه بتاعه مش
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+297
+00:36:05,600 --> 00:36:09,660
+هستيهي الدوران اذا همشي في نفس الاتجاه السرعة مش
+
+298
+00:36:09,660 --> 00:36:15,820
+هستيهي الدوران الجزئية هذه طيب
+
+299
+00:36:25,130 --> 00:36:29,150
+ممكن احكي .. لما احسب summation of forces استخدم
+
+300
+00:36:29,150 --> 00:36:34,070
+ال radial اللي هو ال radial coordinate system هاخد
+
+301
+00:36:34,070 --> 00:36:36,990
+summation of forces بتجاه ال radial direction و
+
+302
+00:36:36,990 --> 00:36:40,710
+summation of forces بتجاه ال theta direction هتكون
+
+303
+00:36:40,710 --> 00:36:46,190
+summation of forces بتجاه ال radial بسوء m ar بسوء
+
+304
+00:36:46,190 --> 00:36:48,930
+m r w minus r theta dot تربيع و summation of
+
+305
+00:36:48,930 --> 00:36:51,830
+forces بتجاه ال theta direction بسوء m r theta
+
+306
+00:36:51,830 --> 00:36:54,270
+double dot زي اتنين r dot theta dot
+
+307
+00:36:59,800 --> 00:37:09,340
+إذا كان محصلة القوة اللى بتأثر على الجسم اتجاهها
+
+308
+00:37:09,340 --> 00:37:15,540
+أو خط عملها بيمر في مركز الإحداثيات معناته عزم هذه
+
+309
+00:37:15,540 --> 00:37:23,100
+القوة المحصلة حوالين O أشهر ساوية صفريعني احنا
+
+310
+00:37:23,100 --> 00:37:26,140
+الحالة لو عندنا سطح حلو كانت المحصلة الكوية اللي
+
+311
+00:37:26,140 --> 00:37:33,840
+بتأثر على جسم محصلة خط عملها بمر في O معناه moment
+
+312
+00:37:33,840 --> 00:37:38,020
+حوالي O هتكون إيش ساوي؟ Zero يعني إذا كانت ال M O
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+313
+00:37:38,020 --> 00:37:47,900
+بالساوية Zero بالساوية DHO by DT إذا ال
+
+314
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+differential بالساوية Zero معناه ال H O إيش
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+315
+00:37:50,680 --> 00:37:51,280
+بالساوية؟
+
+316
+00:37:54,820 --> 00:38:02,260
+constant يعني الزخم الزاوي is conserved زخم الزاوي
+
+317
+00:38:02,260 --> 00:38:06,960
+is conserved اتطلعوا على اليوتيوب امثلة على ال
+
+318
+00:38:06,960 --> 00:38:10,580
+angular momentum هتشوفوا حالات بتبين conservation
+
+319
+00:38:10,580 --> 00:38:14,690
+of angular momentumيعني مثلا هتشوفوا أحد
+
+320
+00:38:14,690 --> 00:38:22,430
+الفيديوهات في سفينة فضاء شخص بيكون بيلف يصير له
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+321
+00:38:22,430 --> 00:38:29,210
+rotation لأن بيفرد إيديه زي هيك سرعته تبطأ بضم
+
+322
+00:38:29,210 --> 00:38:34,370
+حاله زي هيك سرعته بزيه يصير لف أسرع هذا جاي من ال
+
+323
+00:38:34,370 --> 00:38:37,930
+conservation of angular momentum تطلعوا على
+
+324
+00:38:37,930 --> 00:38:40,870
+اليوتيوب على بفتح بس تكتب conservation of angular
+
+325
+00:38:40,870 --> 00:38:42,330
+momentum هتشوف فيديوهات كتير
+
+326
+00:38:56,190 --> 00:39:01,810
+أه طبعا لاحظ ان هو بيحاول انه يقلل حجمه .. يقلل
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+327
+00:39:01,810 --> 00:39:07,450
+حجمه و يخلي تدفق الهواء انسيابي بتفريج كتير مع ..
+
+328
+00:39:07,450 --> 00:39:10,650
+في فيديو برضه موجود على اليوتيوب لهذا المثال بس
+
+329
+00:39:10,650 --> 00:39:14,850
+كانت .. بس هذا بتحكي علشان اللي هو مقامة الهواء
+
+330
+00:39:21,580 --> 00:39:26,460
+صحيح طيب إذا
+
+331
+00:39:26,460 --> 00:39:30,740
+كانت ال conservation of angular momentum لجسم
+
+332
+00:39:30,740 --> 00:39:35,480
+بتحرك على هذا المصار و خد في اللحظة لما كان عند P
+
+333
+00:39:35,480 --> 00:39:41,720
+O و حالة لما كان عند Pو ال forces are always
+
+334
+00:39:41,720 --> 00:39:45,240
+central محاصرة القوة بتأثر باتجاه ال central O
+
+335
+00:39:45,240 --> 00:39:48,200
+معناته بيكون عندك conservation of angular momentum
+
+336
+00:39:48,200 --> 00:39:56,040
+معناته HO هتكون تستوى H عند O بتستوى H .. H عند PO
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+337
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+بتستوى H عند P معناته هيكون عند RMV sin Phi هيها
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+338
+00:40:03,280 --> 00:40:03,900
+هذه Phi
+
+339
+00:40:06,640 --> 00:40:12,480
+هتساوي R نود M V نود سين فاي هتروح ال M مع ال M او
+
+340
+00:40:12,480 --> 00:40:16,200
+ممكن احكي ال H O بيساوي M R Square تتا دوت اذا
+
+341
+00:40:16,200 --> 00:40:21,860
+قسمت على M ال M is constant بيسرندي R Square تتا
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+342
+00:40:21,860 --> 00:40:26,700
+دوت بيساوي ايش constant اللي بيساوي H small H
+
+343
+00:40:26,700 --> 00:40:29,900
+small هي ال angular momentum الزخم الزاوي لكل وحدة
+
+344
+00:40:29,900 --> 00:40:33,460
+كتلة جاي
+
+345
+00:40:33,460 --> 00:40:34,040
+سؤال؟
+
+346
+00:40:36,830 --> 00:40:40,350
+نتعرف علشان جديد اللي هو Newton's law of
+
+347
+00:40:40,350 --> 00:40:46,650
+gravitation ال force of gravitation بنشوفه في حالة
+
+348
+00:40:46,650 --> 00:40:50,630
+الأجسام بتدور حوالين يعني كتلة صغيرة بتدور حوالين
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+349
+00:40:50,630 --> 00:40:56,770
+كتلة كبيرة يعني مثال دوران الكواكب حوالين الشمس أو
+
+350
+00:40:56,770 --> 00:41:00,950
+حتى دوران الأقمار الصناعية حوالين الأرض بيكون هذه
+
+351
+00:41:00,950 --> 00:41:04,070
+الأجسام تحت أثير قوة مركزية
+
+352
+00:41:06,820 --> 00:41:10,960
+الان اذا عندك جسمين جسم كتلته M capital جسم كتلته
+
+353
+00:41:10,960 --> 00:41:16,440
+M small والمسافة بينهم R كل واحد من الجسمين بيأثر
+
+354
+00:41:16,440 --> 00:41:25,170
+على الآخر بقوة F minus Fالقوة هذه قيمتها تُعطى
+
+355
+00:41:25,170 --> 00:41:28,730
+بالعلاقة F بساوية G في M capital M small على R
+
+356
+00:41:28,730 --> 00:41:32,690
+square الـ G اللي هي constant of gravitation اللي
+
+357
+00:41:32,690 --> 00:41:38,070
+هو بساوية 66.73×10-12 متر مكعب على kilogram second
+
+358
+00:41:38,070 --> 00:41:43,190
+square هذا الـ Newton's law of gravitation، تشوف
+
+359
+00:41:43,190 --> 00:41:51,860
+مثلًا الـ G is constant، universalاللي بتتغير ال G
+
+360
+00:41:51,860 --> 00:41:56,360
+is universal constant ال G small بتتغير من كوكبه
+
+361
+00:41:56,360 --> 00:42:08,260
+لكوكبه يعني ال G هي universal constant ال
+
+362
+00:42:08,260 --> 00:42:15,240
+G small يعني ال changes يعني يعني on the moon على
+
+363
+00:42:15,240 --> 00:42:24,320
+القمرis different than earth يعني مختلفة عن الأرض
+
+364
+00:42:24,320 --> 00:42:28,860
+مختلفة عن الزحل مختلفة عن الظهرة مختلفة عن كوكب لا
+
+365
+00:42:28,860 --> 00:42:33,660
+كوبة ال G small لكن ال G ال G يعني عندي على الأرض
+
+366
+00:42:33,660 --> 00:42:40,040
+لو كان عندي جسم على الأرض هاي الكرة الأرضية وعندي
+
+367
+00:42:40,040 --> 00:42:47,320
+جسم عليها وهي مركز الأرض والمسافة هذه R capital
+
+368
+00:42:48,120 --> 00:42:54,240
+حكينا أننا سنأثر بعض بـ Forces F و Minus F الـ F
+
+369
+00:42:54,240 --> 00:43:01,720
+هتكون في الحالة هذه وزن الجسم اللي هي M في G بستوي
+
+370
+00:43:01,720 --> 00:43:11,820
+M Small M Capital على R تربيع في جهزم جهزم جهزم
+
+371
+00:43:11,820 --> 00:43:16,460
+جهزم جهزم جهزم حيروح عندي M مع M هتكون عندي G
+
+372
+00:43:17,920 --> 00:43:24,980
+بيساوة M G على R square ال R بتاعة الأرض ال M
+
+373
+00:43:24,980 --> 00:43:27,700
+بتاعة الأرض احنا عارفينها و ال G بتاعة الأرض
+
+374
+00:43:27,700 --> 00:43:31,440
+عارفينها و ال R عارفينها بنحسب ال gravitation
+
+375
+00:43:31,440 --> 00:43:36,500
+constant للكولة الأرضية G على فرض انه الكولة
+
+376
+00:43:36,500 --> 00:43:37,400
+الأرضية كرة
+
+377
+00:43:51,170 --> 00:44:02,330
+نشوف مثال طيب
+
+378
+00:44:02,330 --> 00:44:09,610
+a block B هذا block of mass M كتلة M can slide
+
+379
+00:44:09,610 --> 00:44:15,120
+freely on a frictionless arm OAالـ Block B ممكن
+
+380
+00:44:15,120 --> 00:44:20,480
+ينزلك بدون احتكاك على الإدراع OA which rotates in
+
+381
+00:44:20,480 --> 00:44:23,620
+a horizontal plane at a constant rate θ dot
+
+382
+00:44:23,620 --> 00:44:29,220
+الإدراع هذا بدور في المستوى الأفقي بدور بالشكل هذا
+
+383
+00:44:29,220 --> 00:44:34,980
+مش في الرأس يعني الوزن جاي عمودي على الصفحة مش
+
+384
+00:44:34,980 --> 00:44:43,830
+لتحت بدور بمعدل ثابت سرعة زاوية θ dot constantB is
+
+385
+00:44:43,830 --> 00:44:51,170
+released at the distance RO from O تم إطلاق B كان
+
+386
+00:44:51,170 --> 00:44:58,810
+مثلا ممسوك بالخيط و فجأه عملت cut express
+
+387
+00:44:58,810 --> 00:45:03,950
+as a function of R the component of VR of the
+
+388
+00:45:03,950 --> 00:45:11,950
+velocity of B along OA نحسب VR نحسب VR
+
+389
+00:45:13,920 --> 00:45:16,280
+عشان احنا مثلا اذاك لازم نعمل free body diagram
+
+390
+00:45:16,280 --> 00:45:23,820
+هاي الجسم طبعا
+
+391
+00:45:23,820 --> 00:45:28,840
+هاخد المستوى الصفحى اللى هو بمثل المستوى الأفقي
+
+392
+00:45:28,840 --> 00:45:32,400
+الوزن هكون عمودي على الصفحى مش هبين اندي في ال
+
+393
+00:45:32,400 --> 00:45:39,200
+free body diagram يعني الوزن هكون لجوه طيب
+
+394
+00:45:42,000 --> 00:45:45,160
+هو هكالي frictionless فش احتكاك معناه بس فى عندى
+
+395
+00:45:45,160 --> 00:45:50,420
+normal force اذا هو بدور بهذا الاتجاه هيكون عندى
+
+396
+00:45:50,420 --> 00:45:56,320
+high normal force هذا
+
+397
+00:45:56,320 --> 00:46:01,920
+الزاوية ثتا
+
+398
+00:46:01,920 --> 00:46:05,280
+انا
+
+399
+00:46:05,280 --> 00:46:11,540
+باخد ال block B ال block B هيكون له
+
+400
+00:46:14,920 --> 00:46:23,460
+مركبتين هستخدم ريدال كواردينيتز هتكون عند MAR
+
+401
+00:46:23,460 --> 00:46:26,680
+و
+
+402
+00:46:26,680 --> 00:46:40,960
+MAθ و المحاور تاعته هد ER و هد Eθ
+
+403
+00:46:42,510 --> 00:46:49,250
+هي كانت رسمت free pedagram بالكامل اللي
+
+404
+00:46:49,250 --> 00:46:53,690
+انا أخدته تجاه ال radial direction submission لل
+
+405
+00:46:53,690 --> 00:47:03,810
+forces على أي حال ال AR تجاهه بالعكس
+
+406
+00:47:03,810 --> 00:47:08,530
+نعم
+
+407
+00:47:10,260 --> 00:47:12,800
+ممكن تكون في هذه الاتجاه و في هذا الاتجاه
+
+408
+00:47:12,800 --> 00:47:24,720
+summation لل F R بالسوء M A R و أنا عندي هيكون هذه
+
+409
+00:47:24,720 --> 00:47:28,340
+اتجاه الموجب
+
+410
+00:47:28,340 --> 00:47:44,730
+في فرصة اتجاه ال E R مافيش سفر بالسوء Mفى AR R
+
+411
+00:47:44,730 --> 00:47:49,510
+Double Dot Minus
+
+412
+00:47:49,510 --> 00:47:54,830
+R Theta Dot تربيع يعني حسينا ان دي R Double Dot
+
+413
+00:47:54,830 --> 00:47:59,510
+Minus R Theta Dot تربيع بيستوي سفر يعني هيكون ان
+
+414
+00:47:59,510 --> 00:48:10,440
+دي ال R Double Dot عبارة عن D By Dt لR Dotاللي هي
+
+415
+00:48:10,440 --> 00:48:19,380
+VR minus R theta dot تربيع بتساوي سفر يعني هتكون
+
+416
+00:48:19,380 --> 00:48:36,720
+عند D VR by DT بتساوي R theta dot تربيع لأ
+
+417
+00:48:36,720 --> 00:48:42,040
+نعمacceleration ده كنستان تزايده في R كمان مرة ال
+
+418
+00:48:42,040 --> 00:48:51,280
+AR ضمن كنستان؟ لأ ال .. ال AR زيرو ال M لإن مافيش
+
+419
+00:48:51,280 --> 00:48:56,580
+عندي friction هان تمام عشان انا اتزاوج ال VR هي ال
+
+420
+00:48:56,580 --> 00:49:04,040
+R ثيتا دوت تربية كنستان كمان .. ايوة اتفضل ال R
+
+421
+00:49:04,040 --> 00:49:09,530
+ثيتا دوت تربية كنستانأيوة صحيح هدي constant لأ ال
+
+422
+00:49:09,530 --> 00:49:15,270
+R مش constant ال R مش constant لأن أنا جبتها على
+
+423
+00:49:15,270 --> 00:49:20,490
+جهة التانية انا كان عندي DVR by DT minus R to the
+
+424
+00:49:20,490 --> 00:49:23,510
+dot التربيع بالسوء صفر جبت R to the dot التربيع
+
+425
+00:49:23,510 --> 00:49:28,950
+على جهة التانية صارت موجة لأن انا هضرب في DR على
+
+426
+00:49:28,950 --> 00:49:46,180
+DR يعني هسير عندي DVR by DRدر با دي تي ايش
+
+427
+00:49:46,180 --> 00:49:52,700
+هي VR دي
+
+428
+00:49:52,700 --> 00:50:00,700
+VR با دي R ثتا Dot تربيع
+
+429
+00:50:03,390 --> 00:50:12,750
+هعمل فصل للمتغيرات حضر الطرفين VR DVR
+
+430
+00:50:12,750 --> 00:50:16,450
+بالساوية
+
+431
+00:50:16,450 --> 00:50:28,390
+R theta node dot تربيع DR هعمل تكامل R node to any
+
+432
+00:50:28,390 --> 00:50:35,120
+Rوهنا هو احنا بدنا ال VR كانت في البداية صفر من
+
+433
+00:50:35,120 --> 00:50:46,340
+صفر ل VR يعني هكون عندي VR تربيع على اتنين بتساوي
+
+434
+00:50:46,340 --> 00:50:55,120
+θ تحكم constant في
+
+435
+00:50:55,120 --> 00:51:03,590
+R تربيععلى اتنين من R node ل R حيروح تحسين عندي VR
+
+436
+00:51:03,590 --> 00:51:14,630
+تربيع هتكون theta node تربيع في R تربيع minus R
+
+437
+00:51:14,630 --> 00:51:22,720
+node تربيع يعني VRهتكون theta ند dot جزر التربيع
+
+438
+00:51:22,720 --> 00:51:33,040
+لR تربيع minus R ند تربيع هذا VR المطلوب
+
+439
+00:51:33,040 --> 00:51:38,400
+التاني طلب the magnitude of the horizontal force
+
+440
+00:51:38,400 --> 00:51:46,120
+exerted on B by the arm OA اللي هو بده N معناته
+
+441
+00:51:48,220 --> 00:51:54,520
+معنى التحقق summation of forces باتجاه الـθيتا
+
+442
+00:51:54,520 --> 00:52:01,360
+سواء M A ثيتا تجاه
+
+443
+00:52:01,360 --> 00:52:09,280
+الثيتا ستكون عندي ايش N مستوى M A ثيتا اللي هي R
+
+444
+00:52:09,280 --> 00:52:20,070
+ثيتا double dot زائد اتنين R dottheta dot لما
+
+445
+00:52:20,070 --> 00:52:25,010
+حكينا theta dot ايش الساوية ساوية
+
+446
+00:52:25,010 --> 00:52:29,670
+constant صح؟ معنى ال theta دول دوت ايش الساوية سفر
+
+447
+00:52:29,670 --> 00:52:42,170
+ستكون معناته اتنين ام ار دوت ايش هي VR في ال theta
+
+448
+00:52:42,170 --> 00:52:49,460
+dot يعني هتكون اتنين امtheta dot حضره في VR التي
+
+449
+00:52:49,460 --> 00:53:09,720
+هي theta dot جزر التربية ايه ل R تربية في
+
+450
+00:53:09,720 --> 00:53:10,180
+اي سؤال
+
+451
+00:53:15,180 --> 00:53:15,920
+أعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/jP6MQ-ZzAbE_raw.json b/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/jP6MQ-ZzAbE_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..35ccedfb346fe8ee986dd1abc5173958e7d14ab5
--- /dev/null
+++ b/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/jP6MQ-ZzAbE_raw.json
@@ -0,0 +1 @@
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"probability": 0.783203125}, {"start": 179.79, "end": 179.93, "word": " في", "probability": 0.56005859375}, {"start": 179.93, "end": 180.27, "word": " الحالة", "probability": 0.9772135416666666}, {"start": 180.27, "end": 180.41, "word": " هذه", "probability": 0.413818359375}, {"start": 180.41, "end": 180.83, "word": " بتكون", "probability": 0.957275390625}, {"start": 180.83, "end": 181.59, "word": " ال", "probability": 0.72900390625}, {"start": 181.59, "end": 181.83, "word": " theta", "probability": 0.5166015625}, {"start": 181.83, "end": 182.29, "word": " بيستوى", "probability": 0.9177734375}, {"start": 182.29, "end": 182.57, "word": " theta", "probability": 0.5263671875}, {"start": 182.57, "end": 182.81, "word": " not", "probability": 0.634765625}, {"start": 182.81, "end": 183.23, "word": " زاد", "probability": 0.6376953125}, {"start": 183.23, "end": 183.67, "word": " omega", "probability": 0.7333984375}, {"start": 183.67, "end": 184.21, "word": " في", "probability": 0.86865234375}, 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"probability": 0.8583984375}, {"start": 818.04, "end": 820.74, "word": " هتكون", "probability": 0.9308268229166666}, {"start": 820.74, "end": 821.18, "word": " سرعة", "probability": 0.9371744791666666}, {"start": 821.18, "end": 821.68, "word": " الدوران", "probability": 0.9671223958333334}, {"start": 821.68, "end": 822.08, "word": " Omega", "probability": 0.5732421875}, {"start": 822.08, "end": 823.52, "word": " cross", "probability": 0.77490234375}, {"start": 823.52, "end": 826.48, "word": " RBA", "probability": 0.76416015625}, {"start": 826.48, "end": 828.72, "word": " يعني", "probability": 0.870361328125}, {"start": 828.72, "end": 830.38, "word": " VB", "probability": 0.91796875}, {"start": 830.38, "end": 831.66, "word": " السرعة", "probability": 0.8523763020833334}, {"start": 831.66, "end": 832.32, "word": " الكلية", "probability": 0.7698567708333334}, {"start": 832.32, "end": 833.56, "word": " هتكون", "probability": 0.9611002604166666}, {"start": 833.56, "end": 834.12, "word": " تساوي", "probability": 0.84912109375}, {"start": 834.12, "end": 835.4, "word": " VA", "probability": 0.5693359375}, {"start": 835.4, "end": 836.94, "word": " زائد", "probability": 0.6707356770833334}, {"start": 836.94, "end": 837.06, "word": " اللي", "probability": 0.577392578125}, {"start": 837.06, "end": 837.2, "word": " هي", "probability": 0.8740234375}, {"start": 837.2, "end": 837.62, "word": " VBA", "probability": 0.9267578125}, {"start": 837.62, "end": 837.78, "word": " اللي", "probability": 0.93603515625}, {"start": 837.78, "end": 837.9, "word": " هي", "probability": 0.8916015625}, {"start": 837.9, "end": 838.26, "word": " Omega", "probability": 0.84326171875}, {"start": 838.26, "end": 839.9, "word": " cross", "probability": 0.89208984375}, {"start": 839.9, "end": 842.1, "word": " RBA", "probability": 0.956298828125}], "temperature": 1.0}, {"id": 33, "seek": 87274, "start": 849.72, "end": 872.74, "text": "طبعا الجسم لو كان بدور حوالين A هذا محور الدوران معناته VBA هتكون عمودية على الخط الواصل بين A وB يعني هذه زي وإيش تسعين درجة يعني لو عم بدي أعملها ع شكل .. ع شكل vector هذه VA", "tokens": [9566, 3555, 3615, 995, 25724, 38251, 45164, 25961, 47525, 13063, 11331, 2407, 6027, 9957, 316, 23758, 3714, 5016, 13063, 32748, 13063, 7649, 20449, 8315, 47395, 691, 9295, 8032, 2655, 30544, 6225, 2304, 2407, 16254, 3660, 15844, 33962, 9566, 2423, 2407, 33546, 1211, 49374, 316, 4032, 33, 37495, 22653, 29538, 30767, 1829, 4032, 28814, 1829, 8592, 6055, 3794, 3615, 9957, 11778, 47341, 3660, 37495, 22653, 45164, 6225, 2304, 4724, 16254, 5551, 25957, 1211, 11296, 6225, 13412, 28820, 4386, 6225, 13412, 28820, 8062, 29538, 18527], "avg_logprob": -0.25223213576135184, "compression_ratio": 1.6021505376344085, "no_speech_prob": 0.0, "words": [{"start": 849.72, "end": 850.64, "word": "طبعا", "probability": 0.9676513671875}, {"start": 850.64, "end": 851.56, "word": " الجسم", "probability": 0.915283203125}, {"start": 851.56, "end": 852.28, "word": " لو", "probability": 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860.48, "end": 861.78, "word": " الخط", "probability": 0.979248046875}, {"start": 861.78, "end": 862.34, "word": " الواصل", "probability": 0.9326171875}, {"start": 862.34, "end": 862.64, "word": " بين", "probability": 0.88134765625}, {"start": 862.64, "end": 862.8, "word": " A", "probability": 0.9521484375}, {"start": 862.8, "end": 863.1, "word": " وB", "probability": 0.7161865234375}, {"start": 863.1, "end": 863.52, "word": " يعني", "probability": 0.85400390625}, {"start": 863.52, "end": 863.68, "word": " هذه", "probability": 0.383056640625}, {"start": 863.68, "end": 863.84, "word": " زي", "probability": 0.90478515625}, {"start": 863.84, "end": 864.26, "word": " وإيش", "probability": 0.610595703125}, {"start": 864.26, "end": 865.54, "word": " تسعين", "probability": 0.82757568359375}, {"start": 865.54, "end": 866.0, "word": " درجة", "probability": 0.99560546875}, {"start": 866.0, "end": 868.7, "word": " يعني", "probability": 0.919921875}, {"start": 868.7, "end": 868.84, "word": " لو", "probability": 0.84619140625}, {"start": 868.84, "end": 869.0, "word": " عم", "probability": 0.82275390625}, {"start": 869.0, "end": 869.1, "word": " بدي", "probability": 0.28497314453125}, {"start": 869.1, "end": 869.34, "word": " أعملها", "probability": 0.9036865234375}, {"start": 869.34, "end": 869.46, "word": " ع", "probability": 0.45361328125}, {"start": 869.46, "end": 869.82, "word": " شكل", "probability": 0.862060546875}, {"start": 869.82, "end": 869.98, "word": " ..", "probability": 0.321533203125}, {"start": 869.98, "end": 870.22, "word": " ع", "probability": 0.7626953125}, {"start": 870.22, "end": 870.54, "word": " شكل", "probability": 0.9658203125}, {"start": 870.54, "end": 871.04, "word": " vector", "probability": 0.85791015625}, {"start": 871.04, "end": 872.28, "word": " هذه", "probability": 0.70849609375}, {"start": 872.28, "end": 872.74, "word": " VA", "probability": 0.6923828125}], "temperature": 1.0}, {"id": 34, "seek": 89763, "start": 880.01, "end": 897.63, "text": "و هاد VBA هي اللي هي دموها زي هاد VBA و احنا حكينا VB بصوة VA زي VBA معناته هاد هيكون VB", "tokens": [2407, 8032, 18513, 691, 9295, 39896, 13672, 1829, 39896, 11778, 2304, 2407, 11296, 30767, 1829, 8032, 18513, 691, 9295, 4032, 1975, 5016, 8315, 11331, 4117, 1829, 8315, 691, 33, 4724, 9381, 2407, 3660, 18527, 30767, 1829, 691, 9295, 20449, 8315, 47395, 8032, 18513, 39896, 30544, 691, 33], "avg_logprob": -0.34114583643774193, "compression_ratio": 1.4285714285714286, "no_speech_prob": 0.0, "words": [{"start": 880.01, "end": 880.27, "word": "و", "probability": 0.91162109375}, {"start": 880.27, "end": 880.61, "word": " هاد", "probability": 0.26348876953125}, {"start": 880.61, "end": 881.43, "word": " VBA", "probability": 0.688720703125}, {"start": 881.43, "end": 881.75, "word": " هي", "probability": 0.72900390625}, {"start": 881.75, "end": 881.83, "word": " اللي", "probability": 0.806640625}, {"start": 881.83, "end": 881.93, "word": " هي", "probability": 0.6748046875}, {"start": 881.93, 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"probability": 0.8248697916666666}, {"start": 891.55, "end": 891.73, "word": " هاد", "probability": 0.892822265625}, {"start": 891.73, "end": 892.21, "word": " هيكون", "probability": 0.739013671875}, {"start": 892.21, "end": 897.63, "word": " VB", "probability": 0.906005859375}], "temperature": 1.0}, {"id": 35, "seek": 91580, "start": 905.98, "end": 915.8, "text": "وعرفنا we define VBA بالـ cross product لسرعة الزاوية مع ال RBA ال RBA هي المسافة الواصلة بين نقطة A و نقطة B", "tokens": [2407, 3615, 28480, 8315, 321, 6964, 691, 9295, 20666, 39184, 3278, 1674, 5296, 3794, 2288, 27884, 6024, 110, 995, 2407, 10632, 20449, 2423, 497, 9295, 2423, 497, 9295, 39896, 9673, 3794, 31845, 3660, 2423, 2407, 33546, 37977, 49374, 8717, 47432, 3660, 316, 4032, 8717, 47432, 3660, 363], "avg_logprob": -0.19628906281044087, "compression_ratio": 1.2692307692307692, "no_speech_prob": 0.0, "words": [{"start": 905.98, "end": 906.56, "word": "وعرفنا", "probability": 0.7127685546875}, {"start": 906.56, "end": 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"probability": 0.904541015625}, {"start": 912.88, "end": 913.18, "word": " هي", "probability": 0.90771484375}, {"start": 913.18, "end": 913.74, "word": " المسافة", "probability": 0.97705078125}, {"start": 913.74, "end": 914.08, "word": " الواصلة", "probability": 0.9095458984375}, {"start": 914.08, "end": 914.24, "word": " بين", "probability": 0.91650390625}, {"start": 914.24, "end": 914.62, "word": " نقطة", "probability": 0.9879557291666666}, {"start": 914.62, "end": 914.78, "word": " A", "probability": 0.912109375}, {"start": 914.78, "end": 914.9, "word": " و", "probability": 0.97509765625}, {"start": 914.9, "end": 915.38, "word": " نقطة", "probability": 0.8624674479166666}, {"start": 915.38, "end": 915.8, "word": " B", "probability": 0.98388671875}], "temperature": 1.0}, {"id": 36, "seek": 96675, "start": 938.99, "end": 966.75, "text": "طيب .. انا عندى هنا رد .. رد ab موصول بطرف ب block بتحرك اتجاه الأفقي و block بتحرك عن بيه في اتجاه الرأسي", "tokens": [9566, 1829, 3555, 4386, 1975, 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"word": " رد", "probability": 0.986328125}, {"start": 951.39, "end": 951.83, "word": " ab", "probability": 0.185546875}, {"start": 951.83, "end": 958.93, "word": " موصول", "probability": 0.9393310546875}, {"start": 958.93, "end": 959.45, "word": " بطرف", "probability": 0.9388020833333334}, {"start": 959.45, "end": 959.91, "word": " ب", "probability": 0.9755859375}, {"start": 959.91, "end": 960.35, "word": " block", "probability": 0.46875}, {"start": 960.35, "end": 962.33, "word": " بتحرك", "probability": 0.9485677083333334}, {"start": 962.33, "end": 962.61, "word": " اتجاه", "probability": 0.8358154296875}, {"start": 962.61, "end": 963.05, "word": " الأفقي", "probability": 0.75390625}, {"start": 963.05, "end": 964.03, "word": " و", "probability": 0.85546875}, {"start": 964.03, "end": 964.31, "word": " block", "probability": 0.9482421875}, {"start": 964.31, "end": 964.91, "word": " بتحرك", "probability": 0.9733072916666666}, {"start": 964.91, "end": 965.21, "word": " عن", "probability": 0.39599609375}, {"start": 965.21, "end": 965.49, "word": " بيه", "probability": 0.6608072916666666}, {"start": 965.49, "end": 965.61, "word": " في", "probability": 0.435302734375}, {"start": 965.61, "end": 965.99, "word": " اتجاه", "probability": 0.973876953125}, {"start": 965.99, "end": 966.75, "word": " الرأسي", "probability": 0.947509765625}], "temperature": 1.0}, {"id": 37, "seek": 98868, "start": 967.66, "end": 988.68, "text": "Va هيكون هذه اتجاهها و Vb أكيد هيكون نفسي لتحت هاي Vb لحظة Va على الأقل اتجاه Va بيستويش اتجاه Vb معناته الجسم", "tokens": [53, 64, 39896, 30544, 29538, 1975, 2655, 7435, 40294, 11296, 4032, 691, 65, 5551, 4117, 25708, 39896, 30544, 8717, 36178, 1829, 5296, 2655, 33753, 8032, 47302, 691, 65, 5296, 5016, 19913, 3660, 16822, 15844, 16247, 4587, 1211, 1975, 2655, 7435, 40294, 16822, 4724, 1829, 14851, 45865, 8592, 1975, 2655, 7435, 40294, 691, 65, 20449, 8315, 47395, 25724, 38251], "avg_logprob": -0.2538400373216403, "compression_ratio": 1.5, "no_speech_prob": 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عبارة عن Omega في المسافة هدى RBA اللي هي L", "tokens": [40228, 22653, 691, 9295, 4724, 1829, 3794, 995, 45865, 18527, 7603, 9725, 4032, 39319, 8315, 6225, 9640, 5172, 9957, 691, 9295, 6225, 3555, 9640, 3660, 18871, 27645, 8978, 9673, 3794, 31845, 3660, 8032, 3215, 7578, 497, 9295, 13672, 1829, 39896, 441], "avg_logprob": -0.2780877869753611, "compression_ratio": 1.1440677966101696, "no_speech_prob": 0.0, "words": [{"start": 1138.39, "end": 1138.87, "word": "يعني", "probability": 0.85009765625}, {"start": 1138.87, "end": 1139.59, "word": " VBA", "probability": 0.792236328125}, {"start": 1139.59, "end": 1142.13, "word": " بيساوي", "probability": 0.4912109375}, {"start": 1142.13, "end": 1142.75, "word": " VA", "probability": 0.427490234375}, {"start": 1142.75, "end": 1144.35, "word": " tan", "probability": 0.650390625}, {"start": 1144.35, "end": 1144.83, "word": " theta", "probability": 0.21875}, {"start": 1144.83, "end": 1148.43, "word": " واحنا", "probability": 0.699462890625}, {"start": 1148.43, "end": 1148.91, "word": " عارفين", "probability": 0.990234375}, {"start": 1148.91, "end": 1150.63, "word": " VBA", "probability": 0.852294921875}, {"start": 1150.63, "end": 1151.01, "word": " عبارة", "probability": 0.9302978515625}, {"start": 1151.01, "end": 1151.11, "word": " عن", "probability": 0.994140625}, {"start": 1151.11, "end": 1151.53, "word": " Omega", "probability": 0.59033203125}, {"start": 1151.53, "end": 1155.31, "word": " في", "probability": 0.953125}, {"start": 1155.31, "end": 1157.73, "word": " المسافة", "probability": 0.97705078125}, {"start": 1157.73, "end": 1158.15, "word": " هدى", "probability": 0.611572265625}, {"start": 1158.15, "end": 1159.45, "word": " RBA", "probability": 0.8134765625}, {"start": 1159.45, "end": 1160.31, "word": " اللي", "probability": 0.87255859375}, {"start": 1160.31, "end": 1160.55, "word": " هي", "probability": 0.8525390625}, {"start": 1160.55, "end": 1160.89, "word": " L", "probability": 0.81787109375}], "temperature": 1.0}, {"id": 44, "seek": 119073, "start": 1163.19, "end": 1190.73, "text": "بيستوى VA tan θ يعني omega السرعه الزاوية هتكون VA على ال tan θ و VB انا غلطان على الفكرة هنا", "tokens": [3555, 1829, 14851, 2407, 7578, 18527, 7603, 12622, 37495, 22653, 10498, 21136, 2288, 3615, 3224, 6024, 110, 995, 2407, 10632, 8032, 2655, 30544, 18527, 15844, 2423, 7603, 12622, 4032, 691, 33, 1975, 8315, 32771, 1211, 9566, 7649, 15844, 27188, 4117, 25720, 34105], "avg_logprob": -0.3361191846603571, "compression_ratio": 1.2956521739130435, "no_speech_prob": 0.0, "words": [{"start": 1163.19, "end": 1163.71, "word": "بيستوى", "probability": 0.52265625}, {"start": 1163.71, "end": 1164.31, "word": " VA", "probability": 0.468505859375}, {"start": 1164.31, "end": 1165.77, "word": " tan", "probability": 0.63671875}, {"start": 1165.77, "end": 1166.87, "word": " θ", "probability": 0.587890625}, {"start": 1166.87, "end": 1167.89, "word": " يعني", "probability": 0.814453125}, {"start": 1167.89, "end": 1168.29, 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غلطان", "probability": 0.973876953125}, {"start": 1190.03, "end": 1190.15, "word": " على", "probability": 0.64599609375}, {"start": 1190.15, "end": 1190.45, "word": " الفكرة", "probability": 0.8271484375}, {"start": 1190.45, "end": 1190.73, "word": " هنا", "probability": 0.73388671875}], "temperature": 1.0}, {"id": 45, "seek": 122138, "start": 1193.08, "end": 1221.38, "text": "هذا VB وهذا VBA هنا نصلح تان ثيتا بالساوية VB على VA يعني VB بالساوية VA تان ثيتا هذه قيمة VB", "tokens": [3224, 15730, 691, 33, 37037, 15730, 691, 9295, 34105, 8717, 9381, 1211, 5016, 6055, 7649, 38637, 36081, 995, 20666, 3794, 995, 2407, 10632, 691, 33, 15844, 18527, 37495, 22653, 691, 33, 20666, 3794, 995, 2407, 10632, 18527, 6055, 7649, 38637, 36081, 995, 29538, 12174, 32640, 3660, 691, 33], "avg_logprob": -0.35299744897959184, "compression_ratio": 1.5252525252525253, "no_speech_prob": 0.0, "words": [{"start": 1193.08, "end": 1193.48, "word": "هذا", "probability": 0.7138671875}, {"start": 1193.48, "end": 1194.0, "word": " VB", "probability": 0.546142578125}, {"start": 1194.0, "end": 1197.36, "word": " وهذا", "probability": 0.798828125}, {"start": 1197.36, "end": 1198.2, "word": " VBA", "probability": 0.96044921875}, {"start": 1198.2, "end": 1200.86, "word": " هنا", "probability": 0.2364501953125}, {"start": 1200.86, "end": 1202.64, "word": " نصلح", "probability": 0.71063232421875}, {"start": 1202.64, "end": 1205.98, "word": " تان", "probability": 0.48065185546875}, {"start": 1205.98, "end": 1206.38, "word": " ثيتا", "probability": 0.613525390625}, {"start": 1206.38, "end": 1207.14, "word": " بالساوية", "probability": 0.6040771484375}, {"start": 1207.14, "end": 1210.32, "word": " VB", "probability": 0.9326171875}, {"start": 1210.32, "end": 1211.86, "word": " على", "probability": 0.5625}, {"start": 1211.86, "end": 1212.64, "word": " VA", "probability": 0.82470703125}, {"start": 1212.64, "end": 1213.86, "word": " يعني", "probability": 0.8408203125}, {"start": 1213.86, "end": 1214.52, "word": " VB", "probability": 0.960205078125}, {"start": 1214.52, "end": 1216.46, "word": " بالساوية", "probability": 0.868115234375}, {"start": 1216.46, "end": 1217.06, "word": " VA", "probability": 0.91015625}, {"start": 1217.06, "end": 1218.78, "word": " تان", "probability": 0.7095947265625}, {"start": 1218.78, "end": 1219.28, "word": " ثيتا", "probability": 0.875}, {"start": 1219.28, "end": 1220.6, "word": " هذه", "probability": 0.362548828125}, {"start": 1220.6, "end": 1220.98, "word": " قيمة", "probability": 0.9627278645833334}, {"start": 1220.98, "end": 1221.38, "word": " VB", "probability": 0.7220458984375}], "temperature": 1.0}, {"id": 46, "seek": 124985, "start": 1222.56, "end": 1249.86, "text": "و في عندي برضه cosine theta بساوة VA على VBA معناته VBA بساوة VA على cosine theta", "tokens": [2407, 8978, 18871, 16254, 4724, 43042, 3224, 23565, 9725, 4724, 3794, 995, 2407, 3660, 18527, 15844, 691, 9295, 20449, 8315, 47395, 691, 9295, 4724, 3794, 995, 2407, 3660, 18527, 15844, 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" connecting", "probability": 0.95361328125}, {"start": 2258.93, "end": 2259.25, "word": " rod", "probability": 0.57470703125}, {"start": 2259.25, "end": 2259.77, "word": " PD", "probability": 0.44921875}], "temperature": 1.0}, {"id": 82, "seek": 228806, "start": 2264.22, "end": 2288.06, "text": "study the connecting rod BD and في ال connecting rod VBD فعند VB لا تساوي VD", "tokens": [28349, 88, 264, 11015, 8685, 363, 35, 293, 8978, 2423, 11015, 8685, 691, 33, 35, 6156, 3615, 41260, 691, 33, 20193, 6055, 3794, 995, 45865, 691, 35], "avg_logprob": -0.26785715562956675, "compression_ratio": 1.0963855421686748, "no_speech_prob": 0.0, "words": [{"start": 2264.22, "end": 2265.62, "word": "study", "probability": 0.784423828125}, {"start": 2265.62, "end": 2267.02, "word": " the", "probability": 0.75634765625}, {"start": 2267.02, "end": 2268.5, "word": " connecting", "probability": 0.90185546875}, {"start": 2268.5, "end": 2268.88, "word": " rod", "probability": 0.77685546875}, {"start": 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{"start": 2456.86, "end": 2457.14, "word": " b", "probability": 0.98779296875}, {"start": 2457.14, "end": 2458.98, "word": " لتلاتة", "probability": 0.74462890625}], "temperature": 1.0}, {"id": 89, "seek": 247100, "start": 2460.0, "end": 2471.0, "text": "بدي على تمانية صين الأربعين و انها بحسب Beta", "tokens": [3555, 16254, 15844, 46811, 7649, 10632, 20328, 9957, 16247, 25513, 3615, 9957, 4032, 16472, 11296, 4724, 5016, 35457, 33286], "avg_logprob": -0.4046875134110451, "compression_ratio": 0.987012987012987, "no_speech_prob": 0.0, "words": [{"start": 2460.0, "end": 2460.98, "word": "بدي", "probability": 0.334716796875}, {"start": 2460.98, "end": 2461.2, "word": " على", "probability": 0.828125}, {"start": 2461.2, "end": 2461.82, "word": " تمانية", "probability": 0.97509765625}, {"start": 2461.82, "end": 2463.32, "word": " صين", "probability": 0.58001708984375}, {"start": 2463.32, "end": 2465.3, "word": " الأربعين", "probability": 0.882080078125}, {"start": 2465.3, "end": 2467.54, 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new file mode 100644
index 0000000000000000000000000000000000000000..47443d02b2d82ac016db7c27ce1f560e6f165a73
--- /dev/null
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@@ -0,0 +1 @@
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"الان موقع C بيتغير بدلوش ثابت يعني لو صار الرد صار هنا صار رد زي هيك هتصير instant center هنا واضح انه موقع ال instant center متغير", "tokens": [6027, 7649, 3714, 30543, 3615, 383, 4724, 1829, 2655, 17082, 13546, 47525, 1211, 2407, 8592, 38637, 16758, 2655, 37495, 22653, 45164, 20328, 9640, 34892, 3215, 20328, 9640, 34105, 20328, 9640, 12602, 3215, 30767, 1829, 39896, 4117, 8032, 2655, 9381, 13546, 9836, 3056, 34105, 4032, 46958, 5016, 16472, 3224, 3714, 30543, 3615, 2423, 9836, 3056, 44650, 17082, 13546], "avg_logprob": -0.2758620710208498, "compression_ratio": 1.5255474452554745, "no_speech_prob": 0.0, "words": [{"start": 865.39, "end": 866.15, "word": "الان", "probability": 0.781982421875}, {"start": 866.15, "end": 866.91, "word": " موقع", "probability": 0.97265625}, {"start": 866.91, "end": 867.25, "word": " C", "probability": 0.52294921875}, {"start": 867.25, "end": 869.05, "word": " بيتغير", "probability": 0.745458984375}, {"start": 869.05, "end": 869.59, "word": " بدلوش", 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عند ال instant center بتكون السرعة at the instant center Vc بتكون تستوى Zero هذا لا يعني ال acceleration تستوى Zero this does not mean ان A C بشكل عام بتسويش Zero ال acceleration نقطة C بتسويش Zero", "tokens": [40228, 22653, 8978, 5296, 5016, 19913, 3660, 19446, 25961, 34105, 8978, 5296, 5016, 19913, 3660, 19446, 6055, 7649, 10632, 20328, 9640, 34105, 3714, 30543, 3615, 2423, 9836, 3056, 44650, 17082, 13546, 43242, 2423, 9836, 3056, 39894, 30544, 21136, 2288, 27884, 412, 264, 9836, 3056, 691, 66, 39894, 30544, 6055, 14851, 2407, 7578, 17182, 23758, 20193, 37495, 22653, 2423, 17162, 6055, 14851, 2407, 7578, 17182, 341, 775, 406, 914, 16472, 316, 383, 4724, 8592, 28820, 6225, 10943, 39894, 3794, 45865, 8592, 17182, 2423, 17162, 8717, 47432, 3660, 383, 39894, 3794, 45865, 8592, 17182], "avg_logprob": -0.22899865014578707, "compression_ratio": 1.84037558685446, "no_speech_prob": 0.0, "words": [{"start": 887.78, "end": 888.08, "word": "يعني", "probability": 0.871826171875}, {"start": 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"word": "نشوف", "probability": 0.8326822916666666}, {"start": 923.2, "end": 924.14, "word": " مثال", "probability": 0.953125}, {"start": 924.14, "end": 935.92, "word": " نرجع", "probability": 0.9290364583333334}, {"start": 935.92, "end": 936.14, "word": " نفس", "probability": 0.935546875}, {"start": 936.14, "end": 936.72, "word": " المثلة", "probability": 0.92236328125}, {"start": 936.72, "end": 938.62, "word": " السابقة", "probability": 0.9786783854166666}, {"start": 938.62, "end": 940.08, "word": " خمس", "probability": 0.8190104166666666}, {"start": 940.08, "end": 940.38, "word": " عشر", "probability": 0.37347412109375}, {"start": 940.38, "end": 940.82, "word": " اتنين", "probability": 0.9110107421875}, {"start": 940.82, "end": 941.42, "word": " the", "probability": 0.244873046875}, {"start": 941.42, "end": 941.76, "word": " double", "probability": 0.9248046875}, {"start": 941.76, "end": 942.2, "word": " gear", "probability": 0.947265625}, {"start": 942.2, "end": 942.64, "word": " 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{"start": 1866.34, "end": 1866.7, "word": " already", "probability": 0.444091796875}, {"start": 1866.7, "end": 1867.3, "word": " عرفها", "probability": 0.8740234375}, {"start": 1867.3, "end": 1868.52, "word": " اللى", "probability": 0.5985107421875}, {"start": 1868.52, "end": 1868.64, "word": " هى", "probability": 0.833740234375}, {"start": 1868.64, "end": 1869.06, "word": " 200", "probability": 0.82568359375}, {"start": 1869.06, "end": 1869.5, "word": " Pi", "probability": 0.1396484375}, {"start": 1869.5, "end": 1870.4, "word": " و", "probability": 0.78076171875}, {"start": 1870.4, "end": 1870.54, "word": " ال", "probability": 0.576171875}, {"start": 1870.54, "end": 1870.76, "word": " BC", "probability": 0.787109375}, {"start": 1870.76, "end": 1871.22, "word": " عرفها", "probability": 0.9415690104166666}, {"start": 1871.22, "end": 1871.62, "word": " معناته", "probability": 0.5659586588541666}, {"start": 1871.62, "end": 1872.14, "word": " بحسب", "probability": 0.81298828125}, {"start": 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"probability": 0.842578125}, {"start": 1897.79, "end": 1898.01, "word": " اللي", "probability": 0.56640625}, {"start": 1898.01, "end": 1898.27, "word": " هو", "probability": 0.9453125}, {"start": 1898.27, "end": 1899.27, "word": " الصراع", "probability": 0.6969401041666666}, {"start": 1899.27, "end": 1899.61, "word": " الزاوية", "probability": 0.847314453125}, {"start": 1899.61, "end": 1899.71, "word": " ل", "probability": 0.84326171875}, {"start": 1899.71, "end": 1900.01, "word": " VD", "probability": 0.71435546875}, {"start": 1900.01, "end": 1900.25, "word": " في", "probability": 0.87939453125}, {"start": 1900.25, "end": 1900.93, "word": " المسافة", "probability": 0.9644775390625}, {"start": 1900.93, "end": 1901.09, "word": " من", "probability": 0.935546875}, {"start": 1901.09, "end": 1901.23, "word": " ال", "probability": 0.93359375}, {"start": 1901.23, "end": 1901.45, "word": " incense", "probability": 0.2354736328125}, {"start": 1901.45, "end": 1901.99, "word": " center", "probability": 0.7119140625}, {"start": 1901.99, "end": 1903.17, "word": " C", "probability": 0.78564453125}, {"start": 1903.17, "end": 1903.89, "word": " لنقطة", "probability": 0.949951171875}, {"start": 1903.89, "end": 1904.29, "word": " D", "probability": 0.9755859375}, {"start": 1904.29, "end": 1906.33, "word": " Omega", "probability": 0.6064453125}, {"start": 1906.33, "end": 1906.65, "word": " VD", "probability": 0.970947265625}], "temperature": 1.0}, {"id": 65, "seek": 193320, "start": 1910.54, "end": 1933.2, "text": "على bc في cd وانا عندى bc معروفة و cd معروفة وانا بتبحسب ال VD هدى هى ال instance center طريقة ال instance center method عشان اعمل velocity analysis ل rigid bodies طيب بتحلوا المثال اربعة سبعين تمانين و تمانية تمانين و خمسة وتسعين", "tokens": [3615, 23942, 272, 66, 8978, 269, 67, 4032, 7649, 995, 43242, 7578, 272, 66, 20449, 32887, 5172, 3660, 4032, 269, 67, 20449, 32887, 5172, 3660, 4032, 7649, 995, 39894, 49628, 35457, 2423, 691, 35, 8032, 3215, 7578, 8032, 7578, 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1916.02, "word": " bc", "probability": 0.7286376953125}, {"start": 1916.02, "end": 1916.66, "word": " معروفة", "probability": 0.9169921875}, {"start": 1916.66, "end": 1916.84, "word": " و", "probability": 0.96142578125}, {"start": 1916.84, "end": 1917.2, "word": " cd", "probability": 0.779541015625}, {"start": 1917.2, "end": 1917.56, "word": " معروفة", "probability": 0.8798828125}, {"start": 1917.56, "end": 1917.66, "word": " وانا", "probability": 0.6210123697916666}, {"start": 1917.66, "end": 1918.18, "word": " بتبحسب", "probability": 0.6971028645833334}, {"start": 1918.18, "end": 1918.48, "word": " ال", "probability": 0.91357421875}, {"start": 1918.48, "end": 1918.84, "word": " VD", "probability": 0.540283203125}, {"start": 1918.84, "end": 1919.24, "word": " هدى", "probability": 0.5577799479166666}, {"start": 1919.24, "end": 1919.34, "word": " هى", "probability": 0.97705078125}, {"start": 1919.34, "end": 1919.48, "word": " ال", "probability": 0.89306640625}, {"start": 1919.48, "end": 1919.82, "word": " instance", "probability": 0.408935546875}, {"start": 1919.82, "end": 1920.38, "word": " center", "probability": 0.7958984375}, {"start": 1920.38, "end": 1921.74, "word": " طريقة", "probability": 0.9765625}, {"start": 1921.74, "end": 1921.9, "word": " ال", "probability": 0.82275390625}, {"start": 1921.9, "end": 1922.06, "word": " instance", "probability": 0.427734375}, {"start": 1922.06, "end": 1922.34, "word": " center", "probability": 0.8408203125}, {"start": 1922.34, "end": 1922.62, "word": " method", "probability": 0.98828125}, {"start": 1922.62, "end": 1922.96, "word": " عشان", "probability": 0.97802734375}, {"start": 1922.96, "end": 1923.46, "word": " اعمل", "probability": 0.9329427083333334}, {"start": 1923.46, "end": 1924.58, "word": " velocity", "probability": 0.890625}, {"start": 1924.58, "end": 1925.4, "word": " analysis", "probability": 0.82958984375}, {"start": 1925.4, "end": 1926.06, "word": " ل", "probability": 0.9462890625}, {"start": 1926.06, "end": 1926.96, "word": " rigid", "probability": 0.9765625}, {"start": 1926.96, "end": 1927.36, "word": " bodies", "probability": 0.900390625}, {"start": 1927.36, "end": 1928.3, "word": " طيب", "probability": 0.9020182291666666}, {"start": 1928.3, "end": 1928.66, "word": " بتحلوا", "probability": 0.695068359375}, {"start": 1928.66, "end": 1929.1, "word": " المثال", "probability": 0.9811197916666666}, {"start": 1929.1, "end": 1929.46, "word": " اربعة", "probability": 0.660400390625}, {"start": 1929.46, "end": 1929.96, "word": " سبعين", "probability": 0.9486083984375}, {"start": 1929.96, "end": 1930.54, "word": " تمانين", "probability": 0.90625}, {"start": 1930.54, "end": 1930.78, "word": " و", "probability": 0.73291015625}, {"start": 1930.78, "end": 1931.02, "word": " تمانية", "probability": 0.73291015625}, {"start": 1931.02, "end": 1931.34, "word": " تمانين", "probability": 0.8487955729166666}, {"start": 1931.34, "end": 1931.5, "word": " و", "probability": 0.994140625}, {"start": 1931.5, "end": 1932.34, "word": " خمسة", "probability": 0.91064453125}, {"start": 1932.34, "end": 1933.2, "word": " وتسعين", "probability": 0.9063720703125}], "temperature": 1.0}, {"id": 66, "seek": 195464, "start": 1933.92, "end": 1954.64, "text": "عادة المثال هذه مستوها أعلى مستوى الامتحانات بحيث هيكون تكون تخشوا على امتحان الأمور سهل تكون بالنسبة لكم المحاضرة الجاي هنكمل اللي هو ال acceleration analysis ل general plan motion اعطيكوا العفو", "tokens": [3615, 18513, 3660, 9673, 12984, 6027, 29538, 3714, 14851, 2407, 11296, 5551, 3615, 23942, 3714, 14851, 2407, 7578, 2423, 10943, 2655, 5016, 7649, 9307, 4724, 5016, 1829, 12984, 39896, 30544, 6055, 30544, 6055, 9778, 8592, 14407, 15844, 1975, 2304, 2655, 5016, 7649, 16247, 2304, 13063, 8608, 3224, 1211, 6055, 30544, 20666, 1863, 35457, 3660, 5296, 4117, 2304, 9673, 5016, 46958, 25720, 25724, 47302, 8032, 1863, 24793, 1211, 13672, 1829, 31439, 2423, 17162, 5215, 5296, 2674, 1393, 5394, 1975, 3615, 9566, 1829, 4117, 14407, 18863, 5172, 2407], "avg_logprob": -0.21282327791740155, "compression_ratio": 1.61, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 1933.92, "end": 1934.38, "word": "عادة", "probability": 0.9892578125}, {"start": 1934.38, "end": 1934.8, "word": " المثال", "probability": 0.89453125}, {"start": 1934.8, "end": 1935.0, "word": " هذه", "probability": 0.2498779296875}, {"start": 1935.0, "end": 1935.54, "word": " مستوها", "probability": 0.7618408203125}, {"start": 1935.54, "end": 1935.88, "word": " أعلى", "probability": 0.7896321614583334}, {"start": 1935.88, "end": 1936.4, "word": " مستوى", "probability": 0.90234375}, {"start": 1936.4, "end": 1937.36, "word": " الامتحانات", "probability": 0.861572265625}, {"start": 1937.36, "end": 1938.42, "word": " بحيث", "probability": 0.9853515625}, {"start": 1938.42, "end": 1938.96, "word": " هيكون", "probability": 0.799072265625}, {"start": 1938.96, "end": 1939.66, "word": " تكون", "probability": 0.609619140625}, {"start": 1939.66, "end": 1940.4, "word": " تخشوا", "probability": 0.7960205078125}, {"start": 1940.4, "end": 1940.5, "word": " على", "probability": 0.58642578125}, {"start": 1940.5, "end": 1940.78, "word": " امتحان", "probability": 0.9455078125}, {"start": 1940.78, "end": 1941.24, "word": " الأمور", "probability": 0.9607747395833334}, {"start": 1941.24, "end": 1941.56, "word": " سهل", "probability": 0.88134765625}, {"start": 1941.56, "end": 1941.82, "word": " تكون", "probability": 0.722900390625}, {"start": 1941.82, "end": 1942.1, "word": " بالنسبة", "probability": 0.916748046875}, {"start": 1942.1, "end": 1943.06, "word": " لكم", "probability": 0.5924479166666666}, {"start": 1943.06, "end": 1946.48, "word": " المحاضرة", "probability": 0.96630859375}, {"start": 1946.48, "end": 1946.84, "word": " الجاي", "probability": 0.781494140625}, {"start": 1946.84, "end": 1947.52, "word": " هنكمل", "probability": 0.95849609375}, {"start": 1947.52, "end": 1947.64, "word": " اللي", "probability": 0.921875}, {"start": 1947.64, "end": 1948.34, "word": " هو", "probability": 0.98583984375}, {"start": 1948.34, "end": 1949.22, "word": " ال", "probability": 0.564453125}, {"start": 1949.22, "end": 1949.84, "word": " acceleration", "probability": 0.9404296875}, {"start": 1949.84, "end": 1950.5, "word": " analysis", "probability": 0.82666015625}, {"start": 1950.5, "end": 1950.88, "word": " ل", "probability": 0.259033203125}, {"start": 1950.88, "end": 1951.14, "word": " general", "probability": 0.853515625}, {"start": 1951.14, "end": 1951.66, "word": " plan", "probability": 0.93017578125}, {"start": 1951.66, "end": 1952.44, "word": " motion", "probability": 0.91748046875}, {"start": 1952.44, "end": 1954.32, "word": " اعطيكوا", "probability": 0.7818196614583334}, {"start": 1954.32, "end": 1954.64, "word": " العفو", "probability": 0.7413736979166666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1954.9111875, "duration_after_vad": 1716.497499999996}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/pDahJvkpbFE.srt b/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/pDahJvkpbFE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6519eb4131cecfcc974336b08c653f5e39227366
--- /dev/null
+++ b/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/pDahJvkpbFE.srt
@@ -0,0 +1,2552 @@
+1
+00:00:06,020 --> 00:00:14,760
+هنحل اسئلة امتحان سرعة السؤال الأول كان the motion
+
+2
+00:00:14,760 --> 00:00:27,380
+of a particle is defined by the relation اللي 
+
+3
+00:00:27,380 --> 00:00:27,880
+هي X
+
+4
+00:00:37,550 --> 00:00:42,250
+عندي حركة particle معرفة بالمعادلة x اتناشر t
+
+5
+00:00:42,250 --> 00:00:55,210
+تكعيب ناقص ثمانية عشر t تربيع زائد اثنين t زائد
+
+6
+00:00:55,210 --> 00:00:55,770
+خمسة
+
+7
+00:00:58,770 --> 00:01:01,930
+x and t are expressed in meters and seconds
+
+8
+00:01:01,930 --> 00:01:05,650
+respectively determine the position and velocity
+
+9
+00:01:05,650 --> 00:01:08,390
+when the acceleration of the particle is equal to
+
+10
+00:01:08,390 --> 00:01:12,590
+zero اوجد ال position والسرعة لما ال acceleration
+
+11
+00:01:12,590 --> 00:01:22,110
+بالساوية صفر يعني بده v and x when a تساوي صفر
+
+12
+00:01:22,110 --> 00:01:30,550
+معناته أنا هشتق أول شيء احسب ال v بسرعة dx على dt
+
+13
+00:01:30,550 --> 00:01:39,070
+هتساوي  زائد
+
+14
+00:01:39,070 --> 00:01:52,190
+اثنين وال a dv by dt تساوي اثنين وسبعين t ناقص ستة و
+
+15
+00:01:52,190 --> 00:01:52,670
+ثلاثين
+
+16
+00:01:56,230 --> 00:02:02,830
+a equal 0 when 72t
+
+17
+00:02:02,830 --> 00:02:12,290
+-30 = 0 يعني t بساوية نصف 
+
+18
+00:02:12,290 --> 00:02:16,670
+find x
+
+19
+00:02:16,670 --> 00:02:30,570
+and v at t بساوية نصف secondيعني هيكون عندي x هتكون
+
+20
+00:02:30,570 --> 00:02:43,050
+اثنا عشر في نصف تكعيب ناقص ثمانية عشر في نصف تربيع زائد
+
+21
+00:02:43,050 --> 00:02:55,890
+اثنين في نصف زائد خمسة  أكيد بيطلع الجواب و v هتكون 
+
+22
+00:02:55,890 --> 00:03:05,630
+ستة وثلاثين في نصف تربيع ناقص ستة وثلاثين في نصف
+
+23
+00:03:05,630 --> 00:03:14,170
+زائد اثنين 
+x 
+
+24
+00:03:14,170 --> 00:03:23,350
+ثلاثة متر وال v هذا
+
+25
+00:03:23,350 --> 00:03:23,910
+السؤال الأول
+
+26
+00:03:27,680 --> 00:03:46,440
+السؤال الثاني السؤال 
+
+27
+00:03:46,440 --> 00:03:55,340
+الثاني a truck travels 220 meters in 10 seconds
+
+28
+00:03:56,480 --> 00:04:00,940
+while being decelerated at a constant rate of 0.6
+
+29
+00:04:00,940 --> 00:04:19,880
+m per second squared خلّي نلخص المسألة عندي 
+
+30
+00:04:19,880 --> 00:04:27,570
+ال truckبمشي ب 220 متر في عشر ثواني طبعا كان في
+
+31
+00:04:27,570 --> 00:04:33,450
+الأول ماشي هو كان له سرعة ابتدائية طبعا بمشي بعجلة
+
+32
+00:04:33,450 --> 00:04:37,690
+تناقصية قيمتها 0.6 meters per second بدنا 
+
+33
+00:04:37,690 --> 00:04:42,930
+نجد ال initial velocity أول شيء لازم ألخص المثلّثات و
+
+34
+00:04:42,930 --> 00:04:44,930
+أحط محاور إحداثيات عند هاي ال truck
+
+35
+00:04:56,760 --> 00:05:00,600
+هاي ال a وهاي
+
+36
+00:05:00,600 --> 00:05:05,900
+ال v نود لازم
+
+37
+00:05:05,900 --> 00:05:15,300
+اعرف ال positive x axis هاي
+
+38
+00:05:15,300 --> 00:05:19,340
+ال x هاي
+
+39
+00:05:19,340 --> 00:05:22,500
+ال y هذا ال origin تبعي
+
+40
+00:05:26,070 --> 00:05:33,170
+الـ a معطنيها بتساوي الـ a معاكس ال x axis minus
+
+41
+00:05:33,170 --> 00:05:42,470
+0.6  هو
+
+42
+00:05:42,470 --> 00:05:51,710
+مشي مسافة delta x 220 متر في زمن delta t 
+
+43
+00:05:54,410 --> 00:06:04,110
+بساوي او t عشرة seconds بده
+
+44
+00:06:04,110 --> 00:06:10,110
+v0 عارف
+
+45
+00:06:10,110 --> 00:06:15,450
+المسافة أنا عارف الزمن عارف ال acceleration يعني
+
+46
+00:06:15,450 --> 00:06:23,070
+delta x هتكون  v0 t زائد
+
+47
+00:06:24,870 --> 00:06:34,630
+½ a t تربيع delta x عندي 220 تساوي v نود في عشر ثواني
+
+48
+00:06:34,630 --> 00:06:46,470
+ناقص نصف في ستة من عشرة في عشرة تربيع ومنها بحسب ال
+
+49
+00:06:46,470 --> 00:06:52,910
+v نود أنا عندي مئة ثلاثمئة
+
+50
+00:06:56,980 --> 00:07:02,740
+نصف يعني 250 يعني
+
+51
+00:07:02,740 --> 00:07:08,420
+خمسة وعشرين متر في الثانية هذه ال v naught
+
+52
+00:07:08,420 --> 00:07:14,760
+المطلوب الثاني ال final velocity يعني v at t equal
+
+53
+00:07:14,760 --> 00:07:18,960
+10 v at
+
+54
+00:07:18,960 --> 00:07:28,890
+t equal 10 second هنحكي v تساوي v naught زائد a في t
+
+55
+00:07:28,890 --> 00:07:36,090
+ال v naught عندي خمسة وعشرين ناقص ستة من عشرة في
+
+56
+00:07:36,090 --> 00:07:40,230
+عشرة the
+
+57
+00:07:40,230 --> 00:07:46,790
+distance 
+
+58
+00:07:46,790 --> 00:07:50,530
+travelled during the first one point five second
+
+59
+00:07:51,300 --> 00:07:59,900
+المسافة اللي مشيها خلال أول واحد ونصف ثانية هدل
+
+60
+00:07:59,900 --> 00:08:06,740
+بيه؟ بيه؟ سيه؟ بده ال distance؟
+
+61
+00:08:06,740 --> 00:08:14,200
+traveled يعني
+
+62
+00:08:14,200 --> 00:08:19,480
+for 1.5 second
+
+63
+00:08:22,430 --> 00:08:33,830
+دلتا x مظبوط زائد
+
+64
+00:08:33,830 --> 00:08:42,650
+نصف a t تربيع يعني هتكون عند v نود خمسة وعشرين
+
+65
+00:08:42,650 --> 00:08:51,170
+في واحد ونصف ناقص نصف في ستة من عشرة
+
+66
+00:08:54,870 --> 00:09:06,270
+في واحد ونصف تربيع يعني يعني
+
+67
+00:09:06,270 --> 00:09:12,970
+تساوي ثلاثين ونصف  عن دهان اه كم بيطلع 36.
+
+68
+00:09:27,930 --> 00:09:34,510
+متر بس في لحظة وملاحظة على النقطة هذه احنا عندنا 
+
+69
+00:09:34,510 --> 00:09:41,110
+v بشكل عام سواء v نود زائد a في t يعني ال v هتساوي
+
+70
+00:09:41,110 --> 00:09:48,990
+خمسة وعشرين ناقص ستة من عشرة t متى
+
+71
+00:09:48,990 --> 00:09:54,950
+v بيساوي صفر؟ هذه .. هذه .. ما لهاش خاصة الحل هذه
+
+72
+00:09:54,950 --> 00:10:00,480
+إضافة v بيساوي .. لما v بيساوي صفر سينادي خمسة و
+
+73
+00:10:00,480 --> 00:10:07,680
+عشرين ناقص ستة من عشرة t بيساوي صفر يعني ال t 41.
+
+74
+00:10:07,680 --> 00:10:12,120
+666
+
+75
+00:10:12,120 --> 00:10:16,720
+second لأنه
+
+76
+00:10:16,720 --> 00:10:21,320
+حكى لي احسب لي ال distance travelled during fifty
+
+77
+00:10:21,320 --> 00:10:21,780
+seconds
+
+78
+00:10:25,440 --> 00:10:29,620
+في فرق بين ال position vector بين ال position
+
+79
+00:10:29,620 --> 00:10:36,320
+vector و ال distance travelled ال
+
+80
+00:10:36,320 --> 00:10:42,320
+position vector بوجد موقع من مركز إحداثيات مركز
+
+81
+00:10:42,320 --> 00:10:45,940
+إحداثيات في أي لحظة هذا ال position vector ال
+
+82
+00:10:45,940 --> 00:10:49,860
+distance travelled يديش مسافة مشيها مثلا أنا مشيت
+
+83
+00:10:49,860 --> 00:10:58,920
+بهذا ال .. وصلت للباب مشيت مثلا ثلاثة متر ورجعت هاي
+
+84
+00:10:58,920 --> 00:11:05,620
+يا سلام كمان أربعة متر سبع ومشيت كمان مترين تسعة
+
+85
+00:11:05,620 --> 00:11:09,420
+الآن
+
+86
+00:11:09,420 --> 00:11:13,000
+هاي مركز الإحداثيات ورايه هذا .. هذا الموقع
+
+87
+00:11:13,000 --> 00:11:16,420
+تبعيه بس المسافة اللي مشيتها ايه كمان؟ تسعة
+
+88
+00:11:18,490 --> 00:11:22,770
+فمعناته اللي بيحدد الفترات .. المسافات اللي مشيتها
+
+89
+00:11:22,770 --> 00:11:26,670
+.. أنا كنت ماشي .. ماشي في الأول .. مشيت ثلاثة ..
+
+90
+00:11:26,670 --> 00:11:32,030
+أكيد حصل لحالة توقف .. سكون ..
+
+91
+00:11:32,030 --> 00:11:35,410
+بعدين هرجع .. أعكس الاتجاه .. لا يمكن أعكس الاتجاه
+
+92
+00:11:35,410 --> 00:11:40,170
+إلا لما أسافر distance travelled بشوف الفترات
+
+93
+00:11:40,170 --> 00:11:43,470
+بقسم الفترات اللي بتكون السرعة يعني مثلا بحكي
+
+94
+00:11:43,470 --> 00:11:47,350
+distance travelled لو لو كانت t بساوية خمسين
+
+95
+00:11:47,350 --> 00:11:53,490
+second هحكي ال distance travelled بيساوي delta x
+
+96
+00:11:53,490 --> 00:12:02,680
+واحد زائد delta x اثنين delta x واحد هتكون  في t
+
+97
+00:12:02,680 --> 00:12:08,120
+من صفر لحد واحد وأربعين فاصلة ستة ستة سبعة seconds
+
+98
+00:12:08,120 --> 00:12:16,620
+و delta x اثنين في t من واحد وأربعين فاصلة ستة
+
+99
+00:12:16,620 --> 00:12:23,660
+ستة سبعة لحد الخمسين وبجمع قيمهم المطلقة يعني
+
+100
+00:12:23,660 --> 00:12:28,080
+بجمع delta x واحد زي delta x اثنين هذا ال distance
+
+101
+00:12:28,080 --> 00:12:28,980
+travelled
+
+102
+00:12:32,030 --> 00:12:40,010
+طيب هذا السؤال الثاني السؤال 
+
+103
+00:12:40,010 --> 00:12:55,430
+الثالث block
+
+104
+00:12:55,430 --> 00:13:04,400
+b أنا عندي ثلاث بلوكات a و b و c look a و b و c 
+
+105
+00:13:04,400 --> 00:13:08,500
+المفروض
+
+106
+00:13:08,500 --> 00:13:13,440
+أول شيء أول ما أطلع المسائل زي هيك بده أحط المرجعيات
+
+107
+00:13:13,440 --> 00:13:25,300
+بتاعتنا عندي هاي أول مرجع هذا
+
+108
+00:13:25,300 --> 00:13:25,920
+هسميها
+
+109
+00:13:33,230 --> 00:13:43,510
+ya وهدى yb و
+
+110
+00:13:43,510 --> 00:13:49,470
+الدعم الكهامر جاية هى هدى
+
+111
+00:13:49,470 --> 00:13:55,790
+هتكون ايش xc 
+
+112
+00:13:55,790 --> 00:13:59,250
+طيب
+
+113
+00:13:59,250 --> 00:14:12,930
+block b أنا عندي ثلاثة بلوكات a و b و c هي عندي a هي
+
+114
+00:14:12,930 --> 00:14:19,170
+block a block
+
+115
+00:14:19,170 --> 00:14:27,430
+b و block c 
+
+116
+00:14:29,500 --> 00:14:32,120
+block b moves downward with a constant velocity of 
+
+117
+00:14:32,120 --> 00:14:42,500
+20 mm per second block b بتحرك اللي هو vb موجب ولا 
+
+118
+00:14:42,500 --> 00:14:48,500
+سالب؟ vb
+
+119
+00:14:48,500 --> 00:14:52,360
+شو ساوي؟
+
+120
+00:14:52,360 --> 00:14:56,220
+عشرين لأن اتجاه الموجب بتاع المحاور الواي vb تساوي
+
+121
+00:14:56,220 --> 00:15:04,680
+20 mm per second وهذه شاملها 
+
+122
+00:15:04,680 --> 00:15:09,600
+constant يعني
+
+123
+00:15:09,600 --> 00:15:17,860
+a b تساوي صفر ال t equals zero في البداية block
+
+124
+00:15:17,860 --> 00:15:23,440
+a is moving upward with a constant acceleration
+
+125
+00:15:23,440 --> 00:15:25,780
+يعني بتتحرك لأعلى
+
+126
+00:15:29,360 --> 00:15:38,500
+تتحرك لأعلى و constant و
+
+127
+00:15:38,500 --> 00:15:45,860
+velocity تلاتين يعني va va صفر هذه لأن ال time 
+
+128
+00:15:45,860 --> 00:15:54,060
+equal zero معطينيها كم؟ عشرين؟ تلاتين؟ سالب 30 
+
+129
+00:15:54,060 --> 00:15:57,320
+mm per second لأنها عكس المحاور
+
+130
+00:16:01,030 --> 00:16:05,490
+knowing that is العلم at t equal three seconds
+
+131
+00:16:05,490 --> 00:16:17,570
+slider c at t equal ثلاثة seconds slider
+
+132
+00:16:17,570 --> 00:16:21,770
+c هذا has
+
+133
+00:16:21,770 --> 00:16:24,730
+moved 57 mm to the right يعني
+
+134
+00:16:24,730 --> 00:16:25,630
+delta xc
+
+135
+00:16:29,510 --> 00:16:35,310
+الـ 57 ملي متر تحرك في خلال ثلاث ثواني ماشي الـ 57
+
+136
+00:16:35,310 --> 00:16:40,350
+ملي متر تحرك 
+
+137
+00:16:40,350 --> 00:16:45,310
+في خلال ثلاث ثواني ماشي الـ 57 ملي متر تحرك في
+
+138
+00:16:45,310 --> 00:16:45,930
+خلال ثلاث ثواني ماشي الـ 57 ملي متر تحرك في خلال
+
+139
+00:16:45,930 --> 00:16:47,290
+ثلاث ثواني ماشي الـ 57 ملي متر تحرك في خلال ثلاث
+
+140
+00:16:47,290 --> 00:16:47,390
+ثواني ماشي الـ 57 ملي متر تحرك في خلال ثلاث ثواني 
+
+141
+00:16:47,390 --> 00:16:47,930
+ماشي الـ 57 ملي متر اتحرك في خلال تلت ثواني ماشي
+
+142
+00:16:47,930 --> 00:16:50,450
+الـ 57 ملي متر اتحرك في خلال تلت ثواني ماشي الـ 57 
+
+143
+00:16:50,450 --> 00:16:57,350
+ملي متر اتحرك في خلال 
+
+144
+00:16:57,350 --> 00:17:04,570
+تلت ثواني ماشي طبعا ايه ايش نوع الحركة هنا؟ البلوكات
+
+145
+00:17:04,570 --> 00:17:07,870
+مربطة مع بعض من خلال الحبال المعنى انها حركة
+
+146
+00:17:07,870 --> 00:17:12,190
+مرتبطة صح؟ المعنى انك تحاول تجد علاقة بينها أنا 
+
+147
+00:17:12,190 --> 00:17:20,810
+عندي هذا ال واحد ال اتنين ال تلاتة الاربعة الخمسة
+
+148
+00:17:20,810 --> 00:17:29,930
+الستة السبعة والثمانية هيكون عندي ال واحد
+
+149
+00:17:32,930 --> 00:17:43,830
+زائد L2 زائد L3 زائد L4 زائد L5 زائد L6 زائد L7
+
+150
+00:17:43,830 --> 00:17:51,990
+زائد L8 بالساوية constant مظبوط؟
+
+151
+00:17:51,990 --> 00:17:53,970
+طبعا ممكن تعملوها شفويا بس كشفونها شفويا
+
+152
+00:17:53,970 --> 00:17:59,130
+بتنعمل بالطريقة هادية الواحد هتكون الواحد و اتنين
+
+153
+00:17:59,130 --> 00:18:09,310
+و التلاتة XA صح؟ يعني هيكون دي XA YA ZA
+
+154
+00:18:09,310 --> 00:18:26,090
+زاد ZA زاد ZA زاد 4 5 6 و 7 YB زاد YB زاد YB زاد
+
+155
+00:18:26,090 --> 00:18:39,700
+YB زاد YB زاد L8 XC بالساوية
+
+156
+00:18:39,700 --> 00:18:47,380
+constant يعني هيكون تلاتة ZA زاد
+
+157
+00:18:47,380 --> 00:18:58,700
+أربعة YB زاد XC بالساوية constant يعني
+
+158
+00:19:00,210 --> 00:19:06,990
+اشتقاق أو أو ده خلي دلتاس حاسب ان تلاتة Delta ZA
+
+159
+00:19:06,990 --> 00:19:21,390
+زاد أربع Delta YB زاد Delta XC بالساوية صفر و
+
+160
+00:19:21,390 --> 00:19:34,710
+بطلع كمان عندي تلاتة VA زائد أربع VB زائد VC بيساوي
+
+161
+00:19:34,710 --> 00:19:49,330
+صفر وعندي تلاتة AA زائد أربع AB زائد AC بيساوي صفر
+
+162
+00:19:49,330 --> 00:19:55,070
+لكن في واحد منهم بيتحرك بـ constant velocity بمعناته 
+
+163
+00:19:55,070 --> 00:19:58,890
+ال acceleration بتاعته ايش يستوي؟ صفر هذه بتساوي 
+
+164
+00:19:58,890 --> 00:20:02,970
+صفر
+
+165
+00:20:02,970 --> 00:20:09,750
+يعني هتكون عندي تلاتة a a زي
+
+166
+00:20:09,750 --> 00:20:18,610
+ال a c بالساوية صفر يعني عندي هاي المعادلات هذه 
+
+167
+00:20:18,610 --> 00:20:31,160
+معادلة واحد هذه اتنينوها دياش تلاتة طيب احنا وجدنا 
+
+168
+00:20:31,160 --> 00:20:35,940
+relationship بين حركة البلوكات a و b و c نرجع
+
+169
+00:20:35,940 --> 00:20:47,800
+لمطلوب بده هو ال initial velocity ل block c طيب 
+
+170
+00:20:48,730 --> 00:20:51,770
+بالنسبة لـ block A بتحرك بـ constant acceleration 
+
+171
+00:20:51,770 --> 00:20:59,150
+و النيشال اللي كانت سرعته تلاتين second بالنسبة لـ
+
+172
+00:20:59,150 --> 00:21:05,970
+B بتحرك بسرعة ايش؟ بسرعة ايش؟ constant معناه هتكون
+
+173
+00:21:05,970 --> 00:21:09,630
+Delta YB
+
+174
+00:21:09,630 --> 00:21:13,290
+ايش هتكون الساوية؟
+
+175
+00:21:15,870 --> 00:21:28,670
+D T في VB صح يب بيساوي يب نود زائد VB في T يعني انا
+
+176
+00:21:28,670 --> 00:21:35,130
+هتكون عندي هتكون بعد تلاتة ثواني اللي هي تلاتة في
+
+177
+00:21:35,130 --> 00:21:38,710
+عشرين ستين ملي ملي
+
+178
+00:21:56,630 --> 00:22:03,870
+طيب عندي هى المعطينة تلاتة a a زاد a c هو بيحكيلي a
+
+179
+00:22:03,870 --> 00:22:08,130
+a constant فمعناته a c هتكون ايش constant لأن a c
+
+180
+00:22:08,130 --> 00:22:15,970
+هتكون تساوي minus تلاتة a a معناته a c بيساوي ايش
+
+181
+00:22:15,970 --> 00:22:20,290
+constant كيف هنجيب a c
+
+182
+00:22:25,530 --> 00:22:35,610
+معطيني الزمن ومعطيني ال delta X C لأن
+
+183
+00:22:35,610 --> 00:22:42,050
+في عندي علاقات هنا نعم
+
+184
+00:22:42,050 --> 00:22:48,270
+هي نفسها صحيح ثابتة صحيح لأن أنا كنت اشتي تحكي أنت
+
+185
+00:22:48,270 --> 00:22:59,670
+تعود في المعادلة هذه الآن تلاتة هنا تلاتة VA زائد 
+
+186
+00:22:59,670 --> 00:23:08,030
+أربع VB زائد VC بالساوية صفر حدث anytime المعنى 
+
+187
+00:23:08,030 --> 00:23:17,890
+التلاتة VA ند زائد أربع VB ند زائد VC ند بالساوية
+
+188
+00:23:17,890 --> 00:23:26,840
+صفر VA ند كم كانت؟ تلاتة في سالب تلاتين زائد أربع
+
+189
+00:23:26,840 --> 00:23:36,820
+في عشرين زائد VC ند ساوية صفر معناه VC ند عشرة ملي
+
+190
+00:23:36,820 --> 00:23:42,900
+متر per second هذا المطلوب الأول المطلوب الثاني
+
+191
+00:23:42,900 --> 00:23:47,440
+the accelerations of A and C
+
+192
+00:23:49,460 --> 00:23:52,880
+بالنسبة للـ C أنا أصبحت أعرف الصورة المبتدئية و
+
+193
+00:23:52,880 --> 00:24:00,820
+أعرف الزمن و أعرف Delta X Delta X C بالساوية VC
+
+194
+00:24:00,820 --> 00:24:09,200
+Nod T زائد نص AC T تربيعي مظبوط؟ خليكوا معايا
+
+195
+00:24:09,200 --> 00:24:21,770
+Delta X C 57 بالساوية عشرة في تلاتة زائد نص في AC
+
+196
+00:24:21,770 --> 00:24:30,450
+في تلاتة تربيع ومنها بحسب ال AC عند هنا سبعة و
+
+197
+00:24:30,450 --> 00:24:35,970
+خمسين ناقص تلاتين سبعة و عشرين السبعة و عشرين على 
+
+198
+00:24:35,970 --> 00:24:43,630
+التسعة تلاتة في اتنين ستة تطلع AC ستة millimeter
+
+199
+00:24:43,630 --> 00:24:53,200
+per second عندي هين a a هتكون تساوي minus a c على
+
+200
+00:24:53,200 --> 00:24:59,200
+تلاتة يعني هتكون minus ستة على تلاتة تساوي نقص
+
+201
+00:24:59,200 --> 00:25:06,740
+اتنين millimeter per second تربيع هذا 
+
+202
+00:25:06,740 --> 00:25:11,240
+المطلوب الثاني المطلوب الثالث the change in 
+
+203
+00:25:11,240 --> 00:25:15,200
+position of block a after five second
+
+204
+00:25:20,760 --> 00:25:29,760
+after at t equals five seconds هتكون عندي delta yb
+
+205
+00:25:29,760 --> 00:25:35,320
+ايش بتساوي أو
+
+206
+00:25:35,320 --> 00:25:42,380
+احنا delta
+
+207
+00:25:42,380 --> 00:25:54,670
+ya هيكون عندي VA ند في T زائد نص AA في T تربيع
+
+208
+00:25:54,670 --> 00:26:05,930
+هيكون عندي VA ند اللي هو ناقص تلاتين في الخمسة زائد 
+
+209
+00:26:05,930 --> 00:26:08,990
+نص
+
+210
+00:26:08,990 --> 00:26:19,280
+في AA ناقص اتنين في خمسة تربيع يعني هيكون سالب
+
+211
+00:26:19,280 --> 00:26:24,040
+مية و خمسين ناقص 
+
+212
+00:26:24,040 --> 00:26:31,020
+ايش خمسة و عشرين يعني Delta YA هيكون minus مية و
+
+213
+00:26:31,020 --> 00:26:38,060
+خمس و سبعين ملي متر هيكون
+
+214
+00:26:38,060 --> 00:26:38,760
+السؤال خلص
+
+215
+00:26:44,250 --> 00:26:51,910
+في أي سؤال؟ السؤال
+
+216
+00:26:51,910 --> 00:26:52,890
+الرابع
+
+217
+00:27:15,640 --> 00:27:21,260
+الآن problem number four three children تلت أطفال
+
+218
+00:27:21,260 --> 00:27:29,480
+اللي هو طفل a و b و c are throwing snowballs فيه
+
+219
+00:27:29,480 --> 00:27:37,720
+ثلج بيمسكوه بيرموا مع بعض كتل ثلج child a طفل a
+
+220
+00:27:37,720 --> 00:27:41,840
+throws a snowball with a horizontal ballistic
+
+221
+00:27:41,840 --> 00:27:50,340
+field طفل A بيرمي كورة الثلج بسرعة أفقية V0 if the
+
+222
+00:27:50,340 --> 00:27:56,580
+snowball just passes over the head of child B إذا 
+
+223
+00:27:56,580 --> 00:28:02,400
+كانت الكورة بتمر من فوق رأس الطفل B and hits child
+
+224
+00:28:02,400 --> 00:28:07,280
+C بتضرب في child C يعني بتمر من .. بتمر هيك بتضرب
+
+225
+00:28:07,280 --> 00:28:16,970
+في C Determine the value of V0 يعني
+
+226
+00:28:16,970 --> 00:28:21,710
+خليني ألخص البسألة أول شيء لازم أحط محاولة
+
+227
+00:28:21,710 --> 00:28:27,850
+إحداثية صح مظبوط يعني بدي أحط أنا عنده هنا و بدي
+
+228
+00:28:27,850 --> 00:28:36,450
+أحطها عند A هذا ال X وهذا
+
+229
+00:28:36,450 --> 00:28:36,810
+ال Y
+
+230
+00:28:40,170 --> 00:28:44,250
+هذا ال origin يعني 
+
+231
+00:28:44,250 --> 00:28:50,650
+بدت الكورة ال origin بتاعها zero او خلينا نحط عشان
+
+232
+00:28:50,650 --> 00:29:00,690
+تكون أكثر دقة x
+
+233
+00:29:00,690 --> 00:29:01,910
+y هو هذا ال origin
+
+234
+00:29:06,630 --> 00:29:13,430
+طبعا في دي حركة بتجاه الأفق وحركة بتجاه الرأس عند
+
+235
+00:29:13,430 --> 00:29:20,590
+ال horizontal direction
+
+236
+00:29:20,590 --> 00:29:24,050
+وفي
+
+237
+00:29:24,050 --> 00:29:28,550
+عند ال vertical direction
+
+238
+00:29:40,070 --> 00:29:43,090
+أول شيء في ال horizontal direction على فرض إهمال
+
+239
+00:29:43,090 --> 00:29:52,850
+مقاومة الهواء هتكون دي uniform velocity
+
+240
+00:29:52,850 --> 00:29:58,970
+الآن
+
+241
+00:29:58,970 --> 00:30:06,170
+V X هتكون تساوي ايش في الحالة دي V naught V naught
+
+242
+00:30:06,170 --> 00:30:07,730
+X اللي هي V naught لنا أفقية
+
+243
+00:30:11,650 --> 00:30:22,070
+في ال vertical direction uniform acceleration
+
+244
+00:30:22,070 --> 00:30:26,370
+ay
+
+245
+00:30:26,370 --> 00:30:33,730
+بصفة و minus 9.806 meter per second square
+
+246
+00:30:36,860 --> 00:30:48,780
+و V Y node Zero معناه 
+
+247
+00:30:48,780 --> 00:30:53,900
+هين هيكون ال X بتساوي
+
+248
+00:30:53,900 --> 00:31:01,100
+V node في T وهين
+
+249
+00:31:01,100 --> 00:31:01,560
+ال Y
+
+250
+00:31:05,510 --> 00:31:11,350
+Y0 هتكون تساوي Y0
+
+251
+00:31:11,350 --> 00:31:12,550
+هتكون Zero في الحلقة دي
+
+252
+00:31:12,550 --> 00:31:33,370
+Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0 Y0
+
+253
+00:31:34,890 --> 00:31:40,430
+T تربيع يعني ال Y بتساوي ناقص أربعة بون تسعة صفر
+
+254
+00:31:40,430 --> 00:31:50,650
+تلاتة T تربيع هذه معادلة واحد هذه معادلة اتنين 
+
+255
+00:31:50,650 --> 00:31:53,870
+اللي
+
+256
+00:31:53,870 --> 00:32:01,290
+أنا فيه عندي مبين لما نصل بي عند بي معطيني ال X و
+
+257
+00:32:01,290 --> 00:32:01,590
+ال Y
+
+258
+00:32:04,710 --> 00:32:13,110
+عند بي عند
+
+259
+00:32:13,110 --> 00:32:26,890
+بي كوان دي x بالساوية سبعة متر و
+
+260
+00:32:26,890 --> 00:32:28,290
+عندك هين عند بي
+
+261
+00:32:33,450 --> 00:32:40,350
+كون دي Y بالساوية سالب واحد صح تحت المحاور سالب
+
+262
+00:32:40,350 --> 00:32:45,490
+واحد بالساوية سالب اربعة point تسعة صفر تلاتة
+
+263
+00:32:45,490 --> 00:32:51,970
+تربيع معناته T ايش بتكون تساوي واحد على اربعة
+
+264
+00:32:51,970 --> 00:32:59,090
+point تسعة صفر تلاتة تحت الجذر معناته هنا هتكون دي
+
+265
+00:33:02,050 --> 00:33:09,110
+أربعة خمسة واحد أخدت جذر؟ أربعة خمسة واحد second
+
+266
+00:33:09,110 --> 00:33:17,290
+هين هيكون عندي سبعة بيساوي V نوت T already وجدناها
+
+267
+00:33:17,290 --> 00:33:24,050
+صح؟ اليابونت أربعة خمسة واحد منها بحسب ال V نوت
+
+268
+00:33:24,050 --> 00:33:25,550
+خمسة عشر؟
+
+269
+00:33:28,450 --> 00:33:32,750
+meter per second هذا المطلوب الأول المطلوب الثاني
+
+270
+00:33:32,750 --> 00:33:38,390
+بده distance D مناسب
+
+271
+00:33:38,390 --> 00:33:45,970
+لزمن النقطة C صح؟ at C
+
+272
+00:33:45,970 --> 00:33:50,810
+and C
+
+273
+00:33:50,810 --> 00:34:01,240
+يكون ال Y كم تساوي minus تلاتة بتساوي minus 4
+
+274
+00:34:01,240 --> 00:34:22,160
+point 903 T تربيع و T منها بتطلع point
+
+275
+00:34:22,160 --> 00:34:26,320
+second
+
+276
+00:34:28,430 --> 00:34:34,890
+عند C بيكون
+
+277
+00:34:34,890 --> 00:34:44,750
+دي X بيساوي V نوت قردة حسبته خمسة عشر و نص ال
+
+278
+00:34:44,750 --> 00:34:52,130
+X تكون تساوي سبعة زائد D سبعة 
+
+279
+00:34:52,130 --> 00:34:58,130
+زائد D هتكون تساوي خمسة عشر و نص ال time اللى هو 
+
+280
+00:34:58,130 --> 00:35:15,030
+point سبعة ثمانية اتنين و منها بحسب ال D كام 
+
+281
+00:35:15,030 --> 00:35:21,330
+خمسة point متر
+
+282
+00:35:26,370 --> 00:35:31,370
+في أي سؤال؟ the
+
+283
+00:35:31,370 --> 00:35:38,730
+two blocks shown في عندي بلوكين a و b الوزن بتاع a
+
+284
+00:35:38,730 --> 00:35:44,310
+مائة
+
+285
+00:35:44,310 --> 00:35:51,270
+كيلو جرام و
+
+286
+00:35:51,270 --> 00:35:51,770
+mb
+
+287
+00:35:55,040 --> 00:36:00,420
+ثلاثمائة كيلو جرام start
+
+288
+00:36:00,420 --> 00:36:04,720
+from rest النظام الذي تكون من a و b بدأ من السكون
+
+289
+00:36:04,720 --> 00:36:08,840
+start
+
+290
+00:36:08,840 --> 00:36:12,800
+from
+
+291
+00:36:12,800 --> 00:36:15,060
+rest
+
+292
+00:36:20,430 --> 00:36:22,550
+the horizontal plane and the pulley are
+
+293
+00:36:22,550 --> 00:36:27,610
+frictionless مستوى الأفقي ليس به احتكاك والبكرات
+
+294
+00:36:27,610 --> 00:36:32,430
+ملساء and the pulley is assumed to be of
+
+295
+00:36:32,430 --> 00:36:39,690
+negligible mass سنهمل كتلة البكرة determine the
+
+296
+00:36:39,690 --> 00:36:44,770
+acceleration of each block and the tension in the
+
+297
+00:36:44,770 --> 00:36:48,030
+cord أوجد ال acceleration لكل block و الشد في
+
+298
+00:36:48,030 --> 00:36:48,530
+الحبل
+
+299
+00:36:52,630 --> 00:36:59,750
+أول شيء طبعاً عشان نعرف ال acceleration بلزم أني
+
+300
+00:36:59,750 --> 00:37:03,310
+أدرس ال kinematic of motion هندسة الحركة أنا ممكن
+
+301
+00:37:03,310 --> 00:37:08,070
+أدرس هندسة الحركة بدون الرجوع لل forces وبعد ما
+
+302
+00:37:08,070 --> 00:37:10,730
+عرفتها ليه ال acceleration ممكن أحسب ال tension في
+
+303
+00:37:10,730 --> 00:37:19,430
+الحبل طيب الحركة ايه مرتبطة بحركة بيه مرتبطة بها
+
+304
+00:37:19,430 --> 00:37:21,310
+ممكن أنا أعمل reference frame
+
+305
+00:37:25,590 --> 00:37:32,810
+أسمي هذا ال X Axis وهذا
+
+306
+00:37:32,810 --> 00:37:40,290
+ال Y Axis وهذا سيكون YB
+
+307
+00:37:40,290 --> 00:37:45,870
+وهذا سيكون XA
+
+308
+00:37:57,850 --> 00:38:03,190
+Automatic هتكون XA زي اثنين YB بالساوية constant
+
+309
+00:38:03,190 --> 00:38:08,850
+مظبوط؟ XA زي
+
+310
+00:38:08,850 --> 00:38:20,130
+اثنين YB بالساوية constant إذا بشتق كمان مرة بيصير
+
+311
+00:38:20,130 --> 00:38:31,680
+عندي ايه؟ VA زي اثنين VB بالساوية صفر و AA زيادة
+
+312
+00:38:31,680 --> 00:38:41,300
+اثنين AB بالساوية صفر يعني هذه معادلة واحد هذه
+
+313
+00:38:41,300 --> 00:38:54,520
+اثنين هذه ثلاث  طيب
+
+314
+00:38:58,860 --> 00:39:13,900
+سأعمل block او free body diagram ل A ايه
+
+315
+00:39:13,900 --> 00:39:24,060
+ايش ال forces بتأثر على ايه وزنه لتحت اللي هو M A
+
+316
+00:39:24,060 --> 00:39:32,680
+G وفي رد الفعل من الأرض na وفي الحبل الذي يحاول
+
+317
+00:39:32,680 --> 00:39:40,320
+يشد بهذا الاتجاه T هذا
+
+318
+00:39:40,320 --> 00:39:48,000
+هيصير هيعطيني
+
+319
+00:39:48,000 --> 00:39:54,560
+acceleration ma
+
+320
+00:39:54,560 --> 00:39:57,940
+aa
+
+321
+00:40:14,140 --> 00:40:16,480
+اللي هو حافظت على نفس ال system هاي عندي هاي X
+
+322
+00:40:16,480 --> 00:40:21,860
+وهاي Y
+
+323
+00:40:21,860 --> 00:40:28,720
+summation
+
+324
+00:40:28,720 --> 00:40:31,940
+لل
+
+325
+00:40:31,940 --> 00:40:39,540
+forces باتجاه ال Y في
+
+326
+00:40:39,540 --> 00:40:43,830
+اتجاه ال Y في حركة عندي؟ معناته مافي اكسلايش في
+
+327
+00:40:43,830 --> 00:40:49,090
+التجارب يعني هي صفر يعني
+
+328
+00:40:49,090 --> 00:40:52,590
+سأكون عند
+
+329
+00:40:52,590 --> 00:40:56,130
+Mg
+
+330
+00:40:56,130 --> 00:41:10,790
+M A G minus N A سوا صفر يعني N A هتكون تساوي ما مش
+
+331
+00:41:10,790 --> 00:41:15,350
+لازم أعنيك المعلومة هاد على أي حال na بالساوية ما
+
+332
+00:41:15,350 --> 00:41:25,350
+التي هي مائة في تسعة point ثمانية صفر ستة يعني
+
+333
+00:41:25,350 --> 00:41:33,370
+هتكون تساوي تسعمائة وثمانين point ستة نيوتن هذا
+
+334
+00:41:33,370 --> 00:41:36,330
+باتجاه ال wire summation
+
+335
+00:41:38,060 --> 00:41:46,260
+of forces باتجاه ال X بالساوية
+
+336
+00:41:46,260 --> 00:41:59,900
+M A في ال A A بتجاه ال X سأكون
+
+337
+00:41:59,900 --> 00:42:06,540
+سالباً T بالساوية
+
+338
+00:42:06,540 --> 00:42:22,910
+سالباً ma a a يعني سيكون عندي ال T بتساوي مائة
+
+339
+00:42:22,910 --> 00:42:26,370
+a
+
+340
+00:42:26,370 --> 00:42:33,210
+a هاي معادلة a ش اربع
+
+341
+00:42:41,120 --> 00:42:46,320
+طيب سنعمل ال free body diagram لل
+
+342
+00:42:46,320 --> 00:42:59,440
+block B block B ايش
+
+343
+00:42:59,440 --> 00:43:04,080
+ال force بتأثر على block B عندي
+
+344
+00:43:04,080 --> 00:43:07,980
+هنا وزنه
+
+345
+00:43:07,980 --> 00:43:09,180
+اللي mb
+
+346
+00:43:13,280 --> 00:43:16,840
+حسب المحاولات التي وضعتها هم منطق يمشوا يعني ال
+
+347
+00:43:16,840 --> 00:43:22,940
+acceleration بتاعهم متعاكسين طيب
+
+348
+00:43:22,940 --> 00:43:30,040
+دقيق الأرقام هذه كلها و الإشارات؟ في أي سؤال؟
+
+349
+00:43:30,040 --> 00:43:35,820
+بعدين حالياً في حسب نظام الجامعة الآن مافيش محاضرات
+
+350
+00:43:35,820 --> 00:43:41,910
+أحد 3 من 11 ل 12 ونصف فراغ جامعي و السبت 24 ال
+
+351
+00:43:41,910 --> 00:43:42,750
+11 ل 12
+
+352
+00:44:01,750 --> 00:44:05,510
+الكتاب ال .. الكتاب بيجي كتاب واحد نفس الكتاب
+
+353
+00:44:05,510 --> 00:44:10,690
+بيكون أول عشر شباتر استاتيكا بعدين بيجي ال 11 ..
+
+354
+00:44:10,690 --> 00:44:16,630
+الشبتر 11 لحد الشبتر 17 ديناميكا الكتاب بتاع بير و
+
+355
+00:44:16,630 --> 00:44:21,290
+بتاع .. بتاع مريم و بتاع هبلر و الكتب المشهورة نفس
+
+356
+00:44:21,290 --> 00:44:28,270
+النظام فكيف تحكي لملهاش خاص طيب
+
+357
+00:44:28,270 --> 00:44:28,810
+نكمل
+
+358
+00:44:32,290 --> 00:44:38,110
+the twelve pound block B هذا block B starts from
+
+359
+00:44:38,110 --> 00:44:43,630
+rest بدأ من السكون block B and slides on the
+
+360
+00:44:43,630 --> 00:44:49,150
+thirty pound wedge A ينزلق على block A which is
+
+361
+00:44:49,150 --> 00:44:53,230
+supported by a horizontal surface block A جاي على
+
+362
+00:44:53,230 --> 00:45:00,450
+مستوى أفقي neglecting friction إذا تم إهمال
+
+363
+00:45:00,450 --> 00:45:04,990
+الاحتكاك determine the acceleration of the wedge
+
+364
+00:45:04,990 --> 00:45:07,850
+يعني ال acceleration ل block A و ال acceleration
+
+365
+00:45:07,850 --> 00:45:12,950
+of the block اللي هو B بده ال acceleration ل A و
+
+366
+00:45:12,950 --> 00:45:20,070
+ال acceleration ل B طيب
+
+367
+00:45:20,070 --> 00:45:30,350
+معناته أنا سأعمل three body diagrams ل A و ل B عند
+
+368
+00:45:30,350 --> 00:45:30,930
+هاي A
+
+369
+00:45:38,900 --> 00:45:45,580
+ماذا يؤثر على A؟ وزنه
+
+370
+00:45:45,580 --> 00:45:53,740
+الوزن
+
+371
+00:45:53,740 --> 00:45:58,820
+الوزن الوزن الوزن الوزن
+
+372
+00:45:58,820 --> 00:46:02,760
+الوزن
+
+373
+00:46:02,760 --> 00:46:05,060
+الوزن الوزن الوزن الوزن الوزن الوزن الوزن الوزن
+
+374
+00:46:05,060 --> 00:46:08,220
+الوزن الوزن الوزن الوزن
+
+375
+00:46:10,270 --> 00:46:17,310
+وفي رد الفعل من block B N 2 ولا يوجد احتكاك في
+
+376
+00:46:17,310 --> 00:46:26,050
+احتكاك هو يقول لي لا يوجد احتكاك هذا حيث ساوى
+
+377
+00:46:26,050 --> 00:46:31,830
+ال
+
+378
+00:46:31,830 --> 00:46:35,870
+A مسموح له بالتحرك باتجاه الأفقي ما أنت تقولين دي هنا
+
+379
+00:46:35,870 --> 00:46:38,570
+M A
+
+380
+00:46:43,060 --> 00:47:00,000
+AA هذا بالنسبة لـ Block A بالنسبة لـ Block B Block
+
+381
+00:47:00,000 --> 00:47:09,720
+B فيه بيأثر وزنه WB
+
+382
+00:47:14,410 --> 00:47:21,330
+وفي رد الفعل من A على B يعني عكس N2 هذا
+
+383
+00:47:21,330 --> 00:47:28,590
+هذا
+
+384
+00:47:28,590 --> 00:47:32,370
+تساوي ثلاثين
+
+385
+00:47:32,370 --> 00:47:36,150
+درجة هذا تساوي
+
+386
+00:47:52,920 --> 00:48:04,580
+مش اتجاه ال acceleration بتاعة A بتاعة B لتحت ما
+
+387
+00:48:04,580 --> 00:48:10,220
+هو A هيكون ماشي و B بنزلق عليه معناته لتحت هد مش
+
+388
+00:48:10,220 --> 00:48:13,240
+سرعة مش ال acceleration بتاعة B ال B بالنسبة ل A
+
+389
+00:48:13,240 --> 00:48:26,140
+يعني أنا سأحكي التالي انه ABك vector بيستوي a a زاد a
+
+390
+00:48:26,140 --> 00:48:32,680
+b بالنسبة ل a صح؟
+
+391
+00:48:32,680 --> 00:48:41,400
+a a كيف اتجاهها؟ هاي اتجاه a؟ a a هاي اتجاهها و
+
+392
+00:48:41,400 --> 00:48:45,680
+a b a لتحت
+
+393
+00:48:52,450 --> 00:48:58,150
+بزاوية ثلاثين درجة معناته
+
+394
+00:48:58,150 --> 00:49:03,090
+AB بيكون عبّر عنها بال two components فعلا مباشرة
+
+395
+00:49:03,090 --> 00:49:10,470
+أنه أحكي هذه تساوي و
+
+396
+00:49:10,470 --> 00:49:15,550
+في لها مركب لتحت هذه
+
+397
+00:49:15,550 --> 00:49:26,800
+كلها تنتيل مع بعض AB معناته هتكون هذه AA في mb
+
+398
+00:49:26,800 --> 00:49:37,300
+وهذا a b a في mb واضح
+
+399
+00:49:37,300 --> 00:49:43,480
+هذا b
+
+400
+00:49:43,480 --> 00:49:48,560
+مش مش ماشي حر لحاله الآن a ماشي بهذا الاتجاه
+
+401
+00:49:49,730 --> 00:49:53,150
+وبنزلق بالنسبة له معناته ببساطة هبقى أنا اي بي
+
+402
+00:49:53,150 --> 00:49:57,750
+بيستوي a a زاد a b a هاي المراكبة هي حاطط هدول
+
+403
+00:49:57,750 --> 00:50:02,550
+بدل a b حاطيتهم هنا هاي a a وهذه a b a اللي هو ال
+
+404
+00:50:02,550 --> 00:50:08,030
+vector الصم ل a a و a b a هم مثله a b هتكون معناته
+
+405
+00:50:08,030 --> 00:50:16,310
+هذه هتكون تساوي mb في a b وهي a b هتكون a a mb
+
+406
+00:50:16,310 --> 00:50:18,330
+زاد a b a في mb
+
+407
+00:50:23,860 --> 00:50:32,600
+هذه الزاوية ثلاثين درجة وهذه
+
+408
+00:50:32,600 --> 00:50:36,920
+ثلاثين
+
+409
+00:50:36,920 --> 00:50:41,060
+درجة خلنا
+
+410
+00:50:41,060 --> 00:50:45,640
+نُحط المحاور أنا عشان يكون شيء كامل بده أحط ال X
+
+411
+00:50:45,640 --> 00:50:49,240
+موجب وال Y موجب
+
+412
+00:50:59,200 --> 00:51:04,840
+Summation of forces باتجاه ال Y في
+
+413
+00:51:04,840 --> 00:51:10,480
+حركة باتجاه ال Y؟ مافيش ما تتحركش معناه Summation
+
+414
+00:51:10,480 --> 00:51:17,880
+of forces مش هيكون ساوى سفر وأنا حددت لتجاه الموجب
+
+415
+00:51:17,880 --> 00:51:20,980
+ده أنا ده من المرجعيات مهمة كتير عندي أنا حاطب
+
+416
+00:51:20,980 --> 00:51:25,380
+المرجعية هنا وبرضه بحطها هنا لما أكتب المعادلة ال
+
+417
+00:51:25,380 --> 00:51:32,860
+Summation of forces سيكون عندي N واحد minus WA
+
+418
+00:51:32,860 --> 00:51:38,720
+minus
+
+419
+00:51:38,720 --> 00:51:49,460
+N2 Cos 30 بيساوي
+
+420
+00:51:49,460 --> 00:51:57,200
+ايش؟ صفر WA
+
+421
+00:51:57,200 --> 00:51:58,160
+أكبر ما أعطينيها
+
+422
+00:52:01,750 --> 00:52:10,070
+ثلاثين W A ثلاثين
+
+423
+00:52:10,070 --> 00:52:19,670
+pound و W B مستوى اثنا عشر pound يعني أنا هكون عندي
+
+424
+00:52:19,670 --> 00:52:24,030
+N واحد ناقص
+
+425
+00:52:24,030 --> 00:52:28,030
+N اثنين cos  الثلاثين
+
+426
+00:52:31,040 --> 00:52:39,580
+بتساوي W A التي هي ثلاثين هذه
+
+427
+00:52:39,580 --> 00:52:44,700
+معادلة واحدة باتجاه
+
+428
+00:52:44,700 --> 00:52:50,200
+الـ X summation of forces باتجاه
+
+429
+00:52:50,200 --> 00:52:58,340
+الـ X بيساوي M A A باتجاه الـ X
+
+430
+00:53:02,420 --> 00:53:14,260
+هيكون طبعًا عندي N2 N2 sin 30 هتساوي
+
+431
+00:53:14,260 --> 00:53:23,180
+M A A يعني
+
+432
+00:53:23,180 --> 00:53:33,500
+هتساوي M A عبارة عن 30 هذا وزن بدي أحوله لكتلة هقسم
+
+433
+00:53:33,500 --> 00:53:48,940
+على 32.2 a a يعني أنتم أنتم
+
+434
+00:53:48,940 --> 00:53:54,500
+sin الـ 30 بتساوي
+
+435
+00:53:54,500 --> 00:54:09,640
+30 على 32.2 من 10 a a هي معادلة اثنين نجي
+
+436
+00:54:09,640 --> 00:54:15,400
+لجسم B نعم
+
+437
+00:54:15,400 --> 00:54:21,900
+بالضبط هاي نجي
+
+438
+00:54:21,900 --> 00:54:27,480
+لـ .. أول شيء هاد المفهوم هاد كيف اجت؟ طيب
+
+439
+00:54:35,690 --> 00:54:40,090
+هذه اتجاه الـ X هذه
+
+440
+00:54:40,090 --> 00:54:46,090
+اتجاه الـ Y إحنا دايمًا لازم نوثق و نوثق صح أن أحط
+
+441
+00:54:46,090 --> 00:54:49,610
+المرجع هذا جزء من عملية التوثيق إحنا أي عمل بتكون
+
+442
+00:54:49,610 --> 00:54:55,110
+من ست خطوات ايش حكينا هي الخطوات؟ جمع البيانات
+
+443
+00:54:55,110 --> 00:55:02,350
+وتحليلها تعمل خطة تنفذ الخطة تتأكد أن شغلك صح
+
+444
+00:55:02,350 --> 00:55:04,650
+التحكم التوثيق
+
+445
+00:55:06,060 --> 00:55:09,700
+اللي هو ايش بعد التوثيق reflection أو linkage تحسين
+
+446
+00:55:09,700 --> 00:55:14,860
+منحنى التعلم بتاعك وتطرح حلول أو تحسين الحال
+
+447
+00:55:14,860 --> 00:55:19,740
+لمثائق مشابهة مستقبليًا فإحنا جزء من العملية أن نوثق
+
+448
+00:55:19,740 --> 00:55:23,280
+صح summation
+
+449
+00:55:23,280 --> 00:55:28,880
+للـ forces باتجاه الـ X summation للـ forces لاتجاه
+
+450
+00:55:28,880 --> 00:55:39,320
+الـ X هاي لاتجاه الموجة بيساوي M B A B باتجاه الـ X
+
+451
+00:55:39,320 --> 00:55:55,260
+اتجاه الـ X عندي minus N2 sin 30 minus N2
+
+452
+00:55:55,260 --> 00:55:57,820
+sin 30
+
+453
+00:56:08,510 --> 00:56:14,990
+N B A A ناقص
+
+454
+00:56:14,990 --> 00:56:32,550
+N B A B بالنسبة لـ A Cos 30 يعني
+
+455
+00:56:32,550 --> 00:56:33,950
+ناقص N2
+
+456
+00:56:37,050 --> 00:56:48,570
+Sin 30 هتساوي M B 12 على
+
+457
+00:56:48,570 --> 00:57:01,150
+32.2 12 a a ناقص 12 على 32.2 12 a b a في cos 30
+
+458
+00:57:01,150 --> 00:57:04,450
+هذه
+
+459
+00:57:04,450 --> 00:57:12,470
+المعادلة رقم ايه؟ رقم ثلاثة بس هكتبها بصيغة هدق
+
+460
+00:57:12,470 --> 00:57:20,510
+أظبطها هتكون هدق and two sine الثلاثين ناقص ثلاثين
+
+461
+00:57:20,510 --> 00:57:25,450
+على اثنين و ثلاثين و اثنين من عشرة a a بالساوية
+
+462
+00:57:25,450 --> 00:57:37,330
+سفير هدق هتكون minus and two sine الثلاثين ناقص
+
+463
+00:58:01,310 --> 00:58:06,330
+عندي so far أكمل معادلة عندي معادلة واحدة اثنتين
+
+464
+00:58:06,330 --> 00:58:11,790
+ثلاثة كم مجهول عندي N واحد و N اثنين و A A و A B A
+
+465
+00:58:11,790 --> 00:58:14,830
+عندي أربع مجاهيل و ثلاث معادلات ما أنا أنا محتاج
+
+466
+00:58:14,830 --> 00:58:22,210
+معادلة رابعة معادلة رابعة هاخد
+
+467
+00:58:22,210 --> 00:58:27,490
+summation باتجاه الـ Y summation للـ forces باتجاه
+
+468
+00:58:27,490 --> 00:58:32,070
+الـ Y بتساوي
+
+469
+00:58:32,070 --> 00:58:33,670
+M B
+
+470
+00:58:35,750 --> 00:58:45,790
+A B باتجاه الـ Y باتجاه الـ Y هكون دي N2 Cos ال
+
+471
+00:58:45,790 --> 00:58:54,510
+30 minus W B بتساوي
+
+472
+00:58:54,510 --> 00:59:03,610
+minus M B A B A Sin
+
+473
+00:59:07,490 --> 00:59:18,610
+الثلاثين يعني أنا هكون عند N2 Cos 30 زائد
+
+474
+00:59:18,610 --> 00:59:32,810
+هجيب هذين N B 12 على 32.2 A B A Sin 30 بتساوي W B
+
+475
+00:59:32,810 --> 00:59:33,710
+12
+
+476
+00:59:37,520 --> 00:59:45,900
+هذه معادلة ايه؟ أربعة لأن
+
+477
+00:59:45,900 --> 00:59:48,940
+عندي أربع معادلات وأربع مجاهيل بدي أصفطهم تحت بعض
+
+478
+00:59:48,940 --> 00:59:54,140
+أول معادلة N1
+
+479
+00:59:54,140 --> 01:00:00,500
+minus
+
+480
+01:00:00,500 --> 01:00:02,300
+N2
+
+481
+01:00:05,970 --> 01:00:12,530
+cos 30 بتساوي
+
+482
+01:00:12,530 --> 01:00:22,450
+30 المعادلة الثانية هادئ
+
+483
+01:00:22,450 --> 01:00:30,370
+المعادلة
+
+484
+01:00:30,370 --> 01:00:33,770
+الثانية هتكون عند n 2 cos 30
+
+485
+01:00:41,490 --> 01:00:49,410
+ناقص ثلاثين على اثنين و ثلاثين .2 a a
+
+486
+01:00:49,410 --> 01:00:59,830
+بالساوية ايش صفر المعادلة الثالثة ناقص ان اثنين
+
+487
+01:00:59,830 --> 01:01:04,110
+ناقص
+
+488
+01:01:04,110 --> 01:01:08,130
+ان اثنين sin الثلاثين
+
+489
+01:01:11,000 --> 01:01:20,440
+ناقص اثنا عشر على اثنين و ثلاثين .2 A A زائد
+
+490
+01:01:20,440 --> 01:01:30,600
+اثنا عشر على اثنين و ثلاثين .2 A B A بتساوي
+
+491
+01:01:30,600 --> 01:01:34,400
+cos
+
+492
+01:01:34,400 --> 01:01:39,600
+الثلاثين بتساوي
+
+493
+01:01:41,110 --> 01:01:51,010
+صفر المعادلة الرابعة لها دي and two cos
+
+494
+01:01:51,010 --> 01:01:56,970
+الثلاثين زائد
+
+495
+01:01:56,970 --> 01:02:07,950
+اثنا عشر على اثنين وثلاثين .2 A B A sine
+
+496
+01:02:07,950 --> 01:02:08,650
+الثلاثين
+
+497
+01:02:11,970 --> 01:02:18,310
+بساوة اثنا عشر هدول
+
+498
+01:02:18,310 --> 01:02:21,510
+أربع معادلات اعونها أنا عملتهم هيك عشان أعملهم على
+
+499
+01:02:21,510 --> 01:02:29,170
+شكل مصفوفة الطرف هذا الثوابت يعني هدا كانها a x
+
+500
+01:02:29,170 --> 01:02:36,400
+بساوة b و ايه هذا مصفوفة مربعة و الـ X هذا ال vector
+
+501
+01:02:36,400 --> 01:02:41,520
+of variables و الـ B ال vector of constants هذا
+
+502
+01:02:41,520 --> 01:02:44,260
+أساس الـ .. الـ .. الـ linear algebra و أساس الـ
+
+503
+01:02:44,260 --> 01:02:48,140
+finite element هذا كل الشغل هذا طيب هيكون عندي هين
+
+504
+01:02:48,140 --> 01:02:54,480
+لو أعمل مصفوفة واحد
+
+505
+01:02:57,910 --> 01:03:02,510
+ناقص cos الثلاثين ناقص cos الثلاثين اللي هي جزء
+
+506
+01:03:02,510 --> 01:03:09,550
+ثلاثة على اثنين صح ان
+
+507
+01:03:09,550 --> 01:03:18,210
+واحد ان اثنين و صفر صفر صح المعادلة الثانية صفر
+
+508
+01:03:18,210 --> 01:03:25,450
+cos الثلاثين نص وهنا
+
+509
+01:03:25,450 --> 01:03:26,730
+عندي ناقص ثلاثين
+
+510
+01:03:30,190 --> 01:03:35,850
+على اثنين و ثلاثين و اثنين و عشرة و صفر المعادلة
+
+511
+01:03:35,850 --> 01:03:45,150
+الثالثة صفر و ناقص نص و
+
+512
+01:03:45,150 --> 01:03:52,690
+ناقص اثنا عشر على اثنين و ثلاثين و اثنين و عشرة و
+
+513
+01:03:52,690 --> 01:03:57,090
+اثنا عشر على
+
+514
+01:03:57,090 --> 01:04:03,010
+اثنين و ثلاثين و اثنين من عشرة في cos ثلاثة على
+
+515
+01:04:03,010 --> 01:04:11,590
+اثنين المعادلة الرابعة اللي هي صفر cos ثلاثة على
+
+516
+01:04:11,590 --> 01:04:15,930
+اثنين و
+
+517
+01:04:15,930 --> 01:04:23,790
+صفر و
+
+518
+01:04:23,790 --> 01:04:25,890
+ستة
+
+519
+01:04:27,630 --> 01:04:37,130
+على اثنين و ثلاثين و اثنين من عشرة N واحد
+
+520
+01:04:37,130 --> 01:04:53,730
+N اثنين A A و A B A هتساوي ثلاثين صفر صفر اثنا عشر
+
+521
+01:04:56,050 --> 01:04:57,830
+الحاجات اللي ممكن تعملها is reduce,
+
+522
+01:05:02,150 --> 01:05:04,470
+draw,
+
+523
+01:05:08,410 --> 01:05:16,710
+echelon form أو ممكن تعمل triangular
+
+524
+01:05:26,510 --> 01:05:33,130
+بعدين solve four
+
+525
+01:05:33,130 --> 01:05:43,490
+n واحد n اثنين a a و a b a هذا
+
+526
+01:05:43,490 --> 01:05:52,930
+المصطلح سميها ايه هذي x هذي ايه بيه الـ x هتساوي
+
+527
+01:05:56,120 --> 01:06:00,440
+A inverse في
+
+528
+01:06:00,440 --> 01:06:03,960
+B نعم
+
+529
+01:06:03,960 --> 01:06:12,340
+أشوف
+
+530
+01:06:12,340 --> 01:06:17,320
+إذا في Mathematica هنا نازل شوية بس
+
+531
+01:06:28,790 --> 01:06:32,030
+طيب على أي حال هتحلوها على الـ math lab أو الـ
+
+532
+01:06:32,030 --> 01:06:37,450
+mathematics حتة وممكن تحلوها بطريقة تقليدية انه
+
+533
+01:06:37,450 --> 01:06:43,150
+شوية تحل اثنتين اثنتين بتخليهم ثلاثة variables بعدين
+
+534
+01:06:43,150 --> 01:06:45,830
+ثلاثة variables بتخليهم بتحل .. بيصير لك two
+
+535
+01:06:45,830 --> 01:06:50,770
+variables بعدين ايش one variable اللي هو في الواقع
+
+536
+01:06:50,770 --> 01:06:55,030
+أنت بتكون سويت ايش reduced row at four يعني الـ row
+
+537
+01:06:55,030 --> 01:07:16,970
+at four هتصير مصبوغة هيك الشكلحسيت شكل المصوفة حلها
+
+538
+01:07:16,970 --> 01:07:24,170
+يدوي حلها يدوي طيب فأنت بتخلي أنا بكون عندي هذا ال
+
+539
+01:07:24,170 --> 01:07:29,610
+term بتطرح و تجمع الصفوف بيصير ان دي بس هذا مبين في
+
+540
+01:07:29,610 --> 01:07:34,970
+الأول بتحل الأول آخر variable بعدين هذا بتكون يعني
+
+541
+01:07:34,970 --> 01:07:40,110
+أول ثلاثة صفر بعدين هنا اثنين صفر بعدين هنا واحد
+
+542
+01:07:40,110 --> 01:07:46,310
+صفر بتحل أول معادلة الثاني بتحل الثاني الثالث جبر
+
+543
+01:07:46,310 --> 01:07:54,200
+خطي طيب في أي سؤال هذا بندول the bob of a two meter
+
+544
+01:07:54,200 --> 01:07:59,420
+pendulum طول الحبل تاع البندول اثنين متر describes
+
+545
+01:07:59,420 --> 01:08:02,440
+an arc of a circle in a vertical plane يعني
+
+546
+01:08:02,440 --> 01:08:07,940
+البندول بتحرك في المستوى الرأسي if the tension in
+
+547
+01:08:07,940 --> 01:08:11,760
+the cord is 2.5 times the weight of the
+
+548
+01:08:11,760 --> 01:08:16,040
+bob for the position shown لما كانت زوايا ثلاثين
+
+549
+01:08:16,040 --> 01:08:20,360
+درجة إذا كان الشد في الحبل بيساوي اثنين و نصف ضعف
+
+550
+01:08:20,360 --> 01:08:21,840
+الوزن
+
+551
+01:08:24,030 --> 01:08:29,330
+find the velocity وجد السرعة and acceleration of
+
+552
+01:08:29,330 --> 01:08:33,470
+the ball in that position يعني وجد ال acceleration
+
+553
+01:08:33,470 --> 01:08:41,030
+للكورة هذه و السرعة لما تكون الزاوية ثلاثين درجة
+
+554
+01:08:41,030 --> 01:08:45,950
+إذا كنا عارفين إن الوزن أو الشد بيساوي اثنين و نصف
+
+555
+01:08:45,950 --> 01:08:46,610
+الوزن
+
+556
+01:08:50,340 --> 01:08:53,680
+مثال زي هيك بحكي عن شد ووزن معناته لازم نعمل free
+
+557
+01:08:53,680 --> 01:09:01,620
+body diagram هاي عندي هاي
+
+558
+01:09:01,620 --> 01:09:14,480
+البندول ايش ال forces بتأثر على البندول M G و
+
+559
+01:09:14,480 --> 01:09:19,040
+شد في اتجاه الحبل و هذه الزاوية
+
+560
+01:09:21,980 --> 01:09:28,900
+ثلاثين درجة الآن
+
+561
+01:09:28,900 --> 01:09:35,940
+نتيجة هذا الحصيلة دي هتكون طبعا لها مركبتين أصلا ليش
+
+562
+01:09:35,940 --> 01:09:43,000
+أنا أخد tangential و normal من ايه
+
+563
+01:09:43,000 --> 01:09:48,840
+normal و
+
+564
+01:09:48,840 --> 01:09:56,600
+ايه tangential والزاوية هي دي تلاتين
+
+565
+01:09:56,600 --> 01:10:07,780
+درجة وعرف عندي هي ET وها
+
+566
+01:10:07,780 --> 01:10:14,660
+دي E normal هي كأننا وصفت المثلث بشكل كامل حاطط
+
+567
+01:10:14,660 --> 01:10:18,640
+محاور إحداثيات وحاطط كل ال forces و ال
+
+568
+01:10:18,640 --> 01:10:20,260
+accelerations بيبين كل شيء عندي
+
+569
+01:10:28,630 --> 01:10:32,890
+طيب مجموع ال forces في اتجاه ال normal direction
+
+570
+01:10:32,890 --> 01:10:40,910
+هأخد و في اتجاه ال tangent summation لل FN بهذا
+
+571
+01:10:40,910 --> 01:10:45,010
+الاتجاه بالمثل
+
+572
+01:10:45,010 --> 01:10:50,210
+M A Normal إذا كان لدي ال T
+
+573
+01:11:03,530 --> 01:11:15,670
+هتكون Mg cos T minus Mg cos 30 هسميها θ التي هي 30
+
+574
+01:11:15,670 --> 01:11:19,810
+cos θ بالمثل
+
+575
+01:11:19,810 --> 01:11:29,210
+M a normal V
+
+576
+01:11:29,210 --> 01:11:33,170
+square على L M
+
+577
+01:11:34,580 --> 01:11:40,120
+خليها a normal ال T هو بيحكي ال T بيساوي اتنين و
+
+578
+01:11:40,120 --> 01:11:48,460
+نص الوزن يعني ال T بيساوي اتنين و نص Mg minus Mg
+
+579
+01:11:48,460 --> 01:11:55,960
+cosine theta سواء M a normal معناته a normal
+
+580
+01:12:04,980 --> 01:12:17,140
+تكون اتنين و نص في تسعة point تمانية صفر ستة ناقص
+
+581
+01:12:17,140 --> 01:12:23,640
+تسعة
+
+582
+01:12:23,640 --> 01:12:32,960
+point تمانية صفر ستة في اتنين و نص ناقص
+
+583
+01:12:32,960 --> 01:12:34,000
+كوساين التلاتين
+
+584
+01:12:38,540 --> 01:12:44,540
+هتطلع كم؟ meter
+
+585
+01:12:44,540 --> 01:12:50,720
+per second square وهي اتجاهها و بتعمل زاوية ايش
+
+586
+01:12:50,720 --> 01:12:56,560
+هذه
+
+587
+01:12:56,560 --> 01:13:01,960
+a normal a normal ايش بالثانوية برضه؟
+
+588
+01:13:01,960 --> 01:13:09,510
+V square على L صح؟ معناته ال V هتكون جذر التربيعي ل
+
+589
+01:13:09,510 --> 01:13:18,050
+a normal في L يعني ال V تساوي جذر التربيعي ل 16
+
+590
+01:13:18,050 --> 01:13:27,790
+point صفر اثنين اثنين ال L كم تساوي اثنين
+
+591
+01:13:27,790 --> 01:13:29,430
+متر per second
+
+592
+01:13:37,550 --> 01:13:43,110
+هدي E normal بدنا لسه نجيب ال a tangential
+
+593
+01:13:43,110 --> 01:13:53,630
+صح؟ معناه هنجيب summation of forces في اتجاه ال
+
+594
+01:13:53,630 --> 01:14:01,430
+tangential direction بالمثل م a tangential هيكون
+
+595
+01:14:01,430 --> 01:14:03,490
+عندي mg sin 30
+
+596
+01:14:10,920 --> 01:14:24,560
+بيساوي MA tangential يعني AT نصف و نص ال G ل 4.903
+
+597
+01:14:24,560 --> 01:14:29,780
+متر على second square معناته أنا عندي
+
+598
+01:14:40,530 --> 01:14:45,010
+A tangential وعندي
+
+599
+01:14:45,010 --> 01:14:48,770
+A normal
+
+600
+01:14:48,770 --> 01:14:58,510
+وعندي
+
+601
+01:14:58,510 --> 01:15:02,370
+هنا A
+
+602
+01:15:02,370 --> 01:15:02,970
+tangential
+
+603
+01:15:08,710 --> 01:15:15,830
+المحصلة لها دي a a
+
+604
+01:15:15,830 --> 01:15:22,710
+هتكون جذر التربيعي ل a normal تربيع زائد a
+
+605
+01:15:22,710 --> 01:15:27,650
+tangential تربيع هتساوي جذر التربيعي لستة عشر point صفر
+
+606
+01:15:27,650 --> 01:15:35,310
+اثنين اثنين تربيع زائد أربعة point تسعة صفر ثلاثة
+
+607
+01:15:35,310 --> 01:15:36,090
+تربيع
+
+608
+01:15:39,190 --> 01:15:44,570
+هتطلع كم؟ ستة عشر
+
+609
+01:15:44,570 --> 01:15:54,970
+point سبعة خمسة خمسة سبعة خمسة خمسة متر
+
+610
+01:15:54,970 --> 01:16:04,830
+per second square الزاوية هذه هذه
+
+611
+01:16:07,720 --> 01:16:14,040
+بنسميها beta تان
+
+612
+01:16:14,040 --> 01:16:23,000
+انفرس ل a normal على a tangential يعني تان انفرس ل
+
+613
+01:16:23,000 --> 01:16:28,980
+16.022 على 4.903
+
+614
+01:16:52,810 --> 01:17:00,930
+تسعة و ثمانية تسعة و ثمانية تلاتة و سبعين هذه
+
+615
+01:17:00,930 --> 01:17:05,890
+زاوية تلاتة و سبعين وهذه زاوية أكم
+
+616
+01:17:05,890 --> 01:17:12,530
+هذه تلاتين صح معناته
+
+617
+01:17:12,530 --> 01:17:20,830
+A هتكون تساوي ستة عشر point سبعة خمسة خمسة متر على
+
+618
+01:17:20,830 --> 01:17:26,640
+ثانية تربيع و بتعمل مع الأفق زاوية
+
+619
+01:17:26,640 --> 01:17:34,200
+43 درجة
+
+620
+01:17:34,200 --> 01:17:43,160
+عرف
+
+621
+01:17:43,160 --> 01:17:49,300
+الزمن أنت؟ ايه ماشي بتحلها بالطريقة اللي بتحكيها
+
+622
+01:17:53,020 --> 01:17:59,620
+بس .. كمان
+
+623
+01:17:59,620 --> 01:18:05,720
+مرة السؤال .. كمان مرة السؤال انه جالنا عند ال ها
+
+624
+01:18:05,720 --> 01:18:10,080
+دي كانت عند ال T زيرو تساوي تلاتين درجة ايش ال ..
+
+625
+01:18:10,080 --> 01:18:15,760
+تلاتين زاوية تلاتين درجة اه بيقولك عند ال T مثلا
+
+626
+01:18:15,760 --> 01:18:18,860
+أربعة أو أي T هنحسن ان ال V نوت هي ال V اللي
+
+627
+01:18:18,860 --> 01:18:30,390
+طلعناها الآن السؤال هل ال AT constant افحص
+
+628
+01:18:30,390 --> 01:18:33,870
+شوف إذا ال AT constant بيكون ممكن تحل بالطرق
+
+629
+01:18:33,870 --> 01:18:38,290
+التقليدية انه في اتجاه التنجيش ال direction V
+
+630
+01:18:38,290 --> 01:18:44,730
+بالمثل اعمل المعادلة الحركة لحالك as a function
+
+631
+01:18:44,730 --> 01:18:50,050
+of θ طبعا اكيد linear for a small angle اكيد بتكون
+
+632
+01:18:50,050 --> 01:18:50,630
+constant
+
+633
+01:18:54,340 --> 01:18:59,380
+افحصها، افحص ليها، رد لي الخبر المرة الجاية طيب سؤال
+
+634
+01:18:59,380 --> 01:19:06,400
+تاني تلاتة
+
+635
+01:19:06,400 --> 01:19:11,160
+و أربعين، هذه كلها تلاتة و سبعين، و هذه كلها أكم؟
+
+636
+01:19:11,160 --> 01:19:14,480
+تلاتين، معناته هذه أكم؟ تلاتة و أربعين، اللي هي
+
+637
+01:19:14,480 --> 01:19:17,060
+تلاتة و سبعين ناقص تلاتين، تلاتة و أربعين
+
+638
+01:19:25,620 --> 01:19:27,620
+طيب محاضرة جاية بنكمل
diff --git a/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/t4tgqiSXs1o_postprocess.srt b/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/t4tgqiSXs1o_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c10ae54cb038590efe9c59076d72b248f1c53d6c
--- /dev/null
+++ b/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/t4tgqiSXs1o_postprocess.srt
@@ -0,0 +1,1404 @@
+1
+00:00:05,380 --> 00:00:08,040
+بسم الله الرحمن الرحيم السلام عليكم و رحمة الله و
+
+2
+00:00:08,040 --> 00:00:11,720
+بركاته اليوم هنكمل المحاضرة في ال .. اللي هو
+
+3
+00:00:11,720 --> 00:00:16,420
+المحاضرة الفاترة تتحكي عن ال principle of work and
+
+4
+00:00:16,420 --> 00:00:19,640
+energy المحاضرة هنحكي عن ال principle of impulse
+
+5
+00:00:19,640 --> 00:00:23,720
+and momentum طبعا في ال principle of impulse and
+
+6
+00:00:23,720 --> 00:00:27,560
+momentum احنا نربط بين .. في الحل المفسير نربط بين
+
+7
+00:00:27,560 --> 00:00:34,930
+الزمن و السرعة و ال forcesو هنتعرف على مصطلحات
+
+8
+00:00:34,930 --> 00:00:39,530
+تتضمن impulsive motion و التصادمات انا عندهين
+
+9
+00:00:39,530 --> 00:00:46,990
+rigid body عندى محاولة احداثيات X و Y عندى
+
+10
+00:00:46,990 --> 00:00:51,190
+الصراعات ل different particles على ال body عندى
+
+11
+00:00:51,190 --> 00:00:55,350
+مجموعة من القوة الخارجية بتأثر على الجسم نتيجة
+
+12
+00:00:55,350 --> 00:00:58,650
+القوة الخارجية اكيد ال .. ال .. ال momentum ل
+
+13
+00:00:58,650 --> 00:01:03,110
+different particles forming the body هتتغيربشكل
+
+14
+00:01:03,110 --> 00:01:09,730
+عام الزخم واحد زائد ال summation لل external
+
+15
+00:01:09,730 --> 00:01:12,910
+impulse من واحد لاتنين بالساوية الزخم اتنين يعني
+
+16
+00:01:12,910 --> 00:01:16,630
+system momentum واحد زائد system external impulse
+
+17
+00:01:16,630 --> 00:01:19,970
+من واحد لاتنين بالساوية system momentum اتنين
+
+18
+00:01:23,510 --> 00:01:31,730
+الـ momentum of particles forming ال body ممكن
+
+19
+00:01:31,730 --> 00:01:34,870
+تكون مكوّن من جزءين جزء اللي هو linear momentum
+
+20
+00:01:34,870 --> 00:01:38,830
+linear momentum لكل الجسم بالساوية ال mass بتاعته
+
+21
+00:01:38,830 --> 00:01:46,350
+في صورة المركز الثقل زاد couple hg بالساوية اللي
+
+22
+00:01:46,350 --> 00:01:53,030
+هو I في Omegaال I هي ال moment of inertia في حالة
+
+23
+00:01:53,030 --> 00:01:58,950
+plan motion for
+
+24
+00:01:58,950 --> 00:02:01,130
+a rigid body which is symmetrical with respect to
+
+25
+00:02:01,130 --> 00:02:04,110
+the reference frame بتكون ال HG بسوء I في Omega
+
+26
+00:02:04,110 --> 00:02:09,690
+معناته الممنتع للجسم مكون جزء ان جزء due to زخم
+
+27
+00:02:09,690 --> 00:02:14,040
+الخطو due to الزخم الزاوية جزئية due to الزخم
+
+28
+00:02:14,040 --> 00:02:16,800
+الخطي هتكون linear momentum اللي هي ال mass في
+
+29
+00:02:16,800 --> 00:02:21,920
+سرعة مركز استقل الجزئية ال notch عن الزخم الزاوية
+
+30
+00:02:21,920 --> 00:02:24,940
+HG بالساوية I في Omega I اللي هي المتوبة ان هي حول
+
+31
+00:02:24,940 --> 00:02:27,900
+المركز استقل و ال Omega هي السرعة الزاوية للجسم
+
+32
+00:02:27,900 --> 00:02:30,820
+طبعا هذا في حالة rigid body symmetrical with
+
+33
+00:02:30,820 --> 00:02:32,780
+respect to the reference plane
+
+34
+00:02:36,530 --> 00:02:41,030
+هندرس ال plan motion of a rigid body في البداية
+
+35
+00:02:41,030 --> 00:02:48,750
+كان عندي الجسم له linear momentum MV1 و angular
+
+36
+00:02:48,750 --> 00:02:56,710
+momentum I omega 1 مؤثر عليه external forces FDT
+
+37
+00:02:56,710 --> 00:03:03,150
+عندها F force 1 F2 F3 ويلهم زخم F1DT
+
+38
+00:03:03,150 --> 00:03:09,240
+F2DT F3DTنتجة الـ External forces هيتغير الذخم
+
+39
+00:03:09,240 --> 00:03:11,060
+الخطي والذخم الزاوية
+
+40
+00:03:19,710 --> 00:03:23,190
+طبعا ال system البياني دي هذا يعبر عن تلت معادلات
+
+41
+00:03:23,190 --> 00:03:27,970
+معادل للمومنتا في اتجاه ال X axis للمومنتا في
+
+42
+00:03:27,970 --> 00:03:32,870
+اتجاه ال Y axis والمعادلة التالتة ال moment of
+
+43
+00:03:32,870 --> 00:03:37,490
+momenta and impulses about a given point المعنى
+
+44
+00:03:37,490 --> 00:03:40,950
+تلت معادلات معادلة في ال X ومعادلة في ال Y ومعادلة
+
+45
+00:03:40,950 --> 00:03:46,330
+اللي هي عزم الذخم
+
+46
+00:03:46,330 --> 00:03:48,690
+بالنسبة لأي نقطة انا باختارها
+
+47
+00:03:52,650 --> 00:03:58,430
+في حالة non-centroidal rotation في
+
+48
+00:03:58,430 --> 00:04:02,690
+حالة non-centroidal rotation انا فيه عندهين جسم
+
+49
+00:04:02,690 --> 00:04:12,610
+بدور حوالي نقطة O وهي مركز psychologyهتكون سرعة
+
+50
+00:04:12,610 --> 00:04:18,710
+مركزي او زخم لمركز ثقل هتكون M في V و في الواحد
+
+51
+00:04:18,710 --> 00:04:23,290
+اللي .. اللي .. اللي عنده اللي هو زخم زاوية I في
+
+52
+00:04:23,290 --> 00:04:30,870
+Omega I في Omega لو أخدت العزم حوالين O العزم
+
+53
+00:04:30,870 --> 00:04:41,450
+حوالين Oهيكون عندي ال MV في R زاد
+
+54
+00:04:41,450 --> 00:04:46,070
+I في Omega و V عبارة عن Omega في R يعني هتكون MR
+
+55
+00:04:46,070 --> 00:04:49,830
+Square يعني هتصفي ال I حوالين O يعني هيكون عندي I
+
+56
+00:04:49,830 --> 00:04:54,130
+O Omega واحد زاد اللي هو ال
+
+57
+00:04:57,030 --> 00:05:00,910
+الزخم اللي هو ال .. ال .. ال .. ال impulse الزاوية
+
+58
+00:05:00,910 --> 00:05:05,570
+من واحد لاتنين M O D T بيساوي الزخم الزاوية I O
+
+59
+00:05:05,570 --> 00:05:14,670
+Omega 2 حوالين O طيب
+
+60
+00:05:14,670 --> 00:05:17,170
+وين ال no external forces؟
+
+61
+00:05:19,120 --> 00:05:21,540
+acts on a rigid body or a system which was لمّا
+
+62
+00:05:21,540 --> 00:05:24,160
+مافيش عندك قوة خارجية بتأثر على الجسم أو نظام
+
+63
+00:05:24,160 --> 00:05:30,020
+الأجسام الجاسية بتكون الزخم عند ال time واحد
+
+64
+00:05:30,020 --> 00:05:33,920
+بالساوية الزخم عند ال time اتنين في الحالة هات
+
+65
+00:05:33,920 --> 00:05:37,420
+بيكون عندك conservation in both linear momentum او
+
+66
+00:05:37,420 --> 00:05:41,210
+conservation of angularmomentum يعني هكون L واحد
+
+67
+00:05:41,210 --> 00:05:45,570
+بيستوي L اتنين وH O واحد بيستوي H O two طبعا هذه
+
+68
+00:05:45,570 --> 00:05:50,310
+في حال كان مافيش قوة خارجية مؤثرة على ال rigid
+
+69
+00:05:50,310 --> 00:05:56,330
+body او ال system of rigid bodies اذا
+
+70
+00:05:56,330 --> 00:06:01,930
+كان sum مجموعة ال sum of angular impulses path
+
+71
+00:06:01,930 --> 00:06:06,780
+through اذا كان ال impulses بتمر في النقطة Oاللي
+
+72
+00:06:06,780 --> 00:06:10,260
+احنا هناخد ال moment حواليها في الحالة هذه طالما
+
+73
+00:06:10,260 --> 00:06:14,560
+ال impulses الخط عملها بيمر في النقطة اللي هناخد
+
+74
+00:06:14,560 --> 00:06:20,000
+العزم حواليها معناته تعملش عزم معناته ال angular
+
+75
+00:06:20,000 --> 00:06:25,300
+momentum is conserved لكن مش بالضرورة تكون ال
+
+76
+00:06:25,300 --> 00:06:27,960
+linear momentum conserved في حالة ان some angular
+
+77
+00:06:27,960 --> 00:06:32,140
+impulses بتمر في النقطة O about which we take
+
+78
+00:06:32,140 --> 00:06:36,620
+moments في الحالة هذهاللي we have conservation of
+
+79
+00:06:36,620 --> 00:06:40,260
+angular momentum but not conservation in linear
+
+80
+00:06:40,260 --> 00:06:44,640
+momentum يعني h o واحد بيستوى h o اتنين شوف نحل
+
+81
+00:06:44,640 --> 00:06:51,300
+الأمثلة هذا المثال سبق وحلناه باستخدام principle
+
+82
+00:06:51,300 --> 00:06:54,620
+of impulse and momentum خلينا نراجعه ال system is
+
+83
+00:06:54,620 --> 00:06:59,160
+at rest النظام هذا كان في حالة السكون في البداية
+
+84
+00:06:59,160 --> 00:07:04,260
+whensix newton meter moment is applied يعني عندي
+
+85
+00:07:04,260 --> 00:07:11,700
+هنا M ال
+
+86
+00:07:11,700 --> 00:07:17,820
+M قيمتها ستة نيوتن متر ال M قيمتها
+
+87
+00:07:17,820 --> 00:07:23,920
+ستة نيوتن مرة neglecting friction إذا تم اهمة
+
+88
+00:07:23,920 --> 00:07:30,140
+الاحتكار أو جدdetermine the time required for gear
+
+89
+00:07:30,140 --> 00:07:33,580
+B to reach an angular velocity of 600 rpm او دي
+
+90
+00:07:33,580 --> 00:07:38,040
+الزمن اللازم عشان السرعة الزاوية للgear B اتوصل
+
+91
+00:07:38,040 --> 00:07:43,060
+600 rpm طبعا معطيني ال mass ل A و ال rate of
+
+92
+00:07:43,060 --> 00:07:45,920
+gyration ل A و ال mass ل B و ال rate of gyration ل
+
+93
+00:07:45,920 --> 00:07:51,700
+B اللي منهم باحسب ال I ال moment of inertia ل A و
+
+94
+00:07:51,700 --> 00:07:55,000
+ال moment of inertia ل B يعني على السريع معطيني ال
+
+95
+00:07:55,000 --> 00:08:02,820
+M Aاللي هي عشرة كيلو جرام و ال MB اللي هي تلاتة
+
+96
+00:08:02,820 --> 00:08:12,620
+كيلو جرام و ال KA معطينيها اتين ملي متر و ال KB
+
+97
+00:08:12,620 --> 00:08:21,570
+معطينيها تمانين ملي متر من هدول بحسب ال IAاللي هي
+
+98
+00:08:21,570 --> 00:08:31,670
+M A K A تربية هتكون ال M A اللي هي عشرة
+
+99
+00:08:31,670 --> 00:08:36,150
+في point اتنين تربية يعني هتكون point four
+
+100
+00:08:36,150 --> 00:08:43,190
+kilogram متر تربية وال I B هتكون M B
+
+101
+00:09:01,530 --> 00:09:07,010
+الحسابات هتفيد بعد شوية الان سيكون لدي ال system
+
+102
+00:09:07,010 --> 00:09:08,150
+momentum واحد
+
+103
+00:09:12,320 --> 00:09:23,020
+بدي أخد كل واحد لحالي لو أخدت a لحالي هاي a وهاي
+
+104
+00:09:23,020 --> 00:09:28,820
+بي
+
+105
+00:09:28,820 --> 00:09:33,320
+عند
+
+106
+00:09:33,320 --> 00:09:39,120
+هنا هكون عندي ay وعندي
+
+107
+00:09:39,120 --> 00:09:39,720
+ax
+
+108
+00:09:54,020 --> 00:10:01,320
+في البداية عندي هيكون هذا بي هذا اي هذا بي
+
+109
+00:10:01,320 --> 00:10:05,240
+طبعا مركز ثقل بي مركز ثقل اي سرعته مصفر يعني عنده
+
+110
+00:10:05,240 --> 00:10:11,060
+هيكون عندي اي اي اي اي اي اي اي اي اي اي اي اي اي
+
+111
+00:10:11,060 --> 00:10:11,220
+اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي
+
+112
+00:10:11,220 --> 00:10:11,440
+اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي
+
+113
+00:10:11,440 --> 00:10:12,720
+اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي
+
+114
+00:10:12,720 --> 00:10:20,940
+اي اي اي اي اي اي اي اي اي اي
+
+115
+00:10:20,940 --> 00:10:26,590
+اي اي اي اي اي اي اي اي اي اي ازائد خلال الفترة
+
+116
+00:10:26,590 --> 00:10:36,890
+هذه هي a هي b هي
+
+117
+00:10:36,890 --> 00:10:51,110
+a هيكون عندى هنا ay في ال time في delta t وعندي ax
+
+118
+00:10:52,940 --> 00:11:00,760
+في Delta T وعندي هنا رد الفعل By في Delta T وعندي
+
+119
+00:11:00,760 --> 00:11:10,480
+Bx في Delta T وعندي ال moment M
+
+120
+00:11:10,480 --> 00:11:23,710
+Delta T وفي tangential force وعندي هناF Delta T
+
+121
+00:11:23,710 --> 00:11:34,610
+وفي عكسة H F Delta T هتساوي After
+
+122
+00:11:34,610 --> 00:11:39,850
+some time T هتكون
+
+123
+00:11:39,850 --> 00:11:48,550
+عندهان I B Omega B اتنين
+
+124
+00:11:50,050 --> 00:12:00,230
+و IA أميجا A واحد هاي
+
+125
+00:12:00,230 --> 00:12:04,850
+عند ال positive x axis هاي ال positive y axis
+
+126
+00:12:24,860 --> 00:12:30,720
+لو اخدت بي بي لحاله واخدت ال moment حوالين اللي هو
+
+127
+00:12:30,720 --> 00:12:33,640
+انا هاكون طبعا system moment واحد زاد ال impulse
+
+128
+00:12:33,640 --> 00:12:35,880
+واحد لاتنين نحكي اتنين كتاب جديد على ال equation
+
+129
+00:12:35,880 --> 00:12:44,240
+system system moment واحد
+
+130
+00:12:44,240 --> 00:12:50,320
+زاد ال impulse واحد لاتنين بس هو ال system moment
+
+131
+00:12:50,320 --> 00:12:53,680
+اتنين
+
+132
+00:12:56,300 --> 00:13:04,560
+ان اخد الجسم بيه اللي هو جير جير بيه خد ال moment
+
+133
+00:13:04,560 --> 00:13:12,080
+حوالين ال moment حوال نقطة بيه
+
+134
+00:13:12,080 --> 00:13:19,740
+حيكون عنده بالنسبة ل بيه عنده حيكون M طبعا
+
+135
+00:13:19,740 --> 00:13:21,960
+ال initial ما كان دي I او مجبرة اتوا M
+
+136
+00:13:24,800 --> 00:13:30,480
+مافيش هذه الصفر يعني نحكي و نكتبها و بعدين نسفرها
+
+137
+00:13:30,480 --> 00:13:36,560
+اي بي
+
+138
+00:13:36,560 --> 00:13:48,860
+اميجا بي واحد زائد ام دلتا تي
+
+139
+00:13:48,860 --> 00:13:49,800
+ناقص
+
+140
+00:13:52,340 --> 00:14:05,300
+ف دلتا تي في ر بي بالساوية اي بي
+
+141
+00:14:05,300 --> 00:14:16,200
+اوميجا باتنين طبعا هذه هتكون Zero
+
+142
+00:14:16,200 --> 00:14:27,130
+انا كنت Zeroزاد ستة دلتا T ماينوس F انا مش عارفها
+
+143
+00:14:27,130 --> 00:14:39,850
+F دلتا T RB اللي هي في مية في point واحد بس
+
+144
+00:14:39,850 --> 00:14:46,310
+I B I B انا حسبتها هي point O واحد تسعة اتنين
+
+145
+00:14:46,310 --> 00:14:49,470
+Omega B اتنين
+
+146
+00:14:51,340 --> 00:14:59,700
+هذا بالنسبة ل B بالنسبة ل A جير A هيكون
+
+147
+00:14:59,700 --> 00:15:10,700
+عنده IA Omega A واحد زائد طبعا مافيش عنده moment
+
+148
+00:15:10,700 --> 00:15:14,580
+هعتبر
+
+149
+00:15:14,580 --> 00:15:20,320
+هيك موجب موجب
+
+150
+00:15:23,580 --> 00:15:28,360
+زائد F Delta
+
+151
+00:15:28,360 --> 00:15:35,280
+T في R A بالساوية
+
+152
+00:15:35,280 --> 00:15:49,540
+I A Omega A اتنين هذا سيكون سفر فهو F Delta T
+
+153
+00:15:52,690 --> 00:15:58,750
+فى R A A F Delta T فى R A اللى هو point اتنين خمسة
+
+154
+00:15:58,750 --> 00:16:08,110
+بالسوء I A اللى هي point اربعة Omega A اتنين يعني
+
+155
+00:16:08,110 --> 00:16:14,210
+هذه عند المعادلة رقم واحد هذه المعادلة رقم اتنين
+
+156
+00:16:14,210 --> 00:16:25,250
+لو جمعت واحد مع اتنين واحدزاد اتنين هتكون عندهين
+
+157
+00:16:25,250 --> 00:16:34,270
+هتروح هذه او بده احكي من اتنين مش هنجمع يعني هضرب
+
+158
+00:16:34,270 --> 00:16:47,290
+يعني من اتنين هتكون F Delta T بالساوية واحد
+
+159
+00:16:47,290 --> 00:16:50,850
+point ستة omega
+
+160
+00:16:52,180 --> 00:16:56,540
+ا اتنين اتنين
+
+161
+00:16:56,540 --> 00:16:56,840
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+162
+00:16:56,840 --> 00:17:02,200
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+163
+00:17:02,200 --> 00:17:04,560
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+164
+00:17:04,560 --> 00:17:09,480
+اتنين اتنين اتنين
+
+165
+00:17:09,480 --> 00:17:10,520
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+166
+00:17:10,520 --> 00:17:13,040
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+167
+00:17:13,040 --> 00:17:17,400
+اتنين اتنين اتن
+
+168
+00:17:18,910 --> 00:17:27,450
+مظبوط بالسواء point o 192 omega b 2 الآن في علاقة
+
+169
+00:17:27,450 --> 00:17:34,930
+بين omega a و omega b عندي ر a omega a بالسواء ر
+
+170
+00:17:34,930 --> 00:17:40,390
+بي omega بي يعني انا هيكون عندى ر a اللي هي 250
+
+171
+00:17:43,070 --> 00:17:51,710
+omega a بالثومية omega b يعني omega a هتكون
+
+172
+00:17:51,710 --> 00:17:59,410
+الثومية عمتين وخمسين هتسوى أربع من عشرة omega b
+
+173
+00:17:59,410 --> 00:18:06,050
+يعني هيحيكون عندهين ستة delta T ناقص واحد ستة من
+
+174
+00:18:06,050 --> 00:18:11,150
+عشرة في point واحد point واحد ستة من عشرةفي omega
+
+175
+00:18:11,150 --> 00:18:22,970
+a اتنين في اربعة من عشرة omega b اتنين بتساوي
+
+176
+00:18:22,970 --> 00:18:32,090
+point o 192 omega b اتنين انا omega b اتنين
+
+177
+00:18:32,090 --> 00:18:39,870
+معطينيها omega b اتنيناللي بيستوى ستين ستمية ر بي
+
+178
+00:18:39,870 --> 00:18:46,730
+ام بدي احول ال radians per second هتكون ستمية في
+
+179
+00:18:46,730 --> 00:18:56,350
+اتنين في by تقسيم ستين تطلع اتنين ستين bond تمانية
+
+180
+00:18:56,350 --> 00:19:02,330
+تلاتة اتنين bond تمانية تلاتة اتنين radian per
+
+181
+00:19:02,330 --> 00:19:26,230
+secondيعني سأكون ستة دلتا T بتساوي تطلع
+
+182
+00:19:26,230 --> 00:19:26,910
+point O
+
+183
+00:19:29,760 --> 00:19:35,300
+تمنية تلاتة اتنين اميجا بي اتنين يعني هتكون point
+
+184
+00:19:35,300 --> 00:19:40,720
+o تمانية تلاتة اتنين اميجا بي اتنين اتنين وستين
+
+185
+00:19:40,720 --> 00:19:48,660
+point تمانية تلاتة اتنين ومنها بحسب delta T في
+
+186
+00:19:48,660 --> 00:19:55,840
+اتنين وستين point تمانية تلاتة اتنين يساوي تقسيم
+
+187
+00:19:55,840 --> 00:19:58,980
+ستة تطلع point تمانية سبعة واحد
+
+188
+00:20:02,020 --> 00:20:07,240
+second معناته بعد بون تمانية سبعة واحد second
+
+189
+00:20:07,240 --> 00:20:15,960
+بتوصل سرعة ال gear بي ستمية rpm هذا
+
+190
+00:20:15,960 --> 00:20:19,160
+المطلوب الأول المطلوب التاني بده ال tangential
+
+191
+00:20:19,160 --> 00:20:25,060
+force exerted by gear B on gear A بده ال F T يعني
+
+192
+00:20:25,060 --> 00:20:29,320
+لو من هنا من هنا ال F هتكون تساوي
+
+193
+00:20:32,900 --> 00:20:40,600
+من هنا ال F هتكون واحد point ستة في omega a اتنين
+
+194
+00:20:40,600 --> 00:20:47,100
+اللي هي في point اربعة omega a اتنين اللي هي point
+
+195
+00:20:47,100 --> 00:20:59,310
+اربعة في point اربعة omega b اتنين على delta Tهي
+
+196
+00:20:59,310 --> 00:21:04,270
+هتكون واحد point ستة في أربع من عشرة في اتنين و
+
+197
+00:21:04,270 --> 00:21:09,930
+ستين point تمانية تلات اتنين على delta T اللي هي
+
+198
+00:21:09,930 --> 00:21:13,190
+point تمانية سبعة واحدة
+
+199
+00:21:41,640 --> 00:21:43,480
+نحل مسألة تانية
+
+200
+00:22:35,570 --> 00:22:41,310
+انحل مسألة تانية a uniform sphere of mass m and
+
+201
+00:22:41,310 --> 00:22:44,130
+radius r is projected along a rough horizontal
+
+202
+00:22:44,130 --> 00:22:47,550
+surface with a linear velocity v1 and no angular
+
+203
+00:22:47,550 --> 00:22:56,030
+velocity عندي سفير كتلتها m مص كترة r تم القائها
+
+204
+00:22:56,030 --> 00:23:01,520
+على سطح خشن بسرعة ابتدائية v1و في البداية ماكانش
+
+205
+00:23:01,520 --> 00:23:03,820
+.. ماكانش ال rotation speed يعني كانت omega واحد
+
+206
+00:23:03,820 --> 00:23:10,300
+بالساوية سفر يعني v واحد and v واحد معطاه omega
+
+207
+00:23:10,300 --> 00:23:17,880
+واحد بالساوية سفر كان معامل احتكاك coefficient of
+
+208
+00:23:17,880 --> 00:23:23,400
+kinetic friction بين الكورة والسطح mu k معطين
+
+209
+00:23:23,400 --> 00:23:30,620
+معامل احتكاك بين الكورة والسطحdetermine the time
+
+210
+00:23:30,620 --> 00:23:34,940
+at which the sphere will start rolling without
+
+211
+00:23:34,940 --> 00:23:37,860
+sliding طبعا هو أول ما حدثها حدثها ب linear
+
+212
+00:23:37,860 --> 00:23:44,850
+velocityهيكون في البداية في عند sliding شوية شوية
+
+213
+00:23:44,850 --> 00:23:48,590
+بتحاول ت slide and roll slide roll slide roll يعني
+
+214
+00:23:48,590 --> 00:23:53,310
+slide and roll لحد ما تاخد لنصها و تصير complete
+
+215
+00:23:53,310 --> 00:23:56,530
+rolling motion فهو بده the time at which the
+
+216
+00:23:56,530 --> 00:23:59,610
+sphere will start rolling without slipping يعني في
+
+217
+00:23:59,610 --> 00:24:03,370
+الفترة من بداية الحركة اللي كانت complete sliding
+
+218
+00:24:05,120 --> 00:24:08,520
+لا لحد مثلا complete rolling يعني ماكنش فيه
+
+219
+00:24:08,520 --> 00:24:11,100
+sliding يعني في الفترة بين complete sliding و
+
+220
+00:24:11,100 --> 00:24:14,020
+complete rolling كان فيه خليط من ال sliding و ال
+
+221
+00:24:14,020 --> 00:24:17,320
+rolling بدنا نوجد الزمن هذا من بداية ال complete
+
+222
+00:24:17,320 --> 00:24:22,960
+sliding ل ال complete rolling طبعا
+
+223
+00:24:22,960 --> 00:24:30,140
+الكورة في الفترة في البداية كانلها
+
+224
+00:24:30,140 --> 00:24:32,840
+MV1
+
+225
+00:24:37,100 --> 00:24:41,840
+و I Omega
+
+226
+00:24:41,840 --> 00:24:47,580
+واحد هذا الزخم زاد في الفترة من time واحد ل time
+
+227
+00:24:47,580 --> 00:24:59,060
+اتنين كانت تحت تأثير وزنها W في Delta T وفي رد
+
+228
+00:24:59,060 --> 00:25:04,780
+الفعل N Delta T
+
+229
+00:25:06,920 --> 00:25:20,580
+و فى عندى friction اللى هم U K N Delta T هتساوى
+
+230
+00:25:20,580 --> 00:25:31,740
+فى النهاية هكون عندى M
+
+231
+00:25:31,740 --> 00:25:33,820
+V2
+
+232
+00:25:36,500 --> 00:25:43,580
+و I أميجا اتنين يعني
+
+233
+00:25:43,580 --> 00:25:51,900
+عندي system momenta واحد زاد
+
+234
+00:25:51,900 --> 00:26:00,020
+ال impulse واحد لاتنين بالسواء ال system momenta
+
+235
+00:26:00,020 --> 00:26:02,160
+اتنين
+
+236
+00:26:18,720 --> 00:26:21,740
+أت position 2 لما سنة complete rolling بيصيح علاقة
+
+237
+00:26:21,740 --> 00:26:28,680
+بين V2 و Omega 2 يعني هتكون V2 بالسوء R Omega 2
+
+238
+00:26:47,630 --> 00:26:56,570
+عند هاي ال X و هاي ال Y X
+
+239
+00:26:56,570 --> 00:27:01,550
+و ال Y طبعا
+
+240
+00:27:01,550 --> 00:27:06,790
+في اتجاه ال Y along ال Y along ال Y direction
+
+241
+00:27:06,790 --> 00:27:11,370
+هيكون
+
+242
+00:27:11,370 --> 00:27:14,070
+عنده سفر
+
+243
+00:27:16,940 --> 00:27:24,940
+-W Delta T زائد
+
+244
+00:27:24,940 --> 00:27:35,820
+N Delta T مافيش حركة زخمة اتجاه الواحد بالساوية
+
+245
+00:27:35,820 --> 00:27:42,180
+سفر معناته ال N بالساوية W
+
+246
+00:27:48,750 --> 00:27:56,150
+باتجاه ال X هكون
+
+247
+00:27:56,150 --> 00:28:05,550
+عندي MV1-MUK
+
+248
+00:28:05,550 --> 00:28:14,710
+N Delta T بيساوي
+
+249
+00:28:14,710 --> 00:28:18,290
+MV2
+
+250
+00:28:21,270 --> 00:28:27,150
+م V اتنين يعني
+
+251
+00:28:27,150 --> 00:28:30,650
+انا هاكون عندي
+
+252
+00:28:30,650 --> 00:28:40,930
+م V واحد ناقص م U K م G اللي هي الوزن ال N اللي هي
+
+253
+00:28:40,930 --> 00:28:49,590
+م G Delta
+
+254
+00:28:49,590 --> 00:28:50,010
+T
+
+255
+00:28:54,960 --> 00:29:05,900
+بالساوية MV2 يعني اذا اختصر ال M سيكون V1-UKG
+
+256
+00:29:05,900 --> 00:29:10,960
+Delta T بساوية
+
+257
+00:29:10,960 --> 00:29:12,380
+V2
+
+258
+00:29:25,020 --> 00:29:40,900
+هذا مركز تقع الـ G لو
+
+259
+00:29:40,900 --> 00:29:46,820
+أخدت ال moment حول الـ G moment of moment about
+
+260
+00:29:46,820 --> 00:30:05,140
+الـ G و اعتبرت هذا موجبهكو عندى I Omega 1 زائد
+
+261
+00:30:05,140 --> 00:30:10,440
+R UKN
+
+262
+00:30:10,440 --> 00:30:16,320
+Delta T بتساوي
+
+263
+00:30:16,320 --> 00:30:22,720
+I Omega 2 طبعا هذا سفر
+
+264
+00:30:25,600 --> 00:30:37,300
+مانا أضحك واندي R ميو كيه ال N M G دلتا
+
+265
+00:30:37,300 --> 00:30:45,860
+T بتسوى ال I للاسفير اللي هي اتنين على خمسة
+
+266
+00:30:45,860 --> 00:30:50,360
+M R تربيع في ال Omega اتنين
+
+267
+00:30:55,690 --> 00:31:07,050
+يعني هاروح عند ال M مع ال M و R مع R معناه Omega 2
+
+268
+00:31:07,050 --> 00:31:12,770
+Omega
+
+269
+00:31:12,770 --> 00:31:19,730
+2 بتساوي خمسة
+
+270
+00:31:19,730 --> 00:31:34,830
+على اتنين ميو كG Delta T على R و
+
+271
+00:31:34,830 --> 00:31:39,210
+احنا already حكينا ان V2 بيستوي R Omega 2 V2
+
+272
+00:31:39,210 --> 00:31:49,210
+بيستوي Omega 2 في R يعني هتكون تساوي خمسة على
+
+273
+00:31:49,210 --> 00:32:00,240
+اتنين Mu Kج دلتا T وبرضه من هنا طبعا انا اشوف
+
+274
+00:32:00,240 --> 00:32:09,560
+الساوية بتساوي V واحد V
+
+275
+00:32:09,560 --> 00:32:21,140
+واحد minus ميو كي جي دلتا T يعني
+
+276
+00:32:21,140 --> 00:32:27,670
+خمسة اتنينزائد خمسة على الواحد زائد اتنين على
+
+277
+00:32:27,670 --> 00:32:36,110
+اتنين سبعة على اتنين هيكون يعني
+
+278
+00:32:36,110 --> 00:32:42,810
+هيكون دي سبعة على اتنين ميو
+
+279
+00:32:42,810 --> 00:32:42,970
+ك
+
+280
+00:32:45,820 --> 00:32:56,360
+ج دلتا T ساوة V واحد معناته Delta T هتكون تساوية
+
+281
+00:32:56,360 --> 00:33:02,420
+اتنين على
+
+282
+00:33:02,420 --> 00:33:15,530
+سبعة في V واحد على ميو كي جي ميو كي جياحنا حسبنا
+
+283
+00:33:15,530 --> 00:33:19,650
+الزمن اللي عندها بتصل الكورة ل complete rolling
+
+284
+00:33:19,650 --> 00:33:25,310
+motion بتصل ل complete rolling motion هذا المطلوب
+
+285
+00:33:25,310 --> 00:33:29,910
+الأول مطلوب التاني the linear and angular
+
+286
+00:33:29,910 --> 00:33:34,550
+velocities of the sphere at that time خلاص ال time
+
+287
+00:33:34,550 --> 00:33:44,340
+عرفناه معناته احنا من هنا حكينا ان omega 2بالسواق
+
+288
+00:33:44,340 --> 00:33:55,320
+خمسة على اتنين ميو كي في جي على ار في دلتا تي اللي
+
+289
+00:33:55,320 --> 00:34:06,430
+هي اتنين على سبعة اتنين على سبعة V one على ميو كيG
+
+290
+00:34:06,430 --> 00:34:11,270
+يعني UKG مع UKG بتروح مع بعض اتنين مع اتنين
+
+291
+00:34:11,270 --> 00:34:19,450
+بالسبعة Omega 2 هتكون تساوي خمسة على سبعة V واحد
+
+292
+00:34:19,450 --> 00:34:29,270
+على R و V اتنين هتكون Omega 2 R يعني هتكون تساوي
+
+293
+00:34:29,270 --> 00:34:35,150
+خمسة على سبعة V واحد
+
+294
+00:34:40,640 --> 00:34:46,160
+هك تكون حاليا المسألة بشكل مبسط ال I بتاعة ال
+
+295
+00:34:46,160 --> 00:34:49,920
+plate هتكون
+
+296
+00:34:49,920 --> 00:34:55,880
+واحد على اتناش ال mass بتاعة ال plate في المسافة
+
+297
+00:34:55,880 --> 00:35:01,480
+هذه هتسميها A و A في A تربيع زاد A تربيع في A
+
+298
+00:35:01,480 --> 00:35:11,690
+تربيع زاد A تربيع يعني هيكون الساويواحد على ستة
+
+299
+00:35:11,690 --> 00:35:19,170
+and plate ايه التربية يعني هكون واحد على ستة يعني
+
+300
+00:35:19,170 --> 00:35:24,550
+هكون عندي hand نعوض hand and plate and bullet اللي
+
+301
+00:35:24,550 --> 00:35:30,990
+هي point أو خمسة على اتنين و تلاتين و اتنين من
+
+302
+00:35:30,990 --> 00:35:35,010
+عشرة في ال V بتاعة ال bullet اللي هي الف و خمسمية
+
+303
+00:35:37,100 --> 00:35:41,780
+فى اربعتاش على اتناش فعلى ال plate اللى هي واحد
+
+304
+00:35:41,780 --> 00:35:47,080
+على ستة فى ال M بتاعة ال plate اللى هي عشرين على
+
+305
+00:35:47,080 --> 00:35:51,480
+اتنين و تلاتين و اتنين و عشرة فى ال A اللى هي في
+
+306
+00:35:51,480 --> 00:36:00,280
+طمنتاش على اتناش الكل تربيع فى ال Omega بتاعة ال
+
+307
+00:36:00,280 --> 00:36:07,770
+plate اتنين زاد ال M plate اللى هي عشرينعلى اتنين
+
+308
+00:36:07,770 --> 00:36:12,730
+و تلاتين و اتنين من عشرة في ال V بتاعة ال plate
+
+309
+00:36:12,730 --> 00:36:19,170
+اتنين السواء omega لل plate اتنين في تسعة على
+
+310
+00:36:19,170 --> 00:36:22,830
+اتناش يعني
+
+311
+00:36:22,830 --> 00:36:34,230
+في حضربها في تسعة على اتناش omega plate اتنين في
+
+312
+00:36:34,230 --> 00:36:43,920
+تسعةعلى اتناش يعني
+
+313
+00:36:43,920 --> 00:36:52,540
+خلنا نرتب الرقم الأولاني هكون دي point O خمسة في
+
+314
+00:36:52,540 --> 00:36:58,480
+الف و خمسمية في أربعتاش تقسيم اتنين و تلاتين و
+
+315
+00:36:58,480 --> 00:37:02,560
+اتنين و عشرة تقسيم اتناش
+
+316
+00:37:05,070 --> 00:37:14,490
+بطلع عندى اتنين point سبعة واحد سبعة بتساوي عندى
+
+317
+00:37:14,490 --> 00:37:21,630
+هنا عشرين على ستة على اتنين و تلاتين و اتنين و
+
+318
+00:37:21,630 --> 00:37:30,870
+عشرة يساوي في واحد و نص تربيع يساوي
+
+319
+00:37:36,910 --> 00:37:45,670
+زاد عشرين في واحد تمانين تقصي اتنين و تلاتين و
+
+320
+00:37:45,670 --> 00:37:53,130
+اتنين و عشرة تقصي مية و اربع و اربعين يساوي تطلع
+
+321
+00:37:53,130 --> 00:37:54,170
+point الخامسة
+
+322
+00:37:57,550 --> 00:38:02,690
+تمانية اتنين omega plate اتنين وانا بحسب omega
+
+323
+00:38:02,690 --> 00:38:10,310
+plate اتنين بتساوي اتنين point سبعة واحد سبعة
+
+324
+00:38:10,310 --> 00:38:17,210
+تقسيم point خمسة تمانية اتنين بتطلع
+
+325
+00:38:17,210 --> 00:38:24,010
+اربع point ستة ستة تمانية radians per second
+
+326
+00:38:27,910 --> 00:38:31,390
+Bidul impulsive reaction at A assuming that the
+
+327
+00:38:31,390 --> 00:38:36,590
+bullet becomes embedded in 0.0006
+
+328
+00:38:36,590 --> 00:38:44,830
+second طيب
+
+329
+00:38:59,730 --> 00:39:01,990
+عشان أحصل الـ impulse فأنا بدي أخد اللي هو بتجاه
+
+330
+00:39:01,990 --> 00:39:05,150
+ال .. ال .. ال .. ال system منتج بتجاه ال .. ال ..
+
+331
+00:39:05,150 --> 00:39:10,790
+ال x axis هتكون
+
+332
+00:39:10,790 --> 00:39:22,270
+عنده un bullet v bullet واحد زاد ax delta
+
+333
+00:39:22,270 --> 00:39:32,080
+t بس un bullet .. un platev plate اتنين يعني un
+
+334
+00:39:32,080 --> 00:39:37,580
+bullet اللي هي point o خمسة على اتنين و تلاتين
+
+335
+00:39:37,580 --> 00:39:45,460
+point اتنين في الف و خمسمية زائد ax في delta t
+
+336
+00:39:45,460 --> 00:39:52,380
+اللي هي point o o o ستة so un plate اللي هو عشرين
+
+337
+00:39:52,380 --> 00:39:58,250
+على اتنين و تلاتين point اتنينفي v plate اللي هي
+
+338
+00:39:58,250 --> 00:40:06,290
+هتكون تسعة على اتناش اللي
+
+339
+00:40:06,290 --> 00:40:11,710
+هي omega plate اللي هي اربعة بونت ستة ستة تمانية
+
+340
+00:40:11,710 --> 00:40:19,130
+ومنها بحسب ال ax بدي
+
+341
+00:40:19,130 --> 00:40:21,750
+اخد في ال y axis ال y في ال y axis
+
+342
+00:40:27,920 --> 00:40:36,360
+هكون عندى ay delta t minus
+
+343
+00:40:36,360 --> 00:40:44,540
+w plate delta t بتساوي
+
+344
+00:40:44,540 --> 00:40:50,620
+مافيش
+
+345
+00:40:50,620 --> 00:40:52,320
+zero
+
+346
+00:40:58,230 --> 00:41:06,570
+ومنها بحسب ال a y بالساوي w بتاعة ال plate اللي هي
+
+347
+00:41:06,570 --> 00:41:14,750
+عشرين pound هيك حسب ال reaction components طبعا
+
+348
+00:41:14,750 --> 00:41:17,710
+في أمثلة تانية بتوقع أنكوا تطلعوا اللي تفتحوا
+
+349
+00:41:17,710 --> 00:41:21,050
+الكتاب و تطلعوا تحلوا الأمثلة التانية و بالإضافة
+
+350
+00:41:21,050 --> 00:41:24,950
+لإنكوا تحلوا مجموعة من المثال من هيك نكون خلصنا في
+
+351
+00:41:24,950 --> 00:41:25,350
+ال course
+
diff --git a/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/uGFxXwSt91g.srt b/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/uGFxXwSt91g.srt
new file mode 100644
index 0000000000000000000000000000000000000000..de6803d28b1e21899eedff5deb1d572f106e8dbb
--- /dev/null
+++ b/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/uGFxXwSt91g.srt
@@ -0,0 +1,2479 @@
+1
+00:00:04,890 --> 00:00:08,090
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:08,090 --> 00:00:14,590
+اليوم هنكمل .. نحل مزيد من الأمثلة على chapter 16
+
+3
+00:00:14,590 --> 00:00:18,350
+اللي هي force and acceleration analysis of rigid
+
+4
+00:00:18,350 --> 00:00:26,370
+bodies in plane motion هنحل مثال جديد طبعا نطلع على
+
+5
+00:00:26,370 --> 00:00:30,510
+الشكل عندي 
+
+6
+00:00:30,510 --> 00:00:37,360
+نظام بكرات معلق بحبل الجسم A وزنه خمسة pound
+
+7
+00:00:37,360 --> 00:00:44,700
+والجسم B العشرة pound الجسم A معلق على نصف قطر عشرة
+
+8
+00:00:44,700 --> 00:00:54,600
+inch والجسم B معلق على نصف قطر ستة inch لأن لو نطلع
+
+9
+00:00:54,600 --> 00:01:01,440
+بسرعة عشان نتوقع اتجاه الدوران يعني لو أخدت العزم
+
+10
+00:01:01,440 --> 00:01:06,980
+سريعًا حول مركز ثقل G يعني هيكون عندي خمسة في عشرة
+
+11
+00:01:06,980 --> 00:01:14,120
+خمسين وهنا عشرة في ستة ستين مين أكثر؟ ستين ولا
+
+12
+00:01:14,120 --> 00:01:18,160
+خمسين؟ ستين أكثر معناته الحركة هتكون بهذا الاتجاه
+
+13
+00:01:18,160 --> 00:01:25,790
+هتكون الـ rotation بهذا الدوران بهذا الاتجاه طيب الـ
+
+14
+00:01:25,790 --> 00:01:29,210
+pulley weighing twelve pound البكرة هذه وزنها
+
+15
+00:01:29,210 --> 00:01:34,930
+اثنا عشر pound الـ
+
+16
+00:01:34,930 --> 00:01:41,530
+pulley وزنها اثنا عشر pound and
+
+17
+00:01:41,530 --> 00:01:46,090
+having a radius of gyration لنصف قطر العطالة لها
+
+18
+00:01:46,090 --> 00:01:47,270
+ثمانية انش K
+
+19
+00:01:51,630 --> 00:01:57,250
+بساوي ثمانية انش يعني
+
+20
+00:01:57,250 --> 00:02:01,270
+ثمانية على .. يعني ده حولها لقدم ثمانية على اثنا عشر
+
+21
+00:02:01,270 --> 00:02:04,530
+على
+
+22
+00:02:04,530 --> 00:02:11,170
+الأربع فيها الاثنين ثمانية على اثنا عشر كم يعني
+
+23
+00:02:11,170 --> 00:02:19,350
+هتكون ثمانية على اثنا عشر قدم يعني اثنين
+
+24
+00:02:22,590 --> 00:02:29,610
+على ثلاثة قدم على الـ radius and the generation it's
+
+25
+00:02:29,610 --> 00:02:33,570
+connected to two blocks as shown البكرة مربوطة
+
+26
+00:02:33,570 --> 00:02:39,690
+بجسمين a و b من خلال الحبال كما هو مبين معطيني
+
+27
+00:02:39,690 --> 00:02:52,720
+كتلة وزن جسم a و w a هو خمسة pound و w بيهاللي هي
+
+28
+00:02:52,720 --> 00:03:02,820
+عشرة pound assuming
+
+29
+00:03:02,820 --> 00:03:07,520
+no axially friction على فرض أنه عندي المحور هنا
+
+30
+00:03:07,520 --> 00:03:12,540
+مافيش احتكاك determine the angular acceleration of
+
+31
+00:03:12,540 --> 00:03:16,760
+the pulley بدي أنا أوجد العجلة الزاوية للـ pulley و
+
+32
+00:03:16,760 --> 00:03:19,560
+الـ acceleration of each block
+
+33
+00:03:23,380 --> 00:03:29,040
+طبعًا عشان أحل المثال زي هيك هاخد أعمل free body
+
+34
+00:03:29,040 --> 00:03:35,320
+diagram للنظام كله للنظام كله النظام كله
+
+35
+00:03:35,320 --> 00:03:43,940
+هيكون القوة اللي مؤثرة اللي هي عندي ووزن اللي
+
+36
+00:03:43,940 --> 00:03:49,260
+هي WA ووزن الجسم B
+
+37
+00:03:56,270 --> 00:04:01,930
+وعندي وزن البكرة
+
+38
+00:04:06,240 --> 00:04:12,780
+W للـ pulley الشد في الحبال مش هيبين لأنه internal
+
+39
+00:04:12,780 --> 00:04:16,780
+force قوة داخلية لو أخدت الـ free body diagram للـ A
+
+40
+00:04:16,780 --> 00:04:21,620
+لحاله أو الـ B لحاله لازم الشد يبين بس أنا أخدت كل الـ
+
+41
+00:04:21,620 --> 00:04:25,400
+system مع بعضه يعني أنا أخدت الـ block A و B و
+
+42
+00:04:25,400 --> 00:04:30,840
+البكرة مع بعض معناته مش هيبين عندي الـ .. الـ .. الـ
+
+43
+00:04:30,840 --> 00:04:39,420
+tension هذا مركز ثقل G هذا block B هذا block A
+
+44
+00:04:39,420 --> 00:04:47,840
+عندي نصف القطر هذا هذا
+
+45
+00:04:47,840 --> 00:04:54,600
+R ستة انش وهذا R
+
+46
+00:04:54,600 --> 00:04:56,660
+عشرة انش
+
+47
+00:04:59,290 --> 00:05:07,170
+الآن نتيجة هذه القوة هيكون
+
+48
+00:05:07,170 --> 00:05:21,270
+الجسم B بيتحرك بيتحرك حركة انتقالية هيكون لـ مـ ب
+
+49
+00:05:21,270 --> 00:05:24,530
+أب
+
+50
+00:05:27,800 --> 00:05:37,040
+و A هيكون طالع يطلع M
+
+51
+00:05:37,040 --> 00:05:49,760
+A A A هذا الجسم B وهذا
+
+52
+00:05:49,760 --> 00:05:51,380
+الجسم A
+
+53
+00:05:54,320 --> 00:05:58,600
+الآن الـ disk أو البكرة حركتها حركة دورانية حولها
+
+54
+00:05:58,600 --> 00:06:04,360
+مركز ثقلها اللي هو هذا G
+
+55
+00:06:04,360 --> 00:06:15,720
+هيكون للبكرة I للبكرة في ايش في الـ I البكرة في
+
+56
+00:06:15,720 --> 00:06:15,960
+الـ
+
+57
+00:06:23,960 --> 00:06:30,240
+هأحط المحاور هاي X وهاي
+
+58
+00:06:30,240 --> 00:06:33,620
+Y
+
+59
+00:06:49,010 --> 00:06:51,850
+في الـ dynamics إذا رسمت الـ free body diagram صح
+
+60
+00:06:51,850 --> 00:07:02,070
+المثال انحلت وتحصيل حاصل بالسيرة الآن
+
+61
+00:07:02,070 --> 00:07:05,490
+اللي هأسويه
+
+62
+00:07:05,490 --> 00:07:10,470
+هاخد الـ moment حول g الـ moment حول g
+
+63
+00:07:10,470 --> 00:07:22,370
+summation للـ moment حول G هأعتبر بعكس عقارب
+
+64
+00:07:22,370 --> 00:07:30,330
+الساعة موجب هتساوي MG effective
+
+65
+00:07:30,330 --> 00:07:38,730
+نأخذ
+
+66
+00:07:38,730 --> 00:07:41,030
+الجهة اليسار طبعًا هذا الشيء بساوي هذا الشيء
+
+67
+00:07:46,340 --> 00:07:51,300
+الـ .. الـ .. طبعًا الـ .. الوزن بتاع الـ pulley جاي في
+
+68
+00:07:51,300 --> 00:07:55,100
+مركز الثقل بيعملش عزم اللي بيعمل عزم اللي هو
+
+69
+00:07:55,100 --> 00:08:01,520
+الجسم a هي ناقص ناقص
+
+70
+00:08:01,520 --> 00:08:07,380
+انتبه للوحدات عشرة ده حولنا لقدم على اثنا عشر ناقص عشر
+
+71
+00:08:07,380 --> 00:08:08,040
+على اثنا عشر
+
+72
+00:08:18,630 --> 00:08:29,930
+زائد ستة على اثنا عشر W B هذا اللي على الجهة اليسار
+
+73
+00:08:29,930 --> 00:08:36,650
+هتساوي بالنسبة
+
+74
+00:08:36,650 --> 00:08:40,170
+لـ G أنا أخذه من حوالي Markers هيكون I لـ الـ plate
+
+75
+00:08:40,170 --> 00:08:41,930
+في Alpha I
+
+76
+00:08:44,690 --> 00:08:57,150
+الـ Plate في Alpha تاعت الـ Plate زائد
+
+77
+00:08:57,150 --> 00:09:09,290
+الآن الـ M B A B بتاع الـ moment حول J زائد M B A B
+
+78
+00:09:14,810 --> 00:09:30,990
+في ستة على اثنا عشر في ستة على اثنا عشر زائد
+
+79
+00:09:30,990 --> 00:09:34,810
+م
+
+80
+00:09:34,810 --> 00:09:41,970
+اه اه اه في عشر على اثنا عشر
+
+81
+00:09:49,980 --> 00:09:55,940
+طيب و ان دي اللي هي خمسة
+
+82
+00:09:55,940 --> 00:10:00,900
+و بي اللي هي عشرة بدي أحسب الـ I تاعة الـ play ..
+
+83
+00:10:00,900 --> 00:10:07,660
+تاعة الـ .. الـ .. الـ pulley الـ I للـ pulley المعطيني
+
+84
+00:10:07,660 --> 00:10:14,420
+الـ radius and gyration هتكون M K تربيع الـ M تاعة
+
+85
+00:10:14,420 --> 00:10:20,290
+الـ plate اللي هي اثنا عشر على اثنين وثلاثين واثنين من
+
+86
+00:10:20,290 --> 00:10:31,210
+عشرة في الـ K اللي هي اثنين على ثلاثة تربيع
+
+87
+00:10:31,210 --> 00:10:38,950
+تطلع عندي الـ I للـ plate للـ pulley
+
+88
+00:10:59,020 --> 00:11:08,220
+تطلع بوند واحد ستة خمسة ستة بوند واحد ستة خمسة ستة
+
+89
+00:11:08,220 --> 00:11:13,460
+اللي هي هتكون pound
+
+90
+00:11:19,250 --> 00:11:22,610
+pound لأن خلينا نحكي الـ .. الـ .. الـ mass ان الـ
+
+91
+00:11:22,610 --> 00:11:29,470
+mass أو الوزن الـ W اللي هي pound والـ G اللي هي
+
+92
+00:11:29,470 --> 00:11:39,110
+foot على second square في foot square يعني هتكون
+
+93
+00:11:39,110 --> 00:11:46,830
+pound foot second square هاي واحدة
+
+94
+00:11:52,220 --> 00:11:58,660
+هذا الـ I للـ pulley طيب
+
+95
+00:11:58,660 --> 00:12:02,260
+الآن
+
+96
+00:12:02,260 --> 00:12:06,900
+في علاقة بين الـ acceleration لـ block A و الـ angle
+
+97
+00:12:06,900 --> 00:12:20,180
+of acceleration للـ pulley أكيد الـ AA هتساوي
+
+98
+00:12:20,180 --> 00:12:20,680
+Alpha
+
+99
+00:12:24,390 --> 00:12:25,730
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+100
+00:12:25,730 --> 00:12:26,230
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+101
+00:12:26,230 --> 00:12:32,230
+عشرة عشرة عشرة عشرة
+
+102
+00:12:32,230 --> 00:12:34,230
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+103
+00:12:34,230 --> 00:12:34,370
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+104
+00:12:34,370 --> 00:12:35,150
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+105
+00:12:35,150 --> 00:12:36,370
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+106
+00:12:36,370 --> 00:12:50,010
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+107
+00:12:50,010 --> 00:12:53,410
+عش
+
+108
+00:12:59,350 --> 00:13:06,970
+واحد نعوض عن I لـ الـ plate نعوض
+
+109
+00:13:06,970 --> 00:13:13,470
+عن W A و W B I لـ الـ plate و A لـ الـ B و الـ A لـ الـ A
+
+110
+00:13:13,470 --> 00:13:18,390
+و الـ M A و الـ M B في معادلة واحد حسينا اندي التعدى
+
+111
+00:13:18,390 --> 00:13:31,320
+عندي ناقص عشرة على اثنا عشر في W A اللي هي خمسة زائد
+
+112
+00:13:31,320 --> 00:13:41,460
+ستة على اثنا عشر WB اللي هي عشرة بتساوي
+
+113
+00:13:41,460 --> 00:13:50,220
+I للـ plate اللي هي point واحد ستة خمسة ستة الف للـ
+
+114
+00:13:50,220 --> 00:13:53,520
+pulley زائد
+
+115
+00:13:55,740 --> 00:14:03,360
+M بي اللي هي عشرة على اثنين وثلاثين واثنين من
+
+116
+00:14:03,360 --> 00:14:11,640
+عشرة في الـ a بي اللي هي ستة على اثنا عشر الف للـ plate
+
+117
+00:14:11,640 --> 00:14:20,880
+في ستة على اثنا عشر زائد
+
+118
+00:14:20,880 --> 00:14:28,270
+الـ Ma اللي هي خمسة على اثنين وثلاثين واثنين من عشرة
+
+119
+00:14:28,270 --> 00:14:36,490
+في a a اللي هي عشرة على اثنا عشر Alpha تاعت الـ pulley
+
+120
+00:14:36,490 --> 00:14:40,770
+في
+
+121
+00:14:40,770 --> 00:14:44,350
+عشرة على
+
+122
+00:14:44,350 --> 00:14:48,150
+اثنا عشر واضح أن دي مجهول واحد اللي هو Alpha P على
+
+123
+00:14:48,150 --> 00:14:50,370
+الجهة اليمين
+
+124
+00:15:00,280 --> 00:15:08,060
+يعني منها بحسب alpha للـ pulley هتساوي
+
+125
+00:15:44,310 --> 00:15:57,430
+يعني هيكون عندي point 88 هتساوي
+
+126
+00:17:03,500 --> 00:17:13,040
+و أنا بحسب alpha بتاعة الـ pulley هي bond ثمانية تقسم
+
+127
+00:17:13,040 --> 00:17:22,400
+bond ثلاثة خمسة واحد واحد تطلع اثنين bond ثلاثة
+
+128
+00:17:23,990 --> 00:17:31,310
+سبعة ثلاثة radian per second squared في عكس عقارب
+
+129
+00:17:31,310 --> 00:17:37,130
+الساعة هذه الـ alpha بتاعت الـ pulley المطلوب الثاني
+
+130
+00:17:37,130 --> 00:17:46,670
+كان بده الـ acceleration بده
+
+131
+00:17:46,670 --> 00:17:50,230
+الـ acceleration of each block يعني أنا حكينا a a
+
+132
+00:17:53,690 --> 00:18:00,470
+بتساوي عشرة على اثنا عشر الفة للـ pulley يعني عشرة على
+
+133
+00:18:00,470 --> 00:18:05,890
+اثنا عشر في اثنين point ثلاثة سبعة ثلاثة بتساوي
+
+134
+00:18:05,890 --> 00:18:13,990
+بتحسبوها و A لـ B بتساوي ستة على اثنا عشر الفة للـ pulley
+
+135
+00:18:13,990 --> 00:18:19,670
+بتساوي ستة على اثنا عشر في اثنين point ثلاثة سبعة
+
+136
+00:18:19,670 --> 00:18:21,970
+ثلاثة وبتحسبوها
+
+137
+00:18:31,550 --> 00:18:33,090
+طب هنحل مسألة ثانية
+
+138
+00:19:09,290 --> 00:19:14,350
+هنحل مثال ثانية a cord is wrapped around a
+
+139
+00:19:14,350 --> 00:19:17,050
+homogeneous disk of mass 15 kilogram في عندي الـ
+
+140
+00:19:17,050 --> 00:19:25,810
+disk كتلته 15 kilogram لفينا حبل حواليها the cord is
+
+141
+00:19:25,810 --> 00:19:29,790
+pulled upwards with a force T equal 180 Newton  أن
+
+142
+00:19:29,790 --> 00:19:36,950
+شد لأعلى بقوة شد 180 نيوتن يعني عند الـ disk كتلته 
+
+143
+00:19:39,800 --> 00:19:46,020
+خمسة عشر كيلو جرام الـ mass خمسة عشر كيلو جرام
+
+144
+00:19:46,020 --> 00:19:55,880
+والشد في الحبل يستوي مئة وثمانين نيوتن determine
+
+145
+00:19:55,880 --> 00:19:58,860
+the acceleration of the center of the disk من نوجه
+
+146
+00:19:58,860 --> 00:20:02,960
+الـ acceleration لمركز استقل الـ disk و الـ angle
+
+147
+00:20:02,960 --> 00:20:09,120
+acceleration للـ disk و الـ acceleration للحبل طبعا
+
+148
+00:20:09,120 --> 00:20:12,100
+عشان نحل مثل هيك لازم نعمل force analysis يعني
+
+149
+00:20:12,100 --> 00:20:25,640
+لازم نعمل free body diagram free body diagram الـ
+
+150
+00:20:25,640 --> 00:20:29,940
+force بتأثر على الـ disk اللي هو الشد اللي على الـ T
+
+151
+00:20:29,940 --> 00:20:36,020
+و وزنه لتحت
+
+152
+00:20:41,810 --> 00:20:51,350
+اللي هو M في G المعنى هو الـ disk تحت أثر two
+
+153
+00:20:51,350 --> 00:21:02,050
+forces وزنه MG وشد في الحبل T اللي هو نتيجة حصيلة
+
+154
+00:21:02,050 --> 00:21:02,450
+acceleration
+
+155
+00:21:14,650 --> 00:21:19,350
+M في أ
+
+156
+00:21:19,350 --> 00:21:30,350
+هيكون له كمان أي في ألف يعني في أيه له حركتين حركة
+
+157
+00:21:30,350 --> 00:21:34,730
+انتقالية هيكون هو طالع و يطلع و يلف طالع و يلف مع
+
+158
+00:21:34,730 --> 00:21:39,090
+الحبل م
+
+159
+00:21:39,090 --> 00:21:39,950
+أه في ألف
+
+160
+00:22:10,630 --> 00:22:13,430
+لا أظن دائما كل ما أرسم free body diagram لازم أحط
+
+161
+00:22:13,430 --> 00:22:18,210
+المحاور لازم المرجعية تكون واضحة هيك بقدر أنا أعمل
+
+162
+00:22:18,210 --> 00:22:25,970
+analysis  قطر الـ disk  قطر
+
+163
+00:22:25,970 --> 00:22:36,070
+متر يعني قطره متر let's drink beer طيب
+
+164
+00:22:48,830 --> 00:22:50,990
+عشان أجد الـ acceleration للدسك ممكن أحكي
+
+165
+00:22:50,990 --> 00:22:55,270
+summation of forces باتجاه الـ Y بيساوي M في A يعني
+
+166
+00:22:55,270 --> 00:23:03,550
+summation of forces باتجاه
+
+167
+00:23:03,550 --> 00:23:16,550
+الـ Y بيساوي M Ay وهذا هو الاتجاه الموجب اتجاه
+
+168
+00:23:16,550 --> 00:23:17,350
+الـ Y عند الـ T
+
+169
+00:23:21,020 --> 00:23:26,880
+ناقص mg بيساوي
+
+170
+00:23:26,880 --> 00:23:35,840
+MFA نعوض على الـ T الـ
+
+171
+00:23:35,840 --> 00:23:40,760
+T اللي هي مئة وثمانين نيوتن ناقص الـ M عند
+
+172
+00:23:40,760 --> 00:23:49,730
+خمسة عشر في تسعة فاصلة ثمانية صفر ستة بيساوي أما
+
+173
+00:23:49,730 --> 00:23:56,530
+اللي هي خمسة عشر في a وأنا
+
+174
+00:23:56,530 --> 00:24:02,370
+أحسب الـ acceleration الـ a هتكون بيساوي مئة و
+
+175
+00:24:02,370 --> 00:24:06,870
+ثمانين
+
+176
+00:24:06,870 --> 00:24:14,200
+وثمانين ناقص خمسة عشر في تسعة فاصلة ثمانية صفر ستة
+
+177
+00:24:14,200 --> 00:24:21,280
+بيساوى تقسيم خمسة عشر تطلع اثنين فاصلة واحد تسعة أربعة
+
+178
+00:24:21,280 --> 00:24:27,820
+اثنين فاصلة واحد تسعة أربعة meter per second
+
+179
+00:24:27,820 --> 00:24:29,420
+squared يعني اتوجدت الـ acceleration
+
+180
+00:24:35,080 --> 00:24:38,540
+عشان أجد الـ اي انجل اكسلراشن للـ ديسك هاخد الـ
+
+181
+00:24:38,540 --> 00:24:45,080
+moment حوالين جيم، العزم حوالين جيم summation
+
+182
+00:24:45,080 --> 00:24:48,220
+للـ
+
+183
+00:24:48,220 --> 00:24:56,820
+moment حوالين جيم هتكون بيساوي I في Alpha هعتبر
+
+184
+00:24:56,820 --> 00:24:57,900
+clockwise موجب
+
+185
+00:25:04,130 --> 00:25:15,330
+الآن الـ I لديسك I لديسك نصف MR Square نصف
+
+186
+00:25:15,330 --> 00:25:21,450
+MR Square احنا عشان نجيبها المفروض نرجع للجداول
+
+187
+00:25:21,450 --> 00:25:25,990
+عليها الـ I بيساوي نصف لرجع الكتاب هتكون نصف MR
+
+188
+00:25:25,990 --> 00:25:33,090
+Square تأكدوا منها هتكون نصف الكتلة لها خمسة عشر
+
+189
+00:25:34,930 --> 00:25:57,050
+الـ R نصف متر نصف تربيع يعني هتكون خمسة عشر لو
+
+190
+00:25:57,050 --> 00:25:59,470
+واحد فاصلة ثمانية سبعة خمسة واحد
+
+191
+00:26:02,590 --> 00:26:12,110
+كيلو جرام متر تربيع الـ
+
+192
+00:26:12,110 --> 00:26:18,170
+moment حوالين جي الـ mg مابتعمل moment هيكون دي  نصف
+
+193
+00:26:18,170 --> 00:26:29,110
+في T هتساوي I في ألف I اللي هي واحد فاصلة ثمانية
+
+194
+00:26:29,110 --> 00:26:42,660
+سبعة خمسة في ألف يعني نصف في مئة وثمانين بيساوي
+
+195
+00:26:42,660 --> 00:26:51,440
+واحد فاصلة ثمانية سبعة خمسة ألف ومنها باحسب ألف
+
+196
+00:26:51,440 --> 00:26:54,720
+بيساوى
+
+197
+00:27:07,190 --> 00:27:19,830
+ثمانية وأربعين Clockwise
+
+198
+00:27:19,830 --> 00:27:25,890
+هذا المطلوب الثاني المطلوب الثالث الـ acceleration
+
+199
+00:27:25,890 --> 00:27:30,130
+of the cord العجلة بتاعة الحبل الـ acceleration
+
+200
+00:27:30,130 --> 00:27:32,750
+بتاعة الـ cord بتاعة الحبل هتكون نفس الـ
+
+201
+00:27:32,750 --> 00:27:49,200
+acceleration بتاعة a هتكون عندي AA AA
+
+202
+00:27:49,200 --> 00:27:59,180
+كـ vector هتساوى AG اللي
+
+203
+00:27:59,180 --> 00:28:00,120
+هي اتجاهها
+
+204
+00:28:03,050 --> 00:28:17,810
+زائد a a بالنسبة لـ g اللي هتكون يعني
+
+205
+00:28:17,810 --> 00:28:24,730
+هذه a g الـ a ga الـ a a بالنسبة لـ g زائد بدور
+
+206
+00:28:24,730 --> 00:28:30,610
+clockwise هتكون هذه
+
+207
+00:28:30,610 --> 00:28:38,210
+aA بالنسبة لـ G is tangential طبعا فيه normal بس
+
+208
+00:28:38,210 --> 00:28:45,050
+مباشرة بعد ما شدنا ماكان فيه سرعة دورانية
+
+209
+00:28:45,050 --> 00:28:53,730
+للـ desk في عندي A A G normal اللي في الحالة هذه بيساوي
+
+210
+00:28:53,730 --> 00:28:55,130
+صفر
+
+211
+00:29:05,190 --> 00:29:16,030
+الـ A A G هتكون تساوي الـ A A G tangential زائد الـ
+
+212
+00:29:16,030 --> 00:29:20,450
+A A G normal
+
+213
+00:29:20,450 --> 00:29:24,890
+هدف الحل بتاعتنا بيساوي صفر يعني هتكون تساوي الـ A
+
+214
+00:29:24,890 --> 00:29:28,890
+A G tangential هتكون Alpha في R
+
+215
+00:29:32,230 --> 00:29:40,290
+الـ Alpha اللي هي ثمانية وأربعين في نصف اللي هي
+
+216
+00:29:40,290 --> 00:29:46,130
+هتكون أربعة وعشرين متر per second squared يعني
+
+217
+00:29:46,130 --> 00:29:51,210
+هتكون عند الـ AG احنا already حسبناها اثنين فاصلة
+
+218
+00:29:51,210 --> 00:29:59,190
+واحد تسعة أربعة زائد أربعة وعشرين يعني هتكون الـ
+
+219
+00:29:59,190 --> 00:30:06,140
+AA هتكون تساوي ستة وعشرين فاصلة واحد تسعة أربعة meter
+
+220
+00:30:06,140 --> 00:30:11,340
+per second square وهذه اتجاهها
+
+221
+00:30:11,340 --> 00:30:17,740
+طيب
+
+222
+00:30:17,740 --> 00:30:22,940
+حنحل
+
+223
+00:30:22,940 --> 00:30:23,780
+كمان مثال
+
+224
+00:30:57,940 --> 00:31:03,720
+نقرأ المثال Ironiform sphere of mass m and radius
+
+225
+00:31:03,720 --> 00:31:12,400
+r في عند كرة كتلتها m وقطرها r إلى كتلة mass m
+
+226
+00:31:12,400 --> 00:31:19,790
+و قطرها r is projected along a rough horizontal
+
+227
+00:31:19,790 --> 00:31:23,650
+surface with a linear velocity V0 تم القاءها على
+
+228
+00:31:23,650 --> 00:31:32,030
+سطح أفقي خشن بسرعة ابتدائية V0 the coefficient of
+
+229
+00:31:32,030 --> 00:31:34,590
+kinetic friction between the sphere and the
+
+230
+00:31:34,590 --> 00:31:39,090
+surface is Mu K معامل احتكاك الحركي بين الكورة
+
+231
+00:31:39,090 --> 00:31:42,510
+وسطح Mu K
+
+232
+00:31:46,010 --> 00:31:49,610
+يعني تم إلقاء الكورة بسرعة ابتدائية V0 معامل
+
+233
+00:31:49,610 --> 00:31:55,550
+احتكاك الحركي ميو كي determine
+
+234
+00:31:55,550 --> 00:32:01,830
+the time T1 at which the sphere will start rolling
+
+235
+00:32:01,830 --> 00:32:08,430
+without sliding أو دي الزمن T1 اللي عنده الكورة
+
+236
+00:32:08,430 --> 00:32:14,650
+بتبدأ تكون حركتها حركة تدحرج صافي ما فيش فيها sliding
+
+237
+00:32:14,650 --> 00:32:19,450
+فإن أول ما تحدث الكورة بيصير فيها sliding بتحاول تلف
+
+238
+00:32:19,450 --> 00:32:23,610
+بيكون slide و تلف تلف تلف تلف تلف لحد ما تصير طول
+
+239
+00:32:23,610 --> 00:32:27,950
+هذا بيصير إيش تتدحرج يعني الكورة بتبدأ بالـ sliding
+
+240
+00:32:27,950 --> 00:32:34,880
+وشوية شوية الـ sliding بيصير شوية rotation لحد مرحلة
+
+241
+00:32:34,880 --> 00:32:39,500
+ما تصير حركة تدحرجية زي تسنط طول أو تمسك حالها
+
+242
+00:32:39,500 --> 00:32:43,360
+تصير حركة تدحرجية احنا بنوجد الزمن من بداية الحركة
+
+243
+00:32:43,360 --> 00:32:48,540
+لحد ما توصل لحركة تدحرجية كاملة بدون أي انزلاق تدحرج
+
+244
+00:32:48,540 --> 00:32:52,860
+يعني بتكون تلف زي هي تتدحرج على السطح بدون احتكاك
+
+245
+00:32:52,860 --> 00:32:55,980
+زي حركة السيارة وهي ماشية عجلات السيارة بتكون
+
+246
+00:32:55,980 --> 00:33:00,300
+تتدحرج لكن لو ضربت brake خفيف بيكون العجل يلف
+
+247
+00:33:00,300 --> 00:33:05,690
+وينزلق طيب بده الـ time T1 at which the sphere will
+
+248
+00:33:05,690 --> 00:33:11,830
+start rolling without sliding ما
+
+249
+00:33:11,830 --> 00:33:15,250
+زال في الفترة الأولى من بداية الحركة من بداية
+
+250
+00:33:15,250 --> 00:33:20,870
+الحركة لحد ما يستقر عندي pure rolling عندي ..
+
+251
+00:33:20,870 --> 00:33:23,710
+بيكون في الفترة هذه في عندي sliding و rolling مع
+
+252
+00:33:23,710 --> 00:33:28,930
+بعض معناته مافيش علاقة بين الـ acceleration بتاعة
+
+253
+00:33:28,930 --> 00:33:33,660
+الكورة اللي هي الـ linear acceleration و الـ angular
+
+254
+00:33:33,660 --> 00:33:36,780
+acceleration احنا هنعمل free body diagram في الفترة
+
+255
+00:33:36,780 --> 00:33:45,520
+هذه عند الفترة هذه هذه الكورة بيكون يؤثر عليها وزنها
+
+256
+00:33:45,520 --> 00:33:48,740
+MG
+
+257
+00:33:48,740 --> 00:33:56,160
+وفي رد فعل عمودي normal
+
+258
+00:33:56,160 --> 00:33:56,900
+force
+
+259
+00:34:02,180 --> 00:34:06,120
+وفي عندي ميو
+
+260
+00:34:06,120 --> 00:34:12,620
+كي في عندي الاحتكاك طالما في sliding معناته ميو كي
+
+261
+00:34:12,620 --> 00:34:21,300
+في N بتكون عندي ميو كي في N هذا مركز استقل
+
+262
+00:34:21,300 --> 00:34:23,300
+بيساوى
+
+263
+00:34:30,650 --> 00:34:33,790
+طالما في احتكاك بيحاول يخفف من سرعتها مانع الـ X
+
+264
+00:34:33,790 --> 00:34:44,410
+دلوقتي هتكون على جهة الشمال هيكون عندي M في A وفي
+
+265
+00:34:44,410 --> 00:34:51,870
+لها كمان I في
+
+266
+00:34:51,870 --> 00:34:56,650
+Alpha حوالين مركز الثقل
+
+267
+00:34:59,770 --> 00:35:22,630
+حنحكي هذا هو الـ X الموجب هذا هو الـ Y أنا
+
+268
+00:35:22,630 --> 00:35:26,730
+هدرس الحركة من بداية القاء الكورة بسرعة ابتدائية V
+
+269
+00:35:26,730 --> 00:35:34,100
+نود V note لحد ما صار لها a pure rolling motion في
+
+270
+00:35:34,100 --> 00:35:38,220
+الفترة هذه من بداية الإلقاء لحد ما صارت حركة حركة
+
+271
+00:35:38,220 --> 00:35:44,720
+تدحرجية كاملة بيكون عند تدحرج وانزلاق مع بعض وهذا
+
+272
+00:35:44,720 --> 00:35:49,840
+هو الـ free body diagram في الفترة هذه لو أخدت
+
+273
+00:35:49,840 --> 00:35:52,260
+summation of force باتجاه الـ normal direction
+
+274
+00:35:52,260 --> 00:35:53,880
+الكورة ما فيش اللي حركتها تجاه الـ normal
+
+275
+00:36:00,940 --> 00:36:12,780
+باتجاه الـ Y بيساوي MAY حكينا
+
+276
+00:36:12,780 --> 00:36:23,180
+عندي N ناقص MG بيساوي صفر معناته N بيساوي M
+
+277
+00:36:23,180 --> 00:36:23,580
+في G
+
+278
+00:36:29,780 --> 00:36:36,900
+ان بيساوي M في جي هاخد
+
+279
+00:36:36,900 --> 00:36:42,580
+الـ summation of forces باتجاه الـ X summation of forces
+
+280
+00:36:42,580 --> 00:36:49,160
+باتجاه الـ X هنا اعتبرت هذا هو الاتجاه الموجب 
+
+281
+00:36:49,160 --> 00:37:02,480
+بالسواء Max فهذا الاتجاه هيكون عندى ميو K إن ميو K
+
+282
+00:37:02,480 --> 00:37:08,860
+إن بساوة
+
+283
+00:37:08,860 --> 00:37:20,160
+م في A معناته الـ A هعوض
+
+284
+00:37:20,160 --> 00:37:26,760
+أنا طبعا هعوض عن الـ N ميو
+
+285
+00:37:26,760 --> 00:37:36,540
+K في M جيب ساوة M في A هتروح M مع M معناته الـ A
+
+286
+00:37:36,540 --> 00:37:46,880
+هتكون تساوية ميو K في G ميو K في G 
+
+287
+00:38:05,620 --> 00:38:09,820
+طيب الآن هو بدأ بسرعة ابتدائية V Node بدأ بسرعة
+
+288
+00:38:09,820 --> 00:38:13,640
+ابتدائية V Node خليني أعمل معادلة تالتة آخد الـ
+
+289
+00:38:13,640 --> 00:38:25,520
+Moment حوالين الـ G هاي G هاي الـ G summation
+
+290
+00:38:25,520 --> 00:38:35,510
+للـ Moment حوالين G هتكون الساوية I في Alpha و أعتبر 
+
+291
+00:38:35,510 --> 00:38:49,710
+Clockwise موجب يعني هتكون عندي ميو K في N في R لإن 
+
+292
+00:38:49,710 --> 00:38:55,710
+هذا مصبوطر R بتساوي I الـ I للسفير اللي هي اتنين
+
+293
+00:38:55,710 --> 00:39:03,690
+على خمسة I هي أندكتب I بساوي اتنين على خمسة MR
+
+294
+00:39:03,690 --> 00:39:12,470
+تربيعي بساوي اتنين على خمسة MR تربيعي اللي هي I في 
+
+295
+00:39:12,470 --> 00:39:25,430
+الفة خدنا نعوض عن الـ N كنت ميو Kيه N اللي هي MG في 
+
+296
+00:39:25,430 --> 00:39:32,960
+R بساوي اتنين على خمسة MR تربيع في ألفة معناته 
+
+297
+00:39:32,960 --> 00:39:41,640
+الألفة هتساوي طبعا هتروح عند الـ .. هتروح عند M مع
+
+298
+00:39:41,640 --> 00:39:48,900
+M و R مع R يعني الألفة هتكون الساوية خمسة على
+
+299
+00:39:48,900 --> 00:39:55,740
+اتنين خمسة
+
+300
+00:39:55,740 --> 00:39:58,440
+على اتنين مي و K
+
+301
+00:40:03,460 --> 00:40:08,960
+G على R هذه
+
+302
+00:40:08,960 --> 00:40:15,660
+الـ Alpha لاحظوا
+
+303
+00:40:15,660 --> 00:40:19,960
+في الفترة هذه A and Alpha are not related A Alpha
+
+304
+00:40:19,960 --> 00:40:24,660
+يعني A بستويش Alpha في R A and Alpha are not
+
+305
+00:40:24,660 --> 00:40:29,190
+related خلال فترة من بداية الحركة لحد ما صارت 
+
+306
+00:40:29,190 --> 00:40:36,670
+الكورة تتحرك حركة تدحرجية طيب
+
+307
+00:40:36,670 --> 00:40:39,990
+بدأ
+
+308
+00:40:39,990 --> 00:40:48,130
+التحرك لما ألقيته أنا لما ألقيته الكورة ما كانتش
+
+309
+00:40:48,130 --> 00:40:50,430
+تدور يعني Omega Node أنا عندي V Node
+
+310
+00:40:59,600 --> 00:41:06,240
+مطاعنة لإن حاجة أحكي التالي الـ
+
+311
+00:41:06,240 --> 00:41:09,120
+expression صارت معروفة عندي هحكي .. أحكي الـ .. هو
+
+312
+00:41:09,120 --> 00:41:20,640
+صراحة هي V square so V mod square زاد اتنين A في 
+
+313
+00:41:20,640 --> 00:41:26,800
+أو نستخدم الزمن V 
+
+314
+00:41:28,270 --> 00:41:35,290
+بساوي V Not زائد A في T يعني
+
+315
+00:41:35,290 --> 00:41:40,910
+V بساوي
+
+316
+00:41:40,910 --> 00:41:43,950
+V
+
+317
+00:41:43,950 --> 00:41:53,390
+Not زائد الـ A اللي طبعا جايب العكس V
+
+318
+00:41:53,390 --> 00:41:57,710
+Not ناقص الـ A اللي هي Mu K
+
+319
+00:42:00,480 --> 00:42:02,780
+في G في T واحد
+
+320
+00:42:29,270 --> 00:42:38,650
+الـ T بيساوي الـ T واحد بتكون V بيساوي Omega في R 
+
+321
+00:42:38,650 --> 00:42:48,830
+يعني هيكون عندي إن Omega في R بيساوي V Not minus UK
+
+322
+00:42:48,830 --> 00:42:54,610
+في G الآن
+
+323
+00:42:55,550 --> 00:43:04,110
+الـ initial Omega Node كانت تساوي صفر معناته إن 
+
+324
+00:43:04,110 --> 00:43:12,090
+عندي هنا Omega بيساوي Omega Node زاد Alpha في T
+
+325
+00:43:12,090 --> 00:43:17,350
+يعني إحنا هنكون عند الـ Omega بيساوي Omega Node
+
+326
+00:43:17,350 --> 00:43:23,770
+اللي أنا صفر والـ Alpha عندي عبارة عن زاد خمسة على
+
+327
+00:43:23,770 --> 00:43:32,550
+اتنين في ميو K
+
+328
+00:43:32,550 --> 00:43:42,250
+في G على R معناته Omega Omega
+
+329
+00:43:42,250 --> 00:43:51,190
+بساوي خمسة على اتنين ميو K في G على R هذه
+
+330
+00:43:51,190 --> 00:43:52,630
+معادلة واحدة
+
+331
+00:43:56,110 --> 00:44:08,750
+T1 هاي معادلة واحد وهي معادلة اتنين عوض substitute
+
+332
+00:44:08,750 --> 00:44:12,990
+about
+
+333
+00:44:12,990 --> 00:44:24,810
+Omega from معادلة اتنين في معادلة واحدة و كُو عند
+
+334
+00:44:24,810 --> 00:44:28,250
+التالي نعوض المعدل واحد اللي هي عندي خمسة على 
+
+335
+00:44:28,250 --> 00:44:41,030
+اتنين ميو K G على R T واحد في R بيساوي V Node
+
+336
+00:44:41,030 --> 00:44:52,310
+minus ميو K G T واحد هجيب هذا على جهة التانية
+
+337
+00:44:53,500 --> 00:45:01,960
+هيكون عندي هاخد ميو K G
+
+338
+00:45:01,960 --> 00:45:08,640
+T واحد هتروح الـ R مع الـ R هكون عندي خمسة على
+
+339
+00:45:08,640 --> 00:45:17,340
+اتنين زائد واحد هتساوي
+
+340
+00:45:17,340 --> 00:45:22,660
+أش V ند خمسة على اتنين زائد خمسة على خمسة 
+
+341
+00:45:25,830 --> 00:45:28,790
+الواحد اتنين على اتنين اللي هي خمسة على سبعة 
+
+342
+00:45:28,790 --> 00:45:39,930
+معناته هتكون أنديهين خمسة على سبعة UK G T واحد
+
+343
+00:45:39,930 --> 00:45:50,010
+بساوي V Node معناته T واحد هتكون تساوي سبعة 
+
+344
+00:45:50,010 --> 00:46:04,540
+على خمسة V Node على UK في G معناته الزمن عشان نصل 
+
+345
+00:46:04,540 --> 00:46:09,440
+إن تصير حركة الكورة حركة دحرجية فقط ما فيش أي
+
+346
+00:46:09,440 --> 00:46:15,240
+نزلاق عبارة عن سبعة لخمسة V نقطة على UK في G
+
+347
+00:46:21,440 --> 00:46:23,840
+بدأوا linear and angular velocities of the sphere
+
+348
+00:46:23,840 --> 00:46:27,540
+at time T1 أنا خلاص عرفت الـ T1 عشان أوجد الـ
+
+349
+00:46:27,540 --> 00:46:32,080
+linear velocity عشان أوجد الـ linear velocity هعوض
+
+350
+00:46:32,080 --> 00:46:44,800
+في واحد هعوض في هذه المعادلة اللي هي V هتكون
+
+351
+00:46:44,800 --> 00:46:56,280
+ساوى V0 minus Mu KG في T1 اللي هي سبعة على خمسة V 
+
+352
+00:46:56,280 --> 00:47:08,760
+Node على ميو K في G شكلها 
+
+353
+00:47:08,760 --> 00:47:17,120
+مش سبعة على خمسة شكلها خمسة على سبعة هنا
+
+354
+00:47:17,120 --> 00:47:22,410
+عندي خمسة على اتنين يعني أتأكد راجعوا الأرقام ورايا
+
+355
+00:47:22,410 --> 00:47:29,490
+ومنها بحسب اللي هو هتكون خمسة على خمسة ناقص اتنين
+
+356
+00:47:29,490 --> 00:47:32,330
+اتنين
+
+357
+00:47:34,270 --> 00:47:39,650
+على خمسة V Not أنا هذا الرقم هذا الإشارة هذا 
+
+358
+00:47:39,650 --> 00:47:44,150
+الإشارة شاكك فيها راجع الأرقام والإشارات ورايا
+
+359
+00:47:44,150 --> 00:47:50,270
+وإذا في خطأ صحح و ورايا ماشي ما تفرض إن إن هذا 
+
+360
+00:47:50,270 --> 00:48:01,730
+الكلام مقدس بنفس الطريقة بحسب Omega Omega بساوي 
+
+361
+00:48:03,110 --> 00:48:13,590
+خمسة على اتنين ميو K G على R في T واحد اللي هي
+
+362
+00:48:13,590 --> 00:48:18,870
+سبعة على خمسة
+
+363
+00:48:18,870 --> 00:48:34,100
+V Node على ميو K في G يعني هتساوي سبعة على اتنين V
+
+364
+00:48:34,100 --> 00:48:45,600
+Node على R هيك
+
+365
+00:48:45,600 --> 00:48:50,040
+المفروض إحنا نكون حلينا مسائل بشكل كافي يوضح فكرة 
+
+366
+00:48:50,040 --> 00:48:54,100
+كيف يعمل Force Analysis لـ General Plan Motion
+
+367
+00:48:54,100 --> 00:49:01,720
+حلينا مجموعة الأمثلة المختلفة وشوفنا كيف نتعامل مع 
+
+368
+00:49:01,720 --> 00:49:06,010
+أفكار مختلفة هنكمل موضوع جديد 
+
+369
+00:49:35,740 --> 00:49:43,040
+طيب هندرس الحركة المقيدة Constraint Plan Motion
+
+370
+00:49:43,040 --> 00:49:47,520
+حركة مقيدة في مستوى حركة مقيدة يعني الجسم أنا
+
+371
+00:49:47,520 --> 00:49:52,640
+بتحكم في حركته بشكل كامل أمثل على الحركات المقيدة
+
+372
+00:49:52,640 --> 00:50:01,640
+مثلا الـ Truth عندها الـ Truth مع
+
+373
+00:50:01,640 --> 00:50:02,540
+الـ Truth تاني
+
+374
+00:50:05,930 --> 00:50:09,610
+إذا هذا بلف بهذا الاتجاه هذا هيكون بلف باتجاه
+
+375
+00:50:09,610 --> 00:50:13,070
+المعاكس حركة الـ Terce هذا مرتبطة بحركة الـ Terce
+
+376
+00:50:13,070 --> 00:50:18,630
+يعني هذه حركته مقيدة بحركة الـ Terce هذا مثال على
+
+377
+00:50:18,630 --> 00:50:24,150
+حركة مقيدة عندي 
+
+378
+00:50:24,150 --> 00:50:25,390
+مثلا طلع الـ Rod هذا
+
+379
+00:50:29,080 --> 00:50:32,840
+في اعترافه Block A و اعتراف التاني Block B
+
+380
+00:50:37,310 --> 00:50:41,550
+Horizontal Axis و Block B slice على الـ Vertical
+
+381
+00:50:41,550 --> 00:50:47,450
+Axis معناته طرفي الـ Rod محكمين هذا دايما طرف تحرك 
+
+382
+00:50:47,450 --> 00:50:51,150
+أفقي والطرف التاني دايما تحرك رأسي معناته حركة الـ
+
+383
+00:50:51,150 --> 00:50:55,430
+.. الـ .. الـ Rod هذا هي حركة مقيدة لإنها مقيدة حركة
+
+384
+00:50:55,430 --> 00:50:59,970
+الطرف التحتاني باتجاه المحور الأفقي وحركة الطرف 
+
+385
+00:50:59,970 --> 00:51:06,670
+التاني باتجاه الرأس عشان هي بيسميها حركة مقيدة لأ
+
+386
+00:51:06,670 --> 00:51:10,810
+لو عملنا في .. لو عملنا طبعا الجسم هذا الـ .. الـ Rod 
+
+387
+00:51:10,810 --> 00:51:15,750
+هيكون بتحرك حركة مستوي عامة يعني فيه إله انتقال و
+
+388
+00:51:15,750 --> 00:51:21,220
+إله دوران يعني انتقال بعد شوية ماك استقل مش هضل نفس
+
+389
+00:51:21,220 --> 00:51:25,580
+المكان وبعد شوية مش هكون الـ Mail تعرض نفس الـ Mail
+
+390
+00:51:25,580 --> 00:51:28,540
+معناته في Translation و في Rotation في اللحظة اللي
+
+391
+00:51:28,540 --> 00:51:32,500
+إحنا شايفينها كانت الزاوية هذه Theta وكان له
+
+392
+00:51:32,500 --> 00:51:39,760
+Angle Speed Omega و Angle Acceleration Alpha وفي
+
+393
+00:51:39,760 --> 00:51:44,800
+عندي Force P عند الطرف هذا بتأثر بالقوة المؤثرة 
+
+394
+00:51:44,800 --> 00:51:47,820
+عجزة في عندي على فرض إن هذا المستوى أملس وهذا 
+
+395
+00:51:47,820 --> 00:51:52,040
+أملس يعني ما فيش احتكاك كان رد فعل عمودي عند A ورد
+
+396
+00:51:52,040 --> 00:51:57,120
+فعل عمودي عند B وفي وزن الـ Rod W وفي القوة الخارجية 
+
+397
+00:51:57,120 --> 00:52:03,960
+P هذا هيقدر إنّه يصبح الـ Rotation I α وفي عندي Two 
+
+398
+00:52:03,960 --> 00:52:09,740
+Components للـ Inertia أو الـ M A X و M A Y
+
+399
+00:52:15,850 --> 00:52:20,130
+هنشوف مثال هذه
+
+400
+00:52:20,130 --> 00:52:31,090
+حركة مقيدة عندي Rod عندي طرف A في
+
+401
+00:52:31,090 --> 00:52:35,170
+Roller وعندي طرف B في Roller تانية الـ Roller عند 
+
+402
+00:52:35,170 --> 00:52:40,880
+A مسموح للتحرك على المستوى الأفقي و Roll B مصباح 
+
+403
+00:52:40,880 --> 0:52:44,680
+التحرك على المستوى المائل بزاوية 45 درجة معناته 
+
+404
+00:52:44,680 --> 00:52:50,080
+طرفي الـ Rod مقيدي الحركة الطرف A بتحرك أفقا والطرف 
+
+405
+00:52:50,080 --> 00:52:53,420
+B بتحرك على المستوى المائل 45 درجة معناته هذه
+
+406
+00:52:53,420 --> 00:52:58,080
+الحركة حركة مقيدة الـ Rod هتطوله أربع قدم المستوى
+
+407
+00:52:58,080 --> 00:53:05,640
+المائل زاوية مائله 45 درجة نقرأ السؤال The
+
+408
+00:53:05,640 --> 00:53:09,760
+extremities of a four-feet rod weighing fifty
+
+409
+00:53:09,760 --> 00:53:12,580
+pounds can move freely and with no friction along
+
+410
+00:53:12,580 --> 00:53:16,660
+two straight tracks الـ Rod هذا ممكن تحرك بشكل حر
+
+411
+00:53:16,660 --> 00:53:20,220
+على المستوى الأفق والمستوى المائل طبعا هدول
+
+412
+00:53:20,220 --> 00:53:24,160
+مستويين أم لسان يعني ما فيش احتكاك طوله أربع قدم
+
+413
+00:53:24,160 --> 00:53:29,000
+ووزن الـ Rod خمسين Pound W
+
+414
+00:53:30,620 --> 00:53:36,360
+بساوي خمسين Pound the
+
+415
+00:53:36,360 --> 00:53:40,160
+Rod is released with no velocity تم إطلاق الـ Rod 
+
+416
+00:53:40,160 --> 00:53:45,340
+من السكون ما زال تم إطلاقه أكيد هيتحرك هينزلق with
+
+417
+00:53:45,340 --> 00:53:50,000
+no velocity يعني بدأ من السكون from the position
+
+418
+00:53:50,000 --> 00:53:52,640
+shown من الوضعية هذه لما كانت زوايا هذه تلاتين
+
+419
+00:53:52,640 --> 00:53:56,590
+درجة Determine the angular acceleration of the rod
+
+420
+00:53:56,590 --> 00:54:03,370
+وجد السرعة العجل الزاوية للـ Rod والـ Reactions at a 
+
+421
+00:54:03,370 --> 00:54:08,490
+and b ردود الأفعال عند a وb عشان نحل مثل هيك لازم
+
+422
+00:54:08,490 --> 00:54:15,070
+نعمل free body diagram free
+
+423
+00:54:15,070 --> 00:54:22,690
+body diagram طبعا هي عند الطرف a هذا
+
+424
+00:54:22,690 --> 00:54:32,080
+الطرف aو هذا الطرف B الزاوية هذه ثلاثين درجة و هذه
+
+425
+00:54:32,080 --> 00:54:41,460
+خمسة و أربعين درجة هين خمسة و أربعين درجة هين ثلاثين
+
+426
+00:54:41,460 --> 00:54:52,060
+درجة هذه A B هذه أربعة قدم و هذا مركز تقع ال G
+
+427
+00:54:55,400 --> 00:55:14,820
+الحديث دي طيب
+
+428
+00:55:19,850 --> 00:55:22,970
+الآن بدي أحط القوة المؤثرة على الجسم هذا القوة
+
+429
+00:55:22,970 --> 00:55:27,150
+المؤثرة لوش عند a السطح هذا أملس ما فيش احتكاك
+
+430
+00:55:27,150 --> 00:55:30,310
+معناه رد الفعل اللي هتكون عمودي على المستوى هذا
+
+431
+00:55:30,310 --> 00:55:33,090
+فأنا هكون هنا force
+
+432
+00:55:48,300 --> 00:55:54,780
+هذا N A يعني بي حيكون عمودي انتبه مش عمودي على
+
+433
+00:55:54,780 --> 00:55:58,120
+الرد عمودي على المستوى عمودي على المستوى المائل
+
+434
+00:55:58,120 --> 00:56:10,640
+هكون عمودي هذا
+
+435
+00:56:10,640 --> 00:56:14,660
+N N
+
+436
+00:56:14,660 --> 00:56:15,500
+B
+
+437
+00:56:20,720 --> 00:56:32,360
+و في الوزن W
+
+438
+00:56:32,360 --> 00:56:43,540
+وزن الروت هذه هي القوة المؤثرة على الجسم نتيجة
+
+439
+00:56:43,540 --> 00:56:48,040
+هذه القوة المؤثرة على الجسم هيبدأ يتحرك الجسم
+
+440
+00:56:48,040 --> 00:57:01,050
+هيكون lowم ax وم
+
+441
+00:57:01,050 --> 00:57:07,330
+ay
+
+442
+00:57:07,330 --> 00:57:15,370
+وحيكون حركة دوران كمان وإله كمان
+
+443
+00:57:15,370 --> 00:57:18,930
+أي في الف
+
+444
+00:57:23,980 --> 00:57:31,120
+بدأ أحط المحاور هاي ال X و
+
+445
+00:57:31,120 --> 00:57:39,180
+هاي ال Y هيك
+
+446
+00:57:39,180 --> 00:57:45,880
+أنا عملت ال free بدء إجرام كامل بدنا
+
+447
+00:57:45,880 --> 00:57:49,800
+نحسب ال angle acceleration لل .. لل .. لل .. للرد
+
+448
+00:57:49,800 --> 00:58:00,970
+A Bو ال reactions عند a و عند b أنا
+
+449
+00:58:00,970 --> 00:58:06,190
+بدي
+
+450
+00:58:06,190 --> 00:58:13,330
+أحاول المسألة بدي أضرب عصفورين بحجر بدي أطير بدي
+
+451
+00:58:13,330 --> 00:58:18,950
+أعمل معادلة بحيث ال N A و ال N B ما يبينوش يعني
+
+452
+00:58:18,950 --> 00:58:38,210
+بهواي واحدة أشيلهم لأن لو مديت ال N A هذا
+
+453
+00:58:38,210 --> 00:58:43,410
+نقطة C خليني أسميها C خليني بس نطلع على الزوايا
+
+454
+00:58:44,900 --> 00:58:49,540
+عندي هذه الزاوية تسعين
+
+455
+00:58:49,540 --> 00:58:54,400
+هذه ثلاثين وهذه خمسة وأربعين هذه الزاوية خارج
+
+456
+00:58:54,400 --> 00:59:07,000
+المثابرة هذه ثلاثين وهذه خمسة عشر هذه خمسة عشر خمسة عشر
+
+457
+00:59:07,000 --> 00:59:13,840
+والزاوية هذه هذه
+
+458
+00:59:13,840 --> 00:59:14,260
+الزاوية
+
+459
+00:59:17,940 --> 00:59:24,700
+ستين درجة وهذا
+
+460
+00:59:24,700 --> 00:59:30,640
+سيكون خمسة
+
+461
+00:59:30,640 --> 00:59:34,900
+و أربعين درجة معناته
+
+462
+00:59:34,900 --> 00:59:42,920
+مئتين و ثمانين ناقص ستين مئة و عشرين هذا سيكون كم
+
+463
+00:59:42,920 --> 00:59:45,160
+هذا سيكون خمسة و سبعين
+
+464
+00:59:50,140 --> 00:59:56,260
+خمسة وسبعين درجة أنا
+
+465
+00:59:56,260 --> 01:00:02,560
+هاخد العزم حوالين نقطة C هاخد العزم حوالين نقطة C
+
+466
+01:00:02,560 --> 01:00:06,040
+هاخد
+
+467
+01:00:06,040 --> 01:00:11,060
+العزم حوالين نقطة C لما ناخد العزم حوالين نقطة C
+
+468
+01:00:11,060 --> 01:00:16,560
+ال N A بتمر في C و ال N B بتمر في نقطة C باناته ال
+
+469
+01:00:16,560 --> 01:00:18,440
+N A و ال N B مش هيبينه
+
+470
+01:00:23,870 --> 01:00:42,010
+هنعمل هنا عمودي هاسي
+
+471
+01:00:42,010 --> 01:00:49,230
+هادرز ده و خمسة و أربعين و
+
+472
+01:00:49,230 --> 01:00:50,090
+هادرز ستين
+
+473
+01:00:53,930 --> 01:00:58,930
+و هذه خمسة
+
+474
+01:00:58,930 --> 01:01:04,130
+و سبعين و
+
+475
+01:01:04,130 --> 01:01:08,490
+هذه الزاوية خمس
+
+476
+01:01:08,490 --> 01:01:08,910
+عشر
+
+477
+01:01:28,970 --> 01:01:33,730
+الآن لو أخدت ال moment حوالين نقطة G هيكون ال
+
+478
+01:01:33,730 --> 01:01:39,330
+moment of all forces about G بيستوى I في Alpha لكن
+
+479
+01:01:39,330 --> 01:01:41,870
+لو أخدت ال moment حوالين نقطة C هيكون ال moment
+
+480
+01:01:41,870 --> 01:01:50,710
+حوالين ال C I حوالين ال C في Alpha عشان أجد high I
+
+481
+01:01:50,710 --> 01:01:52,870
+حوالين ال C في Alpha بدي أستخدم ال parallel axis
+
+482
+01:01:52,870 --> 01:01:53,250
+theorem
+
+483
+01:02:00,010 --> 01:02:04,990
+معنى الهجة احكي ان M هذي
+
+484
+01:02:04,990 --> 01:02:11,370
+ال trick جديد summation ل
+
+485
+01:02:11,370 --> 01:02:18,070
+ال moment هم أولاً C تعتبر
+
+486
+01:02:18,070 --> 01:02:18,870
+هذا الموجب
+
+487
+01:02:28,140 --> 01:02:39,200
+هتكون ال I حوالين C في Alpha هذا Shortcut لأن
+
+488
+01:02:39,200 --> 01:02:42,620
+بالزمن عشان أعرف ال I حوالين ال C بدي أوصل ال GC
+
+489
+01:02:55,630 --> 01:02:58,930
+واضح عشان دي احسب moments هيلزمني ايش حسابات
+
+490
+01:02:58,930 --> 01:03:09,530
+هندسية لو خدت المثلث ABC هذا طوله أربعة قدم كل
+
+491
+01:03:09,530 --> 01:03:18,090
+زعيم معروفة بدي آخذ المثلث ABC
+
+492
+01:03:18,090 --> 01:03:21,630
+الآن
+
+493
+01:03:21,630 --> 01:03:25,010
+هكون BC على صين ستين
+
+494
+01:03:31,350 --> 01:03:40,910
+هي تساوي AB ع الصين ال 45 بساوي
+
+495
+01:03:40,910 --> 01:03:49,110
+AC ع الصين ال 75 AC هذا ال sign له AC ع الصين ال
+
+496
+01:03:49,110 --> 01:03:54,710
+75 يعني
+
+497
+01:03:54,710 --> 01:04:02,540
+BC أنا مش عارفه يعني BC ع الصين الستين بيساوي AB
+
+498
+01:04:02,540 --> 01:04:09,880
+اللي هو أربعة على sign الخمسة و أربعين بتساوي AC
+
+499
+01:04:09,880 --> 01:04:21,700
+على sign الخمسة وسبعين و منها بحسب BC و بحسب AC
+
+500
+01:04:24,490 --> 01:04:29,070
+BC هيكون أربعة صين ستين على صين خمسة و أربعين و AC
+
+501
+01:04:29,070 --> 01:04:39,110
+بيساوي أربعة صين خمسة وسبعين على صين خمسة و أربعين طيب
+
+502
+01:04:39,110 --> 01:04:44,190
+معناته BC و AC صاروا معروفين عندي
+
+503
+01:04:48,430 --> 01:04:55,150
+احسبوليها تابع وراي و احسبوليها احسب BC و AC
+
+504
+01:04:55,150 --> 01:05:01,410
+بلزمني أحسب كمان CG
+
+505
+01:05:01,410 --> 01:05:13,170
+CG لأخذت المثلث أخذت المثلث ACG
+
+506
+01:05:13,170 --> 01:05:14,550
+أخذت المثلث
+
+507
+01:05:20,120 --> 01:05:32,120
+A C G هذا المثلث لحظة
+
+508
+01:05:32,120 --> 01:05:38,760
+أنا صار معروف عندي A C و A G معروف اللي هو اثنين
+
+509
+01:05:38,760 --> 01:05:43,140
+قدم و الزواهر دي ستين معروفة معناته بأستخدم ال
+
+510
+01:05:43,140 --> 01:05:50,180
+cosine law عشان أحسب ال C Gاللي هو use الـ cosine
+
+511
+01:05:50,180 --> 01:06:04,660
+له اللي هو CG تربيع هاد أضلها حيث هو AG تربيع زائد
+
+512
+01:06:04,660 --> 01:06:12,980
+AC تربيع ناقص
+
+513
+01:06:12,980 --> 01:06:16,240
+اثنين في AG
+
+514
+01:06:18,350 --> 01:06:23,450
+في AC كوساين الزاوية بينهم اللي هي ستين درجة
+
+515
+01:06:23,450 --> 01:06:29,730
+معناته CG حسبناها
+
+516
+01:06:29,730 --> 01:06:39,810
+عوض عن AG عوض
+
+517
+01:06:39,810 --> 01:06:45,400
+عن AG و عن AC و احسبه ال square root تحسبه ال CG
+
+518
+01:06:45,400 --> 01:06:49,400
+معناته ال CG صارت معروفة معناته أنا هيأت كل شيء
+
+519
+01:06:49,400 --> 01:06:52,520
+صار كل شيء معروف عندي إلا أنا هاخد ال moment
+
+520
+01:06:52,520 --> 01:07:01,880
+حوالين C أنا
+
+521
+01:07:01,880 --> 01:07:05,580
+حكيت summation و moment حوالين ال C بيستوى I C في
+
+522
+01:07:05,580 --> 01:07:17,530
+Alpha ال I C ال moment حوالين ال C الـ I C طبقًا
+
+523
+01:07:17,530 --> 01:07:22,610
+للـ Parallel Axis Theory بالـ I C بتساوي
+
+524
+01:07:22,610 --> 01:07:32,750
+الـ I حوالين الـ G زائد ال mass تحت الرد في
+
+525
+01:07:32,750 --> 01:07:36,070
+المسافة اللي هي CG تربيع
+
+526
+01:07:39,820 --> 01:07:42,400
+إذا حد نسي ال parallel axis theorem من الستاتيكا
+
+527
+01:07:42,400 --> 01:07:47,580
+يرجع للستاتيكا يعني ال I حوالين نقطة C بيستوى ال I
+
+528
+01:07:47,580 --> 01:07:50,820
+حوالين G زائد ال ال ال ال ال ال ال ال ال ال ال 
+
+529
+01:07:50,820 --> 01:07:51,400
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال 
+
+530
+01:07:51,400 --> 01:07:52,680
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+531
+01:07:52,680 --> 01:07:53,180
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+532
+01:07:53,180 --> 01:07:54,140
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+533
+01:07:54,140 --> 01:07:57,360
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+534
+01:07:57,360 --> 01:07:57,460
+ال ال ال ال ال ال
+
+535
+01:08:13,400 --> 01:08:18,340
+طيب ال I C صارت معروفة ال M C صنعش المنطقة بقى M C
+
+536
+01:08:18,340 --> 01:08:25,040
+بيصير I في C في Alpha الآن حوالين C عند ال N A و
+
+537
+01:08:25,040 --> 01:08:27,920
+ال N B ما هم ممروا فيه C فشل moment بيضل يعمل
+
+538
+01:08:27,920 --> 01:08:35,990
+moment اللي هو ايش الوزن هيكون عنده المسافة هذه هذا
+
+539
+01:08:35,990 --> 01:08:45,370
+طوله اثنين قدم يعني هتكون هذه المسافة هذه
+
+540
+01:08:45,370 --> 01:09:00,710
+اثنين في cosine الثلاثين والمسافة هذه هذه
+
+541
+01:09:00,710 --> 01:09:01,470
+كلها هذه
+
+542
+01:09:07,060 --> 01:09:19,320
+هذا اثنين ساين الثلاثين معناته هذه هتكون هتكون
+
+543
+01:09:19,320 --> 01:09:30,820
+اللي هي AC و minus اثنين ساين الثلاثين طيب
+
+544
+01:09:30,820 --> 01:09:34,540
+ناخد moment حوالين C Summation of moment from C
+
+545
+01:09:34,540 --> 01:09:39,660
+بيساوي I في C I C في Alpha نأخذ جهة الشمال حكينا N
+
+546
+01:09:39,660 --> 01:09:41,900
+A بتعملش moment و N B بتعملش moment الواحد اللي
+
+547
+01:09:41,900 --> 01:09:50,140
+بيعمل moment اللي هي W في عكس عقارب الساعة W في
+
+548
+01:09:50,140 --> 01:09:59,860
+اثنين cosine الثلاثين درجة بتساوي
+
+549
+01:09:59,860 --> 01:10:13,190
+I C في Alpha الآن ال IG عشان تكون في الصورة IG للرد
+
+550
+01:10:13,190 --> 01:10:20,610
+بيساوي واحد على اثنا عشر M التربيع يعني ال IC هتكون
+
+551
+01:10:20,610 --> 01:10:28,010
+تساوي واحد على اثنا عشر ال M اللي هي W على G طوله
+
+552
+01:10:28,010 --> 01:10:38,030
+التربيع زائد M في CG تربيع IC
+
+553
+01:10:38,030 --> 01:10:45,510
+صارت معروف من أنت بحسب ايش نحسب Alpha we calculate
+
+554
+01:10:45,510 --> 01:10:53,670
+Alpha هذا المطلوب الأول المطلوب الثاني بدي ال
+
+555
+01:10:53,670 --> 01:10:59,090
+reactions عند
+
+556
+01:10:59,090 --> 01:11:01,330
+A
+
+557
+01:11:03,430 --> 01:11:11,990
+و ال reaction عند a و عند b بدوا
+
+558
+01:11:11,990 --> 01:11:23,990
+na و nb الآن عشان أعرف اتجاه ال a ال ax و ال ay ال
+
+559
+01:11:23,990 --> 01:11:29,070
+aa هي اتجاهها هذه
+
+560
+01:11:29,070 --> 01:11:29,610
+aa
+
+561
+01:11:32,410 --> 01:11:39,990
+و هذه a,b
+
+562
+01:11:39,990 --> 01:11:43,230
+a
+
+563
+01:11:43,230 --> 01:11:52,550
+,a و a,b يعني a,a أفقية و a,b مائلة بزاوية خمسة و
+
+564
+01:11:52,550 --> 01:12:03,330
+أربعين خمسة وأربعين درجة ممكن أن أربط a,b مع AA
+
+565
+01:12:03,330 --> 01:12:15,090
+عشان أحسب Alpha يعني هأحكي AB ك
+
+566
+01:12:15,090 --> 01:12:23,530
+vector تعمل زاوية خمسة وأربعين بالساوية
+
+567
+01:12:23,530 --> 01:12:34,300
+AA translation with A  هاتجاهها زائد ABA  هيكون  زاد
+
+568
+01:12:34,300 --> 01:12:42,160
+a b a في tangential هتكون
+
+569
+01:12:42,160 --> 01:12:46,940
+عمودية
+
+570
+01:12:46,940 --> 01:12:50,840
+هتكون
+
+571
+01:12:50,840 --> 01:12:55,800
+عمودية على هذه a b a tangential
+
+572
+01:13:12,260 --> 01:13:23,960
+عمودية هذه تسعين درجة الرد
+
+573
+01:13:23,960 --> 01:13:34,460
+عامل زاوية ثلاثين درجة وانته مع الرأس تعمل ثلاثين
+
+574
+01:13:34,460 --> 01:13:40,300
+درجة زائد a b a normal
+
+575
+01:13:41,910 --> 01:13:51,210
+هتكون في اتجاه ال BA تكون في اتجاه ال
+
+576
+01:13:51,210 --> 01:13:56,390
+BA طبعا أنا في البداية .. بداية الحركة ما بيكون
+
+577
+01:13:56,390 --> 01:13:59,290
+فيه سرعة لل .. سرعة الدورانية بمعناته هذه هتكون
+
+578
+01:13:59,290 --> 01:14:08,270
+إيش الزاوية؟ صفر بمعناته AB اللي بتعمل زاوية خمسة
+
+579
+01:14:08,270 --> 01:14:08,710
+وأربعين
+
+580
+01:14:11,930 --> 01:14:16,290
+بس AA زائد
+
+581
+01:14:16,290 --> 01:14:21,230
+ABA tangential عبارة عن ألف في ألف هتكون
+
+582
+01:14:21,230 --> 01:14:32,750
+أربعة ألف وبتعمل زاوية مع الرأس ثلاثين درجة
+
+583
+01:14:50,940 --> 01:14:55,740
+في نفس المنطق بحسب
+
+584
+01:14:55,740 --> 01:15:06,000
+AG لأنه مش عارف اتجاهها بالسواء AA لهذه اتجاهها 
+
+585
+01:15:06,000 --> 01:15:19,550
+زائد AG بالنسبة لـ A هتكون AA هذه اتجاهها زائد a ga
+
+586
+01:15:19,550 --> 01:15:26,330
+اللي هيتكون اثنين ألفة
+
+587
+01:15:26,330 --> 01:15:32,150
+والزاوية بتاعتها ثلاثين
+
+588
+01:15:32,150 --> 01:15:34,410
+درجة هذه معادلة إيش؟ واحد
+
+589
+01:15:44,100 --> 01:15:50,040
+بعدين هأخذ summation of forces
+
+590
+01:15:50,040 --> 01:15:57,380
+باتجاه الـ Y بيساوي MA
+
+591
+01:15:57,380 --> 01:16:08,860
+Y باتجاه الـ Y هيكون عنده NB Sin 45
+
+592
+01:16:17,860 --> 01:16:28,240
+-W بيساوي الأمر هي W على G زائد
+
+593
+01:16:28,240 --> 01:16:34,480
+W
+
+594
+01:16:34,480 --> 01:16:35,380
+على G في
+
+595
+01:16:40,970 --> 01:16:49,570
+الـ A GY الـ AY هدفه لمركبة هتكون minus اثنين ألفة
+
+596
+01:16:49,570 --> 01:16:56,470
+cosine الثلاثين لحظة عندي ألفة معروفة وده اللي
+
+597
+01:16:56,470 --> 01:17:03,450
+معروف منها بحسب NB بحسب إيش NB
+
+598
+01:17:03,450 --> 01:17:05,870
+بحسب ال NB
+
+599
+01:17:33,200 --> 01:17:38,100
+بعدها هأحكي summation لل
+
+600
+01:17:38,100 --> 01:17:46,040
+forces باتجاه الـ X بالثورة MAX هيكون عنده اللي
+
+601
+01:17:46,040 --> 01:17:52,600
+هي NA لحظة
+
+602
+01:17:52,600 --> 01:17:55,380
+لحظة في إيش غلط هنا نمسح هذا
+
+603
+01:17:58,590 --> 01:18:04,710
+أنا هأخذ باتجاه الـ X summation لل forces باتجاه ال
+
+604
+01:18:04,710 --> 01:18:10,930
+X بتساوي MAX يعني أنا هكون عندي NB cosine NB
+
+605
+01:18:10,930 --> 01:18:17,710
+cosine الخمسة وأربعين بتساوي
+
+606
+01:18:17,710 --> 01:18:24,750
+باتجاه الـ X هكون عندي AA زائد minus
+
+607
+01:18:28,850 --> 01:18:38,110
+اللي هي MW على G في X اللي هي بقرة عن AA-2αSin
+
+608
+01:18:38,110 --> 01:18:43,570
+30 درجة هاي معادلة 2
+
+609
+01:18:53,720 --> 01:18:58,160
+وهأعمل كمان معادلة summation لل forces باتجاه الـ Y
+
+610
+01:18:58,160 --> 01:19:06,000
+بالساوية MAY هكون
+
+611
+01:19:06,000 --> 01:19:11,300
+عندي اللي هو NA زائد
+
+612
+01:19:11,300 --> 01:19:19,260
+NB Sin 45 minus
+
+613
+01:19:19,260 --> 01:19:23,260
+W بالساوية
+
+614
+01:19:24,300 --> 01:19:33,820
+و على جيه في minus اثنين ألفة cosine ثلاثين درجة
+
+615
+01:19:51,200 --> 01:19:55,480
+طيب بتكملوا الحل اعملوا ..كملوا الحل لحالكوا أنا
+
+616
+01:19:55,480 --> 01:20:00,820
+اعطيتكوا الشيء الأساسي بدون أرقام بتكملوها و
+
+617
+01:20:00,820 --> 01:20:06,040
+بتحسبوا الـ accelerator بتحسبوا ال NA و ال NB
+
+618
+01:20:06,040 --> 01:20:12,200
+المحاضرة
+
+619
+01:20:12,200 --> 01:20:16,040
+الجاية بندرس
+
+620
+01:20:16,040 --> 01:20:20,460
+ال non centroidial rotation و rolling motion 
diff --git a/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/uGFxXwSt91g_raw.json b/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/uGFxXwSt91g_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..36700dce13078e8afeb47edc9d1230e465d073fb
--- /dev/null
+++ b/PL9fwy3NUQKwZvX8ccWWIQGuRoAuJoRirA/uGFxXwSt91g_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3201, "start": 4.89, "end": 32.01, "text": "بسم الله الرحمن الرحيم السلام عليكم و رحمة الله اليوم هنكمل .. نحل مزيد من الأمثل على chapter 16 اللي هي force and acceleration analysis of rigid bodies in plan motion هنحل مثال جديد طبعا نطلع على الشكل عندى نظام بكرات", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21136, 37440, 25894, 24793, 4032, 12602, 35571, 3660, 21984, 45595, 20498, 8032, 1863, 24793, 1211, 4386, 8717, 5016, 1211, 3714, 11622, 25708, 9154, 16247, 2304, 12984, 1211, 15844, 7187, 3165, 13672, 1829, 39896, 3464, 293, 17162, 5215, 295, 22195, 7510, 294, 1393, 5394, 8032, 1863, 5016, 1211, 50113, 6027, 10874, 16254, 3215, 23032, 3555, 3615, 995, 8717, 9566, 1211, 3615, 15844, 25124, 28820, 43242, 7578, 8717, 19913, 10943, 4724, 37983, 9307], "avg_logprob": -0.13368056144243406, "compression_ratio": 1.544186046511628, "no_speech_prob": 0.0, "words": [{"start": 4.89, "end": 5.39, "word": "بسم", "probability": 0.87890625}, {"start": 5.39, "end": 5.61, "word": " الله", "probability": 0.95751953125}, {"start": 5.61, "end": 6.21, "word": " الرحمن", "probability": 0.9591471354166666}, {"start": 6.21, "end": 6.59, "word": " الرحيم", "probability": 0.99169921875}, {"start": 6.59, "end": 6.97, "word": " السلام", "probability": 0.93115234375}, {"start": 6.97, "end": 7.39, "word": " عليكم", "probability": 0.955078125}, {"start": 7.39, "end": 7.53, "word": " و", "probability": 0.99560546875}, {"start": 7.53, "end": 7.77, "word": " رحمة", "probability": 0.8165690104166666}, {"start": 7.77, "end": 8.09, "word": " الله", "probability": 0.96923828125}, {"start": 8.09, "end": 9.09, "word": " اليوم", "probability": 0.921875}, {"start": 9.09, "end": 9.89, "word": " هنكمل", "probability": 0.9619140625}, {"start": 9.89, "end": 10.13, "word": " ..", "probability": 0.54931640625}, {"start": 10.13, "end": 12.05, "word": " نحل", "probability": 0.6957600911458334}, {"start": 12.05, "end": 12.65, "word": " مزيد", 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"probability": 0.90380859375}, {"start": 1920.71, "end": 1921.35, "word": " start", "probability": 0.9140625}, {"start": 1921.35, "end": 1921.83, "word": " rolling", "probability": 0.90966796875}, {"start": 1921.83, "end": 1922.57, "word": " without", "probability": 0.935546875}, {"start": 1922.57, "end": 1923.31, "word": " sliding", "probability": 0.96337890625}, {"start": 1923.31, "end": 1923.59, "word": " أو", "probability": 0.0955810546875}, {"start": 1923.59, "end": 1923.73, "word": " دي", "probability": 0.785400390625}, {"start": 1923.73, "end": 1924.19, "word": " الزمن", "probability": 0.9671223958333334}, {"start": 1924.19, "end": 1925.71, "word": " T1", "probability": 0.658203125}, {"start": 1925.71, "end": 1927.05, "word": " اللي", "probability": 0.922119140625}, {"start": 1927.05, "end": 1927.53, "word": " عنده", "probability": 0.99072265625}, {"start": 1927.53, "end": 1928.43, "word": " الكورة", "probability": 0.9806315104166666}, {"start": 1928.43, "end": 1929.27, "word": " بتبدأ", "probability": 0.8836263020833334}, {"start": 1929.27, "end": 1929.69, "word": " تكون", "probability": 0.97900390625}, {"start": 1929.69, "end": 1930.19, "word": " حركته", "probability": 0.8914388020833334}, {"start": 1930.19, "end": 1930.69, "word": " حركة", "probability": 0.9679361979166666}, {"start": 1930.69, "end": 1931.61, "word": " تدحرج", "probability": 0.9100341796875}], "temperature": 1.0}, {"id": 63, "seek": 195021, "start": 1932.71, "end": 1950.21, "text": "صافي مافيش فيها sliding فان أول محدث الكورة بيصير فيها sliding بتحاول تلف بيكون slide و تلف تلف تلف تلف تلف لحد ما تسنط طول هذا بيصير إيش تتدهرج يعني الكورة بتبدأ بال sliding و شوية شوية ال sliding", "tokens": [9381, 31845, 1829, 19446, 41185, 8592, 8978, 11296, 21169, 6156, 7649, 5551, 12610, 3714, 24401, 12984, 33251, 13063, 3660, 4724, 1829, 9381, 13546, 8978, 11296, 21169, 39894, 5016, 995, 12610, 6055, 46538, 4724, 1829, 30544, 4137, 4032, 6055, 46538, 6055, 46538, 6055, 46538, 6055, 46538, 6055, 46538, 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2629.95, "end": 2630.31, "word": " ار", "probability": 0.959716796875}, {"start": 2630.31, "end": 2631.19, "word": " هذه", "probability": 0.10491943359375}, {"start": 2631.19, "end": 2631.83, "word": " معادلة", "probability": 0.96044921875}, {"start": 2631.83, "end": 2632.63, "word": " واحدة", "probability": 0.9716796875}], "temperature": 1.0}, {"id": 87, "seek": 266311, "start": 2636.11, "end": 2663.11, "text": "T1 هاي معادلة واحد وهي معادلة اتنين عوض substitute about omega from معادلة اتنين في معادلة H واحد", "tokens": [51, 16, 8032, 47302, 20449, 18513, 37977, 36764, 24401, 37037, 1829, 20449, 18513, 37977, 1975, 2655, 1863, 9957, 6225, 2407, 11242, 15802, 466, 10498, 490, 20449, 18513, 37977, 1975, 2655, 1863, 9957, 8978, 20449, 18513, 37977, 389, 36764, 24401], "avg_logprob": -0.1916992139071226, "compression_ratio": 1.5151515151515151, "no_speech_prob": 0.0, "words": [{"start": 2636.1099999999997, "end": 2637.5099999999998, "word": "T1", "probability": 0.5655517578125}, {"start": 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"هنشوف مثال هذه حركة مقيدة عندي rod عندي طرف a في roller و عندي طرف b في roller تانية ال roller عند a مسموح للتحرك على المستوى الأفقي", "tokens": [3224, 1863, 8592, 38688, 50113, 6027, 29538, 11331, 31747, 3660, 3714, 4587, 25708, 3660, 18871, 16254, 8685, 18871, 16254, 23032, 28480, 257, 8978, 15948, 4032, 18871, 16254, 23032, 28480, 272, 8978, 15948, 6055, 7649, 10632, 2423, 15948, 43242, 257, 3714, 38251, 2407, 5016, 24976, 2655, 5016, 31747, 15844, 9673, 14851, 2407, 7578, 16247, 5172, 38436], "avg_logprob": -0.2109375037252903, "compression_ratio": 1.5547445255474452, "no_speech_prob": 0.0, "words": [{"start": 3135.85, "end": 3136.31, "word": "هنشوف", "probability": 0.83087158203125}, {"start": 3136.31, "end": 3136.85, "word": " مثال", "probability": 0.967529296875}, {"start": 3136.85, "end": 3140.13, "word": " هذه", "probability": 0.495361328125}, {"start": 3140.13, "end": 3141.27, "word": " حركة", "probability": 0.9635416666666666}, {"start": 3141.27, "end": 3142.37, "word": " 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318096, "start": 3159.62, "end": 3180.96, "text": "و roll B مصباح التحرك على المستوى المائل بزاوية 45 درجة معناته طرفي الرد مقيدي الحركة الطرف A بتحرك أفقه و الطرف B بتحرك على المستوى المائل 45 درجة معناته هذه الحركة حركة مقيدة الرد هتطوله أربع قدم المستوى المائل زاوية مائله 45 درجة", "tokens": [2407, 3373, 363, 3714, 9381, 3555, 39319, 16712, 5016, 31747, 15844, 9673, 14851, 2407, 7578, 9673, 16373, 1211, 4724, 11622, 995, 2407, 10632, 6905, 11778, 47341, 3660, 20449, 8315, 47395, 23032, 28480, 1829, 34892, 3215, 3714, 4587, 25708, 1829, 21542, 31747, 3660, 41950, 28480, 316, 39894, 5016, 31747, 5551, 5172, 4587, 3224, 4032, 41950, 28480, 363, 39894, 5016, 31747, 15844, 9673, 14851, 2407, 7578, 9673, 16373, 1211, 6905, 11778, 47341, 3660, 20449, 8315, 47395, 29538, 21542, 31747, 3660, 11331, 31747, 3660, 3714, 4587, 25708, 3660, 34892, 3215, 8032, 2655, 9566, 12610, 3224, 5551, 25513, 3615, 12174, 40448, 9673, 14851, 2407, 7578, 9673, 16373, 1211, 30767, 995, 2407, 10632, 3714, 16373, 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I", "probability": 0.95751953125}, {"start": 3710.71, "end": 3710.95, "word": " حوالين", "probability": 0.978271484375}, {"start": 3710.95, "end": 3711.03, "word": " ال", "probability": 0.76171875}, {"start": 3711.03, "end": 3711.17, "word": " C", "probability": 0.97119140625}, {"start": 3711.17, "end": 3711.35, "word": " في", "probability": 0.97119140625}, {"start": 3711.35, "end": 3711.57, "word": " Alpha", "probability": 0.97119140625}, {"start": 3711.57, "end": 3711.77, "word": " بدي", "probability": 0.471221923828125}, {"start": 3711.77, "end": 3712.05, "word": " أستخدم", "probability": 0.76361083984375}, {"start": 3712.05, "end": 3712.21, "word": " ال", "probability": 0.95068359375}, {"start": 3712.21, "end": 3712.47, "word": " parallel", "probability": 0.84814453125}, {"start": 3712.47, "end": 3712.87, "word": " axis", "probability": 0.91552734375}, {"start": 3712.87, "end": 3713.25, "word": " theorem", "probability": 0.8642578125}], "temperature": 1.0}, {"id": 126, "seek": 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{"start": 3938.5, "end": 3938.76, "word": " اتنين", "probability": 0.95556640625}, {"start": 3938.76, "end": 3939.24, "word": " قدم", "probability": 0.993408203125}, {"start": 3939.24, "end": 3939.8, "word": " و", "probability": 0.716796875}, {"start": 3939.8, "end": 3940.12, "word": " الزواهر", "probability": 0.65986328125}, {"start": 3940.12, "end": 3940.28, "word": " دي", "probability": 0.501220703125}, {"start": 3940.28, "end": 3940.68, "word": " ستين", "probability": 0.91259765625}, {"start": 3940.68, "end": 3941.48, "word": " معروفة", "probability": 0.95703125}, {"start": 3941.48, "end": 3942.2, "word": " معناته", "probability": 0.4867350260416667}, {"start": 3942.2, "end": 3942.88, "word": " بستخدم", "probability": 0.80291748046875}, {"start": 3942.88, "end": 3943.14, "word": " ال", "probability": 0.869140625}, {"start": 3943.14, "end": 3943.5, "word": " cosine", "probability": 0.60595703125}, {"start": 3943.5, "end": 3943.92, "word": " law", "probability": 0.56591796875}, {"start": 3943.92, "end": 3944.46, "word": " عشان", "probability": 0.94970703125}, {"start": 3944.46, "end": 3944.96, "word": " احسب", "probability": 0.9064127604166666}, {"start": 3944.96, "end": 3945.36, "word": " ال", "probability": 0.9462890625}, {"start": 3945.36, "end": 3945.94, "word": " C", "probability": 0.724609375}, {"start": 3945.94, "end": 3946.58, "word": " G", "probability": 0.89208984375}], "temperature": 1.0}, {"id": 134, "seek": 397624, "start": 3948.02, "end": 3976.24, "text": "اللي هو use الـ cosine له اللي هو CG تربية هاد أضلها حيث هو AG تربية زائد AC تربية ناقص اتنين في AG", "tokens": [6027, 20292, 31439, 764, 2423, 39184, 23565, 46740, 13672, 1829, 31439, 38007, 6055, 25513, 10632, 8032, 18513, 5551, 11242, 1211, 11296, 11331, 1829, 12984, 31439, 28406, 6055, 25513, 10632, 30767, 16373, 3215, 8157, 6055, 25513, 10632, 8717, 995, 4587, 9381, 1975, 2655, 1863, 9957, 8978, 28406], "avg_logprob": -0.3006981459069759, "compression_ratio": 1.347457627118644, "no_speech_prob": 0.0, "words": [{"start": 3948.02, "end": 3948.3, "word": "اللي", "probability": 0.5965576171875}, {"start": 3948.3, "end": 3948.84, "word": " هو", "probability": 0.96435546875}, {"start": 3948.84, "end": 3949.6, "word": " use", "probability": 0.505859375}, {"start": 3949.6, "end": 3949.8, "word": " الـ", "probability": 0.3765869140625}, {"start": 3949.8, "end": 3950.18, "word": " cosine", "probability": 0.603515625}, {"start": 3950.18, "end": 3950.54, "word": " له", "probability": 0.277099609375}, {"start": 3950.54, "end": 3950.68, "word": " اللي", "probability": 0.6798095703125}, {"start": 3950.68, "end": 3950.82, "word": " هو", "probability": 0.982421875}, {"start": 3950.82, "end": 3951.38, "word": " CG", "probability": 0.86083984375}, {"start": 3951.38, "end": 3953.48, "word": " تربية", "probability": 0.8118489583333334}, {"start": 3953.48, "end": 3955.08, "word": " هاد", "probability": 0.4285888671875}, {"start": 3955.08, "end": 3955.76, "word": " أضلها", 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400187, "start": 3978.35, "end": 4001.87, "text": "في AC كوساين الزاوية بينهم اللي هي ستين درجة معناته CG حسبناها عوض عن AG عوض عن AG وعن AC", "tokens": [41185, 8157, 9122, 41779, 995, 9957, 6024, 110, 995, 2407, 10632, 49374, 16095, 13672, 1829, 39896, 8608, 2655, 9957, 11778, 47341, 3660, 20449, 8315, 47395, 38007, 11331, 35457, 8315, 11296, 6225, 2407, 11242, 18871, 28406, 6225, 2407, 11242, 18871, 28406, 4032, 3615, 1863, 8157], "avg_logprob": -0.3027777804268731, "compression_ratio": 1.4326923076923077, "no_speech_prob": 0.0, "words": [{"start": 3978.35, "end": 3978.67, "word": "في", "probability": 0.382568359375}, {"start": 3978.67, "end": 3979.27, "word": " AC", "probability": 0.70068359375}, {"start": 3979.27, "end": 3981.23, "word": " كوساين", "probability": 0.5087890625}, {"start": 3981.23, "end": 3981.81, "word": " الزاوية", "probability": 0.88115234375}, {"start": 3981.81, "end": 3982.19, "word": " بينهم", "probability": 0.955078125}, {"start": 3982.19, "end": 3982.33, 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N B بتعملش moment الواحد اللي بيعمل moment اللي هي W في عكس عقار بالساعة W في اتنين cosine التلاتين درجة بتساوي I C", "tokens": [50, 40879, 399, 295, 1623, 490, 383, 4724, 1829, 3794, 14407, 286, 8978, 383, 286, 383, 8978, 20588, 8717, 47283, 3215, 10874, 3224, 3660, 25124, 2304, 6027, 11331, 4117, 1829, 8315, 426, 316, 39894, 25957, 1211, 8592, 1623, 4032, 426, 363, 39894, 25957, 1211, 8592, 1623, 2423, 14407, 24401, 13672, 1829, 4724, 1829, 25957, 1211, 1623, 13672, 1829, 39896, 343, 8978, 6225, 4117, 3794, 6225, 4587, 9640, 20666, 3794, 995, 27884, 343, 8978, 1975, 2655, 1863, 9957, 23565, 16712, 1211, 9307, 9957, 11778, 47341, 3660, 39894, 3794, 995, 45865, 286, 383], "avg_logprob": -0.2982336963000505, "compression_ratio": 1.5678391959798994, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 4173.26, "end": 4173.88, "word": "Summation", "probability": 0.6329752604166666}, {"start": 4173.88, "end": 4174.02, "word": " of", "probability": 0.92578125}, {"start": 4174.02, 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{"start": 4692.49, "end": 4693.37, "word": " الخمسة", "probability": 0.9344482421875}, {"start": 4693.37, "end": 4693.43, "word": " و", "probability": 0.3818359375}, {"start": 4693.43, "end": 4693.91, "word": " أربعين", "probability": 0.9178466796875}, {"start": 4693.91, "end": 4697.71, "word": " بتساوي", "probability": 0.955322265625}, {"start": 4697.71, "end": 4699.43, "word": " باتجاه", "probability": 0.85150146484375}, {"start": 4699.43, "end": 4699.55, "word": " ال", "probability": 0.97314453125}, {"start": 4699.55, "end": 4699.67, "word": " X", "probability": 0.98681640625}, {"start": 4699.67, "end": 4699.91, "word": " هكون", "probability": 0.862548828125}, {"start": 4699.91, "end": 4700.11, "word": " عندي", "probability": 0.862548828125}, {"start": 4700.11, "end": 4700.39, "word": " A", "probability": 0.7490234375}, {"start": 4700.39, "end": 4700.77, "word": " A", "probability": 0.95703125}, {"start": 4700.77, "end": 4703.37, "word": " زائد", "probability": 0.776611328125}, {"start": 4703.37, "end": 4704.75, "word": " minus", "probability": 0.884765625}], "temperature": 1.0}, {"id": 159, "seek": 472357, "start": 4708.85, "end": 4723.57, "text": "اللي هي M W على G في X اللي هي بقرة عن AA-2αSin 30 درجة هاي معادلة 2", "tokens": [6027, 20292, 39896, 376, 343, 15844, 460, 8978, 1783, 13672, 1829, 39896, 4724, 4587, 25720, 18871, 30680, 12, 17, 1529, 50, 259, 2217, 11778, 47341, 3660, 8032, 47302, 20449, 18513, 37977, 568], "avg_logprob": -0.546875, "compression_ratio": 1.1290322580645162, "no_speech_prob": 0.0, "words": [{"start": 4708.85, "end": 4709.33, "word": "اللي", "probability": 0.72509765625}, {"start": 4709.33, "end": 4709.57, "word": " هي", "probability": 0.5517578125}, {"start": 4709.57, "end": 4709.77, "word": " M", "probability": 0.1746826171875}, {"start": 4709.77, "end": 4710.29, "word": " W", "probability": 0.5029296875}, {"start": 4710.29, "end": 4710.53, "word": " على", "probability": 0.5146484375}, {"start": 4710.53, "end": 4710.89, "word": " G", "probability": 0.92333984375}, {"start": 4710.89, "end": 4712.13, "word": " في", "probability": 0.6845703125}, {"start": 4712.13, "end": 4712.41, "word": " X", "probability": 0.830078125}, {"start": 4712.41, "end": 4712.57, "word": " اللي", "probability": 0.754638671875}, {"start": 4712.57, "end": 4712.69, "word": " هي", "probability": 0.93798828125}, {"start": 4712.69, "end": 4712.97, "word": " بقرة", "probability": 0.4043782552083333}, {"start": 4712.97, "end": 4713.19, "word": " عن", "probability": 0.4365234375}, {"start": 4713.19, "end": 4713.71, "word": " AA", "probability": 0.499755859375}, {"start": 4713.71, "end": 4718.11, "word": "-2αSin", "probability": 0.5072265625}, {"start": 4718.11, "end": 4719.95, "word": " 30", "probability": 0.46826171875}, {"start": 4719.95, "end": 4720.63, "word": " درجة", "probability": 0.92822265625}, {"start": 4720.63, "end": 4720.89, "word": " هاي", "probability": 0.463958740234375}, {"start": 4720.89, "end": 4721.51, "word": " معادلة", "probability": 0.9501953125}, {"start": 4721.51, "end": 4723.57, "word": " 2", "probability": 0.3857421875}], "temperature": 1.0}, {"id": 160, "seek": 476326, "start": 4733.72, "end": 4763.26, "text": "و هعمل كمان معادلة summation لل forces باتجاه ال Y بالساوية M A Y هكون عندي اللي هو N A زاد N B Sin 45 minus W بالساوية", "tokens": [2407, 8032, 25957, 1211, 9122, 2304, 7649, 20449, 18513, 37977, 28811, 24976, 5874, 4724, 9307, 7435, 40294, 2423, 398, 20666, 3794, 995, 2407, 10632, 376, 316, 398, 8032, 30544, 43242, 1829, 13672, 1829, 31439, 426, 316, 30767, 18513, 426, 363, 11187, 6905, 3175, 343, 20666, 3794, 995, 2407, 10632], "avg_logprob": -0.28890626192092894, "compression_ratio": 1.2464788732394365, "no_speech_prob": 0.0, "words": [{"start": 4733.72, "end": 4733.88, "word": "و", "probability": 0.6123046875}, {"start": 4733.88, "end": 4734.14, "word": " هعمل", "probability": 0.91064453125}, {"start": 4734.14, "end": 4734.38, "word": " كمان", "probability": 0.8972981770833334}, {"start": 4734.38, "end": 4734.76, "word": " معادلة", "probability": 0.9420572916666666}, {"start": 4734.76, "end": 4735.34, "word": " summation", "probability": 0.269775390625}, {"start": 4735.34, "end": 4736.46, "word": " لل", "probability": 0.51171875}, {"start": 4736.46, "end": 4737.0, "word": " forces", "probability": 0.90625}, {"start": 4737.0, "end": 4737.7, "word": " باتجاه", "probability": 0.86602783203125}, {"start": 4737.7, "end": 4737.88, "word": " ال", "probability": 0.953125}, {"start": 4737.88, "end": 4738.16, "word": " Y", "probability": 0.5302734375}, {"start": 4738.16, "end": 4739.36, "word": " بالساوية", "probability": 0.684521484375}, {"start": 4739.36, "end": 4739.7, "word": " M", "probability": 0.468505859375}, {"start": 4739.7, "end": 4740.14, "word": " A", "probability": 0.383056640625}, {"start": 4740.14, "end": 4740.62, "word": " Y", "probability": 0.9736328125}, {"start": 4740.62, "end": 4746.0, "word": " هكون", "probability": 0.8525390625}, {"start": 4746.0, "end": 4746.38, "word": " عندي", "probability": 0.56103515625}, {"start": 4746.38, "end": 4746.48, "word": " اللي", "probability": 0.905029296875}, {"start": 4746.48, "end": 4746.76, "word": " هو", "probability": 0.98876953125}, {"start": 4746.76, "end": 4747.14, "word": " N", "probability": 0.65966796875}, {"start": 4747.14, "end": 4747.72, "word": " A", "probability": 0.94873046875}, {"start": 4747.72, "end": 4751.3, "word": " زاد", "probability": 0.719970703125}, {"start": 4751.3, "end": 4751.7, "word": " N", "probability": 0.9658203125}, {"start": 4751.7, "end": 4752.26, "word": " B", "probability": 0.73095703125}, {"start": 4752.26, "end": 4754.72, "word": " Sin", "probability": 0.300537109375}, {"start": 4754.72, "end": 4755.54, "word": " 45", "probability": 0.75634765625}, {"start": 4755.54, "end": 4759.26, "word": " minus", "probability": 0.379150390625}, {"start": 4759.26, "end": 4760.54, "word": " W", "probability": 0.91796875}, {"start": 4760.54, "end": 4763.26, "word": " بالساوية", "probability": 0.97841796875}], "temperature": 1.0}, {"id": 161, "seek": 477382, "start": 4764.3, "end": 4773.82, "text": "و على جيه في minus اتنين الف cosine تلاتين درجة", "tokens": [2407, 15844, 10874, 1829, 3224, 8978, 3175, 1975, 2655, 1863, 9957, 27188, 23565, 6055, 1211, 9307, 9957, 11778, 47341, 3660], "avg_logprob": -0.3206845124562581, "compression_ratio": 1.0, "no_speech_prob": 0.0, "words": [{"start": 4764.3, "end": 4764.82, "word": "و", "probability": 0.24462890625}, {"start": 4764.82, "end": 4765.2, "word": " على", "probability": 0.53564453125}, {"start": 4765.2, "end": 4765.96, "word": " جيه", "probability": 0.6285807291666666}, {"start": 4765.96, "end": 4767.82, "word": " في", "probability": 0.86328125}, {"start": 4767.82, "end": 4768.28, "word": " minus", "probability": 0.2042236328125}, {"start": 4768.28, "end": 4768.76, "word": " اتنين", "probability": 0.9322509765625}, {"start": 4768.76, "end": 4769.2, "word": " الف", "probability": 0.6064453125}, {"start": 4769.2, "end": 4770.94, "word": " cosine", "probability": 0.43896484375}, {"start": 4770.94, "end": 4773.36, "word": " تلاتين", "probability": 0.9266357421875}, {"start": 4773.36, "end": 4773.82, "word": " درجة", "probability": 0.978515625}], "temperature": 1.0}, {"id": 162, "seek": 482046, "start": 4791.2, "end": 4820.46, "text": "طيب بتكملوا الحل اعملوا ..كملوا الحل لحالكوا انا اعطيتكوا الاشي الأساسي بدون أرقام بتكملوها و بتحسبوا ال accelerator بتحسبوا ال N A و ال N B المحاضرة الجاية بندرس ال non centroidial rotation و rolling motion", "tokens": [9566, 1829, 3555, 39894, 24793, 1211, 14407, 21542, 1211, 1975, 25957, 1211, 14407, 4386, 24793, 1211, 14407, 21542, 1211, 5296, 5016, 6027, 4117, 14407, 1975, 8315, 1975, 3615, 9566, 36081, 4117, 14407, 2423, 33599, 1829, 16247, 3794, 32277, 1829, 47525, 11536, 5551, 2288, 4587, 10943, 39894, 24793, 1211, 2407, 11296, 4032, 39894, 5016, 35457, 14407, 2423, 39889, 39894, 5016, 35457, 14407, 2423, 426, 316, 4032, 2423, 426, 363, 9673, 5016, 46958, 25720, 25724, 995, 10632, 44945, 3215, 2288, 3794, 2423, 2107, 1489, 6490, 831, 12447, 4032, 9439, 5394], "avg_logprob": -0.1705582905351446, "compression_ratio": 1.7210526315789474, "no_speech_prob": 0.0, "words": [{"start": 4791.2, "end": 4791.72, "word": "طيب", "probability": 0.9117838541666666}, {"start": 4791.72, "end": 4792.56, "word": " بتكملوا", "probability": 0.811279296875}, {"start": 4792.56, "end": 4793.28, "word": " الحل", "probability": 0.968994140625}, {"start": 4793.28, "end": 4793.76, "word": " اعملوا", "probability": 0.9141845703125}, {"start": 4793.76, "end": 4794.18, "word": " ..كملوا", "probability": 0.7435302734375}, {"start": 4794.18, "end": 4794.54, "word": " الحل", "probability": 0.993408203125}, {"start": 4794.54, "end": 4795.22, "word": " لحالكوا", "probability": 0.9509765625}, {"start": 4795.22, "end": 4795.48, "word": " انا", "probability": 0.750244140625}, {"start": 4795.48, "end": 4795.92, "word": " اعطيتكوا", "probability": 0.8700358072916666}, {"start": 4795.92, "end": 4796.34, "word": " الاشي", "probability": 0.8932291666666666}, {"start": 4796.34, "end": 4797.14, "word": " الأساسي", "probability": 0.9278564453125}, {"start": 4797.14, "end": 4797.6, "word": " بدون", "probability": 0.992919921875}, {"start": 4797.6, "end": 4798.18, "word": " أرقام", "probability": 0.98291015625}, {"start": 4798.18, "end": 4799.72, "word": " بتكملوها", "probability": 0.9462890625}, {"start": 4799.72, "end": 4800.82, "word": " و", "probability": 0.693359375}, {"start": 4800.82, "end": 4801.62, "word": " بتحسبوا", "probability": 0.9422607421875}, {"start": 4801.62, "end": 4801.72, "word": " ال", "probability": 0.91650390625}, {"start": 4801.72, "end": 4802.12, "word": " accelerator", "probability": 0.256591796875}, {"start": 4802.12, "end": 4802.64, "word": " بتحسبوا", "probability": 0.8353271484375}, {"start": 4802.64, "end": 4802.76, "word": " ال", "probability": 0.75244140625}, {"start": 4802.76, "end": 4802.92, "word": " N", "probability": 0.38037109375}, {"start": 4802.92, "end": 4803.28, "word": " A", "probability": 0.59765625}, {"start": 4803.28, "end": 4803.52, "word": " و", "probability": 0.93798828125}, {"start": 4803.52, "end": 4804.06, "word": " ال", "probability": 0.556640625}, {"start": 4804.06, "end": 4804.46, "word": " N", "probability": 0.96826171875}, {"start": 4804.46, "end": 4806.04, "word": " B", "probability": 0.90771484375}, {"start": 4806.04, "end": 4812.2, "word": " المحاضرة", "probability": 0.981689453125}, {"start": 4812.2, "end": 4812.78, "word": " الجاية", "probability": 0.9225260416666666}, {"start": 4812.78, "end": 4816.04, "word": " بندرس", "probability": 0.916259765625}, {"start": 4816.04, "end": 4816.2, "word": " ال", "probability": 0.953125}, {"start": 4816.2, "end": 4816.42, "word": " non", "probability": 0.90380859375}, {"start": 4816.42, "end": 4816.98, "word": " centroidial", "probability": 0.5110677083333334}, {"start": 4816.98, "end": 4817.7, "word": " rotation", "probability": 0.9755859375}, {"start": 4817.7, "end": 4818.76, "word": " و", "probability": 0.80712890625}, {"start": 4818.76, "end": 4819.04, "word": " rolling", "probability": 0.64404296875}, {"start": 4819.04, "end": 4820.46, "word": " motion", "probability": 0.9814453125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 4820.8805625, "duration_after_vad": 3981.1537499999986}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/V5toCkTdsLw_postprocess.srt b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/V5toCkTdsLw_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4a03d2a34800793117ed99f507f1152a76cf2ab0
--- /dev/null
+++ b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/V5toCkTdsLw_postprocess.srt
@@ -0,0 +1,1784 @@
+1
+00:00:04,910 --> 00:00:07,950
+أعوذ بالله السميع العلي من الشيطان الرجيم بسم الله
+
+2
+00:00:07,950 --> 00:00:11,050
+الرحمن الرحيم الحمد لله رب العالمين والصلاة
+
+3
+00:00:11,050 --> 00:00:14,710
+والسلام على أشرف الأنبياء والمرسلين سيدنا محمد بن
+
+4
+00:00:14,710 --> 00:00:18,130
+عبد الله الصادق الأمن ثم أما بعد أحييكم جميعا
+
+5
+00:00:18,130 --> 00:00:21,290
+بتحية الإسلام فالسلام عليكم ورحمة الله تعالى
+
+6
+00:00:21,290 --> 00:00:26,200
+وبركاته كيف حالكوا ناطيبات ان شاء اللهتحذيرنا جيد
+
+7
+00:00:26,200 --> 00:00:31,180
+إن شاء الله؟ عظيم إذا المحاضرة السابقة كنا قد
+
+8
+00:00:31,180 --> 00:00:36,060
+تحدثنا عن موضوع الحجب وعرفنا أن الحجب حجب حرمان
+
+9
+00:00:36,060 --> 00:00:42,700
+وحجب نقصا وهناك من قسمه إلى حجب بالوصف وحجب بالشخص
+
+10
+00:00:42,700 --> 00:00:48,420
+قلنا إن هذا التقسيم ليس دقيقا وليس صائبا وقد جانب
+
+11
+00:00:48,420 --> 00:00:52,560
+الصواب لسبب بسيط وهو أن هناك فرق بين الممنوع
+
+12
+00:00:52,560 --> 00:00:58,020
+والمحجوبذلك أنه وإن كان كل منهما لا يريث إلا أن
+
+13
+00:00:58,020 --> 00:01:03,320
+الممنوع يفقد أهلية الميراث بينما المحجوب لا يمكن
+
+14
+00:01:03,320 --> 00:01:07,960
+أن يفقد أهلية الميراث لذا اقتضى الأمر أن نجعل
+
+15
+00:01:07,960 --> 00:01:13,840
+أقسام الحجب حجب حرمان وحجب نقصان طبعا وهناك من
+
+16
+00:01:13,840 --> 00:01:18,900
+ألحق بهم قسما ثالثا هو الحجب بالاستغراق وهو ما
+
+17
+00:01:18,900 --> 00:01:24,450
+سنتحدث عنه في محاضرتنا هذهقلنا إن الميراث بأصله قد
+
+18
+00:01:24,450 --> 00:01:29,210
+يكون بالفرد وقد يكون بالتعصيب الميراث بالفرد تقدير
+
+19
+00:01:29,210 --> 00:01:34,210
+أما بالتعصيب بغير تقديران بمعنى أن العاصب قد يحوز
+
+20
+00:01:34,210 --> 00:01:39,270
+جميع التركة أو ما تبقى بعد أصحاب الفرودوهذا مما لا
+
+21
+00:01:39,270 --> 00:01:44,810
+خلافة فيه بين الفقهاء طب ماذا لو أنه لم يتبقى أو
+
+22
+00:01:44,810 --> 00:01:49,550
+أنه لم يتبقى شيء بعد أصحاب الفروض لهذا العاصب؟ ما
+
+23
+00:01:49,550 --> 00:01:56,350
+الحال؟ العلماء اتفقوا على أن العاصب يسقط العصبات
+
+24
+00:01:56,350 --> 00:02:02,350
+تسقط إلا في المسألة المشتركة لذلك دعونا نعرف الحجب
+
+25
+00:02:02,350 --> 00:02:06,150
+بالاستغراق قلنا هو استيعاب
+
+26
+00:02:09,040 --> 00:02:14,560
+أصحاب الفروض لجميع
+
+27
+00:02:14,560 --> 00:02:19,900
+التاركة طبعا
+
+28
+00:02:19,900 --> 00:02:23,820
+إذا استوعبوا جميع التاركة شو معناته؟ فتسقط
+
+29
+00:02:23,820 --> 00:02:29,340
+العصابات
+
+30
+00:02:29,340 --> 00:02:35,360
+الا استثناء واحد فقط في المسألة المشتركة
+
+31
+00:02:40,400 --> 00:02:47,500
+وبناء على ذلك نقول لو أن شخص مات و ترك مثلا أم وأخ
+
+32
+00:02:47,500 --> 00:02:47,940
+لأم
+
+33
+00:02:53,410 --> 00:02:59,710
+وكمان نقول مثلا اتنين أخت شقيقة فاللحظة معايا الأم
+
+34
+00:02:59,710 --> 00:03:06,170
+سدس وهنا سدس وهنا جداش طولتين فلو بدنا نحسب
+
+35
+00:03:06,170 --> 00:03:12,190
+المسألة هنلاقي ايش و هن مثلا في أخ لأب عفوا أخ لأب
+
+36
+00:03:12,190 --> 00:03:16,890
+اللي هو العصبة فلو بدى أحسب الأسهم هنا أجد أنهم
+
+37
+00:03:16,890 --> 00:03:21,590
+ستة و المسألة من ستة إذا الفروج استوعبات جميع
+
+38
+00:03:21,590 --> 00:03:25,910
+التاريخةالفروض استوعبت جميع التركة فلم يتبقى شيء
+
+39
+00:03:25,910 --> 00:03:30,390
+للعصابات فتسقط هذا هو الحاجب بالاستغراء مثال أبسط
+
+40
+00:03:30,390 --> 00:03:40,600
+من كده، نقول ماتت وتركت زوج وأخت شقيقة وعم لأبنفس
+
+41
+00:03:40,600 --> 00:03:45,420
+الفكرة الزوج نصف والشقيقة أيضا نصف وهذا هو العصبة
+
+42
+00:03:45,420 --> 00:03:50,300
+فالمسألة من اتنين واحد واحد لم يتبقى شيء للعصبات
+
+43
+00:03:50,300 --> 00:03:54,800
+فتسقط إلا في المسألة المشتركة المسألة المشتركة يا
+
+44
+00:03:54,800 --> 00:03:58,020
+جماعة إلها شروط راح نتحدث عنها لكن بدنا نحكي
+
+45
+00:03:58,020 --> 00:04:04,140
+إبتداء ظهرت إشكاليتها وين؟ في عهدي عمر بن الخطاب
+
+46
+00:04:04,140 --> 00:04:06,140
+رضي الله عنه سماح بدك تسألي؟
+
+47
+00:04:08,940 --> 00:04:15,040
+سلامتك إذا في عهد عمر رضي الله عنه جاء أخوى أشقاء
+
+48
+00:04:15,040 --> 00:04:22,100
+يستفتونه حول مسألة أفرادها زوج و أم و أخوى لأم و
+
+49
+00:04:22,100 --> 00:04:27,320
+هم أي الأشقاءفعوما رضي الله عنه اجتهد في هذه
+
+50
+00:04:27,320 --> 00:04:30,700
+المسألة قال هم مالكمش ولا حاجة الله يسحل عليكم لأن
+
+51
+00:04:30,700 --> 00:04:34,740
+الأولوي لمين؟ لأصحاب الفروض ونبينا صلى الله عليه
+
+52
+00:04:34,740 --> 00:04:39,800
+وسلم يتحدث كلما واضحا ألحقوا الفرائض بأهلها فما
+
+53
+00:04:39,800 --> 00:04:45,300
+باقيا فلأولى رجل ذكى فبالتالي لازم نعطي الزوج و
+
+54
+00:04:45,300 --> 00:04:49,350
+الأم والاخوة لأمه انتوا الله يسحل عليكمهدول الإخوة
+
+55
+00:04:49,350 --> 00:04:52,610
+اللي إجوا يستفتوا عمر رضي الله عنهم مؤدبين خلاص
+
+56
+00:04:52,610 --> 00:04:57,210
+سمعوا كلام أمير المؤمنين و أخدوا حالهم روحهم حلو
+
+57
+00:04:57,210 --> 00:05:01,390
+طبعا هذا الرأي الذي ذهب إليه عمر في بداية الأمر
+
+58
+00:05:01,390 --> 00:05:05,550
+وفقه عليه أبو بكر و ابن عباس و ابن مسعود و من
+
+59
+00:05:05,550 --> 00:05:09,830
+الأئمة الحنفية و الحنابلة لازالوا يأخذون بهذا
+
+60
+00:05:09,830 --> 00:05:13,830
+الرأيالى الآن مذهب الحنافية والحنابلة بإن الأشقاء
+
+61
+00:05:13,830 --> 00:05:19,750
+لا يرثوا بيسقطوا تمام؟ مرتان عرضت المسألة على عمر
+
+62
+00:05:19,750 --> 00:05:24,270
+أيضا رضي الله عنهم في ولايته أيضا اجوا أخوة أشقاء
+
+63
+00:05:24,270 --> 00:05:30,150
+برضه يسألوا ويستفتوا عن هذه المسألة أفلانة ماتت
+
+64
+00:05:30,150 --> 00:05:37,060
+أختنا ماتت وتركت زوج و أم و أخوة لأمه احنافراح عمر
+
+65
+00:05:37,060 --> 00:05:41,600
+رضي الله عنه بدي يفتيهم مثل ما قفته اللي جابلهم
+
+66
+00:05:41,600 --> 00:05:46,920
+قالهم ليس لكم شاق فهدول طلعوا بديش أقول مش مقدمين
+
+67
+00:05:46,920 --> 00:05:51,640
+شوية يعني بس أصحاب حاجة بجاتله يعني بدهم حاجهم نعم
+
+68
+00:05:51,640 --> 00:05:58,360
+كيف؟ كيف احنا نسقط وملناش ولا شاق واخوتنا من أمنا
+
+69
+00:05:58,360 --> 00:06:03,760
+يارسوه؟يا سيدي بيحكوا لا عمر يا سيدي هبقى أنا لا
+
+70
+00:06:03,760 --> 00:06:07,640
+أبا لنا إذا أبونا بيتسبب في إنه إحنا لا ناراس
+
+71
+00:06:07,640 --> 00:06:14,300
+فاعتبر إنه أبونا ميت ألسنا شركاء في الأم مش إحنا و
+
+72
+00:06:14,300 --> 00:06:18,680
+اللي ماتت و هدول إمنا واحدة فاعتبر أب مالناش أب و
+
+73
+00:06:18,680 --> 00:06:23,440
+خلاص و عملنا على هذا الأساس هبقى أنا أبانا حجرا
+
+74
+00:06:24,460 --> 00:06:30,060
+هبقلنا أبانا حمارا، هبقلنا لا أبا لنا فقعدوا يحكوا
+
+75
+00:06:30,060 --> 00:06:35,760
+كذا احتمال وحقيقة كلامهم أقنع سيدنا عمرو إنه فعلا
+
+76
+00:06:35,760 --> 00:06:41,420
+في النهاية إحنا كأشقاء و الإخوة لأمه و الميتة كنا
+
+77
+00:06:41,420 --> 00:06:45,220
+إمنا واحدة فكيف هؤلاء يارثون و نحن لا نارث؟ كيف
+
+78
+00:06:45,220 --> 00:06:50,660
+هذا؟ حينها قال عمرو رضي الله عنه باشتراك جميع
+
+79
+00:06:50,660 --> 00:06:56,980
+الإخوةفي الثلث أشقاء لأم للذكري أو الذكر كالأنثى
+
+80
+00:06:56,980 --> 00:07:01,200
+تماما يعني مافي فارق ل .. لأحدهم على الآخر أو
+
+81
+00:07:01,200 --> 00:07:05,650
+للجنسينباعتبار أنه في الأخوة الأشقاء لذكر يمثله حظ
+
+82
+00:07:05,650 --> 00:07:09,670
+الأنسة يعني و الأخوة لأم اتذكر كالأنسة فهنا أم رضي
+
+83
+00:07:09,670 --> 00:07:15,810
+الله عنه حكم باستوائهم في الثلث باعتبار شو رجح
+
+84
+00:07:15,810 --> 00:07:19,330
+جانب الأم أن أمهم واحدة فخلاص انتوا باعتباركوا
+
+85
+00:07:19,330 --> 00:07:23,230
+أولاد أم إذا الثلث بينكم شو ما كان عددكم و اتذكر
+
+86
+00:07:23,230 --> 00:07:27,590
+كالأنسة تماما فرض يروحوا ماعملوش مشاكل دلهم مؤدبين
+
+87
+00:07:27,590 --> 00:07:33,210
+بعد كده تمام فلحظي معايا هنا إذاالمسألة المشتركة
+
+88
+00:07:33,210 --> 00:07:40,230
+كما قلنا أن أصحاب الفرد استوعبت كل التريكةفلم يبقى
+
+89
+00:07:40,230 --> 00:07:44,430
+شيء للعصابات في الأصل أن تسقط لكن كون هذول أو
+
+90
+00:07:44,430 --> 00:07:51,050
+هؤلاء العصابات هم أخوة أشقاء فلا يسقطون بل يشاركون
+
+91
+00:07:51,050 --> 00:07:57,070
+الإخوة لأم في الثلث لكن في شروط مش دائما مش دائما
+
+92
+00:07:57,070 --> 00:08:01,490
+الأشقاء بدهم يشاركوا الإخوة لأم ففي أربع شروط حتى
+
+93
+00:08:01,490 --> 00:08:06,630
+نقول أن المسألة مشتركةحتى نقول إن المسألة مشتركة
+
+94
+00:08:06,630 --> 00:08:14,590
+لابد من توفر أربعة شروط أول شيء لابد أن يوجد زوج و
+
+95
+00:08:14,590 --> 00:08:19,710
+لما بقول زوج يعني مش زوجة زوج أول شرط أن يكون فيه
+
+96
+00:08:19,710 --> 00:08:24,390
+زوج يارث النصف طبيعي لما بنقول يارث النصف يعني
+
+97
+00:08:24,390 --> 00:08:31,350
+مافي فرع وارث حلو؟ اتنينأن تكون هناك أم أو جدة
+
+98
+00:08:31,350 --> 00:08:35,630
+تريث السدس ومنطقي أنها تاخد سدس لأن في إخوة صح ولا
+
+99
+00:08:35,630 --> 00:08:39,230
+لأ؟ في عدد من الإخوة فالمنطق يقتضي أنها هتاخد
+
+100
+00:08:39,230 --> 00:08:43,550
+السدس فقلنا أم أو جدة لأن الجدة دائما سدس إذا مافي
+
+101
+00:08:43,550 --> 00:08:48,450
+أم والأم سدس إذا في عدد من الإخوة وهنا منطقيا أن
+
+102
+00:08:48,450 --> 00:08:53,230
+تكون الأم سدس باعتبار وجود الإخوة رقم تلاتة أن
+
+103
+00:08:53,230 --> 00:08:56,050
+يكون هناك عدد من الإخوة لأم
+
+104
+00:08:59,170 --> 00:09:07,210
+Half one اذا عدد من الإخوة لأم بمعنى اتنين بينفع
+
+105
+00:09:07,210 --> 00:09:11,570
+سواء اناث او ذكور او اناث ذكور اتنين فاكثر المهم
+
+106
+00:09:11,570 --> 00:09:15,510
+اكتر من واحد ليش؟ لأنه لو قلنا واحد معناته هياخد
+
+107
+00:09:15,510 --> 00:09:19,930
+الصدس هيبقى في باقي صح؟ وبالتالي الأشقاء هياخدوا
+
+108
+00:09:19,930 --> 00:09:24,860
+الباقي وخلصنافطبيعي إنه إذا أخ لأم واحد ماعددش
+
+109
+00:09:24,860 --> 00:09:29,020
+المسألة مشتركة عشان كده بنقول الأربع شروط سوا نرجع
+
+110
+00:09:29,020 --> 00:09:33,480
+نقيد مرة تانية زوج يستحق النصف أم أو جدة إلها
+
+111
+00:09:33,480 --> 00:09:37,820
+سُدُس عدد من الإخوة لأم ذكور أو إينات أو ذكور
+
+112
+00:09:37,820 --> 00:09:44,140
+وإينات اتنين في أكثر الفلوس طبعا والشرط الرابع أن
+
+113
+00:09:44,140 --> 00:09:49,580
+يكون الأشقاء ذكور سواء ركزوا هنا شوية سواء واحد
+
+114
+00:09:50,620 --> 00:09:56,360
+معاه إناس أو ماعوش ركزوا معايا الأشقاء لازم يكون
+
+115
+00:09:56,360 --> 00:10:01,920
+ضمن الأشقاء ذكر لازم يكون الحد الأدنى حتى تكون
+
+116
+00:10:01,920 --> 00:10:07,680
+المسألة مشتركة أن الأشقاء يكون أخ شقيق فأكثر إذا
+
+117
+00:10:07,680 --> 00:10:12,360
+سواء هذا الشقيق معه شقيقات أو ماعوش واحد أو أكتر
+
+118
+00:10:13,130 --> 00:10:16,610
+ولما بنقول لازم يكون على الأقل بناتهم ذكر معناته
+
+119
+00:10:16,610 --> 00:10:20,910
+لو مافيش ذكور وكانت أخد شقيقة مش هيكون فيه عصبات
+
+120
+00:10:20,910 --> 00:10:25,010
+فالشقيقة هتاخد نصف أصلا صح ولا لأ فلا تكون المسألة
+
+121
+00:10:25,010 --> 00:10:29,510
+مشتركة ونفس الأمر يقال فيما لو كانوا الشقيقات
+
+122
+00:10:29,510 --> 00:10:33,630
+تنتين أو أكتر هياخدوا طولتين وبالتالي مافيش عصبات
+
+123
+00:10:33,630 --> 00:10:39,210
+إذا مافي مسألة مشتركةونفس الأمر يقال لو كان في
+
+124
+00:10:39,210 --> 00:10:43,010
+عندي زوجة في المسألة، الزوجة هتاخد الربع وبالتالي
+
+125
+00:10:43,010 --> 00:10:47,010
+هيبقى شئ بعد الإخ والأم، صح ولا لأ؟ طيب الإخ والأم
+
+126
+00:10:47,010 --> 00:10:50,350
+كان واحد، هيبقى شئ بعدهم، إذا لن تسقط العصابات
+
+127
+00:10:51,020 --> 00:10:56,920
+وعليه بنأكد على أنه حتى نعد هذه المسألة مسألة
+
+128
+00:10:56,920 --> 00:11:01,520
+مشتركة لابد من توفر أربعة شروط ذكرناها عسريًا
+
+129
+00:11:01,520 --> 00:11:05,080
+بنتعدل إياهم لأنهم مهمين جدًا نعرفهم يا ميرنا
+
+130
+00:11:05,080 --> 00:11:08,880
+اتفضلي موجود زوج جالس في مصر، موجود ربع مجد ثالث،
+
+131
+00:11:08,880 --> 00:11:13,140
+السادس، موجود عدد من الإخوة اللي قوم يستحقون ثلث،
+
+132
+00:11:13,140 --> 00:11:18,680
+أربعة أن يكون الأشقار بكورة و يفي أن يكونوا شقيًا
+
+133
+00:11:18,680 --> 00:11:31,020
+واحدًا شقيًا؟شقيقا تمام .. تمام مش مشكلة .. تمام
+
+134
+00:11:31,020 --> 00:11:35,160
+أنا كنت مبسوطة ع ميرنا بفكرها بتحكي منها كنت كتير
+
+135
+00:11:35,160 --> 00:11:39,120
+مبسوطة لكن برضه مبسوطة مش مشكلة ميرنا إذا بنقول
+
+136
+00:11:39,120 --> 00:11:47,850
+أول شئ وجود زوج يرفدالنصف مقناته لو زوجة ماعددتش
+
+137
+00:11:47,850 --> 00:11:55,510
+مشتركة طيب اتنين يكون في عندي أم أو جدة تارث السدس
+
+138
+00:11:55,510 --> 00:12:01,410
+ولحظي معايا سدس وهنا مابديش هقول لو كانت تلت لأنه
+
+139
+00:12:01,410 --> 00:12:05,250
+مش هتكون باعتبار في أخوة طبيعي مش هتكون صح ولا لا؟
+
+140
+00:12:05,250 --> 00:12:14,840
+رقم تلاتة ان يكون الإخوة لأم عدد عددوبالتالي لو
+
+141
+00:12:14,840 --> 00:12:20,780
+واحد ماعدتش المسألة مشتركة لأنه لو أخ واحد هياخد
+
+142
+00:12:20,780 --> 00:12:25,180
+السدس وبالتالي هيظل اندباجي بمعنى أن أصحاب الفروض
+
+143
+00:12:25,180 --> 00:12:30,000
+لن يستوفوا جميع التريكة والأمر الرابع أن يكون
+
+144
+00:12:30,000 --> 00:12:39,200
+الأشقاء ذكور سواء واحد فأكثر .. واحد فأكثر معه
+
+145
+00:12:39,200 --> 00:12:40,040
+اناس
+
+146
+00:12:43,490 --> 00:12:50,830
+أو لا وهذا يعني لو كان الأشقاء إناس ماعدتش ..
+
+147
+00:12:50,830 --> 00:12:55,290
+بالظبط ماعدتش المسألة مشتركة لأن الإناس هيارسوا
+
+148
+00:12:55,290 --> 00:12:58,570
+بالفرض و المسألة هتقول موضوع العول هندرسه فيه
+
+149
+00:12:58,570 --> 00:13:03,750
+مابعد علم؟ وبناء على ذلك هناخد صورة المسألة
+
+150
+00:13:03,750 --> 00:13:09,150
+المشتركة و أمتى بتبطي المشتركة المسألة صارت واضحة
+
+151
+00:13:09,150 --> 00:13:18,430
+أظن يعنيالمسألة صورتها العامة زوج أم أو جدة يعني
+
+152
+00:13:18,430 --> 00:13:22,070
+سواء هادي أو هادي بدي أكتب أنا كل الصور المحتملة
+
+153
+00:13:22,070 --> 00:13:32,270
+هال gate وعندي أخوة لأم اتنين فأكثر و بدي أكتبها
+
+154
+00:13:32,270 --> 00:13:40,290
+سواء كلهم ذكور أو اناس أو ذكور واناس معا
+
+155
+00:13:42,890 --> 00:13:49,130
+و بعدين في عندي إيش؟ إخوة أو نقول أخ، شقيق طبعا
+
+156
+00:13:49,130 --> 00:13:54,510
+واحد فأكثر معه
+
+157
+00:13:54,510 --> 00:13:55,650
+شقيقات
+
+158
+00:13:59,380 --> 00:14:03,360
+أو لا تمام؟ شقيقات يعني شقيقة واحدة أو أكتر أو
+
+159
+00:14:03,360 --> 00:14:09,300
+ماعوش أصلا تمام؟ فلحظة لن تخرج المسألة عن صورة من
+
+160
+00:14:09,300 --> 00:14:14,300
+هذه الصورة يعني ممكن أجي أقولك زوج و أم أم أم أم
+
+161
+00:14:14,300 --> 00:14:21,060
+أم مثلا و تلاتة أخ لي أم و أخ شقيق مشتركة أو
+
+162
+00:14:21,060 --> 00:14:28,070
+مشتركة ممكن برضه أقولك زوج و أم أب أبو تلاتة أخت
+
+163
+00:14:28,070 --> 00:14:35,330
+شقيقة و اتنين أخ شقيق برضه مشتركة ممكن أقولك زوج
+
+164
+00:14:35,330 --> 00:14:42,510
+مثلا و أم أب و أقولك أخ لأمه و أخ لأب .. أخ لأم
+
+165
+00:14:42,510 --> 00:14:49,220
+عفوا و أخت لأممثلا أخ شقيق و أخت شقيق برضه مسألة
+
+166
+00:14:49,220 --> 00:14:54,280
+مشترك حلو فشوم كانت الصورة لكن ضمن الضابط اللي
+
+167
+00:14:54,280 --> 00:14:57,780
+وضعناه في المسألة المشتركة وبالتالي بدنا نحلها
+
+168
+00:14:57,780 --> 00:15:05,180
+كالتالي الزوج له النص والجد لها السدس وحتى لو كانت
+
+169
+00:15:05,180 --> 00:15:09,360
+الجد عدد يا جماعة حتى لو الجد كانت عدد نفس الفكرة
+
+170
+00:15:10,510 --> 00:15:16,690
+والاخوة هدول كل ياتهم شو ما كان عددهم كلهم سوى تلت
+
+171
+00:15:16,690 --> 00:15:22,630
+ولما بنقول كلهم سوى تلت الذكر كالأنسا حتى في موضوع
+
+172
+00:15:22,630 --> 00:15:27,110
+الأشقاء بروحش أقول أنه في الأخوة لأم زي بعض الذكر
+
+173
+00:15:27,110 --> 00:15:30,150
+و الإناس بينما في الأشقاء للذكر مثل حافظ الأنسيين
+
+174
+00:15:30,150 --> 00:15:34,630
+لأ هنا كوني دخلتهم كلهم شركة في السدوس عفوا في
+
+175
+00:15:34,630 --> 00:15:39,230
+التلت معناته أنا جعلتهم بيجربوا لبعض بإيش بالأم
+
+176
+00:15:40,410 --> 00:15:45,970
+فكأنهم كلياتهم إخوة لأم كأنه فاشتركوا وشاركوا
+
+177
+00:15:45,970 --> 00:15:50,390
+الإخوة لأم في الثروث و هذه المشاركة تقتضي التساوي
+
+178
+00:15:50,390 --> 00:15:55,730
+بين الذكري و الأنثى فالمسألة من ستة هن تلاتة هن
+
+179
+00:15:55,730 --> 00:16:00,050
+واحد و هن اتنين و الاتنين بدها تتجسم عليهم كلياتهم
+
+180
+00:16:00,050 --> 00:16:04,620
+شوم كان عددهم لو ميةطبعا مثال افتراضي، تمام؟ شو ما
+
+181
+00:16:04,620 --> 00:16:08,440
+كان عددهم التنين بدها تتجسم عليهم، حلو؟ و أنا لما
+
+182
+00:16:08,440 --> 00:16:12,940
+بتحدث عن اتنين ما بتحدث عن اتنين شكل، ربما بتحدث
+
+183
+00:16:12,940 --> 00:16:16,940
+عن ميت ألف دينار، حسب جداش، السهمين هدول إلهم قيمة
+
+184
+00:16:16,940 --> 00:16:23,840
+يعني، اتفضلي سؤالك، شوية سمح، اتفضليهناخد هذا
+
+185
+00:16:23,840 --> 00:16:29,220
+السؤال هناخده اه اه لسه لسه تجلجوش هنعرفه اللي هو
+
+186
+00:16:29,220 --> 00:16:32,600
+المحاضرة الجاية ان شاء الله المحاضرة الجاية بإذن
+
+187
+00:16:32,600 --> 00:16:37,260
+الله ايه سمحت فضل يعني لو كان اكتر من جد تاخد صدر
+
+188
+00:16:37,260 --> 00:16:42,900
+و لو كان مثلا أخوك اكتر منك و لا أه فتديهم طلاب؟
+
+189
+00:16:42,900 --> 00:16:48,020
+اه طبعا اه يعني و من جد تطلت على الصدر؟ كيف طلت
+
+190
+00:16:48,020 --> 00:16:53,400
+على الصدر مافهمتإيش سؤالكي سماح مرة تانية هلجيت لو
+
+191
+00:16:53,400 --> 00:16:58,660
+في عندي جدة خمس جدات بدي أفطر الجدلة فكلهم هياخدوا
+
+192
+00:16:58,660 --> 00:17:03,480
+السدس طب الإخوة لأم مع الأشقاء شو ما كان عددهم
+
+193
+00:17:03,480 --> 00:17:06,520
+كلهم هيشتركوا في التولت هذه هي المسألة المشتركة
+
+194
+00:17:06,520 --> 00:17:09,380
+تمام؟ اه يعني إذا ما .. إنت أخله على الشروط فلو
+
+195
+00:17:09,380 --> 00:17:13,180
+نفسكو مش مشتركة أه طبعا يعني لو في عندي زوجة مثلا
+
+196
+00:17:13,180 --> 00:17:22,270
+أجي أقول زوجة و جدة و ثلاثة أخ لأمو أخ شقيق
+
+197
+00:17:22,270 --> 00:17:30,510
+فالزوجة ربع الجدة ستة و هدول تلت نيجي نحسب المسألة
+
+198
+00:17:30,510 --> 00:17:36,090
+من أتناش هان تلاتة هان اتنين هان أربع اعدي أربع أو
+
+199
+00:17:36,090 --> 00:17:38,650
+تلاتة سبعة أو اتنين تسعة يعني لسه ضايل فيه باقي
+
+200
+00:17:38,650 --> 00:17:43,510
+هذا العصب يعني ضالله باقي بمعنى ما سقطش ما طارش
+
+201
+00:17:43,510 --> 00:17:49,150
+فالمسألة مش مشتركةو نفس الأمر لو كان في عندي مثلا
+
+202
+00:17:49,150 --> 00:17:56,210
+هنا أخ لأم واحد و هات زوج يعني هذا زوج و هذا أخ
+
+203
+00:17:56,210 --> 00:18:00,810
+لأم واحد فهذا نصف و هات سدس فإذا ضايل فيه باقي صح
+
+204
+00:18:00,810 --> 00:18:07,950
+ولا لأ؟ طيب لو المسألة زي كده و هان عدد مثلا لكن
+
+205
+00:18:07,950 --> 00:18:12,590
+هان أخت شقيقة أخت
+
+206
+00:18:12,590 --> 00:18:18,090
+شقيقةفإذا هتاخد نصف وبالتالي المسألة مش مشتركة
+
+207
+00:18:18,090 --> 00:18:25,770
+علم؟ تمام؟ طيب ماذا لو كان بدل الإخوة الأشقاء إخوة
+
+208
+00:18:25,770 --> 00:18:33,130
+لأب؟ هل المسألة تكون مشتركة؟ أيوة الله يفتح عليكم
+
+209
+00:18:33,130 --> 00:18:40,710
+خلّيكم معايا إذا لو كان الإخوة بدل أشقاء إخوة لأب
+
+210
+00:18:41,580 --> 00:18:46,300
+فهل نقول لا يسقطون و يشاركون الإخوة لأم في الثلاث؟
+
+211
+00:18:46,300 --> 00:18:50,260
+بالتأكيد لا، ليش؟ جابل ما أحكي المثال، لأن يا
+
+212
+00:18:50,260 --> 00:18:53,360
+جماعة الإخوة لأب و الإخوة لأم بيجربوش لبعض
+
+213
+00:18:56,830 --> 00:19:01,330
+بجربوش لبعض يعني أنا بدي أجيبلك مثال مثلا خلينا
+
+214
+00:19:01,330 --> 00:19:06,370
+نمثل على عبير عبير هالجيت أبوها متزوجتان تاني
+
+215
+00:19:06,370 --> 00:19:12,710
+فالها أخت تانية اسمها ياسمين من أبوها من أبوها
+
+216
+00:19:12,710 --> 00:19:18,090
+وامها كائنة متزوجة الها أخت اسمها آية تمام فالان
+
+217
+00:19:18,090 --> 00:19:22,510
+آية وعبير امهم واحدة صح؟ طيب حلو عبير وياسمين
+
+218
+00:19:22,510 --> 00:19:27,490
+أبوهم واحد خواتطب الآن بالنسبة ليه؟ يسمين و آية
+
+219
+00:19:27,490 --> 00:19:31,990
+بيجربوا لبعض؟ مطلقا لا في أب مشترك ولا أم مشترك
+
+220
+00:19:31,990 --> 00:19:37,570
+كبيناتهم فكيف لنا أن نجعل الإخوة لأب هنا يحلون محل
+
+221
+00:19:37,570 --> 00:19:41,510
+الأشقاء و يشاركون الإخوة لأم؟ مستحيل .. مستحيل
+
+222
+00:19:41,510 --> 00:19:50,970
+علم؟ تمام وبالتالي لو في عندي زوج و جدة و اتنين أخ
+
+223
+00:19:50,970 --> 00:20:01,800
+لأم و أخت لأبو أخ لأب فبنيجي نقول كده عادي بتحلي
+
+224
+00:20:01,800 --> 00:20:07,300
+طبيعي نصف، سدس، تلت وهدول بتقولي عصبة بالغاية
+
+225
+00:20:07,300 --> 00:20:12,220
+بتيجي تحلي المسألة من ستة، تلاتة، واحد، اتنين،
+
+226
+00:20:12,220 --> 00:20:17,240
+زيروماضال إشي صح ولا لأ؟ يسقطون ما بنروح نقول
+
+227
+00:20:17,240 --> 00:20:20,880
+بنشاركهم هناك شاركناهم مش هدلاك الإخوة جالوا
+
+228
+00:20:20,880 --> 00:20:24,820
+لسيدنا عمار هبقالنا لأب لنا؟ طب هدول لو بدهم
+
+229
+00:20:24,820 --> 00:20:28,700
+يقولوا لأب لنا طب ما هو أصلا الأم بتجرب الكمش؟
+
+230
+00:20:28,700 --> 00:20:33,880
+الأم بتجرب الكمش أصلا مش أمكوا هذه وصلت؟ تمام؟ حلو
+
+231
+00:20:33,880 --> 00:20:38,940
+طيب لو نفس المسألة ومافيش أخ لأب في أخت لأب كده بس
+
+232
+00:20:39,530 --> 00:20:43,850
+هتاخد فرض اقعد تقولي هان محجوبة صح ولا لأ اتفرضها
+
+233
+00:20:43,850 --> 00:20:52,250
+هترفيه ايه يا حبة طبيعي انها صاحبة فرض هنا تمام
+
+234
+00:20:52,250 --> 00:20:58,590
+مية لمية وصلت وصلت يا جماعة جميلة مغيبة خالص مش
+
+235
+00:20:58,590 --> 00:21:03,470
+فاهم ايش بنحكي في اي سؤال يا جميلة لا حتى لها تمام
+
+236
+00:21:03,470 --> 00:21:11,830
+طيب في اي سؤال يا خوات جميلة تمامخلاص إذا هي صورة
+
+237
+00:21:11,830 --> 00:21:15,270
+المسألة زي ما حكينا فبالتالي لو اختل أي شرط هنا
+
+238
+00:21:15,270 --> 00:21:21,910
+زوجة مثلا هنا أخ واحد هان أخت شقيقة مش أخ ماعدتش
+
+239
+00:21:21,910 --> 00:21:27,030
+المسألة مشترك علم؟ تمام نيجي الآن لأصحاب الفرود
+
+240
+00:21:27,030 --> 00:21:30,370
+طبعا في موضوع أصحاب الفرود يا جماعة راح أكون سريعة
+
+241
+00:21:30,370 --> 00:21:35,050
+جدا إلا في موضوع الجد و الأم باعتبار الجد و الجد و
+
+242
+00:21:35,050 --> 00:21:40,410
+الأمالان ليش؟ لأن هذا بكرر المعلومات اللي أخدناها
+
+243
+00:21:40,410 --> 00:21:44,710
+لكن الفكرة أنه هناك يا جماعة لما اتحدثنا عن الفرود
+
+244
+00:21:44,710 --> 00:21:49,150
+إذا بتتذكروا صلوا على رسول الله كنا نتحدث فرض نصف
+
+245
+00:21:49,150 --> 00:21:53,330
+مين بستحقه، إفلانه، علانه، بصر مين، الربع، التمل،
+
+246
+00:21:53,330 --> 00:21:56,870
+التلتين، فهنا لأ بدنا نقول كل وارث إيش حالات
+
+247
+00:21:56,870 --> 00:22:02,130
+ميراثهمن أصحاب الفرود من أصحاب الفرود كل وارث إيش
+
+248
+00:22:02,130 --> 00:22:07,010
+حالات ميراثه فلحظي معايا الفرق بين هاي الموضوع
+
+249
+00:22:07,010 --> 00:22:10,930
+والموضوع السابق أنه قبل كان الأحكام متفرقة هنا
+
+250
+00:22:10,930 --> 00:22:14,750
+بدنا نجمعهم في جانب واحد بس وبالتالي المعلومات مش
+
+251
+00:22:14,750 --> 00:22:20,210
+جديدة أبدا لذلك راح نذكرها ذكر عسرية و نجد فقط end
+
+252
+00:22:20,820 --> 00:22:24,560
+الجد باعتبار أميز بين الجد الصحيح والجد الفاسدة
+
+253
+00:22:24,560 --> 00:22:28,300
+والجد باعتبار لازم نميز بين الجد الصحيح والجد
+
+254
+00:22:28,300 --> 00:22:31,720
+الفاسد وموضوع الأم باعتبار الأم أخدنا حالتين
+
+255
+00:22:31,720 --> 00:22:36,300
+لميراثها وهي إلها تلات حالات، تمام؟ حلو؟ فخلونا ع
+
+256
+00:22:36,300 --> 00:22:40,200
+السريع أول شي نحكي عن الزوج، حالات ميراث الزوج،
+
+257
+00:22:40,200 --> 00:22:45,520
+الزوج هحكي بسرعة أنا نصف أو ربع، نصف إذا لم يكن
+
+258
+00:22:45,520 --> 00:22:52,050
+لزوجته فرع و عارفطب جماعة رجاءً تحكوش معايا تمام؟
+
+259
+00:22:52,050 --> 00:22:55,390
+لما أقول لفلانة اتجاوب، بتجاوب لوحدها منيح؟ إذا
+
+260
+00:22:55,390 --> 00:22:59,990
+الزوج نصف إذا لم يكن لزوجته فرق وارس وإذا كان لها
+
+261
+00:22:59,990 --> 00:23:04,730
+فرق وارس معناته ربع، هي الزوج ميراسه بس يا كذا أو
+
+262
+00:23:04,730 --> 00:23:09,850
+كذا فقط خلصنا، الزوجة ربع أو تمونحالات ميراث
+
+263
+00:23:09,850 --> 00:23:13,990
+الزوجة بس ربع أو طمن ربع إذا زوجها مالوش فرق وارث
+
+264
+00:23:13,990 --> 00:23:18,950
+و طمن إذا إله فرق وارث و الآية واضحة و لكم نصف ما
+
+265
+00:23:18,950 --> 00:23:22,290
+ترك أزواجكم إن لم يكن لهم ولد فإن كان لهم ولد فلكم
+
+266
+00:23:22,290 --> 00:23:26,250
+الربع مما تركنا من بعد وصية يوصينا بيها أو دين و
+
+267
+00:23:26,250 --> 00:23:30,610
+لهم الربع مما تركتم إن لم يكن لكم ولد فإن كان لكم
+
+268
+00:23:30,610 --> 00:23:37,530
+ولد فلهم ثمن تمام جميل نجي للأب الأب يا جماعة
+
+269
+00:23:37,530 --> 00:23:43,830
+ميراثهاما الاصل عصباه اتفجنا ان الاصل في مراسل
+
+270
+00:23:43,830 --> 00:23:48,170
+الاب عصباه لكنه ينتقل من العصبه الى الصدس بوجود
+
+271
+00:23:48,170 --> 00:23:55,910
+الفرع المذكر فالاصل ان الاب عصباه تمام؟عمر الثاني
+
+272
+00:23:55,910 --> 00:24:00,850
+صدوس عند وجود فرع مذكر للميت صدوس زائد عصبة في حال
+
+273
+00:24:00,850 --> 00:24:06,070
+وجود فرع مؤنث للميت وقضية صدوس زائد عصبة قلنا
+
+274
+00:24:06,070 --> 00:24:10,790
+اعملنا هذه التوليفة من باب حماية للأب لأنه خفنا
+
+275
+00:24:10,790 --> 00:24:14,570
+نعطيه عصبة باعتبار فاش ذكره وأو للعصبات فخفنا
+
+276
+00:24:14,570 --> 00:24:18,270
+نعطيه عصبة يحجب بالاستغراق زي ما حكينا قبل شوية
+
+277
+00:24:18,270 --> 00:24:22,910
+يعني مثلا يكون في عنده خليني أقول مثلا خمسة بنت و
+
+278
+00:24:22,910 --> 00:24:28,180
+أمه وزوجةفأو أب فالأب هيطير لو بدنا نقول عصبة
+
+279
+00:24:28,180 --> 00:24:33,100
+باعتبار مش عندي ذكر فلذلك حميناه وقلنا صدزة إذا
+
+280
+00:24:33,100 --> 00:24:38,660
+عصبة حلو؟ طيب نيجي للأم الأم أخدنا حالتين والتالتة
+
+281
+00:24:38,660 --> 00:24:44,000
+الآن جديدة الأم إما تلت إذا الميت مالوش فراوارس
+
+282
+00:24:44,000 --> 00:24:49,240
+ومالوش عدد من الإخسُدُس العكس إذا إله فرع وارث أو
+
+283
+00:24:49,240 --> 00:24:54,980
+عدد من الإخوة والحالة التالتة تلت الباقي هناك تلت
+
+284
+00:24:54,980 --> 00:24:59,020
+التاركة التلت يعني تلت التاركة لما أقول فقط أثلث
+
+285
+00:24:59,020 --> 00:25:07,340
+وأسكت يعني ثلث التاركة بينماتلت الباقي يعني بزيد
+
+286
+00:25:07,340 --> 00:25:11,040
+بعد حدان .. هنحكي مين الحدان هاد .. حلو؟ فالان
+
+287
+00:25:11,040 --> 00:25:15,560
+موضوع أن الأم تأخذ .. هذه شغلة جديدة علينا .. أن
+
+288
+00:25:15,560 --> 00:25:22,860
+الأم تأخذ ثلث الباقي فيما لو كان في عندي مسألة
+
+289
+00:25:22,860 --> 00:25:27,040
+فيها أحد ال .. أو فيها كلا الأبوين مع أحد الزوجين
+
+290
+00:25:28,080 --> 00:25:32,980
+كلا الأبوين يعني أم وأب، كلا الأبوين مع أحد
+
+291
+00:25:32,980 --> 00:25:39,600
+الزوجين حينها الأم بتاخد ثلث الباقي وفلسفة هاي
+
+292
+00:25:39,600 --> 00:25:43,780
+المسألة بسيطة أنه لو بدي أفترض أعطي الأم تلت
+
+293
+00:25:43,780 --> 00:25:46,600
+باعتبار مافيش فرق وارث و مافيش عدد من الإخوة
+
+294
+00:25:46,600 --> 00:25:53,180
+معناته هتاخد أكتر منالأب و لا يتصور باتفاق الفقهاء
+
+295
+00:25:53,180 --> 00:25:57,520
+أن الأم يكون نصيبها أكثر من الأب يعني يختلف مع
+
+296
+00:25:57,520 --> 00:26:01,900
+منطق التشريع أن تكون الأم أكثر من الأب مش جاي مع
+
+297
+00:26:01,900 --> 00:26:06,060
+روح التشريع لذلك العلماء قالوا أنه إلها تلت الباقي
+
+298
+00:26:06,540 --> 00:26:12,220
+وطبعا بيقولك أن الحالة الوحيدة اللي الأم بتأخذ
+
+299
+00:26:12,220 --> 00:26:16,940
+فيها تلت الباقي فيما لو كانت هي و الأب مع أحد
+
+300
+00:26:16,940 --> 00:26:21,300
+الزوجين يعني مسألتين مع أحد الزوجين يعني موجود مع
+
+301
+00:26:21,300 --> 00:26:26,260
+الأب و الأم زوج أو زوجة وبالتالي نيجي نحل على
+
+302
+00:26:26,260 --> 00:26:32,210
+حالنا السابق عادي في عندي زوج مثلا و أم و أبيانحل
+
+303
+00:26:32,210 --> 00:26:36,170
+حالت طبيعي طبعا الأم طبيعي تلت باعتبار شو مافيش
+
+304
+00:26:36,170 --> 00:26:39,850
+فرق وارث و مافيش عدد من الإخوة و هاد عصبة تعالوا
+
+305
+00:26:39,850 --> 00:26:44,350
+نحل المسألة من ستة هان تلاتة و هان اتنين الأب هيظل
+
+306
+00:26:44,350 --> 00:26:50,770
+اللي واحد أي تصور أن الأم تاخد ضعيف الأب مستحيل مش
+
+307
+00:26:50,770 --> 00:26:55,370
+راكبة يعني مش مبلوعة مش مهضومة صح ولا صح؟ تمام
+
+308
+00:26:57,750 --> 00:27:01,510
+طب ما هي يعني لسه انا .. احنا لسه ماحكينا التاصيل،
+
+309
+00:27:01,510 --> 00:27:05,270
+لأ بسيطة ما هو المحاضرة الجاية هنشرحه بالتفصيل
+
+310
+00:27:06,190 --> 00:27:11,270
+بنفعش أستبق الأحداث معلش أنا لحظة معايا حلته حل
+
+311
+00:27:11,270 --> 00:27:15,370
+بسيط جدا يعني هذه مسألة سهلة جدا يعني فانت لحالك
+
+312
+00:27:15,370 --> 00:27:19,870
+بالنظر هتلاقي أنه هذه هتاخد أكتر من هذا بالنظر
+
+313
+00:27:19,870 --> 00:27:25,350
+بعيدا عن التأصيل اللي هندرسه، تمام؟ طيب فهذه الحال
+
+314
+00:27:25,350 --> 00:27:32,130
+غلط العلماء حسوا أن المسألة فيها غلط ف .. و نفس
+
+315
+00:27:32,130 --> 00:27:40,360
+الأمر لو بدنا نقول زوجة و أموأب الزوجة ربع وهادي
+
+316
+00:27:40,360 --> 00:27:47,020
+طول وهاد عصبى برضه هتضل الأم أكثر من الأب okay مش
+
+317
+00:27:47,020 --> 00:27:53,270
+هتكون ضعفه بس أكتر منهفأيضا المسألة لم ترق للعلماء
+
+318
+00:27:53,270 --> 00:27:58,310
+فالسيدنا عمر أول من حكم في مثل هذه المسألة فلذلك
+
+319
+00:27:58,310 --> 00:28:02,930
+هتين المسألتين تسميان المسألتان العمريتان
+
+320
+00:28:02,930 --> 00:28:09,570
+العمريتان لقضاء عمر رضي الله عنه فيهماو أيضًا هناك
+
+321
+00:28:09,570 --> 00:28:14,810
+من أطلق عليهم الغرّوان نسبة إلى الغرّة، الغرّة
+
+322
+00:28:14,810 --> 00:28:18,590
+الوضوح مش دائمًا بنقول الغرّة مقدمة الشيء صح ولا
+
+323
+00:28:18,590 --> 00:28:23,810
+لأ و عادة المقدمة هي الشيء البارز صح ولا صح فلذلك
+
+324
+00:28:23,810 --> 00:28:30,530
+سميت هذه المسألتان بالغرّوان لوضوح الحق فيهم وهو
+
+325
+00:28:30,530 --> 00:28:36,520
+ما سندرسه الآن، تمام؟الأن يا جماعة بدنا نسأل
+
+326
+00:28:36,520 --> 00:28:41,580
+أنفسنا سؤال بنقول في المسألة اللي الأم الأصل
+
+327
+00:28:41,580 --> 00:28:45,300
+ميراثها تلت أمتن الأم تاخد التلت؟ مافي فرق وارث و
+
+328
+00:28:45,300 --> 00:28:48,740
+مافي عدد من الإخوة لأن لو في عدد من الإخوة الأم
+
+329
+00:28:48,740 --> 00:28:53,860
+أخدت تلت وخلصنا بطلت المسألة عمرية أصلا طيب أي عقل
+
+330
+00:28:53,860 --> 00:29:00,880
+مع وجود الأبمع وجود الأب في المسألة أيه تصور أن
+
+331
+00:29:00,880 --> 00:29:05,140
+يكون في عندي .. والأم تلت طبعا والأم تلت ركزي على
+
+332
+00:29:05,140 --> 00:29:08,400
+أن الأم تلت لأنه لو سدس خلصنا مافيش إشكال عندنا
+
+333
+00:29:08,400 --> 00:29:15,080
+أيوع قال أن في عندي مسألة فيها أم وأبو أحد الزوجين
+
+334
+00:29:15,080 --> 00:29:20,560
+معهم صاحب فرض وارس عفوا بدون الزوج معهم صاحب فرض
+
+335
+00:29:20,560 --> 00:29:25,280
+وارس غير أحد الزوجين مستحيل يكون في عنده صاحب فرض
+
+336
+00:29:25,280 --> 00:29:31,340
+حيرث في وجود الأب وطبق الأم تلت إلا أحد الزوجين
+
+337
+00:29:31,340 --> 00:29:36,720
+لأنه لو بدي أفترضهأعيد المسألة مرة تانية، لا يتصور
+
+338
+00:29:36,720 --> 00:29:40,440
+العلماء يقولون، لا يتصور، وفعلا الآن المنطق حيثبت
+
+339
+00:29:40,440 --> 00:29:46,400
+صحيح كلامنا، لا يتصور أنه طالما في أبو أمه، أمه
+
+340
+00:29:46,400 --> 00:29:51,420
+أخدت تلت، لا يتصور أن صاحب الفرض الذي سيرث أن يكون
+
+341
+00:29:51,420 --> 00:29:56,250
+غير الزوجانليش؟ لأن لو بدي أفطرت فيه بنت فالأم
+
+342
+00:29:56,250 --> 00:29:59,790
+ماعداتش صدر، ماعداتش تلت، صح ولا لأ؟ طيب، لو بدي
+
+343
+00:29:59,790 --> 00:30:05,390
+أفطرت فيه إخوة باعتبار هتصير صدوس، فإذا أصلا هم مش
+
+344
+00:30:05,390 --> 00:30:10,800
+هيارثوا، يعني لو هان أخت شقيقةاخد شقيقة أجي أقول
+
+345
+00:30:10,800 --> 00:30:16,060
+نصف؟ لأ محجوبة بالأب فلا ترث فصاحب الفرض الوحيد
+
+346
+00:30:16,060 --> 00:30:21,480
+الذي قد يرث مع وجود الأب و تبقى الأم تلت، مين هو؟
+
+347
+00:30:21,480 --> 00:30:27,760
+الزوج أو الزوجة، بس فقط، فقط، تمام؟ وهتين
+
+348
+00:30:27,760 --> 00:30:34,360
+المسألتين فقط فيما تأخذ الأم ثلث؟ الباقي، تمام؟
+
+349
+00:30:34,360 --> 00:30:40,960
+وصلت؟ فنجي نشوف كيف نحل هالمسألة، هل جيت؟سواء هذه
+
+350
+00:30:40,960 --> 00:30:45,720
+او هذه في
+
+351
+00:30:45,720 --> 00:30:54,760
+عندي زوج قلنا و أم و أب او زوجة و أم و أب فالان يا
+
+352
+00:30:54,760 --> 00:31:01,120
+جماعة العلماء قالوا في هتين المسألتين طبيعي الزوج
+
+353
+00:31:01,120 --> 00:31:07,540
+هياخد فرضه كما هو الأم هتاخد تلت الماقي يعني تلت
+
+354
+00:31:07,540 --> 00:31:14,850
+النصمش الباقي نص؟ صح ولا لأ؟ مش الباقي نصف؟ مش هيك
+
+355
+00:31:14,850 --> 00:31:22,190
+ولا أنا غلطانة؟ حلو إذا انجول تلت الباقيهاد أخد
+
+356
+00:31:22,190 --> 00:31:25,890
+نصف طولة الباقي طبعا بعد أحد الزوشين وبالتالي
+
+357
+00:31:25,890 --> 00:31:31,430
+الزوج أخد نصف جداش ضل بعد النصف نصف فهي هتاخد طولة
+
+358
+00:31:31,430 --> 00:31:36,170
+النصف مش طولة التاريخ طولة النصف طولة النصف جداش
+
+359
+00:31:36,170 --> 00:31:41,590
+سُدس عملية حسابية دائما ال بلغة الحساب أو
+
+360
+00:31:41,590 --> 00:31:46,190
+الرياضيات معناها ضرب طولة
+
+361
+00:31:46,190 --> 00:31:50,370
+النصف اللي هو ستة وروح أش
+
+362
+00:31:54,260 --> 00:32:02,940
+تمام؟ تلت ال نصف يعني سدس حلو؟ طيب و ممكن انحلها
+
+363
+00:32:02,940 --> 00:32:08,340
+حال تاني سهل برضه خليكم معايا انحلها حال طبيعي
+
+364
+00:32:08,340 --> 00:32:17,340
+المسألة هان من اتنين تمام؟ هان واحد و هان ايش؟
+
+365
+00:32:17,340 --> 00:32:24,670
+واحدواحد واحد صح ولا لأ؟ باعتبار نصف طب الواحد
+
+366
+00:32:24,670 --> 00:32:29,630
+بتجسم على تلاتة ما هدول باعتبار بدنا نفترض انه
+
+367
+00:32:29,630 --> 00:32:33,290
+للذاكر يمسله حظ الأنسة يعني تلاتة فبدنا نروح ايش؟
+
+368
+00:32:33,290 --> 00:32:38,110
+ضربين المسألة كلها في تلاتة هان هيصير ستة هان
+
+369
+00:32:38,110 --> 00:32:41,470
+تلاتة و هان تلاتة كيف بدنا نجسم التلاتة على الأب
+
+370
+00:32:41,470 --> 00:32:47,050
+والأم؟ الأم واحد والأب اتنين وخلص تمام؟
+
+371
+00:32:49,970 --> 00:32:53,330
+مش مشكلة المحاضرة الجاية زي ما قرأتلكم آية نيجي
+
+372
+00:32:53,330 --> 00:32:59,150
+لهذه المسألة أسهل الآن في عندي زوجة ربع وهذه تلت
+
+373
+00:32:59,150 --> 00:33:05,590
+الباقي المسألة نقول من أربعة تمام هذه جدش إلها
+
+374
+00:33:05,590 --> 00:33:10,310
+واحد و جدش الباقي تلاتة كيف ننجسم التلاتة سهل واحد
+
+375
+00:33:10,310 --> 00:33:18,610
+اتنين خلصنا صح ولا لا وصلت نعم كمان هذه ماوصلتش
+
+376
+00:33:18,610 --> 00:33:24,260
+طيبجماعة صلوا على رسول الله هلجيت الزوجة إلها رباع
+
+377
+00:33:24,260 --> 00:33:28,520
+صح؟ وإحنا بنقول الأم إلها طولة الباقي يعني طولة
+
+378
+00:33:28,520 --> 00:33:32,860
+التلت أرباع باعتبار الباقي جدش تلت أرباع طب يا
+
+379
+00:33:32,860 --> 00:33:36,240
+سيتي بدناش هذه الفكرة الآن الرباع ناخد المقام
+
+380
+00:33:36,240 --> 00:33:41,540
+نجعله أصل نجعله أصل فإذا جدش الزوجة إلها من أربع
+
+381
+00:33:41,540 --> 00:33:47,220
+واحد لأنه رباع جدش بظل تلاتة التلاتة بدي أجسمها
+
+382
+00:33:47,220 --> 00:33:51,400
+على الأب و الأمفالطبيعي الأب اتنين والأم واحد
+
+383
+00:33:51,400 --> 00:33:59,360
+وخلصنا بس علم؟ علم طيب لو كان مع .. مع الأبوين
+
+384
+00:33:59,360 --> 00:34:04,800
+مثلا إخوة لأم أو إخوة لأب أو كذا هدول okay محجوبين
+
+385
+00:34:04,800 --> 00:34:10,600
+بالأب لكن هذه صارت سدس بطلت المسألة عماريةحلو؟
+
+386
+00:34:10,600 --> 00:34:16,580
+بطلت المسألة عمرية طيب لو اللي كانوا معهم ناس
+
+387
+00:34:16,580 --> 00:34:23,060
+بيأثروش على نصيب الأم يعني الأم هيك هيك هتضلها تلت
+
+388
+00:34:23,060 --> 00:34:29,400
+زي مثلا نقول خمسة عم، خمسة عم شقيق هل المسألة تبقى
+
+389
+00:34:29,400 --> 00:34:33,620
+عمرية ولا تخرج عن كونها عمرية؟ تبقى عمرية لأنهم ما
+
+390
+00:34:33,620 --> 00:34:37,900
+بيأثروا فدول محجوبين وخلصنا ما بيأثروا، مين اللي
+
+391
+00:34:37,900 --> 00:34:43,490
+بيأثروا؟ بس الإخوةعلم؟ تمام؟ هات بالنسبة ليه ميراث
+
+392
+00:34:43,490 --> 00:34:49,190
+الأم؟ طيب، من وين جابوا العلماء إن الأم إلها التلت
+
+393
+00:34:49,190 --> 00:34:54,430
+الباقي مع إن الآية واضحة في دلالتها إن الأم يا سدس
+
+394
+00:34:54,430 --> 00:34:59,330
+يا تلت و لأبويه لكل واحد منهم السدس إن لم يكن له
+
+395
+00:34:59,330 --> 00:35:06,810
+ولد فإن كان له ولد وورثه أبواه فلأمه الثلث فمن وين
+
+396
+00:35:06,810 --> 00:35:13,330
+جبتوا التلت الباقي؟فبنقول أن هذه الآية العلماء
+
+397
+00:35:13,330 --> 00:35:20,610
+فسروها على أنه لأمه الثلث إذا لم يكن معهم أحد
+
+398
+00:35:20,610 --> 00:35:26,170
+الأبوين بينما لو كان أحد الزوجين معهم أو لو كان
+
+399
+00:35:26,170 --> 00:35:32,760
+معهم حدا وارث غير الإخوةفهيأخذوا ثلث الباقي
+
+400
+00:35:32,760 --> 00:35:36,740
+فالعلماء فسروا الآية أن المراد بالثلث هنا في الآية
+
+401
+00:35:36,740 --> 00:35:40,940
+ثلث الباقي في حال وجود أحد الزوجين مع الأبوان
+
+402
+00:35:40,940 --> 00:35:46,660
+تمام؟ علم؟ طيب فإذا
+
+403
+00:35:46,660 --> 00:35:48,220
+المسألة صارت واضحة
+
+404
+00:35:54,090 --> 00:35:57,210
+طب أحوال ميراث الإخ و الإأم على السريع الإخ و
+
+405
+00:35:57,210 --> 00:36:02,590
+الإأم يا جماعة يا سدس يا تلت سدس إذا كان واحد و
+
+406
+00:36:02,590 --> 00:36:06,450
+تلت إذا كانوا عدد بشرط مافيش فرع وارث و مافيش أصل
+
+407
+00:36:06,450 --> 00:36:11,150
+مذكر حلو؟ طيب البنت .. البنت الصلبية إلها تلت
+
+408
+00:36:11,150 --> 00:36:14,530
+حالات للميراث إما النصف إذا كانت واحدة منفردة عن
+
+409
+00:36:14,530 --> 00:36:18,830
+الذكر و الأنثى المماثلين و إما تلتين إذا كانت
+
+410
+00:36:18,830 --> 00:36:23,540
+منفردة عن الذكر المماثلطبعا تنتلف أكثر منفردات عن
+
+411
+00:36:23,540 --> 00:36:27,760
+الذكر المماثل وعصبة بالغير إذا وجد معها المعصب
+
+412
+00:36:27,760 --> 00:36:31,380
+اللي هو الإبن من درجتها الذكر المماثل نيجي لبنات
+
+413
+00:36:31,380 --> 00:36:36,560
+الإبن بنات الإبن أربع حالات يا جماعة النصف إذا لم
+
+414
+00:36:36,560 --> 00:36:40,480
+يوجد معها ذكر أو أنثى مماثلين وذكر أو أنثى أعلى
+
+415
+00:36:40,480 --> 00:36:45,560
+هاي واحد تلتين إذا معهم مش ذكر مماثل ومافيش ..
+
+416
+00:36:45,560 --> 00:36:52,600
+مافيش الأعلىاحنا بنحكي تلتين، مافيش ذكر مماثل و
+
+417
+00:36:52,600 --> 00:36:57,080
+مافيش أعلى، تمام حلو و بتأخذ السدوس سواء واحدة أو
+
+418
+00:36:57,080 --> 00:37:03,980
+أكتر إذا وجدت أمس أعلى مستحقة للنصف و عصبة بالغير
+
+419
+00:37:03,980 --> 00:37:10,680
+تتعصب مع الذكر المماثل أو الأنزل إن احتجت إليه،
+
+420
+00:37:10,680 --> 00:37:15,800
+تمام؟ طبعا بشرط مافيش حدان أعلىأو الذكر أعلى حلو
+
+421
+00:37:15,800 --> 00:37:22,780
+طيب نيجي للاخد الشقيق برضه أربع حلال نصف إذا كانت
+
+422
+00:37:22,780 --> 00:37:26,400
+منفردة عن الذكر والأنثى المماثلين ومنفردة عن الفرع
+
+423
+00:37:26,400 --> 00:37:30,920
+الوارث وعن الأصل المذكر طولتين إذا كانوا تنتين
+
+424
+00:37:30,920 --> 00:37:34,240
+فأكثر منفردات عن الذكر المماثل ومافيش فرع وارث
+
+425
+00:37:34,240 --> 00:37:40,330
+ومافيش أصل مذكر بعدين مين اللي بتقول سدس؟أووا
+
+426
+00:37:40,330 --> 00:37:45,090
+كتقولوا الأخت الشقيقة 6 مستحيل عصبة بالغير إذا كان
+
+427
+00:37:45,090 --> 00:37:49,810
+معها ذكر مماثل اللي هو الأخ الشقيق ومافيش فرع وارث
+
+428
+00:37:49,810 --> 00:37:55,150
+ومافيش أصل مذكر بعدين عصبة مع الغير عند وجود الفرع
+
+429
+00:37:55,150 --> 00:38:01,030
+المؤنث بشرط فش ذكر مماثل ولا أعلى حلو؟ طيب الأخت
+
+430
+00:38:01,030 --> 00:38:04,490
+ليه أب؟ لحظي معايا أنا شريعة لأن كل الكلام أخدناه
+
+431
+00:38:04,490 --> 00:38:10,390
+فش إشي جديدالأخت لأب خمس حلات يا جماعة، خمس حلات
+
+432
+00:38:10,390 --> 00:38:14,890
+للميراث، عندنا النصف إذا كانت واحدة منفردة عن
+
+433
+00:38:14,890 --> 00:38:19,250
+الذكر المماثل وعن الأخ الشقيق و الأخت الشقيقة و
+
+434
+00:38:19,250 --> 00:38:24,230
+الفرق الوارث و الأصل المذكر، طولتين إذا تنتين
+
+435
+00:38:24,230 --> 00:38:32,750
+فأكثر مابعهمشذكر مماثل ماعهمش شقيق أو شقيقة، فيش
+
+436
+00:38:32,750 --> 00:38:37,870
+فرق وارث، فيش أصل، مذكر، تمام؟ سدس إذا كانوا تنتين
+
+437
+00:38:37,870 --> 00:38:41,810
+في أكثر وكان في أخت شقيقة واحدة مستحقة للناس
+
+438
+00:38:41,810 --> 00:38:46,610
+فبيأخذوا السدس تكملة ليه؟الثلاثين والحالة الرابع
+
+439
+00:38:46,610 --> 00:38:51,150
+عصباء بالغير إذا معها أخ لأب طبعا بشرط مافيش أخ
+
+440
+00:38:51,150 --> 00:38:57,930
+شقيق ومافيش فرع وارث مافيش أصل مذكر عصباء مع الغير
+
+441
+00:38:59,650 --> 00:39:04,270
+طبعا مع الفرع المؤنث بشرط مافيش ذكر مماثل ولا ذكر
+
+442
+00:39:04,270 --> 00:39:09,330
+أعلى تمام؟ إذا المخاضرة القادمة بإذن الله نتحدث عن
+
+443
+00:39:09,330 --> 00:39:14,950
+حالات ميراث الجد وحالات ميراث الجدة ثم ندخل مباشرة
+
+444
+00:39:14,950 --> 00:39:19,290
+على تأصيل المسائل بإذن الله رب العالمين إلى هنا
+
+445
+00:39:19,290 --> 00:39:22,370
+نكون قد انتهينا من موضوع محاضرتنا أستغفر الله
+
+446
+00:39:22,370 --> 00:39:26,250
+وأتوب إليه والسلام عليكم ورحمة الله تعالى وبركاته
+
diff --git a/PL9fwy3NUQKwaGIlkTCo2tGndokmJ9ZbKr/7zbUaeBcssU_postprocess.srt b/PL9fwy3NUQKwaGIlkTCo2tGndokmJ9ZbKr/7zbUaeBcssU_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..64c82db25d3c5a63e24b07bf1b335b8d14f4d7c7
--- /dev/null
+++ b/PL9fwy3NUQKwaGIlkTCo2tGndokmJ9ZbKr/7zbUaeBcssU_postprocess.srt
@@ -0,0 +1,3720 @@
+1
+00:00:00,440 --> 00:00:02,620
+موسيقى
+
+2
+00:00:11,860 --> 00:00:14,140
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+3
+00:00:14,140 --> 00:00:17,460
+الصلاة والسلام على رسول الله وبعد أيها الأخوات
+
+4
+00:00:17,460 --> 00:00:19,940
+الكريمات أحيوكم بتحية الإسلام العظيم في السلام
+
+5
+00:00:19,940 --> 00:00:24,820
+عليكم ورحمة الله وبركاته طبعا يسعدنا أن نلتقي في
+
+6
+00:00:24,820 --> 00:00:28,900
+هذا الفصل الدراسي الجديد الفصل الصيفي مع مادة
+
+7
+00:00:28,900 --> 00:00:33,680
+دراسات في القرآن وعلومي طبعا أنا أخوكم في الله
+
+8
+00:00:33,680 --> 00:00:40,280
+الدكتور الأستاذ المساعدكلية أصول الدين قسم التفسير
+
+9
+00:00:40,280 --> 00:00:44,840
+وعلوم القرآن ورئيس قسم التفسير حاليا ضايقلي من
+
+10
+00:00:44,840 --> 00:00:51,720
+عمري شهر واحدفي المادة الدراسات يعني تعتبر من
+
+11
+00:00:51,720 --> 00:00:58,940
+المواد الشيقة جدا و هي تابعة لمتطلبات الجامعة
+
+12
+00:00:58,940 --> 00:01:03,440
+الإسلامية بقسم التفسير و علوم القرآن تحوى معاني
+
+13
+00:01:03,440 --> 00:01:08,700
+كبيرة جدا و طبعا تم الاتفاق على هذه المادة لأن
+
+14
+00:01:08,700 --> 00:01:13,900
+مفردات المادة لابد لكل إنسان مسلم أن يطلع عليها
+
+15
+00:01:14,520 --> 00:01:19,580
+والمفردات المادة طبعا احنا في جانب نظري و في جانب
+
+16
+00:01:19,580 --> 00:01:25,880
+عملي الجانب النظري بدنا نتناول فيه في الفصل الأول
+
+17
+00:01:25,880 --> 00:01:30,800
+و هو تعريف القرآن الكريم نزول القرآن المكي والمدني
+
+18
+00:01:30,800 --> 00:01:36,520
+الناسخ والمنسوخ جمع القرآن الكريم و القضايا
+
+19
+00:01:36,520 --> 00:01:42,950
+المتعلقة بعلوم القرآنوأما الجانب الثاني وهو يتناول
+
+20
+00:01:42,950 --> 00:01:47,490
+جانب التطبيق العملي يعني تطبق صور من صور القرآن
+
+21
+00:01:47,490 --> 00:01:52,070
+الكريم التفسير وهذا التفسير ليس تفسيرا تحليليا
+
+22
+00:01:52,070 --> 00:01:57,830
+بقدر ما هو تفسير موضوي شامل نقف على بعض القضايا
+
+23
+00:01:57,830 --> 00:02:03,890
+وأخمية الصورة في حياة الإنسان الفرد والمجتمع معاه
+
+24
+00:02:04,180 --> 00:02:07,960
+طبعا احنا في انه صورة الإسراء وفي هناك صورة
+
+25
+00:02:07,960 --> 00:02:13,620
+الإسراء طبعا بتحدث عن مقاطع كتيرة ومواضيع اجتماعية
+
+26
+00:02:13,620 --> 00:02:19,580
+راقية حتى نستطيع انه يعني نلقي الضوء عليها من هذا
+
+27
+00:02:19,580 --> 00:02:23,440
+المفهوم ثم الصورة الثانية وهي صورة النور واجتملت
+
+28
+00:02:23,440 --> 00:02:28,940
+على أداب وأحكام تتعلق بالدخول وغض البصر وتيسير سبل
+
+29
+00:02:28,940 --> 00:02:35,470
+الزواج وطلب الآفةوطبعا هنا يعني حتى نعمل على قضية
+
+30
+00:02:35,470 --> 00:02:40,710
+كبح جماح الشهوات من انتشارها في المجتمع ثم الفصل
+
+31
+00:02:40,710 --> 00:02:45,690
+الرابع يتناول اللي هو صورة الحجرات طبعا بالشرح
+
+32
+00:02:45,690 --> 00:02:50,190
+التحليلي لأن هناك كان في تفسير موضوعي لكن صورة
+
+33
+00:02:50,190 --> 00:02:56,390
+الحجرات حتى نأخذ نمط جديد من أمامها التفسير وتركز
+
+34
+00:02:56,390 --> 00:03:00,590
+على قضية الأداباللي يجب أن يتأدبها الإنسان المسلم
+
+35
+00:03:00,590 --> 00:03:04,370
+مع الله سبحانه وتعالى ومع رسوله ومع المجتمع الذي
+
+36
+00:03:04,370 --> 00:03:09,850
+يعيش فيه طلب التثبت من سماع الأخبار ووجوب الإصلاح
+
+37
+00:03:09,850 --> 00:03:14,890
+بين الناس، العمل على توحيد الأمة، كل ذلك سنتناوله
+
+38
+00:03:14,890 --> 00:03:20,280
+في هذه المادة بإذن اللهإذا المادة بتتناول جوانب
+
+39
+00:03:20,280 --> 00:03:24,440
+نظرية ثم جوانب عملية وبناخد من الجوانب العملية
+
+40
+00:03:24,440 --> 00:03:29,020
+صورة الإسراء صورة النور صورة الحجرات وهذه يمكن انا
+
+41
+00:03:29,020 --> 00:03:35,620
+بتصور ان اكثر الصور لها ارتباطبالفتات والمرأة
+
+42
+00:03:35,620 --> 00:03:40,620
+المسلمة يعني ان هذه صور من الصور التي يجب على كل
+
+43
+00:03:40,620 --> 00:03:45,260
+امرأة ان تقف مع هذه الصور لما فيها من فائدة قيمة
+
+44
+00:03:45,260 --> 00:03:48,920
+خاصة صورة النور وصورة الحجرات لانها بتتحدث عن امور
+
+45
+00:03:48,920 --> 00:03:53,560
+شيقة جدا الان سنبدأ بإذن الله سبحانه وتعالى بدنا
+
+46
+00:03:53,560 --> 00:03:57,420
+نلقي اولا مفهوم هذا احنا اتكلمنا عن المساق اما
+
+47
+00:03:57,420 --> 00:04:01,770
+قضية العلاماتأنا مش حابب أتناقض اتحدث في هذا
+
+48
+00:04:01,770 --> 00:04:06,310
+الموضوع كثير و خاصة عند الطالبات لأن الطالبات يعني
+
+49
+00:04:06,310 --> 00:04:13,050
+شوف حتى صار يعني مش عارف هذه الصورة هي إيجابية ولا
+
+50
+00:04:13,050 --> 00:04:17,650
+صورة سيئة مش عارف الان ان كثير من الطالبات تبحث عن
+
+51
+00:04:17,650 --> 00:04:21,490
+العلامة و نص العلامة و قضية المفهوم الإجمالي عند
+
+52
+00:04:21,490 --> 00:04:25,930
+المادة او غيره انا بتصور دي إشكالي و خاصة انه قضية
+
+53
+00:04:25,930 --> 00:04:31,580
+الغيابو انا من الناس اللي يعني شديدى التعامل في
+
+54
+00:04:31,580 --> 00:04:35,680
+قضية الحضور والغياب وانتوا يعني مش طالبات ابتدائى
+
+55
+00:04:35,680 --> 00:04:41,340
+ولا ثانوية بدى اظنى والله اخد حضور غياب في هذه
+
+56
+00:04:41,340 --> 00:04:46,320
+المادة لكن انا في عندي طرق اشد من قضية اللى هو ال
+
+57
+00:04:46,320 --> 00:04:50,120
+.. القضية ال .. ال .. بس اللى اخد الحضور والغياب
+
+58
+00:04:50,120 --> 00:04:56,350
+انا هيكون معايا في بعض الأحيان هيكون طبعايعني في
+
+59
+00:04:56,350 --> 00:05:00,270
+أوقات متفاوتة تختارش على بال الطالب ولا الطالب
+
+60
+00:05:00,270 --> 00:05:04,090
+بأتناول الاسم و بصير أناقش هناك من أنه باخد حضور
+
+61
+00:05:04,090 --> 00:05:09,010
+غياب بصير أختار أسماء عشوائية و بصير أنه في هناك
+
+62
+00:05:09,010 --> 00:05:13,370
+مناقشة فبحط حضور غياب بحط قضية مناقشة فبنجيب
+
+63
+00:05:13,370 --> 00:05:16,510
+عصفرين بحجر هذه واحدةالنقطة الثانية في الأسئلة
+
+64
+00:05:16,510 --> 00:05:20,830
+الموجودة ويريت أنه في المرة القادمة كل طالب يكون
+
+65
+00:05:20,830 --> 00:05:24,450
+مح الكتاب الكتاب هو دراسات في القرآن وعلوم للدكتور
+
+66
+00:05:24,450 --> 00:05:28,930
+الأستاذ الدكتورة لإن هو أستاذ الدكتور زكريا لزميلي
+
+67
+00:05:28,930 --> 00:05:32,330
+والأستاذ الدكتور عصام زهد والدكتور عبد الكريم
+
+68
+00:05:32,330 --> 00:05:35,890
+الدشانوة موجود في مكتبة الجامعة ياريت كل طالبة
+
+69
+00:05:35,890 --> 00:05:40,770
+تجيب الكتاب من المحاضرة القادمة حتى نستطيع أنه نضع
+
+70
+00:05:40,770 --> 00:05:45,740
+بعض الملاحظاتيعني احنا أحيانا في قضية المادة بنحط
+
+71
+00:05:45,740 --> 00:05:51,340
+بعض التفسيرات بعض الاضافات الشروحات و خاصة في قضية
+
+72
+00:05:51,340 --> 00:05:55,620
+الهامش حتى نستطيع أنه نستفيد منها في غالبية الأمور
+
+73
+00:05:55,620 --> 00:06:00,920
+المناقشة أسئلة المناقشة والحوار نضع سين وله إجابة
+
+74
+00:06:00,920 --> 00:06:05,460
+أو ربما أنه يكون هنا السؤال يعني أحيانا في فائدة
+
+75
+00:06:05,460 --> 00:06:09,660
+خارجية فعلى الطالب حتى تستطيع أنهإذا بدها تدرس
+
+76
+00:06:09,660 --> 00:06:12,700
+الكتاب تدرسه في البيت وانا متأكد ان كثير من
+
+77
+00:06:12,700 --> 00:06:16,020
+الطالبات يعني منحهم الله سبحانه وتعالى هبط الذكاء
+
+78
+00:06:16,020 --> 00:06:20,600
+لو هي في البيت راجعت لها لها هتحصل لها 70% ولا 60%
+
+79
+00:06:20,600 --> 00:06:24,420
+يعني من المادة لكن مش شيك المادة المادة هي عبارة
+
+80
+00:06:24,420 --> 00:06:28,000
+عن تلاقوح أفكار هي عبارة عن نقاش عبارة عن حوار
+
+81
+00:06:28,000 --> 00:06:32,740
+وإبفاء جو أو يعني معلومات ممكن تفيد الطالبة في بعض
+
+82
+00:06:32,740 --> 00:06:36,580
+الاستفسارات والهنات هنا و هناكأحنا متفقين ان شاء
+
+83
+00:06:36,580 --> 00:06:40,760
+الله بالعالمين في المرة القادمة يعني هنبدأ في قضية
+
+84
+00:06:40,760 --> 00:06:45,060
+اللي هو المناقش والحوار حتى نستطيع أن نضع النقاط
+
+85
+00:06:45,060 --> 00:06:49,220
+على الحروف من حيث التعريفات الموجودة مادة دراسات
+
+86
+00:06:49,220 --> 00:06:54,720
+في القرآن الكريم وهي طبعا متكونة الفصل الأول علوم
+
+87
+00:06:54,720 --> 00:06:58,940
+القرآن بيجتمع على عدة مباحثالمبحث الأول اللى ..
+
+88
+00:06:58,940 --> 00:07:05,180
+اللى نقف معه اليوم و هو تعريف القرآن .. تعريف
+
+89
+00:07:05,180 --> 00:07:09,100
+القرآن الكريم و حاجة طبيعية أنه إحنا لما بنتكلم عن
+
+90
+00:07:09,100 --> 00:07:13,560
+أي مسألة من المسائل لابد أن نتحدث عن المعنى اللغوي
+
+91
+00:07:13,560 --> 00:07:17,960
+و المعنى الإصطلاحي فاحنا بنقول القرآنهو يعني
+
+92
+00:07:17,960 --> 00:07:22,480
+بالاساس في اللغة جاء على وزن فعلان و هو مشتق من
+
+93
+00:07:22,480 --> 00:07:27,560
+القرأ و القرأ بمعنى الجمع و احنا بنقول احنا لما
+
+94
+00:07:27,560 --> 00:07:34,140
+بنيجي في اللغة بنقول ان القرآن يعني قرأ الماءفي
+
+95
+00:07:34,140 --> 00:07:38,840
+الحوب يعني إذا جمعناه يعني جمعنا الماء في الحوب
+
+96
+00:07:38,840 --> 00:07:43,920
+هذا هو بالمعنى اللغوي وجاءت من الاشتقاق أن القرآن
+
+97
+00:07:43,920 --> 00:07:50,560
+الكريم جاءت من من قرأة بمعنى تلا أو يعني من المقرؤ
+
+98
+00:07:50,560 --> 00:07:55,560
+والتلافة فإذا احنا بنتكلم عن القرآن فهو شامل يعني
+
+99
+00:07:55,560 --> 00:07:59,260
+اشتقاقته شامل هذه المعنات يعني جاء القرآن بمعنى
+
+100
+00:07:59,260 --> 00:08:06,360
+الجمعوبمعنى التلاوة إن علينا جمعه وقرآنه فإذا
+
+101
+00:08:06,360 --> 00:08:12,440
+قرأناه فاتبع قرآنه شوف إن علينا جمعه وقرآنه وكأنه
+
+102
+00:08:12,440 --> 00:08:16,680
+بيأكد على الجامعة والتلاوة شوف هنا جاءت كلمة جامعة
+
+103
+00:08:16,680 --> 00:08:20,240
+اللي هو الجامعة والجامعة احنا سنقف فيه هناك
+
+104
+00:08:20,240 --> 00:08:24,160
+العلماء قبضوا على هذا معنى رائع قالوا الجامعة في
+
+105
+00:08:24,160 --> 00:08:28,370
+الصدور والجامعةفي الصطور والجمع اللي في الصطور
+
+106
+00:08:28,370 --> 00:08:32,930
+يعني الكتابة والقراءة لكن الجمع في قضية الصدر هو
+
+107
+00:08:32,930 --> 00:08:36,670
+التلاوة الحفظ يعني يعني تلاوة القرآن الكريم فمن
+
+108
+00:08:36,670 --> 00:08:41,050
+هنا نفهم أن القول الراجح أن لفظ القرآن يرجع في
+
+109
+00:08:41,050 --> 00:08:44,510
+اشتقاقه إلى معنى الجمع والتلاوة معاه يعني مابنجيش
+
+110
+00:08:44,510 --> 00:08:48,730
+ناخد أنه لو جائك أنت في المعنى وقلت أن القرآن يعني
+
+111
+00:08:48,730 --> 00:08:54,220
+هي مأخوذة من التلاوة وفقط بيكون هذا خطرلأنه لو
+
+112
+00:08:54,220 --> 00:08:57,560
+بدنا نقول تلاوة طب و أين قضية الجامعة الآخر؟ فمعنى
+
+113
+00:08:57,560 --> 00:09:02,300
+ذلك أنه يحوي المعنى يعني معنى أو المعنى يعين و هو
+
+114
+00:09:02,300 --> 00:09:05,480
+قضية الجامعة و قضية التلاوة أما تعريف القرآن في
+
+115
+00:09:05,480 --> 00:09:09,440
+الإصطلاح أنت لو أنا بدأ أسأل شو أنت بتعرف القرآن
+
+116
+00:09:09,440 --> 00:09:16,100
+الكريم؟ نعم
+
+117
+00:09:16,100 --> 00:09:21,110
+إذا هو كلام الله المعجزالان المتعبد بتلوتنا
+
+118
+00:09:21,110 --> 00:09:26,110
+المتعبد بتلوته الذي نزل بوسطة جبريل عليه السلام
+
+119
+00:09:26,110 --> 00:09:32,650
+المنقول إلينا بالتواتر وقيعني بمعنى مبدوء من صورة
+
+120
+00:09:32,650 --> 00:09:38,630
+الفاتحة إلهية إلى صورة الناس هذه هي التعريفات اللي
+
+121
+00:09:38,630 --> 00:09:45,010
+موجودة عندك وهذه من الأمور اللي يجب على كل إنسان
+
+122
+00:09:45,010 --> 00:09:50,000
+مسلم أن يفهم مثل هذا التعريف الجامعالان بدنا نقف
+
+123
+00:09:50,000 --> 00:09:54,160
+معها واحدة واحدة، شوفوا عندما نقول إن هذا كلام
+
+124
+00:09:54,160 --> 00:09:59,500
+الله، معناته لما أنا بفهم كلام الله سبحانه وتعالى
+
+125
+00:10:00,310 --> 00:10:06,890
+إذا أخرج إن كل كلام من كلام البشر و كلام الجن يعني
+
+126
+00:10:06,890 --> 00:10:11,010
+خرج مدام كلام الله يعني خلاص يعني بمعنى الكلام جنس
+
+127
+00:10:11,010 --> 00:10:14,470
+في التعريف و بقول إن وده يعني أخرج إن كلام الإنس و
+
+128
+00:10:14,470 --> 00:10:17,510
+كلام الجن و كلام الملائكة لا دخلة له بالقرآن
+
+129
+00:10:17,510 --> 00:10:23,020
+الكريم لا من قريب ولا من بعيدالمنزل طبعا هنا احنا
+
+130
+00:10:23,020 --> 00:10:25,860
+بنقول انه يعني المنزل على محمد صلى الله عليه وسلم
+
+131
+00:10:25,860 --> 00:10:32,580
+طيب ليش؟ يعني بمعنى أنه حصره لأنه في كلام الله نزل
+
+132
+00:10:32,580 --> 00:10:38,160
+على غير محمد زي؟ التورة زي الإنجيل زي الزبوغ زي
+
+133
+00:10:38,160 --> 00:10:42,540
+صحف إبراهيم وموسى إذا كثير من الكتب يعني معنى ذلك
+
+134
+00:10:42,540 --> 00:10:47,760
+لما نقول المنزل على محمد يعني إعقطنا إش ماله؟إنه
+
+135
+00:10:47,760 --> 00:10:52,800
+اختخصيص بمعنى بس فقط كلام الله الذي جاء به جبريل
+
+136
+00:10:52,800 --> 00:10:57,620
+على قلب محمد صلى الله عليه وسلم طيب لما بنتكلم عن
+
+137
+00:10:57,620 --> 00:11:02,140
+قضية كثيرة احنا بنتكلم عن الفاظ المعجز جون المعجز
+
+138
+00:11:02,140 --> 00:11:08,060
+بلفظه ومعناه ليش طيب القرآن الكريم كلام معجز؟
+
+139
+00:11:13,040 --> 00:11:16,600
+طب أنا بدأ أقوللكم يعني الآن يعني الآن الفرق بين
+
+140
+00:11:16,600 --> 00:11:24,200
+اللي هو الحديث والقرآن الكريم ايش الفرق بينهم؟ اه
+
+141
+00:11:24,200 --> 00:11:28,580
+تفضل الحديث المعنى الإجمالي من الله سبحانه وتعالى
+
+142
+00:11:28,580 --> 00:11:31,860
+أمثلة حياتي من الرسول أما القرآن الكريم الكلام هو
+
+143
+00:11:31,860 --> 00:11:35,460
+ونزل من عند الله سبحانه وتعالى أنا بتكلم من حياتي
+
+144
+00:11:35,460 --> 00:11:40,120
+الإعجاز أنا القرآن بس الحديث
+
+145
+00:11:42,070 --> 00:11:46,270
+بتكلم من وجه الإعجاز، أنا عمال بكرر، يعني بمعنى
+
+146
+00:11:46,270 --> 00:11:51,970
+الحديث كلام الله، مظبوط؟ ومنزل على مين؟ على محمد،
+
+147
+00:11:51,970 --> 00:11:56,050
+والقرآن كلام الله منزل على محمد، لكن في قضية
+
+148
+00:11:56,050 --> 00:12:03,770
+الإعجازيعني بمعنى أن القرآن هو الذي جاء للتحدي
+
+149
+00:12:03,770 --> 00:12:09,570
+يعني بمعنى أنه أعجز العرب والإنس والجن معنى على أن
+
+150
+00:12:09,570 --> 00:12:14,270
+يأتوا بصورة من مثله أو بعشري صور من مثله أو بمثل
+
+151
+00:12:14,270 --> 00:12:20,850
+القرآن الكريم يعني تحدي يعني بمعنى أن التحدي جاء
+
+152
+00:12:20,850 --> 00:12:26,950
+على ثلاثة مراحل أو ليش تحديهم بنيته بالقرآن بمثل
+
+153
+00:12:26,950 --> 00:12:31,950
+القرآنيعني اعطوني قرآن مثله ماجدروش، اتنين تحدهم
+
+154
+00:12:31,950 --> 00:12:39,450
+بعشر صور، تلاتة تحدهم بإيش؟ بصورة واحدةإذا القرآن
+
+155
+00:12:39,450 --> 00:12:45,490
+جاء هنا الإعجاز جاء للتحدي لكن الحديث النبوي جاء
+
+156
+00:12:45,490 --> 00:12:49,550
+للتحدي يعني هل الرسول صلى الله عليه وسلم تحدى
+
+157
+00:12:49,550 --> 00:12:53,830
+الإنس والجن بحديث النبوي إذا هذا فرق اللي احنا
+
+158
+00:12:53,830 --> 00:12:58,470
+بتتكلم عنه عشان أيه جاء للمعجز معناته قضية الإعجاز
+
+159
+00:12:58,470 --> 00:13:04,680
+تعطينا بلفظه ومعناه فالإعجاز خاصيةوليست لوقيدا
+
+160
+00:13:04,680 --> 00:13:09,060
+يعني يمتز بيه بمعنى أن القرآن الكريم أعجز العرب
+
+161
+00:13:09,060 --> 00:13:15,700
+والعجم على أن يأتوا بمثله طيب المتعبد بتلوته ايش
+
+162
+00:13:15,700 --> 00:13:22,440
+معناه المتعبد بتلوته؟ يعني
+
+163
+00:13:22,440 --> 00:13:28,620
+بمعنى أن قضية القرآن الكريم يتعبد به سواء في
+
+164
+00:13:28,620 --> 00:13:34,750
+الصلاة أو في إيش؟أه في غيرها يعني بمعنى في الصلاة
+
+165
+00:13:34,750 --> 00:13:39,570
+الآن أنا جاعل في الصلاة لا يجوز على الإطلاق أني
+
+166
+00:13:39,570 --> 00:13:42,450
+أقرأ حديث نبو و أقول أنا بدأ أتعبد فيه في الصلاة
+
+167
+00:13:42,450 --> 00:13:46,250
+إذا أنا متعبد بتلوتي في الصلاة و في غيرها في غير
+
+168
+00:13:46,250 --> 00:13:53,420
+الصلاة من قرأ القرآن فله بكل حرفحسنة ولا أقول ألف
+
+169
+00:13:53,420 --> 00:13:57,860
+لام ميم حرف و لكن ألف حرف و لام حرف و ميم حرف يعني
+
+170
+00:13:57,860 --> 00:14:01,700
+و أنا فاتح في القرآن الكريم و في البيت قاعد بقرا
+
+171
+00:14:01,700 --> 00:14:06,300
+في الشارع بقرا في السيارة في أي مكان و بقرا القرآن
+
+172
+00:14:06,300 --> 00:14:10,100
+فإيه ليه أجر و إيه ليه تواب و لهذا غنى التعبد
+
+173
+00:14:10,100 --> 00:14:15,060
+بالقرآن لكن لو قرأت أنا كل الأحادث القدسية و كل
+
+174
+00:14:15,060 --> 00:14:20,030
+الأحادث النبويةهل معناه ذلك أنا هذا تعبد؟ إيه لأجر
+
+175
+00:14:20,030 --> 00:14:25,140
+آه، لكن ليس تعبدًا؟شفتوا؟ يعني بمعنى أنه لما بتكلم
+
+176
+00:14:25,140 --> 00:14:30,860
+عن التعبد بتكلم تلاوة يعني أن تلاوة وقراءة القرآن
+
+177
+00:14:30,860 --> 00:14:37,840
+الكريم هي عبادة و لا يصح غير القرآن في قضية الصلاة
+
+178
+00:14:37,840 --> 00:14:42,360
+و بيخرج من هذا قلنا الحديث القدسية وغيرها طيب
+
+179
+00:14:42,360 --> 00:14:47,680
+المنقول إلينا بالتواتر شو معناته التواتر؟ انت
+
+180
+00:14:47,680 --> 00:14:50,820
+خدتوا مصفلح الحديث؟
+
+181
+00:14:52,520 --> 00:14:58,400
+أيوة قولي، إذا
+
+182
+00:14:58,400 --> 00:15:04,480
+هو ما رواه جامع عن جامع عن جامع من بداية السنة إلى
+
+183
+00:15:04,480 --> 00:15:11,340
+آخره طبعا مشوفه الآنمافيش تواطق لم يجمل الصحابة
+
+184
+00:15:11,340 --> 00:15:16,620
+على مين؟ على الكلمة، يعني كلهم بمعنى ثقة، بمعنى
+
+185
+00:15:16,620 --> 00:15:21,220
+صدوق، يعني هؤلاء سلسلة جامعة عن جامعة من الصحابة
+
+186
+00:15:21,220 --> 00:15:26,060
+أو من الرواة من بداية الراوي، يعني الراوي المعاصر
+
+187
+00:15:26,060 --> 00:15:30,210
+مثلاحتى التابعين وقضية الصحابة حتى رسول الله صلى
+
+188
+00:15:30,210 --> 00:15:33,830
+الله عليه وسلم وهذا الجمع هو دليل على قضية نهج
+
+189
+00:15:33,830 --> 00:15:37,990
+قضية الثقة حتى أن بعض العلماء شوفوا الآن لما قالوا
+
+190
+00:15:37,990 --> 00:15:42,930
+ما رواه جمعه عن جمع من أول السنة دي إلى منتهى لم
+
+191
+00:15:42,930 --> 00:15:48,310
+يثبت تواطؤهم على مين على الكذب هذا هو التواتر إذا
+
+192
+00:15:48,310 --> 00:15:54,950
+كتبتي هذه الملاحظة اكتب عندك التواتر في الحمش من
+
+193
+00:15:54,950 --> 00:16:04,200
+تحت في صفحة الستةالتواتر هو ما رواه جامع عن جامع
+
+194
+00:16:04,200 --> 00:16:15,240
+من أول السنة دي إلى منتهى ولم
+
+195
+00:16:15,240 --> 00:16:16,960
+يثبت تواطؤهم على الكلمة
+
+196
+00:16:20,910 --> 00:16:26,650
+السين اللى احنا بدنا ننتبه له احنا فيه عيننا موضوع
+
+197
+00:16:26,650 --> 00:16:33,610
+سين وبتحط ياندك على اللى هو في نفس الصفحة بين
+
+198
+00:16:33,610 --> 00:16:41,910
+الفرق بين تأمين طبلون القرآن
+
+199
+00:16:41,910 --> 00:16:47,570
+الحديث القدسى الحديث النبوي
+
+200
+00:16:52,010 --> 00:16:58,010
+تعمليه لمقارنة بين الثلاثة أولا في شيء بيجمع بين
+
+201
+00:16:58,010 --> 00:17:08,030
+الثلاثة وبعدين يبدأ الافتراق يالا تفضلي القرآن
+
+202
+00:17:08,030 --> 00:17:18,010
+الكريم المعنى واللفظ أو خلينا المعنى واللفظ من عند
+
+203
+00:17:18,010 --> 00:17:18,250
+الله
+
+204
+00:17:22,430 --> 00:17:27,830
+ماشي؟ طيب و الحديث القدسي و الحديث النبوي؟ هنا
+
+205
+00:17:27,830 --> 00:17:32,650
+الحديث القدسي اللفظ
+
+206
+00:17:32,650 --> 00:17:41,570
+من مين؟ اذا المعنى من الله واللفظ من الرسول طب و
+
+207
+00:17:41,570 --> 00:17:46,050
+الحديث النبوي؟
+
+208
+00:17:46,050 --> 00:17:49,230
+نفس الكلام هذا للاثنين
+
+209
+00:17:51,650 --> 00:18:00,190
+طيب خلّيني نشوف كيف
+
+210
+00:18:00,190 --> 00:18:03,750
+انت خدتي؟ قولي ياش خدتي فيه؟ اه
+
+211
+00:18:12,120 --> 00:18:16,340
+الرسول بيحكي بس الضماعة بتكون تعودت على الله
+
+212
+00:18:16,340 --> 00:18:18,960
+سبحانه وتعالى، بس الضماعة في الحديث النبوي بتكون
+
+213
+00:18:18,960 --> 00:18:22,360
+تعودت على الرسول، يعني في ال .. قال رسول الله صلى
+
+214
+00:18:22,360 --> 00:18:25,160
+الله عليه وسلم مثلا أنه عزيزي ما ينفذ، أنه كان
+
+215
+00:18:25,160 --> 00:18:28,560
+ماشي مثلا في الطريق مشاهد مثلا في واحد، فهذا يعني
+
+216
+00:18:28,560 --> 00:18:32,960
+موقف مر بالرسول، أما الحديث القدسي هو إشي بيحكي ..
+
+217
+00:18:32,960 --> 00:18:36,820
+يعني مقمول يعني .. في الحقيقة لو بين علامتين
+
+218
+00:18:36,820 --> 00:18:40,270
+مصريين مثلا عن قول من الله، لأ بس الرسول حكىشوفتوا
+
+219
+00:18:40,270 --> 00:18:43,030
+أنا كنت عمال بديختبر كنت بتقول أخدتوا مادة أصفر من
+
+220
+00:18:43,030 --> 00:18:46,830
+صلاة الحديث، مظبوط؟ طب أنتوا لما بتيجي تتميزوا بين
+
+221
+00:18:46,830 --> 00:18:50,170
+الحديث القدسي و الحديث النبولي، شوف الفرق بين
+
+222
+00:18:50,170 --> 00:18:53,890
+الاتنين، خليني واحدة واحدة، فضل، يارك بس اتعالي
+
+223
+00:18:53,890 --> 00:18:59,050
+صوتك، لأ أنا بتكلم عن اللفظ و المعنى
+
+224
+00:19:02,870 --> 00:19:07,830
+شوفي انا عشان اعطيكي باختصار الراجح وبديش انك انك
+
+225
+00:19:07,830 --> 00:19:14,250
+يعني الان الحديث القدسي زيه زي القرآن بمعنى ان
+
+226
+00:19:14,250 --> 00:19:22,830
+المعنى واللفظ من عند الله المعنى
+
+227
+00:19:22,830 --> 00:19:29,180
+واللفظمن عند الله الحديث انا بعطيك الراجح عشان
+
+228
+00:19:29,180 --> 00:19:33,340
+انتي مش متخصصة دير بالك عشان انت و ادا متطلب احنا
+
+229
+00:19:33,340 --> 00:19:37,440
+في أصول الدين الكلية اللي بنعطيهم علوم القرآن
+
+230
+00:19:37,440 --> 00:19:40,700
+بنفسر بالتفصيل وبالتالي بياخدوا العراء انا بدي
+
+231
+00:19:40,700 --> 00:19:44,520
+اعطيك الرأي الراجح يعني بمعنى القرآن الكريم المعنى
+
+232
+00:19:44,520 --> 00:19:48,040
+واللفظ من عند الله والحديث القدس المعنى واللفظ من
+
+233
+00:19:48,040 --> 00:19:53,540
+عند الله لكن الحديث النبويالمعنى من عند الله
+
+234
+00:19:53,540 --> 00:20:00,020
+واللفظ من من؟ من الرسول فيبقى إيش الفرق بين هذا و
+
+235
+00:20:00,020 --> 00:20:09,500
+هذا؟ الله يبتعليكي هنا متعبد بتلاوته و هذا غير
+
+236
+00:20:09,500 --> 00:20:17,680
+متعبد بتلاوته اتفقنا؟ أنا هي المطلوب منك إذا
+
+237
+00:20:17,680 --> 00:20:23,560
+انتبهي في هناك جامع مشتركبين القرآن وبين الحديث
+
+238
+00:20:23,560 --> 00:20:28,820
+القدسي بأن العلماء القول الراجح قالوا أن اللفظ
+
+239
+00:20:28,820 --> 00:20:34,000
+والمعنى من عند الله المعنى واللفظ من مين؟ من عند
+
+240
+00:20:34,000 --> 00:20:41,060
+الله ولكن القرآن متعبد بتلاوته والحديث ايش ماله؟
+
+241
+00:20:41,060 --> 00:20:45,500
+القدسي غير متعبد بتلاوته طيب، الأثنين الحديث
+
+242
+00:20:45,500 --> 00:20:51,600
+القدسي والحديث النبوي صار هنا متفقين في جزئيةأن
+
+243
+00:20:51,600 --> 00:20:56,500
+المعنى الاتنين هذا صار من عند الله لكن هذا اللفظ
+
+244
+00:20:56,500 --> 00:21:01,480
+من عند الرسول صياغة.ولهذا قال العلماء لا يجوز
+
+245
+00:21:01,480 --> 00:21:09,340
+لراوي الحديث القدسي ان يقول او كما قال.بدو محفوظ
+
+246
+00:21:09,340 --> 00:21:16,260
+حفظا نصيا.في الحديث النبوي ممكن ان اقول او كما قال
+
+247
+00:21:16,260 --> 00:21:20,310
+صلى الله عليه وسلم.أو أروي الحديث بالمعنى، ماشي
+
+248
+00:21:20,310 --> 00:21:25,950
+الحال، لكن في الحديث القدسي لم يجزي العلماء أن
+
+249
+00:21:25,950 --> 00:21:30,430
+نقول بالحديث القدسي أو قلم، على طول بنقول أن قال
+
+250
+00:21:30,430 --> 00:21:36,390
+النبي صلى الله عليه وسلم في حديث مروي عن رب العزة
+
+251
+00:21:36,390 --> 00:21:40,430
+قال، وعلى طول بجيب النص، وهذا الأصل في قضية
+
+252
+00:21:40,430 --> 00:21:45,670
+التعامل حتى عند الدعاء، وعند غيرهم يجب أن يلتزموا
+
+253
+00:21:45,670 --> 00:21:48,930
+بذلكإذا انت فهمتي هذه القضية، هذه سطية، هذه سؤال
+
+254
+00:21:48,930 --> 00:21:52,570
+خارجي، وبديك تنتبهيله وجايكي حياة الصلاة، حياة
+
+255
+00:21:52,570 --> 00:21:55,410
+الفلاح، بديك تركزي على هذه المعاني الرائلة، ودي
+
+256
+00:21:55,410 --> 00:21:59,110
+مقدمة لابد منها، إذا انت فهمتي قضية اللي هي؟
+
+257
+00:21:59,110 --> 00:22:03,730
+النقطة الثانية في شيء، في قضية مهمة، وإحنا بنتعامل
+
+258
+00:22:03,730 --> 00:22:05,930
+مع الأحاديث، أن نفهم
+
+259
+00:22:08,280 --> 00:22:13,320
+في المنقول إلينا بالتواتر أو المنقول إلينا
+
+260
+00:22:13,320 --> 00:22:22,060
+بالإعادة تتصوروا من أنكر حديثا متواترا شو حكمه؟
+
+261
+00:22:22,060 --> 00:22:29,570
+كفريعني صار الحديث المتواتر، هذا بيطينا قوة لا
+
+262
+00:22:29,570 --> 00:22:35,710
+يمكن انكاره، لكن لو بعض الناس أنكر حديث الأحد أو
+
+263
+00:22:35,710 --> 00:22:40,350
+غيره، ربما أنه عليه إثم أو إغمال، لكن مش معناه ذلك
+
+264
+00:22:40,350 --> 00:22:43,630
+أنه خرج من دائرة الإيمان إلى دائرة الكفر، يعني
+
+265
+00:22:43,630 --> 00:22:48,690
+قضية الحديث المتواتر يعتبر من أقوى الحديث احتجاجا
+
+266
+00:22:49,690 --> 00:22:52,870
+منتبهنا على النقطة هذه، إذا خلّينا نشوف الآن
+
+267
+00:22:52,870 --> 00:22:57,870
+التعريف مرة تانية، هو كلام الله المعجز بلفظه
+
+268
+00:22:57,870 --> 00:23:01,870
+ومعناه المنزل على النبي صلى الله عليه وسلم بوسط
+
+269
+00:23:01,870 --> 00:23:05,930
+الجبريل، وهذا اللي بيميز، قال المتعبد بتلاوة
+
+270
+00:23:05,930 --> 00:23:09,790
+والمعجز، وهي اللي ميزتنا من الحديث النبوي والحديث
+
+271
+00:23:09,790 --> 00:23:13,430
+القدسي هو كلام الله، ومنزل على قلب النبي صلى الله
+
+272
+00:23:13,430 --> 00:23:18,300
+عليه وسلم، وجابه وسط الجبريلإذا هنا لكن هنا معجز
+
+273
+00:23:18,300 --> 00:23:23,060
+ومتعبد بتلوته هنا شوفت الآن هي واحدة هي اتنين
+
+274
+00:23:23,060 --> 00:23:28,420
+تلاتة هنا معجزهنا متعبد بالتلوات غير متعبد
+
+275
+00:23:28,420 --> 00:23:32,320
+بالتلوات طبعا معروف وانا معجز لكن هنا لأ الاتنين
+
+276
+00:23:32,320 --> 00:23:36,160
+مش معجزات حتى الحديث القدسي لا يُعتبر إيش ماله؟
+
+277
+00:23:36,160 --> 00:23:41,780
+معجزا يعني الحديث النبوية والقدسية لم يتحدى بها
+
+278
+00:23:41,780 --> 00:23:44,600
+النبي صلى الله عليه وسلم إيش ماله؟ العرب أو الإنس
+
+279
+00:23:44,600 --> 00:23:48,940
+والجن أو غير ذلك لم تأتي للتحدي اتفقنا على هذا
+
+280
+00:23:48,940 --> 00:23:54,040
+الكلام؟ إذا فهمنا؟ خلينا نشوف إن آيات بنقول تعريف
+
+281
+00:23:54,040 --> 00:23:55,980
+القرآن الكريم اصطلاحا
+
+282
+00:24:04,610 --> 00:24:11,430
+على طول بتكتب المبدوء عشان يكتمل لالمبدوء بأول
+
+283
+00:24:11,430 --> 00:24:17,750
+صورة الفاتحة إلى آخر صورة النس وبعض العلماء قال
+
+284
+00:24:17,750 --> 00:24:22,290
+الموجود بين دفتين المصحف يعني الموجود بين الغلاف
+
+285
+00:24:22,290 --> 00:24:26,030
+اللي موجود المجلد اللي عندك من بداية صورة الفاتحة
+
+286
+00:24:26,030 --> 00:24:31,570
+إلى آخر صورة النسالان نتكلم عن قضية القرآن الكريم
+
+287
+00:24:31,570 --> 00:24:39,210
+وتنزلته اولا لو نتكلم عن نزول القرآن الكريم بمعنى
+
+288
+00:24:39,210 --> 00:24:47,610
+نقول نزول القرآن الكريم نزلةتطلق على معنى يعنى،
+
+289
+00:24:47,610 --> 00:24:50,690
+دالبالك هذا الكتاب اللى موجود هو اللى موجود الكتاب
+
+290
+00:24:50,690 --> 00:24:56,050
+يعنى، ملخص نفسه هو هو عشان احنا ملتزمين للاعانة بس
+
+291
+00:24:56,050 --> 00:24:59,470
+لقضية الحفظ والوسيلة من الوسائل اللى كان في النقاش
+
+292
+00:24:59,470 --> 00:25:03,550
+بس بنضيف الأشياء، بمعنى نزلة، ايش معنات نزلة؟
+
+293
+00:25:03,550 --> 00:25:08,270
+شوفوا الكلام في اللغة جاءت الغبوط، احنا بنقول نزلة
+
+294
+00:25:08,270 --> 00:25:12,790
+من أعلى الجبل، مظبوط؟نزل من السيارة، نزل من
+
+295
+00:25:12,790 --> 00:25:18,070
+الطائرة، معناته النزول بمعنى الغبوط من مين؟ من
+
+296
+00:25:18,070 --> 00:25:22,710
+مكان عليه، نزل فلان من الجبل، طالع القرآن الكريم
+
+297
+00:25:22,710 --> 00:25:29,110
+يقول أنزل من السماء ماء، أنزل من السماء، نزل،
+
+298
+00:25:29,110 --> 00:25:34,790
+شفتي؟ قالوا المعنى الثاني بمعنى الحلول، نزلت أهلا
+
+299
+00:25:34,790 --> 00:25:42,040
+وحللت سهلانزلت أهلا وحللت سهلا وقول احنا الآن نزل
+
+300
+00:25:42,040 --> 00:25:47,700
+فلان الى المحطة نزل فلان الى المدينة نزل عندنا
+
+301
+00:25:47,700 --> 00:25:52,780
+ضيفا شوف انها تنزل عندنا ضيفا حلى يعني بمعنى انه
+
+302
+00:25:52,780 --> 00:25:57,760
+حلى عندنا شوفوا القرآن الكريم وقول ربي أنزلني
+
+303
+00:25:57,760 --> 00:26:04,300
+منزلا مباركا وانت خيرالمنزل، شوف الآن يعني بمعنى
+
+304
+00:26:04,300 --> 00:26:11,100
+جاءت كلمة الإنزال بمعنيين، معنى الهبوط ومعنى
+
+305
+00:26:11,100 --> 00:26:17,640
+الإحلال، ماشي؟ أو الحلول، الآن هذا المعنى، هل
+
+306
+00:26:17,640 --> 00:26:23,140
+ينطبق السؤال على القرآن الكريم؟ يعني لما بنقول
+
+307
+00:26:23,140 --> 00:26:27,360
+احنا أنه .. شوف الحلول والهبوط
+
+308
+00:26:28,950 --> 00:26:35,370
+لما نقول نزل القرآن الكريم أو تنزل القرآن الكريم
+
+309
+00:26:35,370 --> 00:26:43,410
+هل بيعني هذا المعنى؟ ليش؟
+
+310
+00:26:43,410 --> 00:26:47,470
+طب وش يعني القرآن الكريم اللي بدي باينه دفتر مصحف
+
+311
+00:26:47,470 --> 00:26:52,090
+شيء ما يديه؟ يعني ما نزلش يعني مش أنه نزل مثلا؟
+
+312
+00:26:52,090 --> 00:26:58,240
+أنا بنقشك، إيه؟الكلام مجازي مش معنى طب ليش يعني
+
+313
+00:26:58,240 --> 00:27:02,620
+احنا مابقدرش نقول نطبق هذا على قضية المعنى الهبوط
+
+314
+00:27:02,620 --> 00:27:06,660
+والحلول؟ ليش .. ليش .. ايش المعنى أن اقول إن
+
+315
+00:27:06,660 --> 00:27:10,960
+القرآن الكريم نزل أي هبط من أعلى من السماوات إلى
+
+316
+00:27:10,960 --> 00:27:15,760
+الأرض؟ أو حل على المسلمين؟ يعني إنه وفق .. يعني
+
+317
+00:27:15,760 --> 00:27:20,060
+يمكن هو بقصد أنه يفت الانتباه مثلا إنه نزل يعني من
+
+318
+00:27:20,060 --> 00:27:23,860
+مكان محدد عالي جدا إلى الأرض، هذا تكليم فيه مبارك
+
+319
+00:27:23,860 --> 00:27:24,520
+على المسلمين
+
+320
+00:27:30,510 --> 00:27:34,730
+يا بنات، مناته القرآن الكريم جُلنا كلام الله، كلام
+
+321
+00:27:34,730 --> 00:27:41,750
+الله مخلوق؟ إذا ليس مجسمًا، إذا مش هينزل، وإذا
+
+322
+00:27:41,750 --> 00:27:46,190
+بدنا نقول حال ضيف، مناته إحنا جسمناه، ومتذكرات قصة
+
+323
+00:27:46,190 --> 00:27:52,790
+المحنة التي تعرض إليها أحمد بن حنبل عندما ضرب ضربا
+
+324
+00:27:52,790 --> 00:27:57,520
+شديدا على أن يقول أن القرآن مخلوق؟القرآن ليس
+
+325
+00:27:57,520 --> 00:28:04,580
+مخلوقا، القرآن هو كلام الله، وكلام الله لا ينفك عن
+
+326
+00:28:04,580 --> 00:28:08,760
+ذات الله، وذات الله لا يمكن تجسيمها، ولا يمكن
+
+327
+00:28:08,760 --> 00:28:13,060
+كذلك، أيش نقول عنها؟ التجسيم، يعني بمعنى أننا نشبه
+
+328
+00:28:13,060 --> 00:28:17,080
+الله سبحانه وتعالى بالمجسمات، معظم الله هذا كفر،
+
+329
+00:28:17,080 --> 00:28:22,180
+وبالتاليإذا لا يليقوا بالقرآن الكريم أن هنا
+
+330
+00:28:22,180 --> 00:28:26,960
+المعنيين تعطينا تشعرنا بقضية المكانية والجسمية
+
+331
+00:28:26,960 --> 00:28:31,220
+وهذا لا يليق بالقرآن الكريم لكن القرآن الكريم
+
+332
+00:28:31,220 --> 00:28:36,200
+الموجود الآن بين أيدينا بين دفتي المصحف هو ليش
+
+333
+00:28:36,200 --> 00:28:40,360
+مانوه؟ هو المخلوق لأنه كتب موجود وورق موجود بيننا
+
+334
+00:28:40,360 --> 00:28:45,550
+لكن كلام الله هو كلام الله الأزليعني اللي لا ينفك
+
+335
+00:28:45,550 --> 00:28:50,530
+عن ذات الله سبحانه وتعالى والله سبحانه وتعالى نقدر
+
+336
+00:28:50,530 --> 00:28:53,330
+نقول والله في كل مكان وكل زمان؟ هذا كلام .. كلام
+
+337
+00:28:53,330 --> 00:28:56,570
+من الجهل لما نقول ربنا في كل زمان وكل مكان ربنا
+
+338
+00:28:56,570 --> 00:29:00,730
+بلا زمان و بلا مكان و بلا بداية و بلا نهاية يعني
+
+339
+00:29:00,730 --> 00:29:05,090
+بمعنى احنا مقدرش نصوره ولا إذا بيبقى زي المخلوقات
+
+340
+00:29:05,090 --> 00:29:09,970
+طيب إيش معناته النزول المقصود في القرآن الكريم؟
+
+341
+00:29:09,970 --> 00:29:15,550
+شوفته الآن؟قول العلماء إلى أن انزال القرآن كان
+
+342
+00:29:15,550 --> 00:29:20,870
+يقصد به ..شوفت الـAlif وBaa يقصد من انزال القرآن
+
+343
+00:29:20,870 --> 00:29:28,410
+انزال حامله ..من هو؟ لأنك لما بنقول نزل القرآن أي
+
+344
+00:29:28,410 --> 00:29:36,290
+نزل جبريل حاملا كلام الله تعالى فهو اللي هو النزول
+
+345
+00:29:36,290 --> 00:29:41,670
+يؤكد على نزول من؟ الشخص الحامليعني نزل بيه الروح
+
+346
+00:29:41,670 --> 00:29:46,110
+الأمين، من هو الروح الأمين؟ جبريل عليه السلام،
+
+347
+00:29:46,110 --> 00:29:52,390
+وكيل يقصد من الإنزال، شوفوا الآن، شوفوا، مهم جدا،
+
+348
+00:29:52,390 --> 00:29:58,070
+واحنا بنتكلم عن قضية النزول، يعني بمعنى لازمة و هو
+
+349
+00:29:58,070 --> 00:30:03,430
+الإعلام، يعني بنقول نزل القرآن للإعلام، بمعنى
+
+350
+00:30:03,430 --> 00:30:11,030
+إنزال القرآن على نبيه إيصاله إليه وإعلامه به،جاءت
+
+351
+00:30:11,030 --> 00:30:17,350
+بمعنى الإعلام إذا ده بنقول الإنزال جاء بمعنى إنزال
+
+352
+00:30:17,350 --> 00:30:22,270
+حامله وهو الروح الأمين أو الإنزال بمعنى يقصد بيه
+
+353
+00:30:22,270 --> 00:30:27,370
+الإعلام فمعنى إنزال القرآن على نبيه يعني إعلام
+
+354
+00:30:27,370 --> 00:30:30,610
+النبي صلى الله عليه وسلم به يعني بالقرآن الكريم
+
+355
+00:30:30,610 --> 00:30:36,670
+طبعا هنا الصين في
+
+356
+00:30:36,670 --> 00:30:39,590
+صفحه سابعة تحت لماذا
+
+357
+00:30:41,200 --> 00:30:45,780
+تم اختيار لفظ
+
+358
+00:30:45,780 --> 00:30:53,100
+الإنزال على القرآن الكريم لش احنا
+
+359
+00:30:53,100 --> 00:30:56,740
+يعني اضفنا كلمة الإنزال على القرآن الكريم
+
+360
+00:31:03,910 --> 00:31:08,290
+يعني تشريف لمين؟ للقرآن الكريم، شرف هذا القرآن
+
+361
+00:31:08,290 --> 00:31:15,230
+وعلو منزلته، وإيش قال هنا؟ وبالحق أنزلناه وبالحق
+
+362
+00:31:15,230 --> 00:31:20,590
+نزل، إذا أولا إحنا بنقول إن بيان شرف هذا القرآن
+
+363
+00:31:20,590 --> 00:31:26,810
+وعلو هذه المنزلةوبقول ومن هنا اختيرت لفظة الإنزال
+
+364
+00:31:26,810 --> 00:31:31,970
+على لفظة الإعلام احنا قلنا انه في معنيين معناته
+
+365
+00:31:31,970 --> 00:31:36,150
+الإنزال ومعناته الإعلام فكلام احنا الاختيار
+
+366
+00:31:36,150 --> 00:31:39,930
+الإنزال يعني بمعنى تم اختيار لفظة الإنزال على قضية
+
+367
+00:31:39,930 --> 00:31:44,770
+الإعلام ليش جاله؟ جاله هذا الشرف علو المكانة
+
+368
+00:31:44,770 --> 00:31:49,410
+معناته ان هو جاي من مكان بعيد وبالتالي اذا ايوة هو
+
+369
+00:31:49,410 --> 00:31:55,080
+رفع لشأن القرآن هو رفع لمين؟طبعا هنا لهذه العلو
+
+370
+00:31:55,080 --> 00:31:59,220
+المنزلة وبالتالي إذا إحنا إفهمنا القرآن الكريم هو
+
+371
+00:31:59,220 --> 00:32:05,680
+عبارة عن قضية إنزاله أي أن القرآن نزل بواسطة جبريل
+
+372
+00:32:05,680 --> 00:32:11,480
+حامل هذا الكلام على وهو كلام الله تعالى وتنزل به
+
+373
+00:32:11,480 --> 00:32:17,460
+على قلب محمد صلى الله عليه وسلم طيب القرآن الكريم
+
+374
+00:32:17,460 --> 00:32:22,120
+هل نزل مرة واحدة بجبريل ونزل على الرسول صلى الله
+
+375
+00:32:22,120 --> 00:32:30,180
+عليه وسلم؟Okay شو رايكم؟ كيف نزل؟ جديش؟تلاتة
+
+376
+00:32:30,180 --> 00:32:36,720
+وعشرين سنة هو في الرواية عشرين سنة ونيف يعني وشوية
+
+377
+00:32:36,720 --> 00:32:42,040
+طبعا القرآن الكريم والدليل انه كان بينزل في
+
+378
+00:32:42,040 --> 00:32:48,000
+مناسبات وكان بينزل في حوادث وبعالج قضايا لهذا
+
+379
+00:32:48,000 --> 00:32:52,380
+القرآن الكريم كان بينزل طيب هنا في القرآن واحنا
+
+380
+00:32:52,380 --> 00:32:56,660
+بنقف مع القرآن الكريم وجدنا انه في آيات كثيرة
+
+381
+00:32:56,660 --> 00:33:00,690
+تحدثت عن ذو القرآنشوفوا الآيات قالت إن أنزلناك في
+
+382
+00:33:00,690 --> 00:33:05,670
+ليلة مباركة و هناك قول الله تعالى يقول إن أنزلناك
+
+383
+00:33:05,670 --> 00:33:10,490
+في ليلة القدر شهر رمضان الذي أنزل فيه القرآن
+
+384
+00:33:10,490 --> 00:33:15,150
+الكريم طب احنا متحيرين مرة الآية بتقول أنزل في
+
+385
+00:33:15,150 --> 00:33:18,970
+ليلة مباركة و مرة بتقول أن أنزل في ليلة القدر و
+
+386
+00:33:18,970 --> 00:33:24,450
+بعدين بتقول أن أنزل في شهر رمضانكيف نوفق ال scene؟
+
+387
+00:33:24,450 --> 00:33:30,290
+السؤال كيف نوفق بين هذه الآيات الثلاثة؟ فبعطينا
+
+388
+00:33:30,290 --> 00:33:33,670
+المباركة هي غيلة القدر
+
+389
+00:33:38,690 --> 00:33:42,350
+إذا احنا عشان نقول ان هنا لا تعارض موجود هيوجد
+
+390
+00:33:42,350 --> 00:33:45,490
+قدامك لا تعارض بين هذه الآيات التلاتة انتبهي
+
+391
+00:33:45,490 --> 00:33:49,810
+فالقرآن الكريم انت لخص السطر هذا اللي مش موجود
+
+392
+00:33:49,810 --> 00:33:57,310
+عندك في خامش في صفحه ثمانية تحت اكتبي نزل القرآن
+
+393
+00:33:57,310 --> 00:34:01,950
+الكريم ليلة القدر
+
+394
+00:34:06,380 --> 00:34:13,840
+تلك الليلة المباركة من شهر رمضان إذا هو القرآن
+
+395
+00:34:13,840 --> 00:34:22,440
+الكريم نزله ليلة القدري هذه الليلة المباركة في شهر
+
+396
+00:34:22,440 --> 00:34:27,740
+رمضان فمعنى ذلك إن هنا مافيش تعارض إنما يتعارض
+
+397
+00:34:27,740 --> 00:34:31,640
+ذاخر هذه الآيات مع الواقع العملي لأن الواقع العملي
+
+398
+00:34:31,640 --> 00:34:36,770
+إيش بيقولإنه كانت بينزل القرآن في نيف وعشرين سنة
+
+399
+00:34:36,770 --> 00:34:41,730
+ما نزلش في ليلة لا واحدة على الإطلاق وإنما كان
+
+400
+00:34:41,730 --> 00:34:47,430
+هناك تنزلات والرأي الراجع عند ابن عباس وجمهور
+
+401
+00:34:47,430 --> 00:34:52,110
+العلماء أن المراد بنزول القرآن في تلك الآيات
+
+402
+00:34:52,110 --> 00:34:59,610
+الثلاثة نزوله جملة واحدة من وين؟ من السماء إلى بيت
+
+403
+00:34:59,610 --> 00:35:04,100
+الأزةيعني الأيات دولة بتتكلموا عن أن نزول القرآن
+
+404
+00:35:04,100 --> 00:35:11,800
+جملة واحدة طيب معنى ذلك أن هذا القرآن شوفوا الكلام
+
+405
+00:35:11,800 --> 00:35:15,680
+اللي احنا بنتكلم فيه أنه تنزل القرآن .. الدليل على
+
+406
+00:35:15,680 --> 00:35:20,480
+نزول القرآن جملة واحدة من السماء و ثم نزوله مفرقا
+
+407
+00:35:20,480 --> 00:35:25,320
+عند أدلة يعني هو لم ينزل جملة واحدة بس فقط وإنما
+
+408
+00:35:25,320 --> 00:35:31,790
+نزل جملة واحدة ثم بعد ذلك ايش ماله؟نزله مفرقة شوف
+
+409
+00:35:31,790 --> 00:35:36,070
+حديث عباس بيقول أنزل القرآن جملة واحدة إلى سماء
+
+410
+00:35:36,070 --> 00:35:42,970
+الدنيا ليلة القدر ثم أنزل بعد ذلك في عشرين سنة ايه
+
+411
+00:35:42,970 --> 00:35:48,690
+يعني؟ وما يزل ورأي الحديث الثاني فصل القرآن من
+
+412
+00:35:48,690 --> 00:35:54,570
+الذكر فوضع في بيت العزة من سماء الدنيا فجعل جبريل
+
+413
+00:35:54,570 --> 00:36:00,120
+ينزل به إلى النبي شوف الحديث هذاهناك في الحديث
+
+414
+00:36:00,120 --> 00:36:05,360
+الأول ابن عباس كإنه أنا بشعر إنه كام مرة نزل
+
+415
+00:36:05,360 --> 00:36:12,720
+القرآن مرتين يعني مرة نزل جملة واحدة من طلاي إلى
+
+416
+00:36:12,720 --> 00:36:21,180
+سناء الدنيا ليلة القدر إلى سناء الدنيا وبعدين نين
+
+417
+00:36:21,180 --> 00:36:27,630
+نزل مفرقة في عشرين سنوات يزيد الحديث التانيانت
+
+418
+00:36:27,630 --> 00:36:34,410
+بيتمعاني فيه؟ اقرأ الحديث يعني
+
+419
+00:36:34,410 --> 00:36:39,590
+فُصل من الذكر مين الذكر؟ يعني من الله إلى وين؟ إلى
+
+420
+00:36:39,590 --> 00:36:45,610
+بيت العزة يعني نزل من الله إلى بيت العزة جملة
+
+421
+00:36:45,610 --> 00:36:51,610
+واحدة اتنين ثم
+
+422
+00:36:51,610 --> 00:36:57,920
+إلى مين؟ إلى الأرضنفس المعنى أنت متأكدة في هنا
+
+423
+00:36:57,920 --> 00:37:03,020
+إضافة قضية فصيلة القرآن من الذكر وهي لأ مش معناته
+
+424
+00:37:03,020 --> 00:37:06,980
+نزل من الله إلى بيت الأعزاب يعني بعدين وضع في ذكر
+
+425
+00:37:06,980 --> 00:37:10,480
+الله عشان أيك أنا بدي أعطيكي ملخص اللي موجود في
+
+426
+00:37:10,480 --> 00:37:18,300
+القرآن عندك في الكتاب شوفي صفحة صفحة 9والراجح في
+
+427
+00:37:18,300 --> 00:37:24,160
+القرآن الكريم له تنزلان شوفتي في الكتاب إيش مكتوب
+
+428
+00:37:24,160 --> 00:37:29,960
+اكتب هنا إنه له ثلاثة تنزلات في الحاشية تحت في
+
+429
+00:37:29,960 --> 00:37:41,260
+صفحة 9 اكتبي الراجح أن القرآن نزل ثلاث تنزلات
+
+430
+00:37:45,890 --> 00:37:50,650
+أن القرآن نزل من الله لأنه كلام الله اللي هتهب
+
+431
+00:37:50,650 --> 00:37:58,630
+نتكلم عليها من الذكر نزل من الله إلى اللوح المحفوظ
+
+432
+00:37:58,630 --> 00:38:10,610
+على طول ما بتحجز شو دليلنا على ذلك بل هو قرآن مجيد
+
+433
+00:38:10,610 --> 00:38:14,610
+في لوح محفوظ
+
+434
+00:38:17,340 --> 00:38:22,640
+إذا شيء طبيعي أن يكون هو كلام الله المرتبط بذات
+
+435
+00:38:22,640 --> 00:38:28,120
+الله لكن الله هنزله إلى اللوح المحفوظ فجاء جبريل
+
+436
+00:38:28,120 --> 00:38:34,880
+فنزل هذا اسمله معناته جملة واحدة اتنين لما بنتكلم
+
+437
+00:38:34,880 --> 00:38:43,100
+عن الجملة الواحدة نزل من اللوح المحفوظ إلى بيت
+
+438
+00:38:43,100 --> 00:38:43,920
+العزة
+
+439
+00:38:46,230 --> 00:38:55,230
+وطبعا هذا بيت العزة وين؟ في السماء الدنيا في
+
+440
+00:38:55,230 --> 00:39:01,990
+المرة الأولى والثانية ماناته نزلاش جملة واحدة
+
+441
+00:39:01,990 --> 00:39:14,380
+التنزل الثالث نزل من بيت العزة إلىقلب النبي صلى
+
+442
+00:39:14,380 --> 00:39:17,760
+الله عليه وسلم إلى الدنيا يعني معروف يانالوين ينزل
+
+443
+00:39:17,760 --> 00:39:27,440
+على قلب النبي صلى الله عليه وسلم مفرقا او في بعض
+
+444
+00:39:27,440 --> 00:39:34,880
+الروات منجما إذا
+
+445
+00:39:34,880 --> 00:39:41,590
+كم مرة نزل القرآن الكريم؟هذا بدّو بالتأكيد انك انت
+
+446
+00:39:41,590 --> 00:39:48,010
+تروي او انه كام مرة او انا اذكري تنزلات القرآن
+
+447
+00:39:48,010 --> 00:39:53,350
+الكريم إذا نزل بداية من الله تعالى إلى اللوح
+
+448
+00:39:53,350 --> 00:39:58,170
+المحفوظ جملة واحدة ثم أنزله الله من اللوح المحفوظ
+
+449
+00:39:58,170 --> 00:40:02,490
+إلى بيت العزةفي السماية الدنيا جملة بعدين جبريل
+
+450
+00:40:02,490 --> 00:40:07,530
+تنزل به مفرقا على قلب النبي صلى الله عليه وسلم
+
+451
+00:40:07,530 --> 00:40:12,270
+شوفوا هذا هو الرأي الراجح في الموضوع وطبعا لو نحن
+
+452
+00:40:12,270 --> 00:40:16,570
+نرجع في البروغان و الإتقان وغيره من كتب علم القرآن
+
+453
+00:40:16,570 --> 00:40:20,550
+نجد هذا المعنى الرائع فعشانك في الامتحان هنا قضية
+
+454
+00:40:20,550 --> 00:40:23,910
+التمييز بين المحاضرة و مش امتحان الان في تلات
+
+455
+00:40:23,910 --> 00:40:29,610
+تنزلات مش سنتينماشي الحال طيب لما بنقول أن القرآن
+
+456
+00:40:29,610 --> 00:40:39,550
+الكريم نزل منجما ماكي الحكمة من تنجيم القرآن ايش
+
+457
+00:40:39,550 --> 00:40:49,750
+ماله؟ منجما او مفرقا ليش؟ تثييل الحفظ تثييل الحفظ
+
+458
+00:40:49,750 --> 00:40:51,030
+ماشي الحال
+
+459
+00:40:54,000 --> 00:41:03,540
+تثبيت فؤاد النبي صلى الله عليه وسلم مسايرة
+
+460
+00:41:03,540 --> 00:41:08,240
+الحوادث المواقف طيب خلينا نشوف واحد واحد الحكمة
+
+461
+00:41:08,240 --> 00:41:12,240
+الأولى تثبيت فؤاد النبي صلى الله عليه وسلم شو يعني
+
+462
+00:41:12,240 --> 00:41:14,620
+تثبيت فؤاد النبي صلى الله عليه وسلم يعني الرسول
+
+463
+00:41:14,620 --> 00:41:20,320
+صلى الله عليه وسلم كان يتعرض إلى أشياء مواقف لكن
+
+464
+00:41:20,320 --> 00:41:28,500
+قبل ذلك جال واحدتجدد الوحي أن في تجدد الوحي وتكرار
+
+465
+00:41:28,500 --> 00:41:32,820
+نزوله من جانب الحق يعني من الله إلى الرسول طلع
+
+466
+00:41:32,820 --> 00:41:36,820
+يملأ قلب النبي صلى الله عليه وسلم سرورا ويشعر
+
+467
+00:41:36,820 --> 00:41:43,180
+بالعناية الإلهية كيف؟
+
+468
+00:41:43,180 --> 00:41:50,120
+لأ مش موقفعامل كل يوم والتاني نازل الواحد كلام
+
+469
+00:41:50,120 --> 00:41:55,000
+ربنا يعني بيعطي سرور وانبساط وانشراع على ذات النبي
+
+470
+00:41:55,000 --> 00:42:00,780
+اجيبلكم مثال اتصوروا الآن احنا في غزان لو انا الآن
+
+471
+00:42:00,780 --> 00:42:06,400
+الدكتور صبح اليازجي كل يوم خميس الناس شايفين ابو
+
+472
+00:42:06,400 --> 00:42:13,860
+العبد هنية وحشيته جايين عندي في البيت شو لها معنى؟
+
+473
+00:42:13,860 --> 00:42:19,630
+قيمتي انا زلم مهممعناته أنا زلم مهم في المجتمع،
+
+474
+00:42:19,630 --> 00:42:28,630
+جايين رئيس الوزراء والحاشية، يعني جايين على واحد
+
+475
+00:42:28,630 --> 00:42:33,610
+صاحب قيمة اجتماعية، مركز اجتماعي، فانا بصير جيمتي،
+
+476
+00:42:33,610 --> 00:42:38,570
+شوفت الآن ولله المثل الأعلىكل يوم جبريل نازل بكلام
+
+477
+00:42:38,570 --> 00:42:43,950
+الله على محمد يعني ان محمد هذي عناية من الله بشخصي
+
+478
+00:42:43,950 --> 00:42:46,250
+محمد صلى الله عليه وسلم، اذا انا فانتوا تثبيت
+
+479
+00:42:46,250 --> 00:42:50,350
+قلبه، اذا مش بس التثبيت بس السؤال، كمان انا بثبت
+
+480
+00:42:50,350 --> 00:42:55,560
+أركاني في المجتمع، انا زلم صاحبمكانة اجتماعية ايه
+
+481
+00:42:55,560 --> 00:42:59,200
+لمركز مرموق عشان هيك الناس بيصيروا ايه اشمالهم
+
+482
+00:42:59,200 --> 00:43:02,880
+عارفين مكانتي بيحبوني وممكن يتعاملوا معايا
+
+483
+00:43:02,880 --> 00:43:05,880
+وبالتالي بيستعملوا .. بيستعملوا كلام في فرق اليوم
+
+484
+00:43:05,880 --> 00:43:11,090
+حتى في المجتمع انه انا بلو اي واحد يعنيمع احترام و
+
+485
+00:43:11,090 --> 00:43:16,750
+تقدير للمراتب و غيره لو واحد مثلا عامل او في اي
+
+486
+00:43:16,750 --> 00:43:19,470
+مجال سواء في ال .. والله بيشتغل على كارنة ولا
+
+487
+00:43:19,470 --> 00:43:22,790
+بيشتغل زبال ولا بيشتغل طبرج ولا بيشتغل كده و واحد
+
+488
+00:43:22,790 --> 00:43:26,650
+جاعت دكتور او طبيب او مهندس او رجل سياسي تبقى
+
+489
+00:43:26,650 --> 00:43:30,090
+اعلام و جاعت فيه مجتمع بتفكر الناس هيسمعه من مين؟
+
+490
+00:43:30,630 --> 00:43:36,170
+هذه معروفة تلقائيًا فانبالكم إذا كان هذا الشخص
+
+491
+00:43:36,170 --> 00:43:41,950
+مربوط بالله مرتبط بالسماء فكان العناية الإلهية
+
+492
+00:43:41,950 --> 00:43:45,950
+بمين؟ بقضية الرسول صلى الله عليه وسلم اتنين قال أن
+
+493
+00:43:45,950 --> 00:43:50,960
+هذا التنزيل نوع من الإعجازتثبيت للنبي صلى الله
+
+494
+00:43:50,960 --> 00:43:57,640
+عليه وسلم ليه؟ لأن الرسول بتحدى في كل مرة كان يأتي
+
+495
+00:43:57,640 --> 00:44:02,060
+القرآن في هذا التنزيل لشكل و تقوي أذر النبي صلى
+
+496
+00:44:02,060 --> 00:44:06,260
+الله عليه وسلميعني جاز بتأيد الرسول في كثير من
+
+497
+00:44:06,260 --> 00:44:12,100
+القضايا، بعدين أن هذا النزول ضحض شبهات كفار قريش،
+
+498
+00:44:12,100 --> 00:44:16,180
+وردًا على الأسئلة، وتسليا، وتسريا للرسول صلى الله
+
+499
+00:44:16,180 --> 00:44:19,460
+عليه وسلم، وتأييد، لما عملهم بيجوا، وفي كل شيء،
+
+500
+00:44:19,460 --> 00:44:21,220
+وعمل الرسول صلى الله عليه وسلم في كل قضايا
+
+501
+00:44:21,220 --> 00:44:23,400
+المسلمين اللي بيتنزع على القناة، شوفتوا، ثلاث
+
+502
+00:44:23,400 --> 00:44:29,480
+أركان من قضية تثبيت، الآنلو أنا قلتلك في السؤال
+
+503
+00:44:29,480 --> 00:44:36,140
+اذكر الحكمة من تنجيم القرآن في نقاط، بتقولي تثبيت
+
+504
+00:44:36,140 --> 00:44:40,040
+قلب النبي صلى الله عليه وسلم، اتنين الحكمة التدرج
+
+505
+00:44:40,040 --> 00:44:45,260
+في تعليم الأمة، ثلاثة مسيرة الأحداث، أربعة تفضيل
+
+506
+00:44:45,260 --> 00:44:49,660
+القرآن على غيرهم الكتب، طب ما أنا أقولك شرح واحدة
+
+507
+00:44:49,660 --> 00:44:56,210
+منها،أو أحيانًا بادكرلك أنه من الحكمة في تنجيم
+
+508
+00:44:56,210 --> 00:44:59,730
+القرآن الكريم تثبيت قلب النبي صلى الله عليه وسلم
+
+509
+00:44:59,730 --> 00:45:06,230
+بيني ذلكإذا فاهمنا؟ سؤال إجمالي، ممكن تحفظه عناصر،
+
+510
+00:45:06,230 --> 00:45:10,350
+لكن في تفصيلي، أنا بدأ أفصل كيف ثبت الرسول صلى
+
+511
+00:45:10,350 --> 00:45:12,550
+الله عليه و سلم أو الله سبحانه وتعالى قلب النبي
+
+512
+00:45:12,550 --> 00:45:14,890
+صلى الله عليه و سلم، بذكر الثلاثة، إذا الحكمة
+
+513
+00:45:14,890 --> 00:45:18,490
+الأولى تثبيت قلب النبي صلى الله عليه و سلم، الحكمة
+
+514
+00:45:18,490 --> 00:45:25,100
+الثانية، التدرج في تربية الأمةعلمًا وعملًا يعني
+
+515
+00:45:25,100 --> 00:45:30,600
+لما بينزل القرآن الكريم مفرق على الأمة جات بيربيهم
+
+516
+00:45:30,600 --> 00:45:35,080
+اولًا بيربيهم عن طريق حفظ القرآن على الأمة التي
+
+517
+00:45:35,080 --> 00:45:39,520
+سير لما بينزل .. وليه هذا ابن مسعود ايش كان بقول؟
+
+518
+00:45:39,520 --> 00:45:44,200
+كنا لما .. نحفظ ال .. لما تتنزل الآيات نحفظ العشر
+
+519
+00:45:44,200 --> 00:45:49,540
+ثم نعمل بها يعني العشر آيات بتتنزل وبيحفظوها و بعد
+
+520
+00:45:49,540 --> 00:45:52,040
+ما بيحفظوها بيبدوا طبقوها بعدين بيبدوا يحفظوا في
+
+521
+00:45:52,040 --> 00:45:56,610
+الآيات التانيةأحنا اليوم طالبة الجامعة الإسلامية،
+
+522
+00:45:56,610 --> 00:46:03,790
+اوف، الله أكبر القرآن الكريم أسجد في القرآن و بتحط
+
+523
+00:46:03,790 --> 00:46:08,410
+تلات أجزاء وأربع أجزاء و تخليهم للتخرج وصار القرآن
+
+524
+00:46:08,410 --> 00:46:13,810
+الكريم كأنه شيء نكد ونقطة سوداء في تاريخ الطالب في
+
+525
+00:46:13,810 --> 00:46:17,780
+الجامعة الإسلامية أو الطالبة، مشكلةالمفروض انه
+
+526
+00:46:17,780 --> 00:46:22,100
+الانشراح انا يمكن ما ذكرتش لكم شوف ان انا طالب
+
+527
+00:46:22,100 --> 00:46:26,200
+التعليم جاي على الجلسة في فرق اني جاي اخد بس فقط
+
+528
+00:46:26,200 --> 00:46:32,640
+عشان اني اتعلم واخد شهادة وفي فرق اني انا جاي اقعد
+
+529
+00:46:32,640 --> 00:46:39,260
+في حلقة علمانت الآن جاي تتعبدي انت مش جاي تاخد
+
+530
+00:46:39,260 --> 00:46:44,120
+علمه بس جاي للعبادة و طول ما انت قاعد الآن بتستمعي
+
+531
+00:46:44,120 --> 00:46:47,580
+ولك ثواب ولك أجر شوف الرسول صلى الله عليه وسلم
+
+532
+00:46:47,580 --> 00:46:52,320
+بيقول كان في صحب من ال .. او في جمع من الصحابة
+
+533
+00:46:52,320 --> 00:46:57,820
+رضوان الله تعالى عليه فقال
+
+534
+00:46:57,820 --> 00:47:04,660
+لهم ألا يحب أحدكم أن يرتع في رياض الجنة يرتع بيلعب
+
+535
+00:47:04,660 --> 00:47:09,350
+يلهوكلهم قالوا بلى يا رسول الله نحب قال عليكم
+
+536
+00:47:09,350 --> 00:47:15,870
+بحلاق العلم فإنها روضة من رياض الجنة وانت جاي
+
+537
+00:47:15,870 --> 00:47:21,310
+وعندك الانشراح والانبساط انك جاي في جلسة علم ربنا
+
+538
+00:47:21,310 --> 00:47:26,190
+بده يعطيك العلم لكن جاي بس عشان يلا أداء مهمة و
+
+539
+00:47:26,190 --> 00:47:31,090
+تخلصي و تروحيهذا اختلف الشعور لذلك انا بقول لما
+
+540
+00:47:31,090 --> 00:47:33,710
+انتوا تجي مكشرين انا بجي مكشر، تجي مبسطين انا
+
+541
+00:47:33,710 --> 00:47:38,170
+مبسط، واحدة تتثوى بما انا بتثوى في زيها، بتنام،
+
+542
+00:47:38,170 --> 00:47:41,430
+وليه هذا تخدش من الاستاذيشي؟ فالقضية مهمة جدا في
+
+543
+00:47:41,430 --> 00:47:47,050
+ان تجي بصدر منشرح، في القضية في الأمل، اليوم لما
+
+544
+00:47:47,050 --> 00:47:50,770
+انا بدي اتكلم عن القرآن الكريم، يجب ان اقراه في
+
+545
+00:47:50,770 --> 00:47:57,270
+القرآن الكريمولقد يسرنا القرآن للذكري فخالم المذكر
+
+546
+00:47:57,270 --> 00:48:04,190
+يسر القرآن ولهذا لا تعجل بيه لسانك إن علينا حتى
+
+547
+00:48:04,190 --> 00:48:07,050
+الرسول كان برادق اللي قلت لهم تتعجل شوية شوية شوية
+
+548
+00:48:07,050 --> 00:48:10,770
+واحدة واحدة وانت بتحفظ شوفوا الآن احنا في طلبة
+
+549
+00:48:10,770 --> 00:48:16,460
+الجامعة مشكلتنا مافيش عندنا وضع برنامجتروحي تضعي
+
+550
+00:48:16,460 --> 00:48:20,620
+برنامج لقضية حفظ القرآن حتى لتلاوة القرآن من باب
+
+551
+00:48:20,620 --> 00:48:24,420
+التعبد والتقرب إلى الله أولادنا ابني كان في صف
+
+552
+00:48:24,420 --> 00:48:29,900
+السادس وحفظ القرآن في شهر و نص في البداية مش خلص
+
+553
+00:48:29,900 --> 00:48:36,200
+الشهر و نص تقريبا و شوية شهر و شوية مش نص وبالتالي
+
+554
+00:48:36,200 --> 00:48:41,390
+كان بس حافظ 15 جزءفلمّا قاجوا بدهم ينزلوا الإعلان
+
+555
+00:48:41,390 --> 00:48:44,930
+ويقولوا خلاص بدهم يراجعوا للي حفظت القرآن صار بيكي
+
+556
+00:48:44,930 --> 00:48:51,290
+كيف ما حفظش القرآن زي زملاده فأقسم أنه يدخل معهم
+
+557
+00:48:51,290 --> 00:48:55,790
+في المسابقة فكان بيوح على المسجد من صلاة الفجر و
+
+558
+00:48:55,790 --> 00:49:01,930
+بيضلوا للإشارة في المسجد كان بيحفظ في اليوم ستين
+
+559
+00:49:01,930 --> 00:49:07,570
+ورقة يبقى انسان دي ست دائم واتفاجأ بعد انتهاء شهر
+
+560
+00:49:07,570 --> 00:49:12,120
+و نص تمامااللي هو اسمه على القائمة فانا استغربت
+
+561
+00:49:12,120 --> 00:49:15,820
+فكرت انه يعني الجامعة بده يرضوني و انه كده بقولهم
+
+562
+00:49:15,820 --> 00:49:19,040
+انتوا كيف عملته؟ قال ابنت كان بيجي أصلاة الفجر
+
+563
+00:49:19,040 --> 00:49:22,620
+بيظل في المسجد بيحفظ ستين ورقة و لما كان بتضغر بده
+
+564
+00:49:22,620 --> 00:49:26,900
+يجيل في جنب الأمود و كان بيتغدى في المسجد وبالتالي
+
+565
+00:49:26,900 --> 00:49:32,280
+إذا طفل بيحفظ ستين ورقة أين طالبة الجامعة
+
+566
+00:49:32,280 --> 00:49:38,820
+الإسلامية من جزء طول الأربع شهور؟شفتوا؟ اللي ربنا
+
+567
+00:49:38,820 --> 00:49:41,440
+بده يقبل على الله سبحانه وتعالى، ربنا بيقبل عليه
+
+568
+00:49:41,440 --> 00:49:45,480
+القرآن الكريم يا بناتنا زي ما أنت بتحفظي في النشيد
+
+569
+00:49:45,480 --> 00:49:49,760
+و بتجهزي حالك عروس فلانة و بتبقى تحفظي في النشيد و
+
+570
+00:49:49,760 --> 00:49:53,320
+بتجهزي حالك و فسطنب و 6 مليون و غير و غيرته طيب
+
+571
+00:49:53,320 --> 00:49:58,670
+بدلك بتجهزي هذا بس عشان تحظري فرحموجود في الدنيا
+
+572
+00:49:58,670 --> 00:50:04,770
+بتكيشي تجهزي حالك حتى تحظري فرحك انتي وتكريمك امام
+
+573
+00:50:04,770 --> 00:50:08,710
+الملائكة و الخلاق يوم القيامة؟طيب بس على الأقل
+
+574
+00:50:08,710 --> 00:50:12,390
+جهزي حالك بقراية القرآن الكريم، إذا احفظي القرآن،
+
+575
+00:50:12,390 --> 00:50:15,710
+وبالتالي احنا بحاجة لإنه افتحي مسجل دائما في
+
+576
+00:50:15,710 --> 00:50:19,090
+القرآن، قول الجزء اللي انت بتحفظيه وخليه يردد،
+
+577
+00:50:19,090 --> 00:50:21,650
+احنا بنحفظ النشيد والأغاني من جد .. من إيش؟ من
+
+578
+00:50:21,650 --> 00:50:26,230
+التكرار، فاحنا خلينا نسمع القرآن الكريم أولا افتحي
+
+579
+00:50:26,230 --> 00:50:30,230
+شريط القرآن، واسمعي شوفي إيش بتلقى الشيخ، وبالتالي
+
+580
+00:50:30,230 --> 00:50:35,990
+بتتعلمي النطق صحولمّا تحفظه، تقرأه، لو كان القرآن
+
+581
+00:50:35,990 --> 00:50:40,550
+مفتوح بين إيدك، لو كل يوم نص ساعة، تشوف الفائدة،
+
+582
+00:50:40,550 --> 00:50:44,050
+الفائدة النفسية، الارتياح النفسي، التأثير النفسي
+
+583
+00:50:44,050 --> 00:50:48,690
+على القلب من القرآن، ثم كذلك انفتاح الذاكرة، تصير
+
+584
+00:50:48,690 --> 00:50:52,210
+عندك قدرة الذكاء ترد دي، وربنا بيشرح لك صدرك،
+
+585
+00:50:52,210 --> 00:50:55,330
+وبالتالي يهيئلك طريقه، وروح ادرس بعد ذلك باقي
+
+586
+00:50:55,330 --> 00:51:00,700
+المواضيعجربى وشوفى تتندميش بيقول اسأله جرب ولا
+
+587
+00:51:00,700 --> 00:51:04,320
+تسأل الطبيب احنا فينا التجربة ميدان وزي تسهيل
+
+588
+00:51:04,320 --> 00:51:08,660
+الحفظ ثم تسهيل الفخم القرآن الكريم والتمهيد وبعدين
+
+589
+00:51:08,660 --> 00:51:13,100
+نتخيل العقائد شوفوا الآن في قضية التدرج أجيب لكم
+
+590
+00:51:13,100 --> 00:51:18,800
+مثال القرآن الكريم بتدرج في قضية الأحكام زي قضية
+
+591
+00:51:18,800 --> 00:51:23,500
+الخمر أولا ايش كان؟
+
+592
+00:51:26,370 --> 00:51:32,530
+تكرهوش الصيف، بعدين انما
+
+593
+00:51:32,530 --> 00:51:38,610
+الخمر و الميسر و الأنصاب و الأزام رزه فاش تانبه،
+
+594
+00:51:38,610 --> 00:51:44,370
+اذا اولا يعني نفش شويه، ماتيجيش اشرب شويه، بعدين
+
+595
+00:51:44,370 --> 00:51:48,830
+ادر بالك ماتيجيش للصلاة و انت ساكرانوشوفوا لو احنا
+
+596
+00:51:48,830 --> 00:51:54,150
+بدنا نجي نتعامل مع قضية التدرج القرآن الرائع في
+
+597
+00:51:54,150 --> 00:51:59,510
+ذلك لوجدنا شيء ملفت للنظر لما انا بدي اشوف
+
+598
+00:51:59,510 --> 00:52:08,030
+الصلاوات صلاة الصبح او الفجر وصلاة الظهر و العصر و
+
+599
+00:52:08,030 --> 00:52:14,250
+بعدين المغرب و العشاء من
+
+600
+00:52:14,250 --> 00:52:18,650
+صلاة الفجر بدي اصليجدّيش المسافة بينهم بينما أقول
+
+601
+00:52:18,650 --> 00:52:22,490
+يعني أسكر و أجي أصلي الظهر ممكن السكر يأثر فيه لأن
+
+602
+00:52:22,490 --> 00:52:25,870
+أنا حريص الصحابة بيختلفوا عننا الحرسين ييجوا على
+
+603
+00:52:25,870 --> 00:52:31,090
+الصلاة طيب أنا يمكن أقول أن أكثر شيء ممكن يسكر
+
+604
+00:52:31,090 --> 00:52:37,190
+فيها هي هذه الفترة، فترة السكر أو شربلكن بين الظهر
+
+605
+00:52:37,190 --> 00:52:39,150
+و العصر مافيش فترة، بين العصر و المجرم مافيش فترة،
+
+606
+00:52:39,150 --> 00:52:45,550
+بين المجرم مافيش فترة، بين العصر
+
+607
+00:52:45,550 --> 00:52:49,150
+و المجرم مافيش فترة، بين العصر و المجرم مافيش
+
+608
+00:52:49,150 --> 00:52:49,270
+فترة، بين العصر و المجرم مافيش فترة، بين العصر و
+
+609
+00:52:49,270 --> 00:52:49,330
+المجرم مافيش فترة، بين العصر و المجرم مافيش فترة،
+
+610
+00:52:49,330 --> 00:52:49,390
+بين العصر و المجرم مافيش فترة، بين العصر و المجرم
+
+611
+00:52:49,390 --> 00:52:49,450
+مافيش فترة، بين العصر و المجرم مافيش فترة، بين
+
+612
+00:52:49,450 --> 00:52:51,430
+العصر و المجرم مافيش فترة، بين العصر و المجرم
+
+613
+00:52:51,430 --> 00:52:55,290
+مافيش فترة، بين العصر و المجرم مافيش فترة، بين الع
+
+614
+00:52:56,450 --> 00:53:00,950
+يقلل ويخفف من قضية السكر ثم بعد ذلك طب ما هو الآن
+
+615
+00:53:00,950 --> 00:53:05,270
+بده الراجل في الفترة هذه من الفجر للظغر مشكلة إيش؟
+
+616
+00:53:05,270 --> 00:53:10,310
+شغل مشكلة عمل مظبوط إذا انشلناها من الخارطة من
+
+617
+00:53:10,310 --> 00:53:13,250
+اللي بس بذكره اللي فلا اللي غالبيته منه مش ماله
+
+618
+00:53:13,250 --> 00:53:16,990
+اللي مشتغلوش ومن كان العربي اللي كان بيقعد في
+
+619
+00:53:16,990 --> 00:53:21,350
+البيت هذي بيكون إيش مثله؟ مذمة وإغانة كان كل العرب
+
+620
+00:53:21,350 --> 00:53:24,840
+أصلا من فيهم برضه يقعد زي إسلامنا اليوم؟لذن هنا
+
+621
+00:53:24,840 --> 00:53:29,640
+شوفتي الفترة اذا من بعد العشاء و طبعا هو اليوم
+
+622
+00:53:29,640 --> 00:53:32,900
+فيله زوجة و فيله ولاد فيله حقوق فيله و كده فيله
+
+623
+00:53:32,900 --> 00:53:37,160
+مسئوليات فبالتالي خفت القضية و بعد ذلك بعد ما
+
+624
+00:53:37,160 --> 00:53:43,060
+الناس بدوا شوية شوية و لما أنزلت انما الخمر و كده
+
+625
+00:53:43,060 --> 00:53:47,820
+رجت بقول الصحابة انه كأراقوا
+
+626
+00:53:49,450 --> 00:53:55,150
+انية وقدور الخمور حتى أن أحدهم كان يمج ما في ثمنه،
+
+627
+00:53:55,150 --> 00:53:58,390
+كان بيشرب، بيذكر، ما حد ما سمع الكلام، مجه،
+
+628
+00:53:58,390 --> 00:54:03,190
+وبالتالي، إذا هنا قضية الاستجابة، مش الاستجابة،
+
+629
+00:54:03,190 --> 00:54:07,830
+سرعة الاستجابة، شفت الفرق بين الجيل الأول وجيلنا؟
+
+630
+00:54:07,830 --> 00:54:13,190
+احنا اليوم بنسمع آيات وحديث ونماذج كثيرة جدا في
+
+631
+00:54:13,190 --> 00:54:18,060
+قضية المجتمع كل يوم تؤكد إلناإن مثل هذه القضايا
+
+632
+00:54:18,060 --> 00:54:23,220
+جريمة في المجتمع وما يترتب عليها من تدمير لكن الآن
+
+633
+00:54:23,220 --> 00:54:27,400
+علينا أن هذا كله أجه أنه على أساس أنه نقف مع
+
+634
+00:54:27,400 --> 00:54:30,940
+الآيات القرآنية تدرج فعشر آيات بنزل لنتيجة حادثة
+
+635
+00:54:30,940 --> 00:54:36,060
+نحفظها نفهمها نأمل فيها ولهذا لما بنقول طالع مثل
+
+636
+00:54:36,060 --> 00:54:42,560
+الذين حملوا التوراة ثم لم يحملوها كمثل الحمار يحمل
+
+637
+00:54:42,560 --> 00:54:44,660
+أسفره حملوا الأمانة
+
+638
+00:54:48,900 --> 00:55:00,480
+ما هو حمل الأمانة؟ أولاً حفظاً ثانياً فهما و
+
+639
+00:55:00,480 --> 00:55:10,140
+إدراكا ثالثا تطبيقا حملوا
+
+640
+00:55:10,140 --> 00:55:15,290
+أمانة الدينأولا، أنا عشان أحمل الدين، لازم أحفظ
+
+641
+00:55:15,290 --> 00:55:19,550
+تعليم الإسلام، تشريع الإسلام، مفاهيم الإسلام،
+
+642
+00:55:19,550 --> 00:55:24,730
+وبعدين بحفظهم، أنا أحفظهم، وبعدين بفهمهم، بتدبرهم،
+
+643
+00:55:24,730 --> 00:55:28,990
+وبعدين بطبق على أرض الواقع، يعني بمعنى كل هذا، لما
+
+644
+00:55:28,990 --> 00:55:37,990
+أنا بدأ أتكلم عنه، بتكلم يعني بمعنى قولا وعملا فأي
+
+645
+00:55:37,990 --> 00:55:43,180
+أمة لم تحفظ دينها ولم تعملالله أعزكم كالحمار، مكتر
+
+646
+00:55:43,180 --> 00:55:48,140
+الحمير بيطلع اليوم، شوفوا هذا المثال نزل صحيح في
+
+647
+00:55:48,140 --> 00:55:55,560
+بني إسرائيل لأنه كان في علوم القرآن خاص،
+
+648
+00:55:55,560 --> 00:56:01,720
+السبب بعدين بيصير أخد حكم العمومحكم العموم يعني
+
+649
+00:56:01,720 --> 00:56:06,540
+كان هو نزل خاص لمسألة و لحدث معين و خاص ببني
+
+650
+00:56:06,540 --> 00:56:10,600
+إسرائيل لكن أخذ حكم العموم أن بني إسرائيل لم
+
+651
+00:56:10,600 --> 00:56:15,340
+يحملوا التوراة لم يحفظوها و لم يعملوا بها فكانوا
+
+652
+00:56:15,340 --> 00:56:20,540
+جاهزين وهذا ينطبق على كل أمة نزل عليها كتابمن قبل
+
+653
+00:56:20,540 --> 00:56:24,840
+الله، فلم يحفظوا ولم يعملوا به، إذا من هنا بنتكلم
+
+654
+00:56:24,840 --> 00:56:27,920
+عن قضية التدرج في القضية، من هنا بنفهم المفاهيم،
+
+655
+00:56:27,920 --> 00:56:30,720
+صارنا بنفهم قضية العقائد، قضية التشريعات، قضية
+
+656
+00:56:30,720 --> 00:56:34,860
+السلوك، الإعادات الحسنة، وبنتكلم عن قضية تثبيت
+
+657
+00:56:34,860 --> 00:56:38,820
+قلوب المسلمين على الصبر، على الوفاة، على التباد،
+
+658
+00:56:38,820 --> 00:56:42,400
+من هنا بتتعلم الصبر، وانا مش شايف اللي اتعرض له
+
+659
+00:56:42,400 --> 00:56:44,680
+المسلمين والتجارب اللي كانت موجودة في القرآن
+
+660
+00:56:44,680 --> 00:56:47,860
+الكريم، كل هذا بيعطيني، وهو تدرج في قضية الفهم.
+
+661
+00:56:48,170 --> 00:56:52,470
+ثلاثة قصيرة الحوادث قصيرة الحوادث الحوادث كانت
+
+662
+00:56:52,470 --> 00:57:02,070
+أحيانا بتصير مثلا حادثة زي حادثة قد
+
+663
+00:57:02,070 --> 00:57:10,910
+سمع الله قولة التي تجادلك وتشتكي لمنيا خولة بنت
+
+664
+00:57:10,910 --> 00:57:15,890
+ثعلب وزوجة أوس ابن الصمت
+
+665
+00:57:19,230 --> 00:57:23,890
+خولة جاءت إلى النبي صلى الله عليه وسلم بعد أن
+
+666
+00:57:23,890 --> 00:57:31,570
+ظاهرها زوجها معناته الظهار بقولها أنت علي كظهر أمي
+
+667
+00:57:32,980 --> 00:57:36,960
+يعني الراجل بيتمتع مع أمه، انت زي أمي تماما، احنا
+
+668
+00:57:36,960 --> 00:57:40,880
+ماكانش عندهم قضية الطلاق زي اليوم اللي صار، عليا
+
+669
+00:57:40,880 --> 00:57:43,120
+الطلاج، ما تدفع عليا الطلاج، لا تأكل عليا الطلاج،
+
+670
+00:57:43,120 --> 00:57:46,440
+ما تدافع عليا الطلاج، كل شي عليا الطلاج، عليا
+
+671
+00:57:46,440 --> 00:57:49,980
+الطلاج، فأصبحت عند الناس وكأنه الراجل بيصيرش راجل
+
+672
+00:57:49,980 --> 00:57:55,160
+إلا لما يحلف طلاجاتأنا جاء عنكم ضيف و متغدى، علي
+
+673
+00:57:55,160 --> 00:57:58,440
+الطلاج لاتأكل، بقى أنا ماكل، ليش تحلف علي طلاج؟
+
+674
+00:57:58,440 --> 00:58:01,400
+يعني هو ضروري يعني؟ هذا كرام كرام؟ نركب في
+
+675
+00:58:01,400 --> 00:58:05,660
+السيارة؟ يا زلم أنت بتصحيش؟ علي الطلاج ما أنت دافع
+
+676
+00:58:06,530 --> 00:58:11,310
+طب وانت بدك تبهدلني قاعد ولا بدك تكرمني؟ بيصيرش
+
+677
+00:58:11,310 --> 00:58:14,510
+أخواتنا الكلمات احنا في قضية كان في الجغلية عندهم
+
+678
+00:58:14,510 --> 00:58:18,910
+قضية قبل تشرية الطلاق كان عندهم ذهار فأول واحد
+
+679
+00:58:18,910 --> 00:58:22,970
+بدوش مرته بيقول انت عليا زي أمي يعني خلاص ومعناته
+
+680
+00:58:22,970 --> 00:58:26,870
+جالها الكلام يعني بيشيرش لاجمة لام عاشرة حتى
+
+681
+00:58:26,870 --> 00:58:31,780
+حقوقها انتهت لغى ولا ولادهاو احنا مشكلة خطيرة جدا
+
+682
+00:58:31,780 --> 00:58:35,200
+عندما نتكلم عن قضية الجاهلية كمان مانتكلمش عن واحد
+
+683
+00:58:35,200 --> 00:58:37,680
+متجوز واحدة واثنتين وثلاثة عندك انجامة انجامتك
+
+684
+00:58:37,680 --> 00:58:41,640
+عليه عندهم الزواج كان يتزوج عشر وعشرين وتلاتين
+
+685
+00:58:41,640 --> 00:58:44,380
+ومافيش إشكالية حتى بعض العرب لما كانوا بيروح
+
+686
+00:58:44,380 --> 00:58:48,160
+زيارات ضيوف خاصة إذا كان من علياء القوم وكبار
+
+687
+00:58:48,160 --> 00:58:52,730
+القوم بيدولوا أجمل بنت عندهم في القبيلةوهذه قضية
+
+688
+00:58:52,730 --> 00:58:57,290
+بيخذها يبتمتع إذا زوجته صارت إذا بدوش يجيها مش مش
+
+689
+00:58:57,290 --> 00:59:01,070
+مشكلة وحتى لو روح بتظلها مربوطة على اسمه يعني هذه
+
+690
+00:59:01,070 --> 00:59:04,990
+زوجته طب يمكن مادخلش بيها يمكن مانجبتش ومارجعش لها
+
+691
+00:59:04,990 --> 00:59:07,330
+خلاص لكن هذه مارت فلانه خلاص وبتظلها مارت فلانه
+
+692
+00:59:07,330 --> 00:59:12,630
+ظلهاقضية الإغانة للمرأة يا بنات العصر اليوم اللي
+
+693
+00:59:12,630 --> 00:59:17,830
+كلكم والله احنا أنا بيجي .. يمكن تلاقي 36 ولا 37
+
+694
+00:59:17,830 --> 00:59:22,190
+جمعية نساوية في قطاع غزة غالبية الجمعية القائمة
+
+695
+00:59:22,190 --> 00:59:26,170
+عليها بنات متفلتات من منهج الإسلام ويدعو يعني إلى
+
+696
+00:59:26,170 --> 00:59:30,150
+قضية الصفور وكذا وكذا وكذا ولانخاطر يجوم المظاهرات
+
+697
+00:59:30,150 --> 00:59:33,350
+يعني احتجاج علينا يمكن انتوا لو انا بقول بس في
+
+698
+00:59:33,350 --> 00:59:37,900
+نقطةلو أن المرأة المسلمة عرفت حقوقها في الإسلام
+
+699
+00:59:37,900 --> 00:59:42,040
+كان لابد أنه احنا للرجال نطلع مظاهرات نطلب حقوقنا
+
+700
+00:59:42,040 --> 00:59:45,720
+من النسوان، عارفين ليش؟ لأن أنتوا أعطاكم الإسلام
+
+701
+00:59:45,720 --> 00:59:51,600
+كل شيء، يكفي أن الإسلام أنقذك من الموتالمرأة كانت
+
+702
+00:59:51,600 --> 00:59:56,260
+توأد المرأة كانت على الأقل متاع عارفين لما يكون
+
+703
+00:59:56,260 --> 00:59:59,240
+واحد من الزوج يتصور لما أقولكم عشر أو خمس عشر ومات
+
+704
+00:59:59,240 --> 01:00:03,620
+الأب ولاد كل زوجة الإخوة من الزوجات المختلفة كل
+
+705
+01:00:03,620 --> 01:00:09,660
+منهم يتسابق على زوجة أبيه أيهم وصل إليها الولد
+
+706
+01:00:09,660 --> 01:00:16,880
+الكبير ووضع عباءته عليها أصبحت ملكا له إن شاء
+
+707
+01:00:16,880 --> 01:00:23,410
+تزوجهاوان شاء أخدمها صارت خادمة وان شاء باعها
+
+708
+01:00:23,410 --> 01:00:27,700
+كالرقيق في السوق شفتوا المرأة إيش كانت؟وانتوا
+
+709
+01:00:27,700 --> 01:00:31,980
+اليوم مشايباتنا طب يا بنات كي عرفوا اسلامكم عشان
+
+710
+01:00:31,980 --> 01:00:36,120
+تعرفوا قضية الاعتزاز احنا بينهم بنت أصول الدين
+
+711
+01:00:36,120 --> 01:00:39,940
+وبنت الشريعة لسه عملتلي على رصة .. بسمي شرط
+
+712
+01:00:39,940 --> 01:00:43,580
+المنديل هذا الصغير حط مانديل بطريقة مش .. و بعدين
+
+713
+01:00:43,580 --> 01:00:46,120
+الدجال بتجيب المنديل بيقصوا في رصة .. بيقصوا في
+
+714
+01:00:46,120 --> 01:00:49,620
+رصة ليش؟ في الآخر عشان أشوف رصة زي الجدوس، رصة
+
+715
+01:00:49,620 --> 01:00:54,160
+اندحبر، هي كده؟يا أخواتنا الكريمات والله إذا بدنا
+
+716
+01:00:54,160 --> 01:00:58,680
+مرضاة الله الطريق موضوع و يكفي إنك انت مفخرة بيننا
+
+717
+01:00:58,680 --> 01:01:02,720
+انت ع فكرة المرأة اللي نشوف بميزها لبسها هو هذا
+
+718
+01:01:02,720 --> 01:01:07,240
+دليل الشرف دليل رفعة المكانة هذه المرأة اللي ..
+
+719
+01:01:07,240 --> 01:01:10,720
+اللي إلها مكانة في القلب و في العقل حقيقة مش قضية
+
+720
+01:01:10,720 --> 01:01:13,680
+أن اليوم نبحث و الله تبحثلي بنتي عن جوال قعدتي
+
+721
+01:01:13,680 --> 01:01:17,380
+تبحثلي عن قضية والله شرب بس موظة إيش صارت الموظة
+
+722
+01:01:17,380 --> 01:01:20,580
+النازلة ان شاء الله هالجد و تحطه و بعدينكمان
+
+723
+01:01:20,580 --> 01:01:23,400
+الجلبة بهذا السيجارة اللى بتلبسوه اللى بتسموه
+
+724
+01:01:23,400 --> 01:01:27,240
+العباية ده المصيبة والجريمة الكبرى اللى جادة بيوصف
+
+725
+01:01:27,240 --> 01:01:31,100
+قضية المرأة هذا مش شيء مصيبة جدا احنا بنفهم ديننا
+
+726
+01:01:31,100 --> 01:01:34,560
+مصيرة حوادث هذه المرأة حلف عليها جوزا انت عليك ظهر
+
+727
+01:01:34,560 --> 01:01:39,160
+أمي وبعد فترة جاي بدوياها وراحت تجري للرسول صلاة
+
+728
+01:01:39,160 --> 01:01:43,740
+وتشتكر فاقبرته القصة ماقدرش ردها فراحت بعد ذلك
+
+729
+01:01:43,740 --> 01:01:49,860
+أرسلهالها فجأت ليش لأنه نزل قول الله سبحانه وتعالى
+
+730
+01:01:49,860 --> 01:01:53,460
+ايه اللي هو قد سمع الله قولة التي تجادل فحل
+
+731
+01:01:53,460 --> 01:01:58,680
+الإشكالية فكان إطعام أولا كان له إيش معلوم؟تحليل
+
+732
+01:01:58,680 --> 01:02:04,660
+رقمها قالت له انا انا في انا عبيده مافيش انا قالش
+
+733
+01:02:04,660 --> 01:02:11,080
+بعدها صيام لسه صيام ستين يوم متتالي شهرين متتالية
+
+734
+01:02:11,080 --> 01:02:17,020
+جوزها أوس بن الصامت كان رجل كبير السن بقدرش يصوم
+
+735
+01:02:17,020 --> 01:02:21,870
+قالتله شيخ كبير جاله طعام ستين مسكينقالتله يا رسول
+
+736
+01:02:21,870 --> 01:02:27,090
+الله احنا فقراء واش احد احنا عندنا فجاء اليها قيل
+
+737
+01:02:27,090 --> 01:02:33,190
+بقف التمر يعني وقال تصدقي بهم على فقراء المسلمين
+
+738
+01:02:33,190 --> 01:02:38,550
+قالت يا رسول الله والله ما بين لبوتيها يعني جبلي
+
+739
+01:02:38,550 --> 01:02:44,050
+المدينة ما بين لبوتيها في كل المدينة ما هناك أحوج
+
+740
+01:02:44,050 --> 01:02:49,090
+مننا اليها قال خديها وكلها انت و جوزكشوفته قضية ..
+
+741
+01:02:49,090 --> 01:02:53,690
+نتكلم عن سماحة الإسلام نتكلم كيف أنه حتى .. احنا
+
+742
+01:02:53,690 --> 01:02:56,310
+المشكلة اليوم بيجي واحد بده يفتي للشيخ على طول
+
+743
+01:02:56,310 --> 01:02:59,890
+بيفتيله و خلصناه اخي بدك تفتي .. شوف أحوال الناس
+
+744
+01:02:59,890 --> 01:03:02,070
+.. إيش اللي عند الناس .. وبعدين بنقلع .. بتقرر ..
+
+745
+01:03:02,070 --> 01:03:04,830
+بتقرر .. وبعدين بتيجي واحد .. بتجيني .. بترجع على
+
+746
+01:03:04,830 --> 01:03:08,970
+المكتب .. بتقولي يا دكتور أنا جايك في إيه لصاحبة و
+
+747
+01:03:08,970 --> 01:03:11,610
+كده .. صاحبة ليه الصاحبة يا بني .. تقولي أنا .. طب
+
+748
+01:03:11,610 --> 01:03:13,670
+و أنت أنا إيش بدي أعرف إنه كده .. و حتى و خاصة
+
+749
+01:03:13,670 --> 01:03:16,950
+بالذات في قضية الطلاقمو بدك تسمعي قضية اللفظ اللي
+
+750
+01:03:16,950 --> 01:03:20,350
+صار، همتيجي تقولي لو الله طلقتها، طب ايش قولتي؟ و
+
+751
+01:03:20,350 --> 01:03:23,820
+ايش قالك جوزي؟و تقولي صاحبتها، مدهش تقول عشان أنا
+
+752
+01:03:23,820 --> 01:03:27,060
+مدهش، خجلانة شوفوا لآن مافيش قضية في الدين، مافيش
+
+753
+01:03:27,060 --> 01:03:30,080
+حرج ولا حياء في الدين إذا أنا بقصد إنه قضية لابد
+
+754
+01:03:30,080 --> 01:03:33,840
+أن نفهم .. شوفوا قضية اليونة، قضية ال .. ال .. ال
+
+755
+01:03:33,840 --> 01:03:36,400
+.. الين في قضية ال .. ال .. والمرونة في قضية
+
+756
+01:03:36,400 --> 01:03:39,640
+التعامل مع نخل هو بالأساس كان عليه جريمة، هو ارتكب
+
+757
+01:03:39,640 --> 01:03:43,240
+جريمة ويجب أن يعاقب لأنه في كفارات، وشوفوا في
+
+758
+01:03:43,240 --> 01:03:46,810
+النهاية طلع مش قادر يؤدي ولا كفارةو بعدين ايش
+
+759
+01:03:46,810 --> 01:03:51,710
+بيسوي؟ اتصور لو ان واحد أجاني و عمره سبعين سنة و
+
+760
+01:03:51,710 --> 01:03:55,090
+لا ثمانين سنة و بيقولي والله انا الآن و انا والله
+
+761
+01:03:55,090 --> 01:03:59,810
+اتطلعت و لا سمعت دارس و انا والله بجيت زمان جتلت
+
+762
+01:03:59,810 --> 01:04:03,870
+واحد او قلت على مرتي انت زي أختي و زي أمي طب ايش
+
+763
+01:04:03,870 --> 01:04:06,910
+هسوي؟ هقول له انا لازم تقرأ قبعة طبعا مافيش ..
+
+764
+01:04:06,910 --> 01:04:11,300
+اتسوقهو جادرسهم سنة ما خمس وسبعين سنة ولا غير غير
+
+765
+01:04:11,300 --> 01:04:11,760
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+766
+01:04:11,760 --> 01:04:13,700
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+767
+01:04:13,700 --> 01:04:14,320
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+768
+01:04:14,320 --> 01:04:15,040
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+769
+01:04:15,040 --> 01:04:16,580
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+770
+01:04:16,580 --> 01:04:17,320
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+771
+01:04:17,320 --> 01:04:21,020
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+772
+01:04:21,020 --> 01:04:22,740
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+773
+01:04:22,740 --> 01:04:32,500
+غير غير
+
+774
+01:04:32,500 --> 01:04:38,600
+غيركل الآيات القرآنية التي جاءت في القرآن الكريم
+
+775
+01:04:38,600 --> 01:04:47,040
+فيها السؤال يسألونك عن الأنفال قل الأنفال يعني
+
+776
+01:04:47,040 --> 01:04:50,880
+بمعنى أن الله تعالى يلقن النبي صلى الله عليه و سلم
+
+777
+01:04:50,880 --> 01:04:55,680
+الإجابة قل يا محمد يسألونك عن الأنفال قل الأنفال
+
+778
+01:04:55,680 --> 01:05:01,760
+يسألونك عن الأهلة قل هي موقيت يسألونك عن إيه؟
+
+779
+01:05:02,780 --> 01:05:08,120
+يسألونك عن الساعة، قول here، من أمرا، الآن في قضية
+
+780
+01:05:08,120 --> 01:05:12,220
+يسألونك عن العفو، قول اللي عفو، الآن إذا في قضايا
+
+781
+01:05:12,220 --> 01:05:21,170
+قول و قول إلا في موطن واحدوإذا سألك عبادي عني فإني
+
+782
+01:05:21,170 --> 01:05:29,650
+قريب أجيب دعوة الداعي لماذا غنسين سؤال لماذا لم
+
+783
+01:05:29,650 --> 01:05:37,610
+يأتي هنا صياغ القرآن بكلمة قل قل يا محمد إني قريب
+
+784
+01:05:37,610 --> 01:05:40,130
+أجيب دعوة الداعي ليه؟ فضل
+
+785
+01:05:44,660 --> 01:05:47,240
+إيش يعني معناته القرب اللي اللي اللي اللي اللي
+
+786
+01:05:47,240 --> 01:05:48,840
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+787
+01:05:48,840 --> 01:05:48,920
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+788
+01:05:48,920 --> 01:05:50,280
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+789
+01:05:50,280 --> 01:05:54,000
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+790
+01:05:54,000 --> 01:05:54,060
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+791
+01:05:54,060 --> 01:05:54,860
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+792
+01:05:54,860 --> 01:05:54,920
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+793
+01:05:54,920 --> 01:06:12,540
+اللي
+
+794
+01:06:12,540 --> 01:06:24,310
+الليسك الغفران تنين كرسي الاعتراف يا
+
+795
+01:06:24,310 --> 01:06:29,550
+سلام واحد عامل البلاوي وبيجي للقسيس في الكنيسة
+
+796
+01:06:29,550 --> 01:06:35,250
+وبجد على كرسي الاعتراف ويبدأ يعدد في الجرائم اللي
+
+797
+01:06:35,250 --> 01:06:40,370
+ارتكبها وبعدين بيطيسك غفران وانتهى احنا هذه جريمة
+
+798
+01:06:40,370 --> 01:06:46,120
+كبرى مش موجودة هنااحنا بدنا ندخّل إذا الإنسان
+
+799
+01:06:46,120 --> 01:06:51,320
+ارتكب كل جرائم الأرض، من قتل، من زنا، من خمر، من،
+
+800
+01:06:51,320 --> 01:06:55,340
+من، من، إلى آخره، مسبنه بين ربه، يا رب تبت إليك
+
+801
+01:06:55,340 --> 01:06:59,740
+وبرفع أكف و أكف الدرع إلى الله، أبواب السماء تفتح.
+
+802
+01:07:00,350 --> 01:07:07,550
+لا واسطة بين العبد وبين ربه عند توبته لا بقول بحق
+
+803
+01:07:07,550 --> 01:07:12,130
+الأنبياء ولا بحق الصالحين لا بده واسط نبي ولا غيره
+
+804
+01:07:12,130 --> 01:07:18,230
+مافيش يقول هنا لكن عنده الهناك لا وليه ده مشكلة
+
+805
+01:07:18,230 --> 01:07:21,750
+خطيرة جدا اجيبلكم النقطة عشان ندخل الموضوع تاني
+
+806
+01:07:21,750 --> 01:07:28,300
+قلوا واحد زمان كان اللي هو اللي القساوسة أغنىالغرب
+
+807
+01:07:28,300 --> 01:07:35,620
+اغنى رجالات الدولة ليه؟ لأن الامبراطور والقياسرة
+
+808
+01:07:35,620 --> 01:07:39,580
+بيرضوا بدون يرضوا مين؟ القسيس بدون يرضوا البابا
+
+809
+01:07:39,580 --> 01:07:44,120
+فاحيانا بيعطوهم قطع أرض بألف الدولمات والهكترات
+
+810
+01:07:44,120 --> 01:07:47,400
+وبيعطوهم من الأموال الكتيرة فانصروا أصحاب رؤوس
+
+811
+01:07:47,400 --> 01:07:50,380
+الأموال كمان انا رايح اخصتك خفران وانا بدأ ادفع
+
+812
+01:07:50,380 --> 01:07:55,990
+مالفدائما شو سك الغفران معناته انت رايع الجنة فأجى
+
+813
+01:07:55,990 --> 01:08:00,550
+واحد من الأباطرة والقياصرة من أغنى الأغنية في ذلك
+
+814
+01:08:00,550 --> 01:08:06,850
+العصر ودخل على القسيس عشان يترى بس جاله شو جاله
+
+815
+01:08:06,850 --> 01:08:12,030
+انا بدي اشتري منك انارة بديش اشتري انا سك غفران
+
+816
+01:08:12,030 --> 01:08:15,670
+بدخل الجنة انا بديش الجنة جاله ايش بتقول جاله زي
+
+817
+01:08:15,670 --> 01:08:19,890
+ما بقولها جاله مقابل ايش جاله بكتب لك كل املاكي
+
+818
+01:08:22,530 --> 01:08:27,230
+عطسك بالنار و طلع اشجال قال يا قوم افعلوا ما شئتم
+
+819
+01:08:27,230 --> 01:08:31,670
+لقد اشتريت النار ماحدش هيروح النار فهذه مهازل لو
+
+820
+01:08:31,670 --> 01:08:35,010
+احنا بننقصها بالمفهوم الحقيقي مصيبة ان احنا نملك
+
+821
+01:08:35,010 --> 01:08:39,930
+نبي ولا اي واحد من المخلوقات حتى لو كان من
+
+822
+01:08:39,930 --> 01:08:43,450
+الملائكة حتى لو كان من الأنبياء هل يملك ان يدخل
+
+823
+01:08:43,450 --> 01:08:48,880
+فلان او يمنع فلان من دخول الجنة؟مستحيل، إذا هذه
+
+824
+01:08:48,880 --> 01:08:55,200
+قضايا التوبة أمر، ولهذا الله سبحانه وتعالى إنك لا
+
+825
+01:08:55,200 --> 01:09:00,660
+تهدي من أحببته، لكن الله هو جمال الرسول كان عنده
+
+826
+01:09:00,660 --> 01:09:05,580
+حرص على أنه عمه أبو طالب أنه يشمله، أنه يموت على
+
+827
+01:09:05,580 --> 01:09:08,720
+الإسلام، وبالتالي يعني الهداية مش منك، حتى لو كنت
+
+828
+01:09:08,720 --> 01:09:15,640
+نبي، أنت داعيةأنت مبلغ، أنت رسول، بتوصل، بس فقط،
+
+829
+01:09:15,640 --> 01:09:18,300
+وإنما الهداية من مين؟ من رب العالمين، إذا انت
+
+830
+01:09:18,300 --> 01:09:21,900
+فاهمتوا الحوادث والأسئلة، وليهذا يسألونك عن الروح،
+
+831
+01:09:21,900 --> 01:09:28,700
+اليهود لما في المدينة أجوهم أهل مكة، أهل مكة يعني
+
+832
+01:09:28,700 --> 01:09:33,490
+كيف احنا بدنا نقدر على محمد؟ مش قادرينفرحوا لأهل
+
+833
+01:09:33,490 --> 01:09:36,690
+اليهود في المدينة جالهم أنتوا أهل كتاب زيكم زي
+
+834
+01:09:36,690 --> 01:09:40,750
+محمد إيش إحنا بدنا نسأل محمد عشان نعجزه؟ قالوا
+
+835
+01:09:40,750 --> 01:09:44,570
+أنتوا سألونا عن ثلاث أمور سألونك عن الروح بعدين
+
+836
+01:09:44,570 --> 01:09:49,850
+قصة أصحاب الكهف و بقوا يسألوا فقالوا لهم إذا أنتوا
+
+837
+01:09:49,850 --> 01:09:52,070
+جوابكم محمد صلى الله عليه وسلم عن هذا الموضوع
+
+838
+01:09:52,070 --> 01:09:57,530
+معناته نبي صحيح وإذا ما جاوبكمش معناته كذبوبالتالي
+
+839
+01:09:57,530 --> 01:10:00,230
+سألوا بتعرفوا قصة أصحاب الكهف من وين للرسول صلى
+
+840
+01:10:00,230 --> 01:10:04,370
+الله عليه وسلم الرجل الأمي والذي لم يطلع على
+
+841
+01:10:04,370 --> 01:10:10,010
+التاريخ كيف عرف ما حصل في زمن أصحاب الكهف؟
+
+842
+01:10:10,010 --> 01:10:12,670
+وبالتالي هنا يسألونك أروح كله؟ أروح من أمر ربي،
+
+843
+01:10:12,670 --> 01:10:16,650
+لذا شفت هنا قضية الأسئلة فكانت تثبيت هي حقيقة لكن
+
+844
+01:10:16,650 --> 01:10:19,350
+مسايرة للحوادث أن الرسول صلى الله عليه وسلم في كل
+
+845
+01:10:19,350 --> 01:10:23,280
+شيء لو عجزة من الإجابةلا كانت هناك مشكلة اذا هنا
+
+846
+01:10:23,280 --> 01:10:30,900
+اثنين طلع هنا قال مجرال الأقضية والواقع والحوادث
+
+847
+01:10:30,900 --> 01:10:35,420
+واحنا لان مقول ان الذين جاءوا بالإفك عصبة منكم لا
+
+848
+01:10:35,420 --> 01:10:39,380
+تحسبوا شرا لكم شوفوا قضية القرآن الكريم جاء يعالج
+
+849
+01:10:39,380 --> 01:10:46,120
+لقضية معينة زوجة النبي القيادة العليا النبي الموحى
+
+850
+01:10:46,120 --> 01:10:51,150
+اليهتتخن في عرضها يا سلام هم اليوم مش قادرين
+
+851
+01:10:51,150 --> 01:10:55,370
+يعيبوا على الإسلام لكن قيادات المسلمين المشايخ
+
+852
+01:10:55,370 --> 01:11:00,250
+والعلماء عملوا سووا الإشعة يعني اليوم أرادوا أن
+
+853
+01:11:00,250 --> 01:11:04,290
+يحاربوا الإسلام في قضية الإشعة وهنا الشيعة على
+
+854
+01:11:04,290 --> 01:11:11,340
+عائشة شوفوا مش يروحوش لمن؟ لأكبر شخصيتينالنبي أو
+
+855
+01:11:11,340 --> 01:11:15,960
+يمكن أقول وزيره أبو بكر الشخصية الثانية في الإسلام
+
+856
+01:11:15,960 --> 01:11:19,660
+لأنه عاش بنت أبي بكر وزوجة النبي وعصابه أصفرين
+
+857
+01:11:19,660 --> 01:11:24,480
+بحجر واتغموها في أرضها ولكن كيف جاء القرآن ليؤالج
+
+858
+01:11:24,480 --> 01:11:28,660
+هذه الواقع أولا جاء عارفين إيش يسوي؟ أنا مابديش
+
+859
+01:11:28,660 --> 01:11:36,880
+أقول يلجم نساء نساء نسوة ونساء
+
+860
+01:11:36,880 --> 01:11:45,950
+ونسوانهذا الجامعه عشان هيك يقطع لسانة النسوان لأن
+
+861
+01:11:45,950 --> 01:11:52,050
+الجريمة من الذي حمل كبر للموضوع حاملة بنت جحش
+
+862
+01:11:52,050 --> 01:11:58,910
+أختيناخد زينب زوجة النبي فهي ما سدقت تسمع احنا زي
+
+863
+01:11:58,910 --> 01:12:03,170
+ما بيقولوا عن ذرة أختها كلمة واخدتها الكلام وطارت
+
+864
+01:12:03,170 --> 01:12:08,230
+فيه وخدت تروج مع أنها صحابية جليلة و هي زوجة جعفر
+
+865
+01:12:08,230 --> 01:12:12,090
+ابن أبي طالبوشوفت أختها؟ وكل إن أختها عبدالله
+
+866
+01:12:12,090 --> 01:12:15,890
+بنجحش لكن الآن هذه الصحابي الجليلة أقدت الدعاية
+
+867
+01:12:15,890 --> 01:12:19,350
+وطارت فيها واحنا اليوم يا سلام نتكلم في أعراض
+
+868
+01:12:19,350 --> 01:12:23,790
+المسلمين وقائع حوادث كانت بتنزل القرآن يعالج حيث
+
+869
+01:12:23,790 --> 01:12:28,150
+كيف يهذب النفس شفت القرآن لإيش أجا؟ عشان يهذب
+
+870
+01:12:28,150 --> 01:12:32,050
+نفسنا عشان الآن يخللنا القضايا ووقائع في مجتمع
+
+871
+01:12:32,050 --> 01:12:36,910
+احنا مش في عالم الملائكة احنا في عالم البشر عالم
+
+872
+01:12:36,910 --> 01:12:42,760
+الشر عالم الجريمةوعالم الإرتقاء الروحي يعني بمعنى
+
+873
+01:12:42,760 --> 01:12:47,120
+إن النافسية البشرية تشمل كل هذه القضايا كذلك نزل
+
+874
+01:12:47,120 --> 01:12:51,380
+من القرآن الكريم ما يلفت انتباه وأنظار المسلمين
+
+875
+01:12:51,380 --> 01:12:58,680
+ويوم حُنين إذ أعجبتكم كثرتكم جايين مغرورين أول مرة
+
+876
+01:12:58,680 --> 01:13:05,360
+وأول حادثة وأول غزوة يجتمع فيها أكبر عدد من
+
+877
+01:13:05,360 --> 01:13:10,510
+المسلمينفي كل المواقع، في كل الغزوات، في كل
+
+878
+01:13:10,510 --> 01:13:16,830
+الحروب، ما كان المسلمون يوما أثر عدد وعدةوكانوا
+
+879
+01:13:16,830 --> 01:13:22,230
+بحقق انتصار إلا في المرة هذه كان عدد المسلمين أقوى
+
+880
+01:13:22,230 --> 01:13:29,750
+فغتروا بكثرتهم وظنوا أن الكثرة ستغنيهم من الله
+
+881
+01:13:29,750 --> 01:13:35,590
+تعالى ولكن ضاقت عليهم الأرض بما راحبت والآن
+
+882
+01:13:35,590 --> 01:13:41,280
+الأعداءأحاطهم من كل الجوانب، ولولا أن الرسول صلى
+
+883
+01:13:41,280 --> 01:13:46,920
+الله عليه وسلم وقف كالجبل وكالطوض الأشم ينادي يا
+
+884
+01:13:46,920 --> 01:13:51,240
+أهل الصمرة أنا النبي، لا كذب، أنا ابن عبد المطلب،
+
+885
+01:13:51,240 --> 01:13:55,900
+حتى جاء إليه الصحابة، فتحولت الهزيمة إلى نصر. إذا
+
+886
+01:13:55,900 --> 01:14:00,620
+شفتوا، يعالج قضايا، جاء القرآن الكريم بيعطيني شيء
+
+887
+01:14:00,620 --> 01:14:05,580
+ومدلول واضح بإنه يلفط أنظار المسلمين إلى تقويم
+
+888
+01:14:05,580 --> 01:14:09,520
+المسار.شوفت القرآن؟ اذا من هنا بناخد الحكمة
+
+889
+01:14:09,520 --> 01:14:16,000
+الثانية الحكمة الرابعة وهي تفضيل القرآن على غيره
+
+890
+01:14:16,000 --> 01:14:21,140
+من الكتب تفضيل القرآن الكريم على غيره من الكتب
+
+891
+01:14:21,140 --> 01:14:28,120
+كيف؟ قال القرآن الكريم فضل غيرك انتبهي جميع الكتب
+
+892
+01:14:28,120 --> 01:14:38,760
+السماوية التي تنزلت على الرسل شو كانت؟جملة واحدة
+
+893
+01:14:38,760 --> 01:14:45,500
+لأنها عبارة عن مواعد وتشريعات بسيطة تلاحظون القرآن
+
+894
+01:14:45,500 --> 01:14:51,500
+الكتب السماوية كانت تنزل على قوميعني وطنية قومية
+
+895
+01:14:51,500 --> 01:14:57,220
+كلهم شعيب ووهود ونوح وغيرهم من الأنبياء والرسل
+
+896
+01:14:57,220 --> 01:15:01,620
+عليه السلام جاءوا لأقوامهم يعني الدعوة محدودة
+
+897
+01:15:01,620 --> 01:15:08,400
+الدعوة وطنية قومية لقومهم ولوطنهم بس فقط إلا رسالة
+
+898
+01:15:08,400 --> 01:15:16,020
+محمد عالميةمش محلية، عالمية للعالمين، للإنس والجن
+
+899
+01:15:16,020 --> 01:15:23,920
+كذلك ولهذا القرآن الكريم جاء جملة واحدة وتميز عن
+
+900
+01:15:23,920 --> 01:15:33,320
+غيره بإيش؟ بأنه نزل مفرقا إذا تفضيل القرآن على
+
+901
+01:15:33,320 --> 01:15:39,100
+غيره بإيش؟ أطول بنزوله مفرقا
+
+902
+01:15:41,960 --> 01:15:49,000
+وبذلك شارك الكتب السماوية في الأولى وانفرض وانفصل
+
+903
+01:15:49,000 --> 01:15:59,600
+في الفضل بالثانية Scene اكتبيه في صفحه 11 تشترك
+
+904
+01:15:59,600 --> 01:16:04,220
+الكتب السماوية مع
+
+905
+01:16:04,220 --> 01:16:05,980
+القرآن الكريم
+
+906
+01:16:08,770 --> 01:16:18,250
+في النزولي جملة واحدة صح ولا غلط؟ يعني انتبهي في
+
+907
+01:16:18,250 --> 01:16:22,570
+الأسئلة انا حاطتك نموذج بس ممكن تجيكي الثانية انه
+
+908
+01:16:22,570 --> 01:16:31,550
+اشترك القرآن الكريم مع الكتب السماوية في وين؟
+
+909
+01:16:31,550 --> 01:16:37,910
+طيب انت قولتي اللي شفت الآن؟تبعتى؟ وين الـ .. ممكن
+
+910
+01:16:37,910 --> 01:16:43,270
+أقولك إنه اشترك معاه في نزوله مفرقا، هتكون الرواي
+
+911
+01:16:43,270 --> 01:16:46,830
+خطأ، إذا اشتركوا في وين؟ في قضية في الجملة واحدة،
+
+912
+01:16:46,830 --> 01:16:51,710
+ومن هنا جاء التفضيل وجاءت الحكمة إنه تفضيل القرآن
+
+913
+01:16:51,710 --> 01:16:55,430
+الكريم، بيان مكانة القرآن، يعني نزوله مفرقا عشان
+
+914
+01:16:55,430 --> 01:17:01,010
+بيانه، لأنه ولا كتاب، شوف أصبح له ميزةتميز عن
+
+915
+01:17:01,010 --> 01:17:05,170
+غيره، مافيش إلا هو الكتاب الوحيد، وبالتالي إذا هنا
+
+916
+01:17:05,170 --> 01:17:09,930
+زاد عليه وهذا تفخيم لشأن هذه الأمة، أمة محمد صلى
+
+917
+01:17:09,930 --> 01:17:15,340
+الله عليه وسلم التي أنزل عليها القرآن الكريمطبعا
+
+918
+01:17:15,340 --> 01:17:21,600
+إلى يعني هنا ننتقل من المبحث الأول والثاني وهو
+
+919
+01:17:21,600 --> 01:17:26,820
+قضية أولا تحدثنا عن معنى القرآن وتعريف القرآن
+
+920
+01:17:26,820 --> 01:17:30,960
+الكريم ثم تناولنا في المبحث الثاني تنزلات القرآن
+
+921
+01:17:30,960 --> 01:17:35,570
+الكريم والحكمة من تنزيل القرآن الكريممفرقا تميز عن
+
+922
+01:17:35,570 --> 01:17:39,590
+غيري من الكتب لأن العامل المشترك بين الكتب السماوي
+
+923
+01:17:39,590 --> 01:17:43,710
+أنها نزلت جملة واحدة لكن تميز عنها القرآن الكريم
+
+924
+01:17:43,710 --> 01:17:47,910
+نكتفي بهذا القدر اليوم وإلى لقاء آخر إن شاء رب
+
+925
+01:17:47,910 --> 01:17:54,210
+العالمين مع المبحث الثالث وهو المكي والمدني سبحانك
+
+926
+01:17:54,210 --> 01:17:58,350
+اللهم بحمدك نشهد أن لا إله إلا أنتنستغفرك ونتوب
+
+927
+01:17:58,350 --> 01:18:01,810
+ليه باسم الله الرحمن الرحيم والعصري إن الإنسان لا
+
+928
+01:18:01,810 --> 01:18:04,790
+في خُسب إلا الذين آمنوا وعملوا الصالحات تواصوا
+
+929
+01:18:04,790 --> 01:18:07,630
+بالحق وتواصوا بالصبر برك الله فيكم وجزاكم الله كل
+
+930
+01:18:07,630 --> 01:18:09,610
+خير والسلام عليكم ورحمة الله تعالى
+
diff --git a/PL9fwy3NUQKwaGIlkTCo2tGndokmJ9ZbKr/C5PHaQWgKtU_postprocess.srt b/PL9fwy3NUQKwaGIlkTCo2tGndokmJ9ZbKr/C5PHaQWgKtU_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2ea5df8459eac94826e3d02f7ee37832898af892
--- /dev/null
+++ b/PL9fwy3NUQKwaGIlkTCo2tGndokmJ9ZbKr/C5PHaQWgKtU_postprocess.srt
@@ -0,0 +1,3292 @@
+1
+00:00:11,220 --> 00:00:13,860
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:13,860 --> 00:00:16,820
+والصلاة والسلام على رسول الله وبعد أيها الإخوات
+
+3
+00:00:16,820 --> 00:00:19,300
+الكريمات أحييكم بتحية الإسلام في السلام عليكم
+
+4
+00:00:19,300 --> 00:00:23,600
+ورحمة الله تعالى وبركاته طبعا نلتقي اليوم مع
+
+5
+00:00:23,600 --> 00:00:28,720
+البرنامج العملي والشق ثاني من المادةأحنا اتكلمنا
+
+6
+00:00:28,720 --> 00:00:32,660
+عن المساق أنه أنهينا الجزء النظري ما يتعلق بعلم
+
+7
+00:00:32,660 --> 00:00:37,540
+القرآن من معنى القرآن الكريم، تنزلات القرآن
+
+8
+00:00:37,540 --> 00:00:41,880
+الكريم، جمع القرآن، أسباب النزول، الناسخ والمنسوخ،
+
+9
+00:00:41,880 --> 00:00:44,520
+الإعجاز، واتكلمنا عن الإعجاز الباني، الإعجاز
+
+10
+00:00:44,520 --> 00:00:49,770
+التشريعي والإعجاز العلميو أُصدر السطار عن هذه
+
+11
+00:00:49,770 --> 00:00:55,070
+القضايا أو المباحث الهامة في حياة الإنسان المسلم
+
+12
+00:00:55,070 --> 00:01:00,630
+والآن سنلجأ إلى البرنامج العملي و أول في الفصل
+
+13
+00:01:00,630 --> 00:01:05,990
+التاني و أول تفسير من المقام أخذ صورة الإسراءوصورة
+
+14
+00:01:05,990 --> 00:01:10,770
+الإسراء احنا في التفسير الموضوعي قسمناها لثلاث
+
+15
+00:01:10,770 --> 00:01:15,070
+مقاطع ما عدا أولا طبعا اتكلمنا عن أهداف الصورة ثم
+
+16
+00:01:15,070 --> 00:01:19,610
+المقطع الأول بيتكلم عن حق الله تعالى مقرنا بحق
+
+17
+00:01:19,610 --> 00:01:25,250
+الوالدين وطبعا هنا اشوف التركيز في الثلاث مقاطعترى
+
+18
+00:01:25,250 --> 00:01:32,750
+ان المؤلف او كتب التفسير او المفسرون اهتموا
+
+19
+00:01:32,750 --> 00:01:37,530
+بالقضايا الاجتماعية والعلاقات البشرية الموجودة
+
+20
+00:01:37,530 --> 00:01:43,470
+شوفوا اول دائرةالدائرة الضيقة وهي دائرة العائلة أو
+
+21
+00:01:43,470 --> 00:01:47,750
+الأسرة وهو بتتكلم عن قضية أن حق الله مقرنا بحق
+
+22
+00:01:47,750 --> 00:01:52,230
+الولدين وهم الدعام الأولى من دعائم الأسرة ثم بعد
+
+23
+00:01:52,230 --> 00:01:55,930
+ذلك تتسع الدائرة إلى خارج الأسرة الأقارب وصلة
+
+24
+00:01:55,930 --> 00:02:00,490
+الأرحام ثم بعد ذلك بتتكلم عن المجتمع الإسلامي من
+
+25
+00:02:00,490 --> 00:02:05,350
+الداخل وكل هذاحتى تكون من البداية احنا لما بنتكلم
+
+26
+00:02:05,350 --> 00:02:13,150
+عن قضية حتى الحياة او المنهج الدعوي في إرساء قواعد
+
+27
+00:02:13,150 --> 00:02:20,470
+الدولة كانوا واحد الفرد اتنين المجتمع اللي هو
+
+28
+00:02:20,470 --> 00:02:27,950
+بيسموه الدولة تلاتة اتنين الحضارة بعدين اربعة
+
+29
+00:02:27,950 --> 00:02:29,470
+الاستخلاف
+
+30
+00:02:31,690 --> 00:02:35,130
+يعني احنا لما نتكلم عن قضية منهجنا، خطتنا ال
+
+31
+00:02:35,130 --> 00:02:40,310
+استراتيجية لقضية هذا المنهج الدعوى الربانى، هاي
+
+32
+00:02:40,310 --> 00:02:43,910
+أربع خطوات، أولا في الفرد المسلم، بعدين باجي
+
+33
+00:02:43,910 --> 00:02:48,290
+المجتمع اللذي تقام على قطيق الدولة، بعدين الحضارة،
+
+34
+00:02:48,290 --> 00:02:51,530
+الأولى لما بتكلم عن قضية الدولة، يعني بتكلم عن
+
+35
+00:02:51,530 --> 00:02:57,290
+قضية الشعب، وبتكلم عن قضية منهج، وبتكلم عن قضية
+
+36
+00:02:57,290 --> 00:03:02,770
+مثلا مقومات الدولة،بعدين تصير الحضارة، الحضارة وهو
+
+37
+00:03:02,770 --> 00:03:06,150
+التي تمثلت في رسالة الرسل من الرسول صلى الله عليه
+
+38
+00:03:06,150 --> 00:03:12,230
+وسلم إلى العالم المحيط و مثل رسالته أرسل رسول إلى
+
+39
+00:03:12,230 --> 00:03:16,290
+بلاد فارس و رسول إلى بلاد الروم و رسول إلى مقوقص
+
+40
+00:03:16,290 --> 00:03:20,430
+عظيم القبط أو الأقباط و حضارات يعني انفتاح على
+
+41
+00:03:20,430 --> 00:03:25,060
+العالم و لما نتكلم عن حضارة تصدير الإسلام إلىاللي
+
+42
+00:03:25,060 --> 00:03:28,780
+هم إيش؟ غير العرب وبالتالي إذا هذه هي الحضارة اللي
+
+43
+00:03:28,780 --> 00:03:32,820
+إحنا بنصدرها لما إحنا بنصير نتعامل وكيفية التعامل
+
+44
+00:03:32,820 --> 00:03:37,900
+مع الآخر شوفتوا في الدولة أعطاني حق حاجة اسمها حق
+
+45
+00:03:37,900 --> 00:03:43,620
+المواطنةيعني بمعنى تعامل المسلمين مع بعضهم البعض،
+
+46
+00:03:43,620 --> 00:03:46,600
+تعامل المسلمين مع أهل الكتاب، تعامل المسلمين مع
+
+47
+00:03:46,600 --> 00:03:51,820
+الوثنيين، فإذا أحسننا التعامل مع هذه الأطراف وهذه
+
+48
+00:03:51,820 --> 00:03:55,400
+الألوان جميعها، فإحنا نستطيع أن نعمل على استثباب
+
+49
+00:03:55,400 --> 00:03:59,060
+أركان الدولة، إذا نحن بحاجة إلى قضية التعامل مع
+
+50
+00:03:59,060 --> 00:04:03,220
+الآخر، وهذا مصطلح اليوم اللي لازم نهتم فيه، نتعامل
+
+51
+00:04:03,220 --> 00:04:06,080
+مع أهل الكتاب، واحنا جولنا أهل الذمة، وأهل الذمة
+
+52
+00:04:06,080 --> 00:04:10,370
+عارفين إيش يعني؟يعني أن هؤلاء في ذمة الله و ذمة
+
+53
+00:04:10,370 --> 00:04:14,590
+الله و هذا كلام أنه احنا بنقول هذا هو الرسالة
+
+54
+00:04:14,590 --> 00:04:18,410
+تبعتنا إذا صرنا مصادرين حضارة و نجحنا في تصديره و
+
+55
+00:04:18,410 --> 00:04:24,260
+عرفنا الآخر من نحنبالتالي احنا نستطيع ان نقيم دولة
+
+56
+00:04:24,260 --> 00:04:28,180
+الاستخلاف الاستخلاف يعني ان الله سبحانه وتعالى ان
+
+57
+00:04:28,180 --> 00:04:32,900
+جائلك في الأرض خليفة يعني بمعنى خلافة الله وخلافة
+
+58
+00:04:32,900 --> 00:04:36,140
+الله مش عشان يرفعلي الاعلام اللتي ما أنزل الله
+
+59
+00:04:36,140 --> 00:04:39,660
+بيها من سلطان وانما راية التوحيد وتشريع الله
+
+60
+00:04:39,660 --> 00:04:43,300
+سبحانه وتعالى يسود وهذا التشريع اللذي يعمل على نشر
+
+61
+00:04:43,300 --> 00:04:47,800
+العدل في الأمم جميعا بدون استثناء وهذه الخطةصورة
+
+62
+00:04:47,800 --> 00:04:51,740
+الإسراء يعني من العلاقات الداخلية يعني إحنا لازم
+
+63
+00:04:51,740 --> 00:04:56,040
+نتكلم عن الفرد و المجتمع و هو إقامة حتى بالكاد لأن
+
+64
+00:04:56,040 --> 00:05:00,240
+مجتمع لا يمكن أن يقام إلا على هذه الأمور و هو
+
+65
+00:05:00,240 --> 00:05:05,280
+المقدمة اللي إحنا بنتحدث فيها شوفوا الأهداف الصورة
+
+66
+00:05:05,280 --> 00:05:10,340
+من أهداف أولا خلينا نشوف الصورة مكيةولم تتحدث عن
+
+67
+00:05:10,340 --> 00:05:13,460
+أمور العقيدة ولا أصول الإيمان زيها زي مجلة الصور
+
+68
+00:05:13,460 --> 00:05:17,020
+المكية من الذاكرين في قضية لما فرقنا بين المكي
+
+69
+00:05:17,020 --> 00:05:23,700
+والمدني وقولنا أن المكي 13 عاما يؤسس النبي صلى
+
+70
+00:05:23,700 --> 00:05:27,380
+الله عليه وسلم الفدايات السليمة التي سيقام عليها
+
+71
+00:05:27,380 --> 00:05:31,950
+صرح الإسلام العظيمواحد بده يبني بيت من أربع طوابق،
+
+72
+00:05:31,950 --> 00:05:36,130
+واحد بده يبني ناطحات، سحاب، هل معقول إن الأساس
+
+73
+00:05:36,130 --> 00:05:40,350
+تبقى البناية والبرج أو الفيلا زي ناطحات السحاب؟
+
+74
+00:05:40,350 --> 00:05:45,960
+الإسلامسيطال عنان السماء، إذا بده قواعد راسيات،
+
+75
+00:05:45,960 --> 00:05:50,740
+عشان هي 13 سنة يؤسس عقيدة، يرسخ التوحيد في نفوس
+
+76
+00:05:50,740 --> 00:05:54,040
+أبناء المسلمين، عشان بعد هيك كل الأشياء بتاتي،
+
+77
+00:05:54,040 --> 00:05:57,740
+وإحنا قلنا الدور الفاتر الدين، عقيدة، شريعة
+
+78
+00:05:57,740 --> 00:06:02,240
+ومعاملة، فعقيدة بالأساس، وهو الجدع، وإحنا رسمنا
+
+79
+00:06:02,240 --> 00:06:07,890
+قضية الشجرة، وبينتلكم عشان إن هذايكون إلك نبراس،
+
+80
+00:06:07,890 --> 00:06:11,590
+يعني إنت لو حفظتي بس هذه الشجرة، شجرة الدين، اللذي
+
+81
+00:06:11,590 --> 00:06:16,130
+ارتضاه الله تعالى للعالمين، هذا اللي هو اللذي ..
+
+82
+00:06:16,130 --> 00:06:20,010
+اللذي يعني إحنا بنكيف معاه. العنصر البارز في
+
+83
+00:06:20,010 --> 00:06:22,550
+الصورة، شخصية الرسول صلى الله عليه وسلم، اللتي
+
+84
+00:06:22,550 --> 00:06:28,110
+برزت من خلال .. ليش؟ لأن لما نتكلم عن أصلا معجزة
+
+85
+00:06:28,110 --> 00:06:31,840
+الإسراء،معجزة الإسرائيل كلها بحالها، ليش؟ تأييد
+
+86
+00:06:31,840 --> 00:06:33,900
+لبي صلى الله عليه وسلم، اتصوروا في سورة الإسرائيل،
+
+87
+00:06:33,900 --> 00:06:37,840
+أنا مانتش أتكلم عن قضية والله يشافر الله، الرسول
+
+88
+00:06:37,840 --> 00:06:40,900
+صلى الله عليه وسلم في السماوات، لكن بدي أولا أن
+
+89
+00:06:40,900 --> 00:06:44,280
+الرسول صلى الله عليه وسلم أسري به من المسجد الحرام
+
+90
+00:06:44,280 --> 00:06:48,080
+إلى المسجد الأخصى، ثم عرج به إلى السماوات، وهو جاي
+
+91
+00:06:48,080 --> 00:06:53,960
+على بيت المقدس، وإذا بمكرمة من الله أن يتنزل جميع
+
+92
+00:06:53,960 --> 00:06:58,530
+الأنبياء والرسل السابقين،وينزلوا إلى بيت المقدس
+
+93
+00:06:58,530 --> 00:07:03,870
+فيصلي بهم النبي صلى الله عليه وسلم إماما ثم بعد
+
+94
+00:07:03,870 --> 00:07:08,790
+ذلك يعرج بيه إلى السماوات وكأن الرسالة انتقلت من
+
+95
+00:07:08,790 --> 00:07:14,350
+كل الأمم الأخرى إلى مين؟إليكم أنتوا يا أتباع محمد
+
+96
+00:07:14,350 --> 00:07:18,450
+الراية سُلمت إليكم لكن المصيبة هل ستبقى الراية
+
+97
+00:07:18,450 --> 00:07:22,150
+مرفوعة و لا بدنا نكسها فدي مشكلة إذا مناته إحنا
+
+98
+00:07:22,150 --> 00:07:26,590
+آخر الرسالات و خاتم الأنبياء و المرسلين حمل الراية
+
+99
+00:07:26,590 --> 00:07:32,490
+و أم جميع الأنبياء يعني بمعنى أننا نحن شهداء على
+
+100
+00:07:32,490 --> 00:07:36,770
+الناس و الرسول علينا شهيدة و هذه الأمة الوسطة اللي
+
+101
+00:07:36,770 --> 00:07:42,630
+بنتكلم عنها وسطية الرسالةثم بعد ذلك أرجى بيه إلى
+
+102
+00:07:42,630 --> 00:07:48,230
+السماوات فأراه الله تعالى من آياته الكبرى رغم أنه
+
+103
+00:07:48,230 --> 00:07:52,410
+رأى من الآيات لكن بعد صدرة المنتهى وإذا يرى عظمة
+
+104
+00:07:52,410 --> 00:07:56,350
+الله وجلال الله وتحدثوا علماء في ذلك لكن وكل ذلك
+
+105
+00:07:56,350 --> 00:08:00,000
+تأيد لمين؟المؤمن بيه، هاي صورة إسراء، يعني كل
+
+106
+00:08:00,000 --> 00:08:03,760
+مرتكز صورة الإسراء تدور على تأييد الله تعالى
+
+107
+00:08:03,760 --> 00:08:06,720
+بالمعجزة الباهرة، قال وهي حادثة الإسراء، هاي
+
+108
+00:08:06,720 --> 00:08:09,420
+الصورة كلها، وإن كانت الصورة تتحدث عن الصلاة مع
+
+109
+00:08:09,420 --> 00:08:12,200
+بني إسرائيل وغيرها، لكن الصلاة مع بني إسرائيل ليش؟
+
+110
+00:08:12,200 --> 00:08:15,000
+مش عشان قضية الدين، وقضية الرسول صلى الله عليه
+
+111
+00:08:15,000 --> 00:08:18,520
+وسلم يتنبأ من خلال صورة الإسراء، وقضينا إلى بني
+
+112
+00:08:18,520 --> 00:08:21,390
+إسرائيل في الكتاب، لا تفسدنا في الأرض مرتين،ولا
+
+113
+00:08:21,390 --> 00:08:24,410
+تعلونه علوًا كبيرا، معناه ذلك أننا نتكلم عن صراع
+
+114
+00:08:24,410 --> 00:08:28,390
+مستقبلي مع يخود في فلسطين وأنكم ستنتصرون والرسول
+
+115
+00:08:28,390 --> 00:08:35,810
+جاعد في مكة يضطهد ويطارد ويعذب مرة واحدةالرسول
+
+116
+00:08:35,810 --> 00:08:40,630
+يطارد، الرسول يقهر، الرسول يعذب، وبيقولك احنا بدنا
+
+117
+00:08:40,630 --> 00:08:45,030
+نفتح فلسطين، وفيه صراع مستقبلي مع يهود في فلسطين،
+
+118
+00:08:45,030 --> 00:08:48,390
+انت عارفين ايش معناته؟ هذا الإعجاز، هذا هو قمة
+
+119
+00:08:48,390 --> 00:08:52,870
+الإيمان، انه مش بس .. والاصل بس تتظبط حالك، بس
+
+120
+00:08:52,870 --> 00:08:57,730
+تحمي أفرادك، سمية تضرب في أعز شيء عندها، في فرجها،
+
+121
+00:08:57,730 --> 00:09:01,090
+برمه، ولا يستطيع أن يحرك، وصبرا اهلا يا سرفان
+
+122
+00:09:01,090 --> 00:09:04,840
+ماقعدكم الجنة، وبعدين؟طب هو لان .. طب بس اتخلص ..
+
+123
+00:09:04,840 --> 00:09:08,120
+طب و المدينة؟ اختصر المدينة و اختصر الصراعات مع
+
+124
+00:09:08,120 --> 00:09:10,980
+فارس و اختصر الصراعات مع بلاد اللي كانت .. و بعدين
+
+125
+00:09:10,980 --> 00:09:14,320
+على طول على بلاد الشام مرة واحدة نقلة .. و ده هو
+
+126
+00:09:14,320 --> 00:09:17,880
+الأمل .. هذا هو الأمل اللي الله سبحانه وتعالى
+
+127
+00:09:17,880 --> 00:09:21,240
+يعطيه للمؤمنين احنا اليوم في غزة حصار .. احنا في
+
+128
+00:09:21,240 --> 00:09:26,470
+غزة اليومتأمر عربي عالمي إسرائيلي و كل العالم
+
+129
+00:09:26,470 --> 00:09:30,210
+متأمر علينا و بيجي واحد شيخ زينا بيطلع على المنظر
+
+130
+00:09:30,210 --> 00:09:33,150
+و بيقول و الله احنا مش بس بدنا نرفع العالم
+
+131
+00:09:33,150 --> 00:09:36,450
+الإسلامي فوق ال .. ال .. ال .. كريبلين خلاص داطر و
+
+132
+00:09:36,450 --> 00:09:38,630
+أنا هل بقول البيت الأبيض؟ لا أنا مابقولش البيت
+
+133
+00:09:38,630 --> 00:09:43,030
+الأبيض و الله سنضع الراية الإسلامية فوق الفاتيكان
+
+134
+00:09:43,740 --> 00:09:48,040
+الفاتيكان عاصمة روميا اللي هي بلد الديني النصراني
+
+135
+00:09:48,040 --> 00:09:52,380
+الفاجر الذي تأمر وزرع اليهود في قلب فلسطين وللأن
+
+136
+00:09:52,380 --> 00:09:55,600
+الغرب متأمر على الأمة الإسلامية سنغرس العالم
+
+137
+00:09:55,600 --> 00:09:59,920
+الإسلامي على الفاتيكان ستفتح القسطنطينية ثم روميا
+
+138
+00:10:00,260 --> 00:10:03,080
+أي هما أولا خلصنا من القساطين اليوم اللي هي
+
+139
+00:10:03,080 --> 00:10:06,320
+أستنبول هنفتح روما بإذن الله سبحانه وتعالى هذه
+
+140
+00:10:06,320 --> 00:10:09,620
+الأمل اللي بنخدم صورة الإسراء النقطة الثانية تعرضت
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+141
+00:10:09,620 --> 00:10:13,820
+صورة الإسراء لمعجزة الإسراء مظاهر التكريم الإلهي
+
+142
+00:10:13,820 --> 00:10:16,980
+لمحمد صلى الله عليه وسلم يقطع هذه المسافات خلال
+
+143
+00:10:16,980 --> 00:10:21,600
+شهرين وطبعا هذا أمر خارق للعادة وغير المألوف عند
+
+144
+00:10:21,600 --> 00:10:26,810
+الناس ولهذا حتى ارتد ما نرتدوازداد إيمانا من آمن
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+145
+00:10:26,810 --> 00:10:31,930
+يعني الصديق جالهم أنتوا يعني أنا بصدق محمد يأتيه
+
+146
+00:10:31,930 --> 00:10:35,850
+الخبر من السماء ولا أصدق محمد أنه سيذهب إلى بيت
+
+147
+00:10:35,850 --> 00:10:40,050
+المقدس أو يقرج به إلى السماء؟ طب مين أولى؟ إذا
+
+148
+00:10:40,050 --> 00:10:43,630
+قضية التصديق أنه عمال بتلقى تعليم من رب السماوات
+
+149
+00:10:43,630 --> 00:10:50,330
+والأرض وخبر ووحي ودستير وتعليم وتشريع وأخلاقو كمين
+
+150
+00:10:50,330 --> 00:10:53,130
+أولى فانا مصدقه في هذا ماتش أصدقه أنه الله عرش بيه
+
+151
+00:10:53,130 --> 00:10:58,530
+إلى السماء إذا هذه قضية تصدق لكن الذين لم يغرس
+
+152
+00:10:58,530 --> 00:11:03,170
+الإيمان في ناس ارتدوا من المؤمنين ارتدوا لأن الوقع
+
+153
+00:11:03,170 --> 00:11:07,210
+الحدث أكبر من تخيلهم العقل البشري احنا زي اليوم
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+154
+00:11:07,210 --> 00:11:09,850
+تقول اللي و الله طلع الجمر طلع كده لأ لأ ما يطلع
+
+155
+00:11:09,850 --> 00:11:14,750
+بس هو عنده لأ طب احنا يمكن نصدق لأن سرنا بنشهد
+
+156
+00:11:14,750 --> 00:11:19,670
+الصواريخ بنشهد الطيرانبنشاهد والله المكوك الفضائي
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+157
+00:11:19,670 --> 00:11:22,930
+لكن هم اللي في عصر الحمار وعصر البقرة وعصر
+
+158
+00:11:22,930 --> 00:11:26,390
+الجاموسة وعصر كده عصر الخيل اللي بيضرب بالخيل أشهر
+
+159
+00:11:26,390 --> 00:11:30,750
+وهو لسه ما موصلش مدينة من المدن إذا عمال بين مكة
+
+160
+00:11:30,750 --> 00:11:33,510
+والمدينة وماجر بيضرب على الخيل اللي بده شهرين
+
+161
+00:11:33,510 --> 00:11:36,870
+فبالك لو بده يطلع من بلاد الشام إلى المغرب أو من
+
+162
+00:11:36,870 --> 00:11:41,380
+المغرب إلى مثلا أندونسيا أو إلى بلاد خوراسيانأو
+
+163
+00:11:41,380 --> 00:11:44,340
+الى الجمهورية الاتحاد السوفيتي اللى هو تاجاكستان و
+
+164
+00:11:44,340 --> 00:11:46,760
+أوسفاكستان و ساماركاند و تاشقاند من الجمهورية
+
+165
+00:11:46,760 --> 00:11:50,780
+الإسلامية إذا شفتوا المسافات هذا بده سنينإذا هذا
+
+166
+00:11:50,780 --> 00:11:53,520
+الكلام اللي احنا بنتكلم عنه فهي صورة الإسراء
+
+167
+00:11:53,520 --> 00:11:57,600
+تأطينا هذا المظهر التكريمي الرائع حيث لا يوجد
+
+168
+00:11:57,600 --> 00:12:00,980
+سيارات ولا طيارات ولا مراكب فضائية ولا غير ذلك
+
+169
+00:12:00,980 --> 00:12:03,720
+قطعت كل هذه المسافات النقطة الثالثة من أهداف
+
+170
+00:12:03,720 --> 00:12:07,960
+الصورة تحدثت الصورة عن بني إسرائيل وما كتب الله
+
+171
+00:12:07,960 --> 00:12:11,380
+عليهم من التشرد والهواد وقضينا إلى بني إسرائيل في
+
+172
+00:12:11,380 --> 00:12:14,770
+الكتابةانتبه، كل الأهداف هذه هتجيكي في الصح و
+
+173
+00:12:14,770 --> 00:12:18,050
+الغلط يعني ممكن تجيكي واحدة منهم في قضية الصح و
+
+174
+00:12:18,050 --> 00:12:21,350
+الغلط و احنا مش معناته انك انت غفلي عن هذا الجانب
+
+175
+00:12:21,350 --> 00:12:25,410
+يعني الأهمية مهمة جدا فيها نقطة الرابعة تحدثت
+
+176
+00:12:25,410 --> 00:12:29,870
+الصورة طالعي عن بعض الآيات الكونية العظيمة و هذا
+
+177
+00:12:29,870 --> 00:12:33,530
+دايما busy في الأسئلةشوفيه؟ إذا الصورة تحدثت عن
+
+178
+00:12:33,530 --> 00:12:37,710
+بعض الآيات الكونية العجيبة التي تدل على عظمة
+
+179
+00:12:37,710 --> 00:12:41,910
+ووحدانية الله و جعلنا الليل والنغار آيتين طبعا
+
+180
+00:12:41,910 --> 00:12:49,430
+فمحونا آية الليل وجعلنا آية النغار مبصرة ليش قال
+
+181
+00:12:49,430 --> 00:12:55,490
+آية النغار مبصرة؟ بس الشمس ماشي ليش الشمس يعني ليش
+
+182
+00:12:55,490 --> 00:12:56,930
+مبصرة؟
+
+183
+00:12:58,730 --> 00:13:04,820
+يعني بمعنى كأنه بيقولك أن الإنسان بلا عمل أعمىفي
+
+184
+00:13:04,820 --> 00:13:09,200
+الليل ما هو بيشوفش فيش شغل فيش كده فهو خلاص انتخاب
+
+185
+00:13:09,200 --> 00:13:14,020
+لكن في النهار يعني بمعنى أن النهار يعطي للإنسان
+
+186
+00:13:14,020 --> 00:13:19,600
+البصيرة في كافة الحياة بل بالعكس سيقوموا بتكاليف
+
+187
+00:13:19,600 --> 00:13:23,360
+الله سبحانه وتعالى له في هذا الضوء في وضع النهار
+
+188
+00:13:23,360 --> 00:13:30,970
+دون غبش وليه ده حتى موسى لما جاء يحاجج قومهاختار
+
+189
+00:13:30,970 --> 00:13:37,270
+يوم الزينا و أن يأتي الناس ضحا طب ليش الناس يأتوا
+
+190
+00:13:37,270 --> 00:13:45,550
+ضحا مش مساء ولا عصرا؟ ليش؟ ما هي كل النهار مبصر
+
+191
+00:13:45,550 --> 00:13:49,550
+لكن ليش وقت الضحك كمان؟ و دي الملاحظة الله أكبر
+
+192
+00:13:49,550 --> 00:13:54,530
+كنتوا بتكون تلقين إيه؟
+
+193
+00:13:54,530 --> 00:13:57,670
+هو بدوا إيه؟ يوم الزينا انت عارف يوم الزينا إيش يا
+
+194
+00:13:57,670 --> 00:14:02,830
+بن؟يعني يوم عيد، كل الناس جاعدين، و هو بده كل
+
+195
+00:14:02,830 --> 00:14:07,830
+الناس ييجوا، مش هو عمال بده حاجز فرعون، و قاصد أنه
+
+196
+00:14:07,830 --> 00:14:11,250
+يوم الزينا، يوم العيد، كل الناس جاعدين، و الضحاة
+
+197
+00:14:11,250 --> 00:14:15,350
+حتى تورا المعجزة واضحة، لا غبشة فيها، بده يضرب،
+
+198
+00:14:15,350 --> 00:14:20,110
+ألقي ما في يمينك، تلقف ما صنعه، إنما صنعه كيدس
+
+199
+00:14:20,110 --> 00:14:25,610
+إيه؟ ساحر، و لا يفلح الساحريعني الآية، آية المعجزة
+
+200
+00:14:25,610 --> 00:14:29,770
+بده ترى في قضية إيه؟ وضح النهار، وقت الضحا، يعني
+
+201
+00:14:29,770 --> 00:14:34,130
+الشمس طالع، مشرقة، الجو ممتاز، كل الناس بيشوفه،
+
+202
+00:14:34,130 --> 00:14:37,950
+بيقدرش يقولك والله إنه ليل وسحرنا وماشوفناش، لأ لأ
+
+203
+00:14:37,950 --> 00:14:42,210
+لأ، الآية واضحة، شفت القضية؟ إذا من هنا لقضية إن
+
+204
+00:14:42,210 --> 00:14:46,470
+هنا دلالة على آيات الله الكولية العجيبة، ثم انتقلت
+
+205
+00:14:46,470 --> 00:14:50,170
+الصورة إلى بعض الآداب الاجتماعيةواللي احنا اتكلمنا
+
+206
+00:14:50,170 --> 00:14:52,690
+فيها في المقاطع الثلاثة، الأداب الاجتماعية
+
+207
+00:14:52,690 --> 00:14:56,430
+والأخلاق الفاضلة، واتي ده القربة حقه والمسكينة
+
+208
+00:14:56,430 --> 00:15:00,650
+وابن السبيل، ولا تبدر تبذير تعاليم رائعة اجتماعية
+
+209
+00:15:00,650 --> 00:15:04,790
+تقعد دعائم للمجتمع اللي هو IHL Muslim، تحدثت
+
+210
+00:15:04,790 --> 00:15:09,530
+الصورة عن البعث والنشوروقالوا اننا كنا اذا كنا
+
+211
+00:15:09,530 --> 00:15:14,090
+عظانا ورفاق ورفاتا انا لم ابعثهم طب انت بتعرف ان
+
+212
+00:15:14,090 --> 00:15:20,670
+القضية هذه قضية العرب بالاساس ولئن سألتهم من خلق
+
+213
+00:15:20,670 --> 00:15:23,890
+السماوات والأرض لا يقول النار؟ اذا هم يؤمنوا
+
+214
+00:15:23,890 --> 00:15:28,250
+باياش؟ الربوبية،
+
+215
+00:15:28,250 --> 00:15:31,250
+بيؤمنوش بلأ كمان ينكروا البعث
+
+216
+00:15:36,360 --> 00:15:39,280
+يعني هم بيؤمنوا بالخلق لكن لا يؤمنوا بالبعث
+
+217
+00:15:39,280 --> 00:15:43,820
+بيؤمنوا أن الله تعالى خلق السماوات و الأرض و خلق
+
+218
+00:15:43,820 --> 00:15:47,360
+الإنسان و بيؤمنوا بهذه القضية لكن لا يؤمنوا بأن
+
+219
+00:15:47,360 --> 00:15:51,900
+الإنسان بعد الموت سيقف بين يدي الله و يبعد طب
+
+220
+00:15:51,900 --> 00:15:57,720
+بتعرفي لو أنا الآن متخيل لا سمح الله أنه مافيش بعث
+
+221
+00:15:58,410 --> 00:16:03,070
+طب مانبزني و بقتل و بعمل كل شي عارفين ليش؟ لأنه
+
+222
+00:16:03,070 --> 00:16:07,030
+مابحاسس .. مافيش حاسس .. معناته خلاص شوفتوا إيش
+
+223
+00:16:07,030 --> 00:16:11,550
+الفرق في قضية الإيمان بالبعث الإيمان بالبعث يقوده
+
+224
+00:16:11,550 --> 00:16:15,590
+إلى الاستقامة لما أنا بدي أعرف إن أنا بعدها الحياة
+
+225
+00:16:15,590 --> 00:16:23,310
+الدنيا سأقف ما لي هذا الكتاب لا يغادر صغيرة ولا
+
+226
+00:16:23,310 --> 00:16:28,410
+كبيرة إلاكل أعمال محصية عليها وبعدين بده حاسب
+
+227
+00:16:28,410 --> 00:16:32,750
+عليها بقدر أعمل باطل بقدر أعمل غلط وبالتالي هذا
+
+228
+00:16:32,750 --> 00:16:36,350
+مدعا إلى الاستقامة إلى الطريق المستقيم ثم سبعة
+
+229
+00:16:36,350 --> 00:16:40,350
+الصورة انتقلت للتحدث عن القرآن الكريم عجزة النبي
+
+230
+00:16:40,350 --> 00:16:44,510
+صلى الله عليه وسلم وقالوا لن نؤمن لك حتى تفجر لنا
+
+231
+00:16:44,510 --> 00:16:50,150
+من الأرض ينبوعا أو تكون لكجنة من نخيل وعين بوتوفين
+
+232
+00:16:50,150 --> 00:16:55,890
+يعني احنا بدك ان صدقك خل هذه الأرض و الصحراء انه
+
+233
+00:16:55,890 --> 00:17:02,370
+جنة هل استجاب لهم النبي صلى الله عليه و سلم؟ ليش؟
+
+234
+00:17:02,370 --> 00:17:08,750
+سؤال لأن الله تبقى بيبعت نبي و بيقعد و بيمنع جزاه
+
+235
+00:17:08,750 --> 00:17:13,570
+وما بيؤمنش القوم بهذه المعجزة الله يبتعد شوفتي؟ لو
+
+236
+00:17:13,570 --> 00:17:20,470
+أن الرسول صلى الله عليه و سلماستجاب لقومه فجعل من
+
+237
+00:17:20,470 --> 00:17:26,590
+الأرض الصحراء جنة وينبيع أنهار ولم يؤمنوا على طول
+
+238
+00:17:26,590 --> 00:17:32,510
+يتنزل عليهم الخسف والمسخ ويؤذبهم الله معناه ذلك
+
+239
+00:17:32,510 --> 00:17:40,570
+أنه سد كل منافذ التوبة وليهذا رحمة من الرسول بقومه
+
+240
+00:17:40,570 --> 00:17:45,130
+مرضيش وقدر أن يدعو الله تعالى فيحقق له هذا الأمر
+
+241
+00:17:46,310 --> 00:17:50,830
+شفتوا؟ يعني شوفوا عظمة الرسول بمعنى هنا قضية أن
+
+242
+00:17:50,830 --> 00:17:54,290
+الله الرسول صلى الله عليه وسلم كان يخاط على قومه
+
+243
+00:17:54,290 --> 00:17:59,490
+رحمة بقومه زي ما شفنا في وين؟ في الطائف لما جاءوا
+
+244
+00:17:59,490 --> 00:18:04,890
+اللي هو ملك الجبال وقال له يا محمد إن شئت أطبقوقفت
+
+245
+00:18:04,890 --> 00:18:08,370
+علي مدين الأخشبين عن الجبلين ولكن الرسول صلى الله
+
+246
+00:18:08,370 --> 00:18:12,910
+عليه وسلم رفض وأبى وقال لعل الله يخرج من أصلابهم
+
+247
+00:18:12,910 --> 00:18:16,230
+من يقولون لا إله إلا الله أو من يوحدون الله تعالى
+
+248
+00:18:16,230 --> 00:18:20,350
+إذا أمل النبي وده أمل الدعاء يعني نحن مش لازم ندعو
+
+249
+00:18:20,350 --> 00:18:25,610
+على الناس ولا لازم ننتقم لأنفسنا كمسلمين حتى مهما
+
+250
+00:18:25,610 --> 00:18:29,470
+حدثيعني احنا مش ثارات، والله يعملوا فينا، سووا
+
+251
+00:18:29,470 --> 00:18:32,410
+فينا مبارا، اليوم يجلدوهم، اليوم ينطخوهم، اليوم
+
+252
+00:18:32,410 --> 00:18:35,090
+يسجلوهم، هذا الكلام مش موجود في المناجة الإسلامية،
+
+253
+00:18:35,090 --> 00:18:41,030
+وإلا كيف سيُكتب لك ثواب الصبر؟ كيف؟ أنا بتفهم، إذا
+
+254
+00:18:41,030 --> 00:18:46,150
+أنا والله يوم ضربوني، وسجنوني،ولمّا مكّن الله
+
+255
+00:18:46,150 --> 00:18:50,670
+تعالى لدولة الإسلام اسجنوهم اضربوهم معناته انت خدت
+
+256
+00:18:50,670 --> 00:18:54,810
+قصاصك في الدنيا وفي الآخراش هتاخد فاشاشي .. اذا
+
+257
+00:18:54,810 --> 00:18:58,390
+اين الثوان؟ اين الأجر؟ شفتوا؟ وليهذا هذا منهج مش
+
+258
+00:18:58,390 --> 00:19:00,950
+معقول عشان هيك طيب ما يجري في العالم اليوم اللي
+
+259
+00:19:00,950 --> 00:19:06,610
+بنشوفه البنات كله تشويه للإسلام مابدهمش بدهمش لا
+
+260
+00:19:06,610 --> 00:19:11,450
+دولة إسلامية ولا منهج إسلامي لأنه لو شافوا منهج
+
+261
+00:19:11,450 --> 00:19:16,270
+الإسلام الناسمستحيل، كبده مطبقه، بتبطل العالم
+
+262
+00:19:16,270 --> 00:19:21,690
+العربي يسوق للغرب، بيبطل العالم العربي يركعوا
+
+263
+00:19:21,690 --> 00:19:25,570
+ويسجدونا زي ما بيقوله للرجل الأبيض المتحضر كما
+
+264
+00:19:25,570 --> 00:19:31,170
+يقوله سابقا، يعني بيبطل احنا عنا عبيد لسياسة تنفيذ
+
+265
+00:19:31,170 --> 00:19:34,970
+السياسات للعالم الغربي وأمريكا اللي اليوم مسيطرة،
+
+266
+00:19:34,970 --> 00:19:40,710
+وجاله عن العالم الثالث المتخلفيا سلام، وانت بيقولك
+
+267
+00:19:40,710 --> 00:19:49,610
+يا متخلفة، شو معناته متخلفة؟ ماتوه؟ قبله؟ مجنون؟
+
+268
+00:19:49,610 --> 00:19:54,800
+معناته متخلفين، عقلياًأحنا متخلفين عقليا في كله،
+
+269
+00:19:54,800 --> 00:19:59,260
+الآن هيك الاتقان، وحقيقة احنا متخلفين، عارفين ليش؟
+
+270
+00:19:59,260 --> 00:20:04,260
+لأن صبرنا هذه المدة الطويلة على قضية الحكام
+
+271
+00:20:04,260 --> 00:20:09,160
+الفاسدين، وكيف أنهم ينشروا الفساد في جسم الأمة،
+
+272
+00:20:09,160 --> 00:20:15,690
+ونخروا في عظام الأمةلكن آن الأوان إنه نفّم إسلامنا
+
+273
+00:20:15,690 --> 00:20:18,810
+حتى إحنا لو فهمنا إسلامنا ماحدش مقدر يسيطر علينا
+
+274
+00:20:18,810 --> 00:20:23,630
+حتى أن الرئيس الدولة أو الخليفة عجبني كلام في
+
+275
+00:20:23,630 --> 00:20:28,470
+الحقيقة للرئيس الجمهورية مرسى لما قال احنا خدم هو
+
+276
+00:20:28,470 --> 00:20:33,090
+بالفعل احنا خدم لما بيكون الخليفة الخليفة خادم
+
+277
+00:20:33,090 --> 00:20:39,610
+يعمل في مؤسسة الشعب وهذه المفاهيم التي يجب أن
+
+278
+00:20:39,610 --> 00:20:43,870
+تعطيهايجب أن تُعاد و تُعطى فرصة حتى من الناس
+
+279
+00:20:43,870 --> 00:20:47,570
+مانضلناش نضغط الغرب تضغط من جانب والشعب اللي لازال
+
+280
+00:20:47,570 --> 00:20:50,950
+مش فاهم دينه بيضغط في جانب تاني إذا لابد أنه نفهم
+
+281
+00:20:50,950 --> 00:20:54,650
+مثل هذه القضايا الموجودة في عصرنا ثم الصورة ختمت
+
+282
+00:20:54,650 --> 00:21:01,050
+بتعظيم الله بالإيمان بوحدانيته وتنزيه الشرك عن
+
+283
+00:21:01,050 --> 00:21:05,910
+زوجة والولد يعني هو ربنا لما نقول والله أن عيسى
+
+284
+00:21:05,910 --> 00:21:11,700
+ابن الله يعني مانعته ربنا إيه له زوجة؟يعني متزوج،
+
+285
+00:21:11,700 --> 00:21:16,480
+يا السلام، والذي متزوج يعني بيعمل عمال البشر، يعني
+
+286
+00:21:16,480 --> 00:21:20,520
+عنده شهوة، وعنده شهوة البطن وشهوة الفرج ومعنده
+
+287
+00:21:20,520 --> 00:21:23,560
+قطية الغضب ومعنده قطية الكثير، معناه ذلك أنه زي
+
+288
+00:21:23,560 --> 00:21:27,280
+البني أدمين، طب وكيف سيكون هو رب العالمين؟معاذ
+
+289
+00:21:27,280 --> 00:21:31,280
+الله شفتوا؟ شفتوا قضية التطاول على ذات الله وعلى
+
+290
+00:21:31,280 --> 00:21:35,260
+عظمة الله واللي بيقول عن الله بس هذا طيب كويس لسه
+
+291
+00:21:35,260 --> 00:21:38,900
+.. لسه احسن من غير .. لأ انا بيقول هذول ان عيسى
+
+292
+00:21:38,900 --> 00:21:41,860
+ابن الله طب فانباركم الذين يقولوا ان عيسى هو الإله
+
+293
+00:21:42,930 --> 00:21:46,950
+إذا هنا مشكلة في المعتقد جاءت صورة الإسراء لتعالج
+
+294
+00:21:46,950 --> 00:21:50,250
+شيء قلوا ادعوا الله او ادعوا الرحمن أي ما تدعوا
+
+295
+00:21:50,250 --> 00:21:54,590
+فله الأسماء الحسنة يعني بمعنى أن الله تعالى منزع
+
+296
+00:21:54,590 --> 00:21:58,670
+عن صفات النقص وصفات العجز يعني لما يكون إنسان
+
+297
+00:21:58,670 --> 00:22:03,170
+وعمال يتزوج وعمال إنسان عادي وبيأكل وبيشرب معناته
+
+298
+00:22:03,170 --> 00:22:07,790
+بحاجة لما بنقول إن هو بدي يأكل لو أنه عطش أو جاه
+
+299
+00:22:07,790 --> 00:22:11,700
+أو بدي يتغورأحنا شفتوا يا بنات احنا بنكون يمكن في
+
+300
+00:22:11,700 --> 00:22:15,520
+البيت أحيانا مافيش تحرج الآن احنا لما بنروح الواحد
+
+301
+00:22:15,520 --> 00:22:19,660
+على الحمام و احنا في الجامعة في المؤسسة نبقى زي
+
+302
+00:22:19,660 --> 00:22:22,540
+الخجلان و رايح و ضبض بحاله و غيره تصور لو احنا
+
+303
+00:22:22,540 --> 00:22:26,120
+بنكون في سفر و جاي طابور و الله و صاف في الطابور
+
+304
+00:22:26,120 --> 00:22:29,680
+ان شاء الله الملوك واقفين و قاجته و حاجة التغوط
+
+305
+00:22:29,680 --> 00:22:32,940
+بيصير يقول لا ولا بدأ أخر ولا أي بنا رئيس ولا زعيم
+
+306
+00:22:32,940 --> 00:22:35,980
+ولا بروح جدام كل العالم مافيش إشكالية شفتوا هذا
+
+307
+00:22:35,980 --> 00:22:40,300
+اسمه ضعف بشريشوف هذا ربنا بأساس مش عشان .. عشان
+
+308
+00:22:40,300 --> 00:22:44,260
+يحسسنا أنك أنت يا إنسان مهما كبرت و مهما كده طلع
+
+309
+00:22:44,260 --> 00:22:48,380
+طلع عشان اللي خلتك تتحرك يا سلام طب و جوع و يعتش
+
+310
+00:22:48,380 --> 00:22:51,320
+صيروا يدوروا على ميه مش هى؟ و من إيش نتكلم عن
+
+311
+00:22:51,320 --> 00:22:55,680
+باقيت الأشياء؟ هذا دليل عيسى دليل ضعف يعني أنت يا
+
+312
+00:22:55,680 --> 00:22:59,740
+إنسان ضعيف طلع الحاجات التافة أنت مش جادر تصمرلك
+
+313
+00:22:59,740 --> 00:23:03,860
+عشر دقايت و غير غلطه ماتكبر على ربنا ليش؟ ولهذا
+
+314
+00:23:03,860 --> 00:23:09,680
+العلماء ماذا قالوا؟ قالوا لو لا المرضلولا المرض
+
+315
+00:23:09,680 --> 00:23:16,500
+ولولا الموت، ما تقطأ ابن آدم رأسه لله قط كان
+
+316
+00:23:16,500 --> 00:23:19,400
+موطّاش رأسه لحدها، كانت تسجل و تسأل الله ربنا؟
+
+317
+00:23:19,400 --> 00:23:25,160
+ليش؟ ما انت خلاص لا تمرض ولا تموت المرض ضعف والموت
+
+318
+00:23:25,160 --> 00:23:29,440
+انتهاء من الحياة الدنيا، مش انتهاء أنا مقدرش، هذا
+
+319
+00:23:29,440 --> 00:23:35,610
+انتهاء اشمل معطوف على شيءمش انتهاء، مش الموت
+
+320
+00:23:35,610 --> 00:23:39,870
+انتهاء، انتهاء من حياة إلى حياة، انتقال، انتهت
+
+321
+00:23:39,870 --> 00:23:43,370
+الحياة الدنيا وبنروح لحياة الآخرة أولها البرزخ
+
+322
+00:23:43,370 --> 00:23:48,990
+لأنه أول منازل الجنة شوةيا روضة من رياض الجنة
+
+323
+00:23:48,990 --> 00:23:53,630
+ونقول آمين يا رب العالمين يا حفرة من خفرة النيران
+
+324
+00:23:53,630 --> 00:23:57,590
+ولا أياده بالله إذا هنا القضية اللي بدنا نفهمها من
+
+325
+00:23:57,590 --> 00:24:02,950
+قضية الان هنقف مع المقطع الأول من صورة الإسراء مين
+
+326
+00:24:02,950 --> 00:24:10,190
+ده تقرأ بصوت حسن جميل ان شاء رب العالمين فضل يا
+
+327
+00:24:10,190 --> 00:24:19,970
+رجل تقولي اسمك اسمك اسمك تسجل اسمكصفاء نوفل تفضلي
+
+328
+00:24:19,970 --> 00:24:26,750
+يا صفاء أرجو بالله من الشيطان الرجيم يا رجل تعالي
+
+329
+00:24:26,750 --> 00:24:36,570
+صوتك باسم الله الرحمن الرحيم لا تجعل مع الله إله
+
+330
+00:24:36,570 --> 00:24:42,310
+آخر فتقعد مذمما مقتولا
+
+331
+00:24:43,480 --> 00:24:57,040
+وقضى ربك ألا تعبدوا إلا إياه وبالوالدين إحسانا إما
+
+332
+00:24:57,040 --> 00:25:10,050
+يبلغن عندك الكبر أحدهما أو كلاهماأحدهما أو كلاهما
+
+333
+00:25:10,050 --> 00:25:22,570
+فلا تقول لهما أف ولا تنهرهما وقل لهما قولا كريما
+
+334
+00:25:22,570 --> 00:25:33,130
+واخفظ لهما جناح الذل من الرحمة وقل رب ارحمهما كما
+
+335
+00:25:33,130 --> 00:25:37,670
+ربحسبك و بارك الله فيك يا عزيزي شوفوا الآيات
+
+336
+00:25:37,670 --> 00:25:42,050
+القرآنية قلنا مقطع الأول حق الله مقرنا بحق
+
+337
+00:25:42,050 --> 00:25:46,690
+الوالدين ووجوب الإحسان إليهم كلمة وجوب الإحسان
+
+338
+00:25:46,690 --> 00:25:54,000
+شوفوا الآن الكلمات قال فتقعدوحط تحتها خط عندك تقعد
+
+339
+00:25:54,000 --> 00:26:03,000
+تقعد
+
+340
+00:26:03,000 --> 00:26:13,420
+تقعد تقعد
+
+341
+00:26:13,420 --> 00:26:17,580
+تقعد تقعد تقعد تقعد تقعد تقعد تقعد تقعد تقعد تقعد
+
+342
+00:26:20,590 --> 00:26:26,390
+به، هذه مشكلة خطيرة لما بنتكلم عن قضية المعانى،
+
+343
+00:26:26,390 --> 00:26:31,470
+الآن هو العاجز الذي لا يستطيع أن يوفر ما يعتش به،
+
+344
+00:26:31,470 --> 00:26:35,850
+إنسان هي العواطلين عن العمل، اللي جاعدين، بس رجال
+
+345
+00:26:35,850 --> 00:26:42,330
+بالصورة والمنظرهذا العاجز، الأصل معناه أنه عاجز عن
+
+346
+00:26:42,330 --> 00:26:48,230
+تحقيق الحياة لأسرته، عاجز على أن يرتقي في مصاف
+
+347
+00:26:48,230 --> 00:26:52,770
+العلماء، عاجز على أن يكون عنصرا فاعلا في المجتمع،
+
+348
+00:26:52,770 --> 00:26:58,350
+إنسان فاشللأ وبالتالي من هنا عندما نتكلم عن المرأة
+
+349
+00:26:58,350 --> 00:27:03,030
+العاملة والمرأة مش معناته اللغان القضاء المصطلح
+
+350
+00:27:03,030 --> 00:27:08,470
+المغلوط وهنا بدنا نفهم انه لما احنا بنقول اشمل
+
+351
+00:27:08,470 --> 00:27:13,510
+المرأة اشملها المرأة العاملة يعني بيفكر العاملة
+
+352
+00:27:13,510 --> 00:27:18,550
+يعني ايش الموظفة وهذه مغالطة كبرى
+
+353
+00:27:21,800 --> 00:27:26,900
+المرأة العاملة يعني الفاعلة التي أخذت دورها
+
+354
+00:27:26,900 --> 00:27:33,920
+الحقيقي في ريادة المجتمع وأول وعلى رأسي وسلم
+
+355
+00:27:33,920 --> 00:27:39,160
+الأولويات عمل البرأة في حياتها الزوجية يعني انا
+
+356
+00:27:39,160 --> 00:27:44,340
+اقول حاجة احنا انت اجرب واسألونا انا متزوج وزوجتي
+
+357
+00:27:44,340 --> 00:27:52,180
+موظفة بندفع ثمن رهيبمقابل هذا الخروج للعمل
+
+358
+00:27:52,180 --> 00:27:57,100
+الوظيفي، ليه؟ و بعدين أنا هذا الكلام احنا اتكلمنا
+
+359
+00:27:57,100 --> 00:28:00,640
+فيه، يقول إن هذا بتفوت من إمرأة إلى أخرى، المرأة
+
+360
+00:28:00,640 --> 00:28:04,160
+اللي عند استعداد هي و زوجها تدفع الضريبة بعد توافق
+
+361
+00:28:04,160 --> 00:28:09,490
+يا بنت، وأنا بنصحكنصيحة لله اي فتاة لابد عند
+
+362
+00:28:09,490 --> 00:28:16,630
+الزواج ان تجلس مع زوجها ويضع خطة عمل لحياتهم شو
+
+363
+00:28:16,630 --> 00:28:20,770
+بتحب شو بحب شو ممكن يلتقوا في الأفكار حتى في تربية
+
+364
+00:28:20,770 --> 00:28:23,750
+الأولاد حتى في تسيير الحياة مين اللي بدي ياخد
+
+365
+00:28:23,750 --> 00:28:27,090
+الأموال ومين بدي يصرف ومين بدي يشتري ومين كده
+
+366
+00:28:27,090 --> 00:28:31,270
+ترتيب أمور حتى في الأمور الحياتية احنا الآن في
+
+367
+00:28:31,270 --> 00:28:34,350
+بداية الحياة المرأة اللي عاملة أصل البيت تربية
+
+368
+00:28:34,350 --> 00:28:39,810
+الأبناءتربية الأبناء لهذا احنا هندور الفات في لقاء
+
+369
+00:28:39,810 --> 00:28:45,070
+بقارن بين جيلنا و جيلكم بنقول انه جيلكم أفضل
+
+370
+00:28:45,070 --> 00:28:50,270
+بملايين المرات ويفرق عن جيل الآباء و الأجداد كما
+
+371
+00:28:50,270 --> 00:28:55,790
+بين السماء و الأرض في الأفضلية انتوا أفضل لكن
+
+372
+00:28:55,790 --> 00:29:01,050
+الجريمة الكبرى انه ينقصكم الأخلاق و القيم
+
+373
+00:29:06,080 --> 00:29:10,280
+تابع، يعني أجيبلك مثال، في العلم مافيش عندهم علم،
+
+374
+00:29:10,280 --> 00:29:15,120
+كانوا جهلة، في الدين كانت بتلاقي عشرين قرية عندهم
+
+375
+00:29:15,120 --> 00:29:19,320
+شيخ واحد وبيجي بيعطيهم بعض الأمور و بعضهم ما عاش
+
+376
+00:29:19,320 --> 00:29:24,710
+ومات ولم يفقه فقه الطهارةأحنا عندنا علم وعندنا
+
+377
+00:29:24,710 --> 00:29:28,290
+قضية أنه سبقونا أبناء نبي كثير يعني مش معقول أنا
+
+378
+00:29:28,290 --> 00:29:31,010
+أروح أتكلم في علم الاقتصاد وعلم الكذا وكذا بجيت
+
+379
+00:29:31,010 --> 00:29:33,790
+شيخ ومدين ووعظ و .. و .. و .. لكن بعرف على
+
+380
+00:29:33,790 --> 00:29:36,250
+الحاسوبة للي أنا أنا بعرفش على الجوال يمكن كتير
+
+381
+00:29:36,250 --> 00:29:42,290
+فهذا كيف لو الأب موجود أو الجد لكن القيم طاعت
+
+382
+00:29:42,290 --> 00:29:48,350
+عندكم أخلاقيات اليوم أخلاق احنا قلنا حتى احنا اللي
+
+383
+00:29:48,350 --> 00:29:52,300
+بدهم يتزوجوا يبدهم يتزوجوا فضائياترموش عيرة و لون
+
+384
+00:29:52,300 --> 00:29:55,520
+القنين حتى عيرة و الشعر عيرة و كله عيرة في عيرة و
+
+385
+00:29:55,520 --> 00:29:59,440
+كله يعني بمعنى شوفوا عارف ايش معناته كذبة بكذبة
+
+386
+00:29:59,440 --> 00:30:04,450
+واحد بتزوج واحدة أخد عامل البداية في كل المواصفاتو
+
+387
+00:30:04,450 --> 00:30:07,010
+احنا بدنا هيك، بدوا الشعر للأشجار و بدوا العين
+
+388
+00:30:07,010 --> 00:30:10,910
+الخضر و بدوا الخصر و بدوا الجمال و نسي الدين، هذا
+
+389
+00:30:10,910 --> 00:30:14,490
+انحطات في القيام كذلك انحطات في القيام عند البنت
+
+390
+00:30:14,490 --> 00:30:19,870
+لما الشاب المتدين صاحب الخلق و المبادئ بتقدم و لو
+
+391
+00:30:19,870 --> 00:30:24,690
+كان حتى خريج جامعة لكن مافيش عمارة، مافيش سيارة،
+
+392
+00:30:24,690 --> 00:30:28,370
+مافيش طيارة، مافيش بعدين ياخدها على الجمركمان
+
+393
+00:30:28,370 --> 00:30:32,530
+بتردعش، بدها أصحاب اللي صارتت و بعدين جديش بدفع
+
+394
+00:30:32,530 --> 00:30:37,110
+مهر كأنه انتي سلعة انا بتصوروا .. انا مابقولش يا
+
+395
+00:30:37,110 --> 00:30:39,210
+أخواتنا الدور اللي فات تكلمنا فيه كثير من القضايا
+
+396
+00:30:39,210 --> 00:30:42,810
+و بدناش ننظر ان كلنا بالغيرة أو فلانا صار كده و
+
+397
+00:30:42,810 --> 00:30:46,170
+كده انا بقول هذا كله ان يعطي من ساعته واحد غني
+
+398
+00:30:46,170 --> 00:30:48,930
+ملياردير شو المن هيعطي خمس تلاف ولا عشر تلاف
+
+399
+00:30:48,930 --> 00:30:54,090
+لزوجته مثلا كمهر؟ واحد غني ملياردير و هو حلو، بده
+
+400
+00:30:54,090 --> 00:30:58,950
+يهديها مال، عنده مليونلو أعطاه عشرة مائة ألف ..
+
+401
+00:30:58,950 --> 00:31:02,930
+بيأثر عليه يعني .. إذا هو حسب طاقته .. طب و واحد
+
+402
+00:31:02,930 --> 00:31:05,830
+ماعندهوش .. أعطانا .. ماجونة الرسول صلى الله عليه
+
+403
+00:31:05,830 --> 00:31:11,120
+وسلم زوج صحابي بسيروانوواحدهم تزوج بحدائه و آخر
+
+404
+00:31:11,120 --> 00:31:15,400
+تزوج بآية و آخر تزوج بخاتم من ذهب من حديد اذا احنا
+
+405
+00:31:15,400 --> 00:31:20,300
+بنتكلم عن قضايا معنوية انت قيمتك اكبر من كل ذلك طب
+
+406
+00:31:20,300 --> 00:31:23,300
+و لما انت بتيجي بدك تبيع حالك و تشتريه يعني نزلك
+
+407
+00:31:23,300 --> 00:31:27,610
+على السوق و تصير زي ال .. مصيرشيا بنت انت اليوم
+
+408
+00:31:27,610 --> 00:31:31,910
+إيه القيمة؟ من هنا بنقول، الآن في قضية المرأة،
+
+409
+00:31:31,910 --> 00:31:33,970
+بدوا يكونوا اللي هدور في هذا الموضوع، هذا اللي
+
+410
+00:31:33,970 --> 00:31:37,830
+بنتكلم عنه، تغيير المجتمع بمفاهيم وقيم، عشان احنا
+
+411
+00:31:37,830 --> 00:31:41,110
+نغرس هذه القيم الموجودة، إذا انت قعد عاجز، أنا
+
+412
+00:31:41,110 --> 00:31:46,470
+بقول المرأة التي لم تشارك في بناء المجتمع أيضا، هي
+
+413
+00:31:46,470 --> 00:31:51,120
+من القاعدة العاجزة التي لا تستطيع التغييرمش بس لأ،
+
+414
+00:31:51,120 --> 00:31:54,520
+إذا انت فمتى إيش معناته؟ العاجز الذي لا يكتسب ما
+
+415
+00:31:54,520 --> 00:31:59,320
+يعيش به مظمومة مأخوذة من الفئل، ذنب، أولامة،
+
+416
+00:31:59,320 --> 00:32:02,820
+فقاعدة مظمومة، إيش بلاي؟ حطي خط، هناك بتقول حط هنا
+
+417
+00:32:02,820 --> 00:32:07,900
+القاعد العاجز الذي لا يكتسب ما يعيش به، في حاجات
+
+418
+00:32:07,900 --> 00:32:12,400
+بتقول أي تصير جامعا على نفسك الذنب وما يتبعه من
+
+419
+00:32:12,400 --> 00:32:15,700
+الله يعني أنت بصير مظموم، و بعدين في عقابه هلاكلك
+
+420
+00:32:15,700 --> 00:32:20,050
+من قبل الله سبحانه وتعالىمخذولة الخذلان من العجز
+
+421
+00:32:20,050 --> 00:32:24,250
+الذي لا نصير لهم يعني انت محدش نصرك و هذا قضية
+
+422
+00:32:24,250 --> 00:32:31,790
+الآية و قضى و قضى جاءت بمعنى فلية بمعنى حكم و فصل
+
+423
+00:32:31,790 --> 00:32:39,210
+حط عليها واحد و قال ابن كفير قضى بمعنى وصى اتنين
+
+424
+00:32:44,110 --> 00:32:50,470
+ثلاثة القرطبين أمر و ألزم و أوجب، هذه ثلاثة، إذا
+
+425
+00:32:50,470 --> 00:32:58,150
+كلمة و قضى ربك ألا تعبده قضى، إذا تشوفي كام معناه،
+
+426
+00:32:58,150 --> 00:33:03,790
+جات حكم و فصل و أوصى أو وصى و أوجب و أمر و ألزم
+
+427
+00:33:04,720 --> 00:33:09,620
+شوفت جديش؟ يعني لما قال الله تعالى و قضى ربك ألا
+
+428
+00:33:09,620 --> 00:33:18,040
+تعبده شوفت الآن بمعنى أن بر الوالدين أمر و واجب و
+
+429
+00:33:18,040 --> 00:33:24,280
+في ألزام فريضة قهر غصب عنك مش بخاطرك حكم بمعنى أن
+
+430
+00:33:24,280 --> 00:33:31,700
+الله حكم من فوق سبع أرقع سبع سماوات أمره بوجوب بر
+
+431
+00:33:31,700 --> 00:33:36,620
+الوالدينيا سلام حدث ولا حرج على ابناء الجامعات من
+
+432
+00:33:36,620 --> 00:33:42,740
+الاحترام العظيم والهيبة للأباء ده بحنا الأباء
+
+433
+00:33:42,740 --> 00:33:47,300
+والامهات أصبحت الأم خادمة عند ابنتها وهذا من
+
+434
+00:33:47,300 --> 00:33:52,300
+السبعة لما بنتكلم عن الأم تالد ربتها كان زمان
+
+435
+00:33:52,300 --> 00:33:55,540
+والله بنقول والله الخدم وبعدين بتبيعها وتشتري ما
+
+436
+00:33:55,540 --> 00:34:01,180
+احنا اليوم لان كام من إنسان موظف جاء عند أمه
+
+437
+00:34:01,180 --> 00:34:07,220
+الخادمة في البيتوياريت انه مثلا يفهم ان الأم قائمة
+
+438
+00:34:07,220 --> 00:34:11,160
+بعمل البيت وهو ومرته برا وقائمة على أمر أبنائه
+
+439
+00:34:11,160 --> 00:34:15,500
+هاتوا تعالى حتى بعد ما براحواشوفتوا الفرق؟
+
+440
+00:34:15,500 --> 00:34:19,980
+الإهانة، مش عيب إن المرأة تخدم ولادها و بتضحي بكل
+
+441
+00:34:19,980 --> 00:34:23,460
+ما تملك من أجل الأولاد و تراهم سعداء، لكن أن يكون
+
+442
+00:34:23,460 --> 00:34:27,820
+الشعور خجلان من أمه، خجلان من أبوه، نحن عنا
+
+443
+00:34:27,820 --> 00:34:33,240
+أساتذة، جامعيين، أطباء، الآن اللي هم مركز اجتماعي،
+
+444
+00:34:33,240 --> 00:34:38,070
+بيعتروا من آبائهم إذا كانوا أميينو لما بيجيوا
+
+445
+00:34:38,070 --> 00:34:42,390
+صحابهم بيجيب الأب لما بيأزم صاحبه بيجيب أبوه يقعد
+
+446
+00:34:42,390 --> 00:34:46,130
+يتفضل حتى على الطعام و الشراب و يعتقل انه هذا الأب
+
+447
+00:34:46,130 --> 00:34:53,030
+انا أبوي ماكنش لا بجرى ولا بكتب و أميلكن هذا يمنع
+
+448
+00:34:53,030 --> 00:34:57,370
+انه بالعكس انا كنت بفتخر انه ييجي و لهذا كثير من
+
+449
+00:34:57,370 --> 00:35:02,630
+القضايا كانت حتى لو الأب كبر و قال و بدأ يقول ما
+
+450
+00:35:02,630 --> 00:35:05,910
+لا يمكن ان يسمع لكن بدك تفهم ان هذا أبوك واحد
+
+451
+00:35:05,910 --> 00:35:09,410
+اتنين تلاتة هذا الأب اللي بنقول عنه أمي هو اللي
+
+452
+00:35:09,410 --> 00:35:13,710
+ربنا و خلانا دكاترة واحنا أصحاب العلم مش قادرين
+
+453
+00:35:13,710 --> 00:35:16,950
+نربي ولادنا يطلعوا أساتذة و يطلعوا دكاترةإذا مين
+
+454
+00:35:16,950 --> 00:35:20,950
+الأفضل؟ هذا الأم الجاخل اللي بنقول عنه خرج أجيال
+
+455
+00:35:20,950 --> 00:35:24,610
+قادة أم .. قادة بتقود مسيرة وإحنا مش قادرين نربي
+
+456
+00:35:24,610 --> 00:35:28,770
+أولادنا زي ما ربونا الأباءشوفتوا وين بر الأباء؟
+
+457
+00:35:28,770 --> 00:35:31,370
+بدنا نفهم إن هذه بنات مش مشكلة وقضيتوا العقوب
+
+458
+00:35:31,370 --> 00:35:34,450
+كثيرة جدا موجودة في هذا الميدان لكن احنا بناخد
+
+459
+00:35:34,450 --> 00:35:39,110
+الإحسان إحسانة .. الإحسان ضد إيش؟ إحسانة ويعني
+
+460
+00:35:39,110 --> 00:35:43,050
+كذلك المراقبة شوفتوا كم معنى للإحسان؟ إذا جاءت
+
+461
+00:35:43,050 --> 00:35:47,050
+بمعنى ضد الإساء حط عليها واحد في صفحة 70 وجاءت
+
+462
+00:35:47,050 --> 00:35:53,280
+بمعنى وقيل الإشارة إلى المراقبةأما كلمة off و لا
+
+463
+00:35:53,280 --> 00:35:59,680
+تقول لهم اف يعني شوف كلمة off جاءت أصل التضجر لكن
+
+464
+00:35:59,680 --> 00:36:03,280
+لما طلع انت بيه؟ طب لو كان هنا بعض الخبار
+
+465
+00:36:06,850 --> 00:36:14,230
+فلعى أُف يعني أنا ببثل التمثيل بمعنى أن هناك هذه
+
+466
+00:36:14,230 --> 00:36:20,510
+الكلمة بمعنى أسلغى ما يسقط من التراب أو الرماد
+
+467
+00:36:20,510 --> 00:36:25,590
+فيقعالطالعين فيش بيقول؟ يسقطوا من تراب أو رماد
+
+468
+00:36:25,590 --> 00:36:29,630
+فينفخوا الإنسان اللي يزولها، هي اللي قلتلك أُف، بس
+
+469
+00:36:29,630 --> 00:36:33,830
+تقولي للأب و لأ، فما بالك الآن اللي بيصفع الأهل و
+
+470
+00:36:33,830 --> 00:36:37,410
+اللي بيضرب الأم و لا ينهر و لا الإساء توجهي
+
+471
+00:36:37,410 --> 00:36:41,990
+الكلمات النابية، عدم الاحترام، إذا هو فيه في
+
+472
+00:36:41,990 --> 00:36:47,430
+القرآن لو وجد كلمة أقل من كلمة أُف، هو فيها أقل من
+
+473
+00:36:47,430 --> 00:36:53,980
+كلمة أُف، يا سلام و أنت متطلع في أمك أنالا تسعر
+
+474
+00:36:53,980 --> 00:36:56,920
+خدك للناس مظبوطا يعني طب و أنت قاعد تتعمل إذا لا
+
+475
+00:36:56,920 --> 00:37:01,520
+الناس فما بالك من الأهل إذا هنا كلمات قرآنية رائعة
+
+476
+00:37:01,520 --> 00:37:07,400
+الأوابين سوف الآن من إيش؟ من أبا و رجع بمعنى رجع
+
+477
+00:37:07,400 --> 00:37:13,540
+لكن الأوابين هذا أبا لكن الأوابين دربارك جمع أوة
+
+478
+00:37:14,750 --> 00:37:20,530
+الأوابين عندك في الكتاب، حطيه، جمع أواب، وكثير
+
+479
+00:37:20,530 --> 00:37:22,990
+القنابة والتوبة والرجوع، ما تقولوش اللي هي
+
+480
+00:37:22,990 --> 00:37:28,490
+الأوابين يعني معناته التائب، لأ، معناته كثير
+
+481
+00:37:28,490 --> 00:37:33,070
+القنابة والتوبة والرجوع، يعني عمل بلحع ربه، الحاح
+
+482
+00:37:33,330 --> 00:37:36,970
+شديد، كثير التوبة، دائما على لساني يا رب تبتوليك،
+
+483
+00:37:36,970 --> 00:37:39,850
+يا رب استغفرني، يعني استغفار، توبة، إنابة، رجوع
+
+484
+00:37:39,850 --> 00:37:43,870
+إلى الله في كل أحواله، هي التوبين، الأوابين، يعني
+
+485
+00:37:43,870 --> 00:37:46,790
+بمعنى مش تابة، أنا توبت وخلصت، بقول يا رب تبتوليك
+
+486
+00:37:46,790 --> 00:37:49,670
+وخلصت، وانتهى الموضوع، لا، أنا كثير، يعني أنا
+
+487
+00:37:49,670 --> 00:37:53,250
+دائم، وهذا القضية حتى أن الله سبحانه وتعالى أنه
+
+488
+00:37:53,250 --> 00:37:56,930
+يمحو هذه قضية الدنوبة الآن، الآن المعنى الإجمالي
+
+489
+00:37:57,940 --> 00:38:01,560
+يعني ببدأ المقطع بأهم قضية تواجه الأمة، ألا وهي
+
+490
+00:38:01,560 --> 00:38:08,020
+قضية التوحيد، قضية التوحيد وهو لأ تجعل يدك لأ تجعل
+
+491
+00:38:08,020 --> 00:38:12,340
+مع الله إله آخر، يعني بدأ بهذه القضية أنها نهت عن
+
+492
+00:38:12,340 --> 00:38:16,500
+الشرك وصغره، وحذرت من هذه العاقبة، ثم بعد ذلك أمر
+
+493
+00:38:16,500 --> 00:38:21,820
+بيش بالإحسان إلى الوالدين، وخاصة إذا بلغ الأبوان
+
+494
+00:38:23,010 --> 00:38:29,510
+اما يبلغنا عندك الكبر احدهم او كده يعني هم موصلون
+
+495
+00:38:29,510 --> 00:38:34,250
+في قضية الشيخوخة لان مكتيش اصلا بيبدأ قضيته بالضعف
+
+496
+00:38:34,250 --> 00:38:38,510
+عند الآباء لما بيكبروا طب و هم اقوياء معروف ان انت
+
+497
+00:38:38,510 --> 00:38:42,710
+اقوياء انت بتسجل تطلع تطلي؟عشان هيك بمعنى انه في
+
+498
+00:38:42,710 --> 00:38:48,510
+وقت الضعف زي ما انت لما كنت ضعيفة غزيلة و كانوا
+
+499
+00:38:48,510 --> 00:38:53,770
+ببروك و يدللوك و يعطوك انت الأن بدك تصدى ما عليك
+
+500
+00:38:53,770 --> 00:38:58,070
+من الجميع و الصحاب اللي حمل أمه جاءت بتوفيها حول
+
+501
+00:38:58,070 --> 00:39:00,890
+الكعبة قالوا يعني انا بقدى
+
+502
+00:39:03,400 --> 00:39:08,760
+جزء من البر قال و الله و لا طلقة من طلقاتها شوف
+
+503
+00:39:08,760 --> 00:39:12,000
+لما عندك طلق الولادة طلقة واحدة ما قدّيت اللي
+
+504
+00:39:12,000 --> 00:39:16,640
+عليها كيف بدك تقدّي كل جميلة يعني ولا شي ولا حاجة
+
+505
+00:39:16,640 --> 00:39:18,880
+و احنا ما شاء الله طول النهار حاملين أهلنا على
+
+506
+00:39:18,880 --> 00:39:22,180
+رؤسنا إذا هنا بدأت الصورة بالتركيز على قضية
+
+507
+00:39:22,180 --> 00:39:26,640
+التوحيد و بعدين لاتجعل مع الله الذي خلقك و رزقك
+
+508
+00:39:26,640 --> 00:39:31,700
+إلها آخر فتكون بذلك مظموما و كأنه بيبين حال الذي
+
+509
+00:39:31,700 --> 00:39:37,750
+تبهييتحلل من دين الله ومن شرع الله وبعدين يفرط في
+
+510
+00:39:37,750 --> 00:39:41,730
+تعاليم الله التي أوجب عليه هذا بيقعد كأنه قاعد في
+
+511
+00:39:41,730 --> 00:39:45,830
+القرنة عاجز عن أن يؤدي دور شفت الإنسان العاجز
+
+512
+00:39:45,830 --> 00:39:49,130
+الكسيح اللي .. اللي هنا؟ مافيش إيه دور هذا هي
+
+513
+00:39:49,130 --> 00:39:54,170
+الحال ومش بس أصلا هو كسيح وضعيف مش قادر يؤدي شيء
+
+514
+00:39:54,170 --> 00:39:59,460
+ومدموم مكروه وبعدين مالوش نصيرشوفتوا هالحالة ما
+
+515
+00:39:59,460 --> 00:40:03,500
+أذلها؟ إنسان لا جادر يعمل إشي و مكروه من الآخرين
+
+516
+00:40:03,500 --> 00:40:07,660
+ولا واحد الناصر ولا واحد مأيده؟ شوفتي بالله
+
+517
+00:40:07,660 --> 00:40:10,060
+الحياة؟ أيات الحياة دي اللي عايشينها؟ والله لو
+
+518
+00:40:10,060 --> 00:40:13,840
+أعطينا مال الدنيا ما أحنا مكافئين في هذه القضية،
+
+519
+00:40:13,840 --> 00:40:19,600
+إذا هنا وقولهالان و قوله هو ايه هو بالوالدين
+
+520
+00:40:19,600 --> 00:40:26,640
+احسانا و قضى ربك ان تحسنه الى الوالدين طلع احسانا
+
+521
+00:40:26,640 --> 00:40:32,500
+كاملا فى الرعاية حط عليها واحد لما انت فى رقم هنا
+
+522
+00:40:32,500 --> 00:40:37,600
+اتنين قوله ايه هو بالوالدين احسانا حط عليها حسين
+
+523
+00:40:37,600 --> 00:40:48,500
+والسؤال لقد اوجب الاسلامالإحسان إلى الوالدين حين
+
+524
+00:40:48,500 --> 00:40:55,300
+قال وقضى ربك أن لا تعبد إلا إياه بالوالدين بيني
+
+525
+00:40:55,300 --> 00:41:00,900
+ذلك So فالان أو جب طلع ايه؟ أولا الإحسان كاملا في
+
+526
+00:41:00,900 --> 00:41:08,850
+الرعايةإثنين في العناية، ثلاثة في المعاملة، إذا
+
+527
+00:41:08,850 --> 00:41:13,470
+هذه المعنى، معنى أوجب الإسلام الإحسان في إيش؟ في
+
+528
+00:41:13,470 --> 00:41:16,990
+الرعاية والعناية والمعاملة، وفي فرق بين الثلاثة؟
+
+529
+00:41:16,990 --> 00:41:22,130
+أه، في فرق، لأنه فيه رعاية وعناية ومعاملةمعاملة
+
+530
+00:41:22,130 --> 00:41:25,930
+سلوك، معاملة اعتقاد، كذا، لكن أحيانا تصل إلى قضية
+
+531
+00:41:25,930 --> 00:41:30,050
+الأشياء المالية، والأشياء في الأخلاق، الكلام، في
+
+532
+00:41:30,050 --> 00:41:33,210
+أشياء ايش ماله؟ الكلام، في أشياء النظر، في أشياء
+
+533
+00:41:33,210 --> 00:41:36,510
+المادة، إذا كل هذه التعاملات، وحنقف مع ذلك، طالع
+
+534
+00:41:36,510 --> 00:41:41,670
+أشجال هو، في الآن السؤال التاني، إما يبلغن عندك
+
+535
+00:41:41,670 --> 00:41:48,090
+الكبر، حُط تحت عندك خط، ما الهدف؟ شون انت استفيد
+
+536
+00:41:48,090 --> 00:41:54,050
+من كلمة عندك، ماذا تعني؟طلع ايش مكتوب؟ تفيده ..
+
+537
+00:41:54,050 --> 00:42:00,510
+ايش مقاله؟ تفيده معنى الالتجاء والاحتماق في حالة
+
+538
+00:42:00,510 --> 00:42:07,310
+الكبر والضعف طلع ايش قال؟ عندك انت
+
+539
+00:42:07,310 --> 00:42:13,290
+طول حياتك وانت عنده و هو اللي بيصرف و هو اللي قايم
+
+540
+00:42:13,290 --> 00:42:19,450
+على أمرك الآن هو أصبح عندك في حالة الضعف موجود
+
+541
+00:42:19,450 --> 00:42:25,020
+عندكفى عذرتك، شو عملتله؟ كلمة عندك تفيد معنى
+
+542
+00:42:25,020 --> 00:42:29,060
+الالتجاء واحتماء إليك في حالة .. هو لما كبره ضعف،
+
+543
+00:42:29,060 --> 00:42:33,720
+التجأ إلك سيبه،
+
+544
+00:42:33,720 --> 00:42:37,860
+يلا نسوان اليوم يتحكموا بمشاهد، نسوان اليوم بناتنا
+
+545
+00:42:37,860 --> 00:42:44,810
+هي المشكلةمش راضي تعتبر ان حماتها و حماها هو أب و
+
+546
+00:42:44,810 --> 00:42:50,330
+أم مش قادر لأمها بتودي كل شي لأختها بتروح و مستئد
+
+547
+00:42:50,330 --> 00:42:55,850
+في صلاة الرحم تاخد كل شي لكن شيء بتعلق بالزوجطب
+
+548
+00:42:55,850 --> 00:43:00,230
+ليش انت بتتودد لأمك بها طريقة بتتوددش لحنكي؟ طب بس
+
+549
+00:43:00,230 --> 00:43:04,690
+على الأقل بدأ أقول إذا كنت تحبينا الزوج و بتعتبر
+
+550
+00:43:04,690 --> 00:43:09,890
+أن هذا زوجك اللي الرابط and علاقة النفس بالنفس و
+
+551
+00:43:09,890 --> 00:43:13,760
+علاقة الروح بالروح بالزوجمش احنا بنقول الزوج الهوى
+
+552
+00:43:13,760 --> 00:43:17,720
+اللى بنتنفسه نستغنيش عنه و هو بقولك نفس الكلام طب
+
+553
+00:43:17,720 --> 00:43:21,620
+طالما انت الهوى اللى بتنفسه و هو الهوى اللى
+
+554
+00:43:21,620 --> 00:43:25,400
+بتتنفسيه طب من باب الحب و الوفاء و الإخلاص للزوج
+
+555
+00:43:25,400 --> 00:43:29,220
+ان احترم أمه احترم أبوه احترم خواته و شوفي بيشوفي
+
+556
+00:43:29,220 --> 00:43:33,320
+مكان تجدش و بدي أبيّلك ان قلة العقل عند النساء
+
+557
+00:43:33,320 --> 00:43:39,960
+والله لو أحسنت التعامل مع الجغيتين لتعيش سلطانة و
+
+558
+00:43:39,960 --> 00:43:44,640
+ملكةبتنحب بالفعل و كل الناس بيقدروها و هذا عبر
+
+559
+00:43:44,640 --> 00:43:46,840
+التجربة هشوفوا .. شوفوا عبر التجربة و تشوفوا
+
+560
+00:43:46,840 --> 00:43:51,140
+العائلات المرأة اللي بيقولها دي قدم ساعد احنا
+
+561
+00:43:51,140 --> 00:43:54,320
+بنقول قدم ساعد حقيقة لإن هي مفتاح من مفاتيح
+
+562
+00:43:54,320 --> 00:43:57,700
+السعادة لأنها تدخل الصراحة شوفوا الآن و احنا كذلك
+
+563
+00:43:57,700 --> 00:44:02,370
+بنتعامل يعني مثلا انه انا لما انا زوجتيبتقبل يد
+
+564
+00:44:02,370 --> 00:44:05,670
+الأم ويد الأب، ما أنا بيفرض عليه نقبل إيد أمها و
+
+565
+00:44:05,670 --> 00:44:09,230
+إيد أبوها، لما أنا هي بتبرق بأخواتي، أنا بصير أنا
+
+566
+00:44:09,230 --> 00:44:13,750
+مرغم أبرق أخواتها، و بالعكس أنت كل ما بررتي أهل
+
+567
+00:44:13,750 --> 00:44:18,060
+الزوج، كل ما كان الزوج بارن بأهل زوجتههذا اللي
+
+568
+00:44:18,060 --> 00:44:21,760
+بنتكلم عنه، بنتكلم عن معاني، تفهم بالك الأب، أنا
+
+569
+00:44:21,760 --> 00:44:26,540
+بقول أن المرأة الصالحة التي تريد مرضاة الله عليها
+
+570
+00:44:26,540 --> 00:44:30,540
+أن تسعى في تحقيق مثل هذه المعالم الطيبة، وقل لهم
+
+571
+00:44:30,540 --> 00:44:34,860
+قولا كريمة، شوف القول الكريم، القول الكريم إيه
+
+572
+00:44:34,860 --> 00:44:40,420
+أكتر من معنى، أول مرتبة من مراتب الرعاية طلعيه،
+
+573
+00:44:40,420 --> 00:44:45,020
+والأدب، حط عليها خطأول مرتبة من مراتب الرعاية
+
+574
+00:44:45,020 --> 00:44:52,720
+والأدام ألا يفضر منه ايش ماله؟ الله أكبر يعني
+
+575
+00:44:52,720 --> 00:44:58,800
+بمعنى أن يكون الكلام الاحترام وهي مرتبة أعلى أن
+
+576
+00:44:58,800 --> 00:45:02,980
+يكون كلامه ايش ماله؟ الاحترام والتقدير والإكرام
+
+577
+00:45:02,980 --> 00:45:09,270
+بالقول الكريمإذا لا تقول له ما أفن خلصها منها يعني
+
+578
+00:45:09,270 --> 00:45:14,110
+ممنوع الإساءة لكن قبل ما تسيء كمان مطلوب منك الآن
+
+579
+00:45:14,110 --> 00:45:20,110
+أن تقول قولا كريما الاحترام والتقدير وادخال السرور
+
+580
+00:45:20,110 --> 00:45:25,050
+طلع القول الكريم هو كل قول يدخل السرور على الأبوين
+
+581
+00:45:25,050 --> 00:45:31,430
+وليس نهي عن التدجرالسنة هي عن تدجر شيء ما تتدجرش
+
+582
+00:45:31,430 --> 00:45:35,150
+ومش بس انت ما تتدجرش منهم كمان مطلوب منك تقول
+
+583
+00:45:35,150 --> 00:45:39,570
+الكلام الطيب كل ما يدخل السرور من كلمات رقيقة انت
+
+584
+00:45:39,570 --> 00:45:43,950
+بتروحي على البيت، اتقبل الأم، اتريحيها، تعمليلها،
+
+585
+00:45:43,950 --> 00:45:47,850
+كل شيء هذا، هذا ادخل كل عمل يدخل السرور على الأخل،
+
+586
+00:45:47,850 --> 00:45:52,570
+فهو قوله طيب، وليه هذا قال عطاء القول الكريم هو
+
+587
+00:45:52,570 --> 00:45:56,930
+القول اللين، يا أبته، يا أمهوغير ذلك من الاسم ال
+
+588
+00:45:56,930 --> 00:45:59,970
+.. او ال .. ال .. الكنية ان تطلق على هذا .. انا
+
+589
+00:45:59,970 --> 00:46:04,390
+بقول هذا كلام من الكلام اللي .. ومن الرحمة كذلك ان
+
+590
+00:46:04,390 --> 00:46:09,510
+تكوني رقيقة، لطيفة، معهما، لا ترفعي العين، ولا
+
+591
+00:46:09,510 --> 00:46:12,530
+يرفض لهم أمر، اللهم أكبر اتوا بنتكلم، بتتكلموا
+
+592
+00:46:12,530 --> 00:46:15,970
+معاكي وانت ما شاء الله ابن الدي بتتكلمي، تملي راسك
+
+593
+00:46:15,970 --> 00:46:22,020
+نبفة، تملي راسك تواضعا، شويةالمجتمع هنا القيم اللي
+
+594
+00:46:22,020 --> 00:46:25,580
+بنتكلم عنها والفرق أنه احنا السابق بدخل البيت و
+
+595
+00:46:25,580 --> 00:46:28,700
+احنا طالعين على المدرسة كنا نقبل أيدي الأب و الأم
+
+596
+00:46:28,700 --> 00:46:32,260
+و الجد و الجدة و احنا راجعين نفس القضية و كان كل
+
+597
+00:46:32,260 --> 00:46:36,000
+ما بنطلع الجامعة .. شوف أول مدرسة تصوري أن الأب و
+
+598
+00:46:36,000 --> 00:46:39,620
+الأم وضع إيده على راسك و يدعو لك بالخير و انت طالع
+
+599
+00:46:39,620 --> 00:46:42,760
+.. رب نبديش وفقك؟ مارضى الله .. مارضى ال .. ال ..
+
+600
+00:46:42,760 --> 00:46:45,480
+ال .. هذا مارضى الله؟ ولا بشيء؟ مارضى الوالدة
+
+601
+00:46:45,480 --> 00:46:49,260
+مارضى الله؟ و العكس صحيح يعني لا يمكن أن يرضى عنك
+
+602
+00:46:49,260 --> 00:46:53,570
+اللهإلا إذا ردوا الأهل صوري وانت طالع الله يسهل
+
+603
+00:46:53,570 --> 00:46:56,450
+عليك وليه؟ ده كانت سبتي الله يرحمها، إيش بجد تقولي
+
+604
+00:46:56,450 --> 00:47:01,530
+دعاء للآن؟ للآن في رنف أذنى رحمة الله تعالى عليها،
+
+605
+00:47:01,530 --> 00:47:06,070
+إيش بتقول؟ الله ينجحك ويربحك و بين عباده لا يضحك
+
+606
+00:47:07,340 --> 00:47:11,420
+شفت هذا الدعاء؟ نجحك و ربحك، نجاح و ربح و عدم
+
+607
+00:47:11,420 --> 00:47:15,040
+فضيحة، شفت الساترة في الدنيا؟ والله لو جبنا كل
+
+608
+00:47:15,040 --> 00:47:17,660
+العلماء اليوم يقولوا هذه العبارات، يختصفوا هذه
+
+609
+00:47:17,660 --> 00:47:21,100
+الجملة، ما هم يقولونها؟ طلع المعنى الرائع، و أنت
+
+610
+00:47:21,100 --> 00:47:24,430
+طالع و أنت نازلةالله يرضى عليك، الله يسهل عليك،
+
+611
+00:47:24,430 --> 00:47:27,850
+شوفت الكلمات الحلوة، هل اليوم احنا البنت بتيجي من
+
+612
+00:47:27,850 --> 00:47:30,210
+الجامعة، بتدخلوا على غرفتها، والابن ماشي وولا
+
+613
+00:47:30,210 --> 00:47:32,370
+يعني، مرة ولادنا بيجيوا مش عارفين ولادنا في الدار
+
+614
+00:47:32,370 --> 00:47:35,530
+ولا مش في الدار، وطلعوا والله مش عارفين، طب وين؟
+
+615
+00:47:35,530 --> 00:47:40,410
+وين البركات؟ وين؟ وين الدعاء؟ ولادنا استغنوا، ليش
+
+616
+00:47:40,410 --> 00:47:43,780
+يعني، هو ماشي يعني بالله دعاء الوالدين؟بطّل يعمل
+
+617
+00:47:43,780 --> 00:47:46,500
+قيمة، هذه القيمة اللي بتكلم عليها قبل شوية، إذا
+
+618
+00:47:46,500 --> 00:47:50,700
+هذه المعاني الرائعة اللي احنا كطلاب علم، اللي
+
+619
+00:47:50,700 --> 00:47:54,240
+اليوم احنا بنتكلم كساتذة، بنتكلم معاكم كأبناءنا،
+
+620
+00:47:54,240 --> 00:47:57,160
+هذه المعاني اللي بدنا نشوفها، الجيل، يا الله أكبر،
+
+621
+00:47:57,160 --> 00:48:00,660
+ربنا هيئ لكم، كل الظروف، احنا عشرة كنا في البيت
+
+622
+00:48:00,660 --> 00:48:08,000
+نام، في الغرفة عشرة، عندنا طاولة؟لمّا جابوا بعد ما
+
+623
+00:48:08,000 --> 00:48:10,820
+صرنا في دائرة الجامعة جابوا شوية خشب وطعانوه و
+
+624
+00:48:10,820 --> 00:48:13,540
+حطوها فى الطاولة و جالوا مبسوطين ان احنا قولنا
+
+625
+00:48:13,540 --> 00:48:17,260
+خاطر ماحدش يمسها الطاولة لإن صارت شيء أثرى او قصدي
+
+626
+00:48:17,260 --> 00:48:23,120
+شيء عظيم جدا او كمان كل واحد كان له خزانة و سرير و
+
+627
+00:48:23,120 --> 00:48:28,540
+laptop و جوال بنتنا كلنا بدنا جوالات و بطلت الجوال
+
+628
+00:48:28,540 --> 00:48:33,120
+يمكن زمان اللى ماكان تسموه شبشب و لا بصراشهبتناقش
+
+629
+00:48:33,120 --> 00:48:35,640
+الحين لأ الفناتة بيفتخروا، بتجيب مين بتجيب جوال
+
+630
+00:48:35,640 --> 00:48:39,000
+أغلى، طب ليش أنت بتشتغلي رئيس الشركة؟ يعني بدك
+
+631
+00:48:39,000 --> 00:48:42,280
+تشتغلي عليها عشان تعمل و تظبطي ولا بدك بس أن أهلك
+
+632
+00:48:42,280 --> 00:48:45,120
+يتصلوا عليك إيه؟ ولا .. آه .. يمكن تطلع صورة
+
+633
+00:48:45,120 --> 00:48:48,290
+صاحبيتك اللي كنت بتكلميها، اللي خاطر، مش إيه؟شوفت
+
+634
+00:48:48,290 --> 00:48:52,230
+وين المعاني؟ انا بقول هذا تراجع فكري، تراجع في
+
+635
+00:48:52,230 --> 00:48:57,210
+مفاخين قيم، انا باخد اتصال، انا مافيش جوال ميت شكل
+
+636
+00:48:57,210 --> 00:49:01,550
+و انا اذا كنت على الأقل أخلي قدراتهم قليلة، باخد
+
+637
+00:49:01,550 --> 00:49:05,310
+شغل هذا، بتعامل معاهوبالتالي بقى اديه لدوره غرض
+
+638
+00:49:05,310 --> 00:49:08,110
+وانتهى الموضوع و لا بس بده فاخر البنات شايفه ات
+
+639
+00:49:08,110 --> 00:49:11,130
+معاه جوال و طب بناتنا اللي قاعدة والخينة حاطة رجل
+
+640
+00:49:11,130 --> 00:49:14,090
+ع رجل و لازم اشوف بلطلون الكابويل و بعدين هى قاعدة
+
+641
+00:49:14,090 --> 00:49:17,230
+و حاطة ال laptop و قاعدة بتشتغل برا قاعدة بتشتغل
+
+642
+00:49:17,230 --> 00:49:19,750
+يجي عشان تفاخر يجيب معاك ال laptop عشان يعنيش وشو
+
+643
+00:49:19,750 --> 00:49:23,430
+المشكلة؟ هو بالفعل ان ال laptop فيه له حاجات طيبة
+
+644
+00:49:23,430 --> 00:49:27,150
+جدا، هل استخدمتيه للدعوة؟بستخدم دي للدعوة عشان
+
+645
+00:49:27,150 --> 00:49:31,530
+اقول والله ربنا بكتبلك أجر وانت تقدمت بعقليتك
+
+646
+00:49:31,530 --> 00:49:35,190
+الفكرية الدعوية انك انت تستخدم ذلك في دعوة الآخرين
+
+647
+00:49:35,190 --> 00:49:39,430
+او على الأقل تجلسي وحط حوالك عشر بنات جاعدة في
+
+648
+00:49:39,430 --> 00:49:43,050
+محاضرة في كلام بتناقش فيه أمور ربك عشان ربنا انه
+
+649
+00:49:43,050 --> 00:49:46,230
+وجد فراغة انك تستغليه و تأثر في قضية ربنا منهم
+
+650
+00:49:46,230 --> 00:49:49,540
+عليكي إذا أهلك أغنياء ماشي الحاللكن إذا أهلك فقراء
+
+651
+00:49:49,540 --> 00:49:52,720
+و بتخليهم يشهدوا و يمدوا الأيد للأخرين عشان يجيبوا
+
+652
+00:49:52,720 --> 00:49:55,580
+لك لابتوب و تبينيه و بعدين كل يوم بدك جي الباب و
+
+653
+00:49:55,580 --> 00:49:58,680
+كل يوم بدك كده و كل يوم بدك تنزلي على الكعبة ..
+
+654
+00:49:58,680 --> 00:50:03,010
+تعرفين الكعبة تبع تلباناتشية؟الكفتيريا من الصبح
+
+655
+00:50:03,010 --> 00:50:06,270
+بيصبن لأنها مش مش مستعدة تجوم الصبح على صلاة الفجر
+
+656
+00:50:06,270 --> 00:50:10,010
+تصلي و بعدين تفطر و تيجي لأ ما هي بتجوم الساعة
+
+657
+00:50:10,010 --> 00:50:12,750
+ثمانية ولا ساعة .. و بيكون المحاضرة تالت ساعة تسعة
+
+658
+00:50:12,750 --> 00:50:15,010
+و بتيجي تجري و .. و .. و .. و .. و .. و .. و .. و
+
+659
+00:50:15,010 --> 00:50:15,590
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+660
+00:50:15,590 --> 00:50:15,610
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+661
+00:50:15,610 --> 00:50:15,870
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+662
+00:50:15,870 --> 00:50:16,970
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+663
+00:50:16,970 --> 00:50:16,990
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+664
+00:50:16,990 --> 00:50:20,670
+.. و .. و .. و .. و .. و .. و .. و ..
+
+665
+00:50:30,360 --> 00:50:33,740
+تعزم حسب مين؟ هو أهلك لما أعطوك .. أعطوك لهذا عشان
+
+666
+00:50:33,740 --> 00:50:37,760
+تعزم صاحباتك ما كلكم في الحال سوا، بدت تنزلين ماشي
+
+667
+00:50:37,760 --> 00:50:40,280
+و ما .. أنا بقول كمان مش عيب أنه البنت لما تيجي
+
+668
+00:50:40,280 --> 00:50:42,760
+تشتر لحالها و غير أغراته، بده تفضل .. تفضل في اللي
+
+669
+00:50:42,760 --> 00:50:45,740
+نصها، ده تبحها، لكن والله يتأروا كمان شكل و اتنين
+
+670
+00:50:45,740 --> 00:50:49,380
+شكل و أهلك من ون يجيبه، شفتوا؟ لكن إيه ده واحدة
+
+671
+00:50:49,380 --> 00:50:52,720
+ربنا منهم و أهلها سمحو لها و جايلين لها أنه انت
+
+672
+00:50:52,720 --> 00:50:55,990
+مسموح لك، يا هي بتطلب إتهابتقول أنا إيه لصديقة
+
+673
+00:50:55,990 --> 00:50:59,830
+وصديقتي ماعنداش ومش مقدرة، إيه بتسمحولي، بتسمحوني
+
+674
+00:50:59,830 --> 00:51:02,710
+يعني في قضية هذا المال اللي بجدمه، لأ؟ ولا بيصير
+
+675
+00:51:02,710 --> 00:51:07,380
+حرام؟أحنا مش قادرين أن نعيش على القيام وكل يوم
+
+676
+00:51:07,380 --> 00:51:10,220
+بقولك و أنت جيل باب و كل يوم تيجي و لو لون الحذاء،
+
+677
+00:51:10,220 --> 00:51:13,360
+لون البلطلون، لون الجميس، لون الجيل باب، لون غطاء
+
+678
+00:51:13,360 --> 00:51:16,140
+الرنس، بتعمل، مافيش أشكالي هنا بس بندور على
+
+679
+00:51:16,140 --> 00:51:18,960
+المظاهر، الكذاب هذا اللي ذبحتنا ذبح و احنا فيه
+
+680
+00:51:18,960 --> 00:51:21,460
+قضايا كتيرة، أنا بقول هذه معاني لو بدك أفعلها
+
+681
+00:51:21,460 --> 00:51:25,220
+معاني رائعة جدا في سورة الإسراء و أخفض و أقول له
+
+682
+00:51:25,220 --> 00:51:31,150
+ربي رحمهما كما ربياني صغيرةشوف الآن بنتكلم عن و
+
+683
+00:51:31,150 --> 00:51:34,650
+أقول ربي ارحمهم كما ربياني صغيرة أنا بدأ أقف مع
+
+684
+00:51:34,650 --> 00:51:38,210
+التلاتة الأول انتبه فوق و أخفض لهم جناح تدلي من
+
+685
+00:51:38,210 --> 00:51:43,350
+الرحمة و أقول ربي ارحمهم كما ربياني صغيرة شوف الآن
+
+686
+00:51:43,350 --> 00:51:47,010
+و أخفض لهم جناح تدلي من الرحمة هو الآن لما بدأ
+
+687
+00:51:47,010 --> 00:51:52,170
+أقولك بيجني الأساليب البيانية او كده ففيها هنا ايش
+
+688
+00:51:52,170 --> 00:51:56,740
+مكتوب هنا مكتوب هنا لها استعارةوانا طبعا استعارة
+
+689
+00:51:56,740 --> 00:52:02,640
+مكنية ليش استعارة مكنية؟ شبه الإنسان بالطائر اللي
+
+690
+00:52:02,640 --> 00:52:05,640
+له جناح، مش هيك؟ وبالتالي إذا أنهنا استعارة مكنية
+
+691
+00:52:05,640 --> 00:52:10,440
+وقال رب ارحمهما كما ربياني صغيره شوفوا الآن بنتكلم
+
+692
+00:52:10,440 --> 00:52:14,180
+عن قضية أنه الموضوع التربة و الرائع اللي موجود في
+
+693
+00:52:14,180 --> 00:52:17,660
+هذه القضية وبقية الكلام الموجود الرائع اللي موجود
+
+694
+00:52:17,660 --> 00:52:19,320
+هنا العبر و العذاب
+
+695
+00:52:22,500 --> 00:52:26,160
+أولا من الدروس والعبار المستفادة من النص، عشان
+
+696
+00:52:26,160 --> 00:52:29,840
+أنهي النص وانقف شوية، الآن التنبيع على منزلة
+
+697
+00:52:29,840 --> 00:52:37,390
+الأبا، صفحة 74الان قضى ربك ألا تعبده إلا إياه جاء
+
+698
+00:52:37,390 --> 00:52:39,750
+في صحاب يقول إن سألة أنت النبي صلى الله عليه وسلم
+
+699
+00:52:39,750 --> 00:52:44,830
+أي الأعمال أحب إلى الله قال الصلاة على وقتها ثم
+
+700
+00:52:44,830 --> 00:52:49,590
+جاء آخر قال ثم أي قال بر الوالدين ثم أي الجهاد في
+
+701
+00:52:49,590 --> 00:52:53,810
+سبيلها شوفوا بر الوالدين بين وين؟ بين الصلاة و بين
+
+702
+00:52:53,810 --> 00:52:59,820
+الجهاد أعظم العبادات عند ربناالصلاة عمود الدين
+
+703
+00:52:59,820 --> 00:53:03,780
+اللي ستسألي عنها يوم القيامة والجهاد سنام الإسلام
+
+704
+00:53:03,780 --> 00:53:09,680
+ثروة الإسلام ولهذا يا أيها الذين آمنوا استجيبوا
+
+705
+00:53:09,680 --> 00:53:15,380
+لله و للرسول إذا دعاكم لما يحييكم دعاكم لمن؟
+
+706
+00:53:15,380 --> 00:53:20,450
+للجهاد والجهاد هو الحياةلمّا بيبقى النداءات اللي
+
+707
+00:53:20,450 --> 00:53:24,190
+مقررة اليوم، وبتكون نسمعها في مقابلة صوت، يا أيها
+
+708
+00:53:24,190 --> 00:53:28,390
+الذين آمن استجيبوا لللغة، إذا دعاكم، لمّا دعاكم؟
+
+709
+00:53:28,390 --> 00:53:33,710
+دعانا إلى الجهاد؟ لأن الجهاد في حياة الأمةهو اللي
+
+710
+00:53:33,710 --> 00:53:37,110
+بيحيي الناس إذا أنا مش ذليل، إذا مش تحت احتلال،
+
+711
+00:53:37,110 --> 00:53:41,590
+فهدي حياتي، أنا عزيز، أنا إنسان كريم، مش أنا ذليل،
+
+712
+00:53:41,590 --> 00:53:45,070
+ماعيشش قضية القخر للاحتلال والدول والإهانة
+
+713
+00:53:45,070 --> 00:53:49,010
+اليومية، بجأة أنا عزيز، مرضيتش بالضايم، ولا بهذا
+
+714
+00:53:49,010 --> 00:53:53,480
+الخضوع والخنوعإن حتى لو كان على حساب أمتي و شعبي
+
+715
+00:53:53,480 --> 00:53:56,640
+إن أنا أساوم و لا كده و أبيع و أشتري الله في
+
+716
+00:53:56,640 --> 00:54:00,040
+العباد و لهذا شيء معين شفتوا الآيات؟ لما أنا بعرف
+
+717
+00:54:00,040 --> 00:54:03,780
+إن حياتي في الدين و لهذا شيء مهم جدا إنه جاءت في
+
+718
+00:54:03,780 --> 00:54:08,400
+البر الوالدين بين قضية الحياة سنام الإسلام الجهاد
+
+719
+00:54:08,400 --> 00:54:11,620
+وبين الصلاة التي ستسألي عنها يوم القيامة الدليل
+
+720
+00:54:11,620 --> 00:54:16,100
+هذا إيش هو؟ أهمية البر وهذا مهم جدا في حياتنا اللي
+
+721
+00:54:16,100 --> 00:54:18,400
+بنشوفها إذا هذا أول استفادة اتنين
+
+722
+00:54:22,920 --> 00:54:31,590
+الان الصين صور المتعددة للإحسانالإحسان إلى الأبوين
+
+723
+00:54:31,590 --> 00:54:34,990
+بالقول، هاي موجودة عندك، الإحسان إلى الأبوين
+
+724
+00:54:34,990 --> 00:54:42,470
+بالفعل بجيم الإحسان إلى الوالدين بالمال، ده حق
+
+725
+00:54:42,470 --> 00:54:46,710
+الطاعة للوالدين، ها الإحسان إلى الوالدين بعد
+
+726
+00:54:46,710 --> 00:54:50,450
+الممات، بعدين أن تخصص الأم على الأب بالحب
+
+727
+00:54:50,450 --> 00:54:53,750
+والمفهام، أنا بتركز على التلاتة الأولى، وهو قضية
+
+728
+00:54:53,750 --> 00:54:57,330
+المال وقضية القول، قضية القول اتكلمنا عنها، أولا
+
+729
+00:54:57,330 --> 00:55:00,770
+ما تقولش اوف، لا تقول له موفهذه الدرجة الأولى،
+
+730
+00:55:00,770 --> 00:55:05,970
+اتنين اختيار الألفاظ المناسبة التي تدخل السرور على
+
+731
+00:55:05,970 --> 00:55:11,440
+مين؟على الأهد، يا أبا تفعل ما تُؤمر، ستجدني إن شاء
+
+732
+00:55:11,440 --> 00:55:14,960
+الله من الصبر، اللهم أكبر، جاي عمال بده يتبحوا، و
+
+733
+00:55:14,960 --> 00:55:19,360
+بعد ذلك قاعد بيبصر، إذا تبهي الإحسان إلى الأبوين
+
+734
+00:55:19,360 --> 00:55:24,780
+بالقول، بأن لا تقول لهم أف، والتاني بالفعل، و جاء
+
+735
+00:55:24,780 --> 00:55:27,820
+هنا طلع الإحسان إلى الوالدين بالفعل، يجب على
+
+736
+00:55:27,820 --> 00:55:32,980
+الأبناء أن يقوموا برعاية والديهم في جميع الأحوالفي
+
+737
+00:55:32,980 --> 00:55:36,880
+مرحلة الشيخوخة والكبر خاصة، يعني معناته في الشباب
+
+738
+00:55:36,880 --> 00:55:40,440
+لأ، كمان في الشباب، بس هنا خاصة لقضية الضعف
+
+739
+00:55:40,440 --> 00:55:43,880
+الموجودة، وقال لها، شوفوا الآن، قال لها يتقدم على
+
+740
+00:55:43,880 --> 00:55:47,740
+والديه بشيء من الأكل والشرب والجلوس والكلام، وقال
+
+741
+00:55:47,740 --> 00:55:51,820
+لها يمشي أمام الأبوينإيه الإماطة الأدى؟ يعني إنه
+
+742
+00:55:51,820 --> 00:55:55,400
+قدامه شوك، قدامه حصلت، إني اتيقت جميل، يا سلام من
+
+743
+00:55:55,400 --> 00:55:58,020
+قضية عقوق الوالدة، يعني إن أنا أتقدم على الأهل و
+
+744
+00:55:58,020 --> 00:56:00,160
+أنا ماشي، و أنت رايحة أنت و أمك في مشوار و أنت
+
+745
+00:56:00,160 --> 00:56:04,460
+ماشي قدامها، مش عارفة، ما شاء الله، هذا عقوقك،
+
+746
+00:56:04,460 --> 00:56:07,520
+قضية الطعام والشراب، حطوا الأكل، كُلوا يا شاء
+
+747
+00:56:07,520 --> 00:56:11,950
+الله، ما هي معروفة، قعدوا في المطبخ، كُلواهذا
+
+748
+00:56:11,950 --> 00:56:16,190
+مشكلة قضية الـ اه في قضية اسمها علاقات لما بنقعد
+
+749
+00:56:16,190 --> 00:56:19,950
+وهنا الأدب منك هنا دور الأم شفت التربية؟ ليش الأم
+
+750
+00:56:19,950 --> 00:56:23,630
+جامعة؟ ليش الأم مدرسة؟ ده للمرأة نفصل المجتمع
+
+751
+00:56:23,630 --> 00:56:27,070
+المرأة كل المجتمع احنا قاعدين بنربي انت بتربي
+
+752
+00:56:27,070 --> 00:56:30,590
+ولهذا عند الطعام اه معروف انه تعالوا بتعلموا
+
+753
+00:56:30,590 --> 00:56:33,530
+الأولاد احنا أسرةوكل أسرة في تعاون، واحد بيحط
+
+754
+00:56:33,530 --> 00:56:35,590
+الشرشة، واحد بيحط الأكل، واحد بيحط الصحون، واحد
+
+755
+00:56:35,590 --> 00:56:39,870
+بيجيب كده، وكذلك بيقعدوا، مينته ولا واحد يمد إيده
+
+756
+00:56:39,870 --> 00:56:43,150
+على الطعام هذا فقط، إلا لما ييجي الأب، شفت دور
+
+757
+00:56:43,150 --> 00:56:47,330
+الأم؟ بتعودوا، ولو أنا جهدت قبل، ممنوع، بس الأمة
+
+758
+00:56:47,330 --> 00:56:52,690
+جاتشإذاً في تعليمات في قضية قيمة من وين؟ هناك
+
+759
+00:56:52,690 --> 00:56:56,330
+نرسلها، عشان هيك مين اللي علمها؟ عشان هيك القيام
+
+760
+00:56:56,330 --> 00:56:59,270
+قاعدة بتزول، شوية شوية، إذا واحدة بالقول، واحدة
+
+761
+00:56:59,270 --> 00:57:03,310
+بإيش؟ إماطة الأم بالفعل، أما قضية اللي هو بالمال
+
+762
+00:57:03,310 --> 00:57:10,210
+على الإبن أن ينفق ماله على أخله، يعني بقضية ويحق
+
+763
+00:57:10,210 --> 00:57:14,130
+للأخ من ماله، أه، من حد ما صير موظف، بيجيبها
+
+764
+00:57:14,130 --> 00:57:17,630
+الراتب وسلم لها المرة، واش بدها المرة تحصل؟ أهله
+
+765
+00:57:17,630 --> 00:57:22,040
+ممشي الحالةهذا مش حاجة جريمة جريمة انت لها طول ما
+
+766
+00:57:22,040 --> 00:57:25,880
+عندك الأكل والشرب والكسوة وكده حتى بدك تحط فيه
+
+767
+00:57:25,880 --> 00:57:29,620
+دهومش يعني انا لو حاطيت فيه ده الوالد مثلا ماتيش
+
+768
+00:57:29,620 --> 00:57:32,620
+اقول اه اقل ولا انا جال ماتش اكل والوالد ماتش اكل
+
+769
+00:57:32,620 --> 00:57:35,770
+شهريا غير انا عندي ومصروف هم عنديلاكل و شرب و
+
+770
+00:57:35,770 --> 00:57:39,550
+التلاج موجود بالعكس طب انا ليش .. ايش المانع لو هم
+
+771
+00:57:39,550 --> 00:57:42,950
+كانوا في طابق لحالهم كمان او في مطبخ و غيره و
+
+772
+00:57:42,950 --> 00:57:45,810
+حطولهم تلاجة و كل اغراض لمباجي و حطولهم اغراضهم
+
+773
+00:57:45,810 --> 00:57:48,550
+لحاله و انا اغراضي لحاله طبخ العام ماشي لحاله و
+
+774
+00:57:48,550 --> 00:57:52,290
+الأكل العام ماشي لحاله لكن هم بدوا حاجة خاصة له و
+
+775
+00:57:52,290 --> 00:57:56,800
+بالان هيمت شيكربس هذا .. والله .. اقولك حتى راتبك
+
+776
+00:57:56,800 --> 00:58:00,800
+جليل بس حاسس الوالد انه انت و الله انا .. و هذول
+
+777
+00:58:00,800 --> 00:58:03,460
+انا .. و الله لو معايش كتير اللي اعطيتك انت عندي
+
+778
+00:58:03,460 --> 00:58:08,100
+بكل الدنيا و انا .. الاب بيقدر كل الظروف، اشي
+
+779
+00:58:08,100 --> 00:58:11,680
+المشكلة؟ اشي المشكلة؟ و هتشوفي بتلاقيها كثيرة جدا،
+
+780
+00:58:11,680 --> 00:58:15,980
+ولهذا احنا مصيبتنا مصيبةأحياناً نغفل هذه الجوانب،
+
+781
+00:58:15,980 --> 00:58:18,700
+إذا من ناحية المالية، وليه هذا الرجل اللي جاء إلى
+
+782
+00:58:18,700 --> 00:58:20,720
+الرسول صلى الله عليه وسلم، جاء الرجل وقال له يا
+
+783
+00:58:20,720 --> 00:58:22,840
+رباه النبي صلى الله عليه وسلم، ماباله؟ يعني ابنه؟
+
+784
+00:58:22,840 --> 00:58:25,280
+بشكي ابنه، قعد بشكيه، فبعتله الرجل، قال له ليش
+
+785
+00:58:25,280 --> 00:58:29,000
+بمانعه؟ أتريد أن تأخذ ماله؟ أنت بتاخذ ماله؟ فقال،
+
+786
+00:58:29,000 --> 00:58:34,500
+ساله يا رسول الله، أنه كان ضعيفا وانا قوي، بذكره،
+
+787
+00:58:34,500 --> 00:58:40,420
+وفقيرا وانا غني، فكنت لا أمنعه شيئا من مالي، كل
+
+788
+00:58:40,420 --> 00:58:46,120
+مالي لهوانا اليوم ضعيف و هو قوي و أنا فقير و هو
+
+789
+00:58:46,120 --> 00:58:51,000
+غني و يدخل علي بماله و بدأ يقول أبيات من الشام و
+
+790
+00:58:51,000 --> 00:58:53,160
+لهذا الرسول صلى الله عليه و سلم قالوا أنت و مالك
+
+791
+00:58:53,160 --> 00:58:58,740
+لأبيك تصوروا هو أنا هو كان ضعيف و أنا قوي طب احنا
+
+792
+00:58:58,740 --> 00:59:02,440
+اليوم قاعدين .. أولادنا صاروا لهم غرف خاصة أولاد
+
+793
+00:59:02,440 --> 00:59:05,600
+.. أولادنا كده بالعكس احنا أنا دكتور بالجامعة
+
+794
+00:59:05,600 --> 00:59:10,230
+أولادي بلبسوا أحسن مني مات مرةوالله أحيانا ان عمري
+
+795
+00:59:10,230 --> 00:59:14,750
+مااشترت الله عزيزي حذاء ب 150 شيكل ولا ب 200 شيكل
+
+796
+00:59:14,750 --> 00:59:17,910
+أولادي بيشتروا ب 150 و 200 شيكل بروح بيشتر الجميس
+
+797
+00:59:17,910 --> 00:59:22,090
+من 70 شيكل و 80 شيكل و مرات 100 شيكل و هذا الكلام
+
+798
+00:59:22,090 --> 00:59:26,270
+احنا عادي بنرضى بأى حاجة الآن احنا بنشتغل على اللى
+
+799
+00:59:26,270 --> 00:59:30,960
+بنسبنا اللون و الكذا وغير أولادنا لأبيشتري الأغلى
+
+800
+00:59:30,960 --> 00:59:35,500
+سعرًا حتى لو كان مش كتير جميل، بيبحث عن الموضوع،
+
+801
+00:59:35,500 --> 00:59:39,020
+يعني انا كتير نفف و بنشتري و بنقولهم هذا و هذا،
+
+802
+00:59:39,020 --> 00:59:41,900
+بيشوف اللون، بيعجب و كل شيء، جيه 100%، لما نيجي
+
+803
+00:59:41,900 --> 00:59:45,700
+ندفع الفلوس، بيجيه مثلا تلاتين شكل ولا خمسين شكل،
+
+804
+00:59:45,700 --> 00:59:51,970
+لا لا بطلتالان نتكلم عن قضية مال عن قضية تعامل
+
+805
+00:59:51,970 --> 00:59:58,110
+الان هذه من الأمور حق الأباء بالقول و بالفعل ثم
+
+806
+00:59:58,110 --> 01:00:01,770
+المال الان الأب طلع شوفي الان في قضية الإحسان إلى
+
+807
+01:00:01,770 --> 01:00:07,410
+الأبوين بالمال وهي رقم G في ال 76 قال توفير يجب
+
+808
+01:00:07,410 --> 01:00:12,150
+على الأبناء أن يبذلوا ما في وسعهم لراحة أبنائهم
+
+809
+01:00:12,150 --> 01:00:19,580
+الراحة طلع نفسية جسدية ماديةنفسية جسدية مادية،
+
+810
+01:00:19,580 --> 01:00:23,880
+شفتي هالمعاني؟ بلى فيه قضية عن طريق الانفاق على
+
+811
+01:00:23,880 --> 01:00:30,360
+الوالدين، توفير كل سبل الراحة سبل الراحة الله
+
+812
+01:00:30,360 --> 01:00:34,840
+أكبر، الناحية النفسية مش حاطية في غرفة تلاتة في
+
+813
+01:00:34,840 --> 01:00:38,840
+تلاتة، ولا أنتوا عايشين في فيلة وغرفة زينجو محتوطة
+
+814
+01:00:38,840 --> 01:00:43,590
+تحتولهذا دخلنا على بعض الناس حاطينه زي .. زي
+
+815
+01:00:43,590 --> 01:00:47,510
+بالفعل .. زي غرفة الفرن اللي كانت زمان وزينجو و
+
+816
+01:00:47,510 --> 01:00:51,490
+الدخنة و الحطب و الهيئة و كمان الغرفة تبعت الجد و
+
+817
+01:00:51,490 --> 01:00:55,990
+لا السيد او اللي كده فهذه مخزن يعني كل .. ايهم
+
+818
+01:00:55,990 --> 01:01:00,870
+اغراضهم حاطينه عندهم و عيششوفتوا العقوق؟ احنا
+
+819
+01:01:00,870 --> 01:01:04,050
+بنتكلم عن قضية من هذه القضايا اللي موجودة حق
+
+820
+01:01:04,050 --> 01:01:08,010
+الطاعة يعني بالاصل أن طاعة الوالدين الإحسان إلى
+
+821
+01:01:08,010 --> 01:01:10,930
+الوالدين بعد الممات أستكفي بهذا القدر و أقف خمس
+
+822
+01:01:10,930 --> 01:01:14,130
+دقائق سبحانك اللهم و بحمدك نشتد والله إلى اللقاء
+
+823
+01:01:14,130 --> 01:01:16,130
+نستغفرك وانتهب
+
diff --git a/PL9fwy3NUQKwaGIlkTCo2tGndokmJ9ZbKr/PEYh7f8lUH4_raw.json b/PL9fwy3NUQKwaGIlkTCo2tGndokmJ9ZbKr/PEYh7f8lUH4_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..40c095e52e25c4020931de7e7f89b2003c4c1365
--- /dev/null
+++ b/PL9fwy3NUQKwaGIlkTCo2tGndokmJ9ZbKr/PEYh7f8lUH4_raw.json
@@ -0,0 +1 @@
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ارتداد، يعني باختلف، لكن اليوم لما احنا بنتكلم و بنعرض الإسلام على الآخرين، وهذه النقطة اللي بنفرق بينها، في فرق بين الآن أن أعرض الإسلام على مشركين أو عبدة أوثان،", "tokens": [37746, 6027, 2655, 6027, 1829, 12399, 36632, 16472, 5016, 23557, 5172, 18871, 32748, 9957, 5551, 8592, 42213, 3224, 24525, 2304, 3224, 1975, 43500, 3215, 18513, 12399, 37495, 22653, 4724, 47283, 2655, 46538, 12399, 44381, 45595, 20498, 5296, 15042, 1975, 5016, 8315, 44945, 2655, 4117, 19528, 4032, 44945, 3615, 43042, 33688, 3794, 37440, 15844, 6024, 95, 34740, 9957, 12399, 37037, 24192, 28239, 47432, 3660, 13672, 1829, 44945, 5172, 2288, 4587, 49374, 11296, 12399, 8978, 6156, 2288, 4587, 49374, 6024, 48506, 14739, 5551, 3615, 43042, 33688, 3794, 37440, 15844, 37893, 31747, 9957, 34051, 6225, 44510, 3660, 34051, 12984, 7649, 12399], "avg_logprob": -0.16714015663272203, "compression_ratio": 1.8974358974358974, "no_speech_prob": 0.0, "words": [{"start": 786.26, "end": 787.24, "word": "وبالتالي،", "probability": 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{"start": 2932.91, "end": 2933.23, "word": " أهداف", "probability": 0.9857177734375}, {"start": 2933.23, "end": 2933.57, "word": " القصة", "probability": 0.9978841145833334}, {"start": 2933.57, "end": 2934.05, "word": " معروفة،", "probability": 0.76171875}, {"start": 2934.05, "end": 2934.33, "word": " أسس", "probability": 0.9554036458333334}, {"start": 2934.33, "end": 2935.21, "word": " البيان،", "probability": 0.864013671875}, {"start": 2935.21, "end": 2935.47, "word": " أسس", "probability": 0.9921875}, {"start": 2935.47, "end": 2936.47, "word": " الدعوة،", "probability": 0.96611328125}, {"start": 2936.47, "end": 2937.37, "word": " تثبيت", "probability": 0.9908447265625}, {"start": 2937.37, "end": 2937.59, "word": " قلب", "probability": 0.9716796875}, {"start": 2937.59, "end": 2937.93, "word": " النبي", "probability": 0.95166015625}, {"start": 2937.93, "end": 2938.15, "word": " صلى", "probability": 0.901123046875}, {"start": 2938.15, "end": 2938.21, "word": " الله", "probability": 0.978515625}, {"start": 2938.21, "end": 2938.45, "word": " عليه", "probability": 0.7373046875}, {"start": 2938.45, "end": 2938.95, "word": " وسلم،", "probability": 0.884765625}, {"start": 2938.95, "end": 2939.25, "word": " بيان", "probability": 0.9713541666666666}, {"start": 2939.25, "end": 2939.63, "word": " العبرة", "probability": 0.7802734375}, {"start": 2939.63, "end": 2940.47, "word": " والعظة،", "probability": 0.7669921875}, {"start": 2940.47, "end": 2940.89, "word": " تصديق", "probability": 0.9779052734375}, {"start": 2940.89, "end": 2941.49, "word": " الأنبياء", "probability": 0.9915771484375}, {"start": 2941.49, "end": 2942.45, "word": " السابقين،", "probability": 0.98525390625}, {"start": 2942.45, "end": 2942.79, "word": " إثبات", "probability": 0.91845703125}, {"start": 2942.79, "end": 2943.17, "word": " الوحي", "probability": 0.9720458984375}, {"start": 2943.17, "end": 2943.41, "word": " إلى", "probability": 0.78759765625}, {"start": 2943.41, "end": 2943.79, "word": " غير", "probability": 0.98876953125}, {"start": 2943.79, "end": 2944.75, "word": " ذلك،", "probability": 0.8671875}, {"start": 2944.75, "end": 2945.27, "word": " سبحانك", "probability": 0.965576171875}, {"start": 2945.27, "end": 2945.49, "word": " اللهم", "probability": 0.707275390625}, {"start": 2945.49, "end": 2945.61, "word": " و", "probability": 0.74853515625}, {"start": 2945.61, "end": 2946.29, "word": " بحمدك،", "probability": 0.88740234375}, {"start": 2946.29, "end": 2946.67, "word": " نشهدك", "probability": 0.83994140625}, {"start": 2946.67, "end": 2946.81, "word": " لا", "probability": 0.64501953125}, {"start": 2946.81, "end": 2947.03, "word": " إله", "probability": 0.97607421875}, {"start": 2947.03, "end": 2947.25, "word": " إلا", "probability": 0.96728515625}, {"start": 2947.25, "end": 2947.79, "word": " أنت،", "probability": 0.8728841145833334}, {"start": 2947.79, "end": 2948.67, "word": " نستغفرك", "probability": 0.9228515625}, {"start": 2948.67, "end": 2949.13, "word": " و", "probability": 0.92333984375}, {"start": 2949.13, "end": 2949.55, "word": " نطلبك", "probability": 0.45001220703125}, {"start": 2949.55, "end": 2949.63, "word": " الله", "probability": 0.33544921875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2950.62925, "duration_after_vad": 2888.904999999991}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwb5JJKeBX9QHGYLiyPfnDQN/zimrrrrHHTo.srt b/PL9fwy3NUQKwb5JJKeBX9QHGYLiyPfnDQN/zimrrrrHHTo.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4a7c4c07a285240fddc9b4bc38cb265cc5459668
--- /dev/null
+++ b/PL9fwy3NUQKwb5JJKeBX9QHGYLiyPfnDQN/zimrrrrHHTo.srt
@@ -0,0 +1,7143 @@
+1
+00:00:03,370 --> 00:00:08,570
+بسم الله الرحمن الرحيم، بنرحب فيكم في اللقاء الأخير
+
+2
+00:00:08,570 --> 00:00:12,250
+في مساق إدارة هندسية اللي هو احنا بندرس فيه 
+
+3
+00:00:12,250 --> 00:00:18,310
+الرياضة والعمل عن بعد في هذا المساق، اليوم هنعرض
+
+4
+00:00:18,310 --> 00:00:22,770
+... يعني نتاج الفصل اللي هي عبارة عن خطط عمل 
+
+5
+00:00:22,770 --> 00:00:27,870
+لمشاريع مقترحة في مجال الرياضة، هنبدأ كل مجموعة
+
+6
+00:00:27,870 --> 00:00:34,650
+منكم عندها تقريبًا حد أقصى 15 دقيقة تعرض فيها فكرة 
+
+7
+00:00:34,650 --> 00:00:39,050
+مشروعها والمقترح، يعني التفاصيل والإحصائيات يمكن 
+
+8
+00:00:39,050 --> 00:00:44,550
+نخفف فيها لأنها بدها وقت لا تنفهم، بس احنا بنتمنالكم 
+
+9
+00:00:44,550 --> 00:00:48,550
+التوفيق وبنتمنالكم بنهاية هذا المساق أنكم 
+
+10
+00:00:48,550 --> 00:00:53,010
+تتوفقوا وتلاقوا الممولين لمقترحات المشاريع تبعتكم
+
+11
+00:00:53,490 --> 00:00:56,650
+فتوكلوا على الله، نبدأ بالمجموعة الأولى مشروع
+
+12
+00:00:56,650 --> 00:01:02,090
+موهبتي، أعضاء الفريق: بسمة السويسي، راشد أبو سلطان، لم
+
+13
+00:01:02,090 --> 00:01:06,950
+يُشرح المشكلة اللي وجدناها، المشكلة الأساسية اللي 
+
+14
+00:01:06,950 --> 00:01:10,370
+احنا واجهناها: صعوبة اختيار التخصص الجامعي لدى
+
+15
+00:01:10,370 --> 00:01:13,290
+الطلاب، فبالتالي صار فيها عندنا تكرار كثير كبير 
+
+16
+00:01:13,290 --> 00:01:16,370
+بالتخصصات، صار في ضياع للخريجين، صار في بطالة
+
+17
+00:01:16,370 --> 00:01:19,590
+فلاقينا إن المشكلة الأساسية في صعوبة اختيار التخصص
+
+18
+00:01:19,590 --> 00:01:23,710
+الجامعي، فعليًا إن الطفل من وهو صغير مش قادر يكتشف
+
+19
+00:01:23,710 --> 00:01:27,510
+مواهبه، فيه مواهب بس للأسف هذه المواهب تندثر مع 
+
+20
+00:01:27,510 --> 00:01:30,850
+الزمن، فاحنا لاقينا إن المشكلة الأساسية اللي احنا
+
+21
+00:01:30,850 --> 00:01:34,410
+بنواجهها إن الأهل مش قادرين يكتشفوا مواهب أطفالهم
+
+22
+00:01:34,680 --> 00:01:39,320
+وبالتالي وجدنا أن الحل عندنا أن نعمل شركة، هذه
+
+23
+00:01:39,320 --> 00:01:44,020
+الشركة بتعمل تطبيقات جوال، بتعمل تلت شغلات، أول حاجة 
+
+24
+00:01:44,020 --> 00:01:47,740
+راح ننشر من خلال هذا التطبيق مجموعة من الاختبارات
+
+25
+00:01:47,740 --> 00:01:51,540
+العلمية المحكمة علميًا، هذه الاختبارات بتعمل على
+
+26
+00:01:51,540 --> 00:01:56,000
+اكتشاف ميول الأطفال المهنية، هذه الاختبارات أكيد 
+
+27
+00:01:56,000 --> 00:02:01,340
+راح يسبقها التحضيرية، مجموعة من الفيديوهات، مجموعة من
+
+28
+00:02:01,340 --> 00:02:04,380
+الألعاب، مجموعة من الدورات اللي لازم يكون الطفل
+
+29
+00:02:04,380 --> 00:02:08,000
+ماخذها لحتى يقدر يتمكن إنه يعمل هذه الاختبارات
+
+30
+00:02:08,000 --> 00:02:11,320
+العلمية اللي راح أقدر من خلالها أنا اكتشف موهبة 
+
+31
+00:02:11,320 --> 00:02:15,180
+الطفل، بالإضافة راح نقدم خدمة اللي هي راح يكون في
+
+32
+00:02:15,180 --> 00:02:19,060
+عينا خبراء نفسيين ومرشدين راح يكونوا على طول 
+
+33
+00:02:19,060 --> 00:02:24,310
+للإجابة على تساؤلات أولياء الأمور، بالإضافة لشغل
+
+34
+00:02:24,310 --> 00:02:28,970
+إضافي راح تكون موجودة عندنا إن أي أهل أي أب بيحس 
+
+35
+00:02:28,970 --> 00:02:32,370
+إنه والله طفل عنده موهبة معينة، بيقدر إنه يصور 
+
+36
+00:02:32,370 --> 00:02:36,030
+فيديو لهذه الـ talent وينشرها عندنا، وبالتالي ممكن
+
+37
+00:02:36,030 --> 00:02:39,930
+بالمستقبل يجي مستثمر معين يقول والله هذه الموهبة 
+
+38
+00:02:39,930 --> 00:02:43,460
+أنا محتاجها عنده ويستثمر له هذه الموهبة، بعد هي 
+
+39
+00:02:43,460 --> 00:02:46,440
+قبلنا نحكي إيش الخلطة السحرية اللي احنا عملناها 
+
+40
+00:02:46,440 --> 00:02:50,120
+لحتى نطلع بالمنتج النهائي، أول حاجة عملناها روحنا
+
+41
+00:02:50,120 --> 00:02:53,760
+جيبنا اختبارات ورقية، لهذه الاختبارات الاكتشاف نور
+
+42
+00:02:53,760 --> 00:02:59,020
+المهنية للأطفال، جربناها بشكل يدوي على مجموعة من 
+
+43
+00:02:59,020 --> 00:03:02,220
+الأطفال، كانت نتائج ممتازة بالنسبة للنتائج الموجودة 
+
+44
+00:03:02,220 --> 00:03:07,190
+من الأشياء المحكمة علميًا، بعد هيك بدنا نحوسب في هذه
+
+45
+00:03:07,190 --> 00:03:10,890
+الاختبارات، نعمل التصاميم اللازمة، نبدأ نبرمج،
+
+46
+00:03:10,890 --> 00:03:13,670
+نشوف الشخصية اللي راح تكون معانا طول الفترة
+
+47
+00:03:16,540 --> 00:03:20,320
+تطبيق، هنعمل مجموعة من أنشطة تحضيرية وهذه راح نحكي
+
+48
+00:03:20,320 --> 00:03:23,180
+عنها في الخطة التسويقية، راح تحكي عنها زميلتي بعد
+
+49
+00:03:23,180 --> 00:03:25,440
+هيك، أوصلنا إيش النتائج، إيش الاختبارات اللي راح
+
+50
+00:03:25,440 --> 00:03:28,380
+تطلع عندنا؟ عندنا نتيجتين مهمتين، النتيجة الأولى 
+
+51
+00:03:28,380 --> 00:03:32,540
+إيش ميول طفلك المهنية؟ والله أنا طفلي عنده ميول 
+
+52
+00:03:32,540 --> 00:03:37,080
+مهنية بالنسبة مثلًا 80% بالهندسة، 70% بالطب، وهكذا
+
+53
+00:03:37,080 --> 00:03:40,900
+يعني بعد هيك بقوله إيش سوق العمل محتاج؟ أنا مش بس 
+
+54
+00:03:40,900 --> 00:03:43,920
+بدي أعرف إيش الميول المهنية عنده، لأ كمان بدي أعرف
+
+55
+00:03:43,920 --> 00:03:47,470
+إيش السوق اللي محتاجه، بعد هي كمان راح نوقف إن والله
+
+56
+00:03:47,470 --> 00:03:51,310
+أنا بس لهنا، لأ أنا كمان بدي أوجه الطفل وأوجه 
+
+57
+00:03:51,310 --> 00:03:54,790
+أولياء أمور الطفل إن والله خذ هذه الدورة لحتى مثلًا 
+
+58
+00:03:54,790 --> 00:03:58,230
+ينزل عنده نسبة الإقناع، خذ هذه الـ ... الـ ... روحها
+
+59
+00:03:58,230 --> 00:04:01,990
+لهذا المركز بيقدم دورات أو مشغلات ممكن تفيد طفلك
+
+60
+00:04:01,990 --> 00:04:07,050
+بالنهاية أي موهبة عندنا بتكون ببذرة صغيرة، لازم احنا
+
+61
+00:04:07,050 --> 00:04:11,570
+نميها لحتى توصل للحصاد المطلوب، مين هم الزبائن اللي
+
+62
+00:04:11,570 --> 00:04:15,630
+احنا متوقعين إنهم راح يكونوا يعني موجهينهم التطبيق
+
+63
+00:04:15,630 --> 00:04:18,490
+تبعنا؟ طبعًا المستهدف المباشر راح يكون عندنا الأطفال 
+
+64
+00:04:18,490 --> 00:04:21,610
+ما بين ثماني لست عشر سنة، بس أكيد الأهالي هم اللي 
+
+65
+00:04:21,610 --> 00:04:23,890
+راح يكونوا مسؤولين يعني إنهم يدفعوا، فهيكونوا 
+
+66
+00:04:23,890 --> 00:04:27,070
+أولياء الأمور برضه وأصحاب المؤسسات والمراكز اللي 
+
+67
+00:04:27,070 --> 00:04:29,810
+راح تعلن عندنا برضه هي راح يكونوا من الفئات
+
+68
+00:04:29,810 --> 00:04:32,570
+المستهدفة، المنطقة الجغرافية اللي احنا بنتوقعها
+
+69
+00:04:33,330 --> 00:04:37,290
+بداية راح تكون قطاع غزة ومثل محافظات الضفة الغربية فلسطين 
+
+70
+00:04:37,290 --> 00:04:40,370
+كاملة، وبعد هي إن شاء الله هننتشر في الوطن العربي 
+
+71
+00:04:40,370 --> 00:04:43,630
+كامل، هتكمل معك وزميلتي روسيا، لازم نتعرف عن
+
+72
+00:04:43,630 --> 00:04:46,490
+المنافسين اللي عندنا في قطاع غزة، مبدئيًا عندنا
+
+73
+00:04:46,490 --> 00:04:51,150
+القطان، الرياض الصغير، والهيزا، شو اللي مميزنا عن 
+
+74
+00:04:51,150 --> 00:04:56,270
+المنافسين؟ أول شيء إن المنافسين مش مبادرين بالنسبة 
+
+75
+00:04:56,270 --> 00:05:00,010
+لأنا لإنه ما فيش حاليًا حد بيقدم خدمة إلكترونية 
+
+76
+00:05:00,010 --> 00:05:04,050
+حاليًا زي ما احنا هنقدم تطبيقات، بالإضافة للخبرة 
+
+77
+00:05:04,050 --> 00:05:07,870
+والإمكانيات والاحتراف اللي هنقدمه في التصاميم اللي
+
+78
+00:05:07,870 --> 00:05:11,890
+هتكون في التطبيقات تبعتنا، والعلاقات المتعددة اللي 
+
+79
+00:05:11,890 --> 00:05:15,810
+هتساعدنا كثير في الترويج والتسويق لمشروعنا
+
+80
+00:05:18,230 --> 00:05:21,570
+أيضًا بالنسبة للاختبارات اللي متقدمة هيكون سمّورنَا 
+
+81
+00:05:21,570 --> 00:05:26,570
+كبيرة لأن العدد متزايد يعني ومش محدود على عدد معين
+
+82
+00:05:26,570 --> 00:05:31,710
+في المستقبل ممكن شو 
+
+83
+00:05:31,710 --> 00:05:34,810
+المصادر اللي هتكون اللي رح تبعنا؟ أول شيء احنا
+
+84
+00:05:34,810 --> 00:05:40,350
+التطبيق تبعنا هيكون هنشر نسخة تجريبية، بعدها هيكون
+
+85
+00:05:40,350 --> 00:05:47,480
+متوفر في المراحل المتقدمة، بالإضافة لإنه المراكز
+
+86
+00:05:47,480 --> 00:05:53,260
+المهتمة بالطفل هتقوم بعمل نشر لِدَوْراتها والأنشطة
+
+87
+00:05:53,260 --> 00:05:57,680
+تبعتها، بحيث إنه احنا أول شيء هنعرف الطفل بموهوبته وبعدين
+
+88
+00:05:57,680 --> 00:06:01,360
+هنوجهه إيش الأنشطة والدورات اللي يلتحق فيها
+
+89
+00:06:01,360 --> 00:06:07,740
+طبعًا المراكز هـ ... هنكون فينا اشتراك شهري لها
+
+90
+00:06:07,740 --> 00:06:11,040
+المراكز، بحيث إن هي بتحصل على التطبيق تبعنا وبتكون 
+
+91
+00:06:11,040 --> 00:06:14,840
+بتوزعه على الأطفال اللي عندها اللي متواجدين في
+
+92
+00:06:14,840 --> 00:06:20,180
+نفس المركز، بعد فترة زمنية طويلة احنا هنكون جمعنا
+
+93
+00:06:20,180 --> 00:06:26,480
+عدد كبير من الأطفال، حددنا وين أماكن توزيعها، هنكون 
+
+94
+00:06:26,480 --> 00:06:32,040
+احنا حددنا وين مثلًا ميوله، وين مواهبه، هي هتُسيّح لنا 
+
+95
+00:06:32,040 --> 00:06:35,920
+Big data ممكن نستفيد منها كثير بالمستقبل، إن والله 
+
+96
+00:06:35,920 --> 00:06:41,720
+لما ه، لأشياء يعني أي حد ببحث عن مواهب أو عن
+
+97
+00:06:41,720 --> 00:06:47,740
+مميّزين، هيكون تطبيقنا ساعد بهذا الجانب، بالنسبة 
+
+98
+00:06:47,740 --> 00:06:51,600
+للحصة السوقية، بنتوقع نحصل على حوالي عشرين بالمئة 
+
+99
+00:06:51,600 --> 00:06:53,120
+من حجم السوق كله
+
+100
+00:06:56,740 --> 00:07:01,820
+شو هو سائل التّصريف والتنمية تبعتنا؟ أول شيء هيكون
+
+101
+00:07:01,820 --> 00:07:07,060
+في عيننا المؤسسات والوزارات هتكون مصدر لتصريف
+
+102
+00:07:07,060 --> 00:07:11,200
+تبعنا، بحيث إن هنكون بنجمع مثلًا طالب مميز من كل
+
+103
+00:07:11,200 --> 00:07:15,900
+مدرسة، وهنكون بإجراء يعني دورات لهم بتنمي 
+
+104
+00:07:15,900 --> 00:07:20,020
+الإبداع والمواهب وعمل بعض الأنشطة والألعاب 
+
+105
+00:07:20,020 --> 00:07:24,560
+اللي بتحفزهم وبتشجعهم على تطبيقنا وعلى فكرة
+
+106
+00:07:24,560 --> 00:07:29,230
+التطبيق تبعنا، بعدهم طبعًا هيكون فيه مشاركة في معارض
+
+107
+00:07:29,230 --> 00:07:34,470
+بشكل دائم ودوري، بحيث إن يضل تطبيقنا قريب من
+
+108
+00:07:34,470 --> 00:07:38,770
+الناس ومن الأهالي، طبعًا هيكون في عندنا مطويات
+
+109
+00:07:38,770 --> 00:07:44,690
+تعريفية بمنتجنا هيتم توزيعها، طبعًا الـ social 
+
+110
+00:07:44,690 --> 00:07:50,690
+media هي جانب فعال كثير بالنسبة لنا، هننشر من خلالها 
+
+111
+00:07:50,690 --> 00:07:55,070
+نشر التطبيق في التلفزيون بشكل كثير، فيديوهات
+
+112
+00:07:55,070 --> 00:07:58,230
+المواهب اللي ذكرتها باسمة إن ممكن أي شخص موهوب
+
+113
+00:07:58,230 --> 00:08:05,390
+يعني يروّج لموهبته وهذا بيزيد يعني فعالية التطبيق
+
+114
+00:08:05,390 --> 00:08:10,070
+بالنسبة لتكاليف التصريف، قسمنا دورات تعريفية 
+
+115
+00:08:10,070 --> 00:08:14,970
+بالإبداع، هتكون نعملها في شكل مثلًا سنوي، مركز أو
+
+116
+00:08:14,970 --> 00:08:20,720
+مشابه، إعلانات فيسبوك وتويتر وإنستجرام قدرناها 
+
+117
+00:08:20,720 --> 00:08:24,580
+التكاليف حوالي 2700 دولار خلال السنة الأولى، أما
+
+118
+00:08:24,580 --> 00:08:27,660
+بالنسبة للمعدات والأجهزة اللي محتاجها ممكن تكون من
+
+119
+00:08:27,660 --> 00:08:32,400
+من المنحة اللي هيموّلونّا إياها أو كمان مساهمات 
+
+120
+00:08:32,400 --> 00:08:36,540
+شخصية، أشياء موجودة عندنا، الأشياء اللي من المنحة
+
+121
+00:08:36,540 --> 00:08:40,160
+احنا بنحتاج لجهاز حاسوب بـ data جودة عالية كمان
+
+122
+00:08:40,160 --> 00:08:44,060
+بنحتاج لـ tablet عشان نحتاج لـ tablet كمان عشان نقعد
+
+123
+00:08:44,060 --> 00:08:49,240
+نعرض عليه الـ ... التطبيق نفسه لإنه ... للأطفال، فيعني 
+
+124
+00:08:49,240 --> 00:08:53,620
+إنه شيء محتاجه بصورة واضحة، فمحتاج لـ tablet كمان
+
+125
+00:08:53,620 --> 00:08:57,120
+الاختبارات نفسها الورقية من ضمن المعدات والأجهزة
+
+126
+00:08:57,120 --> 00:09:01,020
+محتاج جهاز رسم، هذا جهاز الرسم عشان أقعد أرسم
+
+127
+00:09:01,020 --> 00:09:03,860
+character عليه، الـ character اللي هستخدمته
+
+128
+00:09:03,860 --> 00:09:11,130
+للتطبيقات عشان أعرض عليه طريقة جذابة، بحتاج كمان
+
+129
+00:09:11,130 --> 00:09:15,470
+لحساب Google و ... على الـ Google Play وهذه
+
+130
+00:09:15,470 --> 00:09:21,250
+التكاليف حوالي 4000 دولار، أنا من مساهمة شخصية فأنا
+
+131
+00:09:21,250 --> 00:09:25,230
+عندي أجهزة الحواسيب تبعتنا اللي هنبرمج عليها، وأجهزة
+
+132
+00:09:25,230 --> 00:09:29,010
+الهواتف الجوالات اللي هنجرب نطلق عليها اللي هتكون 
+
+133
+00:09:29,010 --> 00:09:33,610
+حوالي 1500 دولار، القّائِدة العاملة ... القّائِدة العاملة
+
+134
+00:09:33,610 --> 00:09:37,790
+احنا نفسنا اللي هنكون المبرمجين والمصممين كمان
+
+135
+00:09:37,790 --> 00:09:41,390
+هنحتاج من برا لرسام اللي هنستخدمه ... هيقعد يرسم 
+
+136
+00:09:41,390 --> 00:09:44,370
+هذا الـ character على جهاز الرسم اللي تحكيّت عنه
+
+137
+00:09:44,370 --> 00:09:48,390
+كمان نحتاج لاستشارة، هذه الاستشارة هتفيدنا 
+
+138
+00:09:48,390 --> 00:09:54,040
+بالخدمات الإرشادية، هيقدم لنا إياها، التطبيقنا عشان 
+
+139
+00:09:54,040 --> 00:09:58,260
+محتاج لواحد مرشد نفسي فـ ... وهذا الـ ... الاستشاري 
+
+140
+00:09:58,260 --> 00:10:02,180
+هيكون بالساعة والتكاليف تبعتّه الإجمالية هتكون 
+
+141
+00:10:02,180 --> 00:10:07,880
+تقريبا سبعة آلاف دولار كمان في تكاليف أخرى عشان نشغل
+
+142
+00:10:07,880 --> 00:10:12,000
+المشروع تبعنا نحتاج صيانة، إنترنت، كهربا، وهذه
+
+143
+00:10:12,000 --> 00:10:18,320
+الأشياء حوالي ألف دولار، المصاريف الإدارية محتاجها 
+
+144
+00:10:18,320 --> 00:10:24,110
+.. تكلفتها إجماليا حوالي ثلاثة آلاف دولار، قال لنا احنا
+
+145
+00:10:24,110 --> 00:10:27,770
+تكاليف تأسيسية عشان نشغل المشروع تبعنا اللي هي
+
+146
+00:10:27,770 --> 00:10:31,930
+معاداة الـarchitecture اللي كنت عنها والمصاريف
+
+147
+00:10:31,930 --> 00:10:35,350
+التكاليف الثانية حوالي خمسة آلاف وخمسمائة دولار،
+
+148
+00:10:35,350 --> 00:10:41,410
+هذه التكاليف التأسيسية عشان نبدأ الاستثمار، الخطة
+
+149
+00:10:41,410 --> 00:10:44,430
+المالية، أنا عندي تكاليف ثابتة وتكاليف متغيرة،
+
+150
+00:10:44,430 --> 00:10:47,930
+التكاليف الثابتة والمتغيرة، في عندنا كهربا، احنا
+
+151
+00:10:47,930 --> 00:10:50,370
+نستخدمش كهربا وهي الكهربا العادية، هذي هتكون 
+
+152
+00:10:50,370 --> 00:10:54,390
+متغيرة، كمان في الأوقات الثانية هيكون عندي .. أنا
+
+153
+00:10:54,390 --> 00:10:59,060
+بقدر .. بعمل اشتراك ثابت من المولد، هيكون تكليفه
+
+154
+00:10:59,060 --> 00:11:03,680
+ثابت، هذي الكهربا من المولد من ضمن التكاليف الثابتة،
+
+155
+00:11:03,680 --> 00:11:06,920
+هلاقي أنا عندي تكاليف ثابتة، الكهربا اللي حكيت
+
+156
+00:11:06,920 --> 00:11:10,780
+عنها من المولد، الإنترنت كمان، الحساب تبع جوجل، وفي
+
+157
+00:11:10,780 --> 00:11:14,540
+عندنا الراتب تبع الرسام والمصاريف الإدارية، و
+
+158
+00:11:14,540 --> 00:11:17,980
+الإيجار، هذه كلها حوالي سبعة آلاف دولار، أما التكاليف
+
+159
+00:11:17,980 --> 00:11:21,420
+المتغيرة، الكهربا اللي حكيت عنها جاية من شركة
+
+160
+00:11:21,420 --> 00:11:25,440
+الكهربا، نحتاج لصيانة وتسويق، ونحتاج كمان 
+
+161
+00:11:25,440 --> 00:11:29,340
+لاستشارة خبير نفسي، هذي التكاليف حوالي أربعة آلاف
+
+162
+00:11:29,340 --> 00:11:34,290
+دولار، المبيعات، بعد ما حكينا كل التكاليف، قد إيش احنا 
+
+163
+00:11:34,290 --> 00:11:38,150
+هندفع الـ .. الـ .. الإيرادات اللي هتطلع معنا
+
+164
+00:11:38,150 --> 00:11:41,450
+للمبيعات خلال السنة الأولى، أنا في عندي أربع
+
+165
+00:11:41,450 --> 00:11:46,230
+تطبيقات على أربع مستويات لعدة مراحل من الثمانية
+
+166
+00:11:46,230 --> 00:11:50,770
+للستة عشر، تكاليف الـ .. الإيرادات والمبيعات اللي
+
+167
+00:11:50,770 --> 00:11:55,330
+هتطلع ليها حوالي أربعة عشر ألف دولار، بالنهاية احنا 
+
+168
+00:11:55,330 --> 00:11:58,550
+لما نيجي نقيم المشروع احنا العائد على الاستثمار
+
+169
+00:11:58,550 --> 00:12:03,290
+بيطلع صفر ربح على التكاليف التأسيسية اللي بيطلع 46%،
+
+170
+00:12:03,290 --> 00:12:07,130
+أما فترة الاسترداد، التكاليف التأسيسية على صفر ربح
+
+171
+00:12:07,130 --> 00:12:12,970
+بيطلع 2.15 اللي هو حوالي سنتين وشهرين عشان نسترد 
+
+172
+00:12:12,970 --> 00:12:17,620
+تكاليف تبعنا، وبالنهاية نختصر المشروع، أنا بتمنى أنه
+
+173
+00:12:17,620 --> 00:12:24,800
+يتم تطبيقه ونسعى أنه ينمي مواهب الأطفال، وينتشر 
+
+174
+00:12:24,800 --> 00:12:27,620
+مش بس على قدر قطاع غزة، ينتشر على مقدار الوطن
+
+175
+00:12:27,620 --> 00:12:31,760
+العربي، اللي هو التطبيق اللي حكينا عنه طول، بسم الله
+
+176
+00:12:31,760 --> 00:12:36,300
+الرحمن الرحيم، هيكون التطبيق تبعنا اسمه المحاسب، 
+
+177
+00:12:36,300 --> 00:12:40,660
+طبعا فريق العمل Islam Mansour و Amal Hamad، هندسة
+
+178
+00:12:40,660 --> 00:12:46,740
+حصوة، أول شيء الشركات اللي طبعا المؤسسات التجارية
+
+179
+00:12:46,740 --> 00:12:50,620
+أو الصغيرة، تعني المشكلة أنه كل شيء بيكون تدوين على
+
+180
+00:12:50,620 --> 00:12:55,100
+ورق، الحسابات والمعاملات بيكون تدوين ورقي، فهذا ما
+
+181
+00:12:55,100 --> 00:12:58,120
+بدنا إياه طبعا الحين، غير هيك لما بتتعامل مع تطبيق
+
+182
+00:12:58,120 --> 00:13:03,800
+بيكون شيء مرتفع السعر، سعر التطبيق بيكون غالي كمان،
+
+183
+00:13:03,800 --> 00:13:09,300
+في عندنا أنه لو مثلا تعاملت مع تطبيق، التطبيق هذا 
+
+184
+00:13:09,300 --> 00:13:14,260
+لو فقدته هتفقد كل البيانات اللي كانت عن التطبيق، كل 
+
+185
+00:13:14,260 --> 00:13:17,740
+الحسابات اللي هتـ .. هيخسرها الشركة، طبعا في شركات
+
+186
+00:13:17,740 --> 00:13:22,900
+تحتاج أنها تحافظ على هذه البيانات، كمان لو مثلا
+
+187
+00:13:22,900 --> 00:13:26,780
+بدي البيانات هذه تكون في أكثر من مكان، مع أكثر من
+
+188
+00:13:26,780 --> 00:13:31,180
+محاسب، هذا الشيء كمان مش موجود فبدنا نعدله،
+
+189
+00:13:33,730 --> 00:13:38,330
+ولو في أحد مثلا المدير بده البيانات يعرضها على نفسه، 
+
+190
+00:13:38,330 --> 00:13:41,850
+كل شيء يكون متابع عليه، يكون متوفر عند
+
+191
+00:13:41,850 --> 00:13:47,170
+المدير، هذا كمان بدنا نوفره، لهيك أجت الفكرة أنه
+
+192
+00:13:47,170 --> 00:13:52,960
+تطبيق محاسب، هنعمله سحابي، التطبيق هيكون سحابي أنه
+
+193
+00:13:52,960 --> 00:13:57,280
+بيدعم كافة .. مختلفة الخصائص، مختلف الـ .. يدعم 
+
+194
+00:13:57,280 --> 00:14:02,780
+مختلف مجالات في المؤسسات، فيقدم الحلول المحاسبية 
+
+195
+00:14:02,780 --> 00:14:08,720
+والمالية للمؤسسات المختلفة باختلاف تخصصها و .. 
+
+196
+00:14:12,320 --> 00:14:15,780
+الفئة اللي هنستهدفها أول شيء، فيه عندنا ثلاث فئات،
+
+197
+00:14:15,780 --> 00:14:22,400
+الشركات الصغيرة الحجم اللي متوفرة بكثرة، هذا الرسمة
+
+198
+00:14:22,400 --> 00:14:27,540
+بتوضح حجم الشركات في قطاع غزة خصوصًا، ثاني شيء 
+
+199
+00:14:27,540 --> 00:14:32,780
+فيه عندنا الشركات الرياضية اللي حاليًا كترت في ..
+
+200
+00:14:32,780 --> 00:14:41,360
+بتزيد عددها في القطاع، اشتريتها، نسيتها، نسيتها، ثالثة
+
+201
+00:14:45,160 --> 00:14:53,900
+أهداف المشروع، طبعًا أهمها تحقيق الدخل، القدرة على
+
+202
+00:14:53,900 --> 00:15:00,400
+استخدام التقنيات، طبعًا هيكون التقنية حديث، تطبيق بيدعم
+
+203
+00:15:00,400 --> 00:15:06,240
+.. بيوفر خدمات مميزة غير عن .. غيرنا من المنافسين، و
+
+204
+00:15:06,240 --> 00:15:09,780
+هيدعم أصحاب المشاريع الصغيرة في دراستهم المالية، و
+
+205
+00:15:09,780 --> 00:15:15,360
+الموازانات ودعم المحتوى العالمي، بسم الله الرحمن
+
+206
+00:15:15,360 --> 00:15:17,940
+الرحيم، احنا أول حاجة تعرّفنا اللي هو فكرة اللي هو 
+
+207
+00:15:17,940 --> 00:15:22,060
+تطبيق المحاسبة كان هو حل كثير من المشاكل بـ ..
+
+208
+00:15:22,060 --> 00:15:24,940
+خصوصًا أنه هنستعمل اللي هي السيرفرات الخارجية
+
+209
+00:15:24,940 --> 00:15:29,400
+لتخزين البيانات، واحنا أي تطبيق موجود يعني الـ ..
+
+210
+00:15:29,400 --> 00:15:32,660
+الـ .. كل تصورات العالم حول اللي هو وجود تطبيقات، و
+
+211
+00:15:32,660 --> 00:15:36,020
+الإنترنت للأشياء فكان اللي هو عندنا اللي هو دراسة
+
+212
+00:15:36,020 --> 00:15:39,460
+للمنافسين الموجودين، فاحنا على السبيل اللي هو أهم 
+
+213
+00:15:39,460 --> 00:15:43,270
+المنافسين اللي هو في سوق العمل، احنا كخدمات بشكل
+
+214
+00:15:43,270 --> 00:15:46,350
+متكامل، هيكون سحابي، يستخدم على الـtablet، ونعمل
+
+215
+00:15:46,350 --> 00:15:50,090
+تزامن للمعلومات في اللي هو على صعيد الشخص اللي هو
+
+216
+00:15:50,090 --> 00:15:53,870
+على الـtablet والجهاز الـcomputer، فهذه الخدمات 
+
+217
+00:15:53,870 --> 00:15:57,910
+بشكل متكامل اللي هي ما .. ما .. ما راح يوفرها أي
+
+218
+00:15:57,910 --> 00:16:02,270
+تطبيق، في بدايات كثير اللي هو كان موجود اللي هو شبيه
+
+219
+00:16:02,270 --> 00:16:07,430
+بتاعتي اللي هو الـ .. خدمات شبيهة لتطبيقنا، في منها
+
+220
+00:16:07,430 --> 00:16:10,590
+عربية وفي منها غير عربية، فدي كانت مشكلة، احنا
+
+221
+00:16:10,590 --> 00:16:15,890
+اللي هو كان دراسة لنا للمنافسين وعناصر المنافسة، و
+
+222
+00:16:15,890 --> 00:16:20,550
+كان في تقييم لهم، بعدين أنه احنا بنحكي ليش احنا 
+
+223
+00:16:20,550 --> 00:16:23,990
+اخترنا هذا المجال مع أنه متواجد زي هيك، بنبناه، نطلع
+
+224
+00:16:23,990 --> 00:16:27,490
+بإيش مميزات لتطبيقنا، أول حاجة اللي هو عمل سحابي
+
+225
+00:16:27,490 --> 00:16:30,470
+وبيعمل على الإنترنت، هيكون كفاءة عالية في حفظ هذه
+
+226
+00:16:30,470 --> 00:16:34,530
+البيانات، اللي هو استخدامه على أجهزة الحاسوب كتطبيق 
+
+227
+00:16:34,530 --> 00:16:38,610
+desktop، وبعدين أن الأجهزة الذكية هي اللي أصبح
+
+228
+00:16:38,610 --> 00:16:42,570
+الكثير يعني .. باتجاه نحو استعمالها، وبيستسهل أكثر
+
+229
+00:16:42,570 --> 00:16:45,510
+من أنه إيه استخدم الحاسوب في هذه الأشياء، وأنا ثالث
+
+230
+00:16:45,510 --> 00:16:48,390
+حاجة اللي هي كانت اللي هي الخدمة اللي هنوفرها، أسأل 
+
+231
+00:16:48,390 --> 00:16:52,730
+محاسبنا، أنه ممكن تسأل وتستشير، أو استفسار بـ ..
+
+232
+00:16:52,730 --> 00:16:55,210
+خصوصًا الأعمال الصغيرة أن هو ما يكونش عندهم الخبرة
+
+233
+00:16:55,210 --> 00:16:58,750
+الواسعة في الحلول المحاسبية المناسبة، فاحنا حابين 
+
+234
+00:16:58,750 --> 00:17:02,250
+نقدم اللي هو .. اللي هي الخدمة أنه يسأل ويستفسر
+
+235
+00:17:02,250 --> 00:17:06,400
+بأي ..خدمة بده يحتاجها، بأي سؤال، وبالـ .. فيه
+
+236
+00:17:06,400 --> 00:17:10,200
+دراسة، فيه معاهد، موازنة، بيقدر يسألنا، وآخر حاجة 
+
+237
+00:17:10,200 --> 00:17:13,120
+أنه أسعارنا تنافسية، أنه إحنا تكون فيه زوايا هتكون
+
+238
+00:17:13,120 --> 00:17:17,220
+مجانية، وأيضًا فيك اشتراك شهري، وأيضًا في فترة
+
+239
+00:17:17,220 --> 00:17:22,170
+تجريبية هتكون للتطبيق اللي هي هتكون مجانية، احنا أول
+
+240
+00:17:22,170 --> 00:17:25,670
+حاجة خطواتي اللي هي خطة العمل، كيف بدأنا هذا العمل،
+
+241
+00:17:25,670 --> 00:17:30,110
+أول شيء عملنا مراحل بدء المشروع، وإيش احتاجنا للبدء،
+
+242
+00:17:30,110 --> 00:17:33,730
+وإيش الخطوات التالية في تطوير وتقديم هذا المشروع 
+
+243
+00:17:33,730 --> 00:17:37,410
+للسوق، أول حاجة اللي احنا عاملنا اللي هي إن شاء
+
+244
+00:17:37,410 --> 00:17:40,470
+الله اللي هو الشركة، وبعدها كانت المرحلة المتوقعة 
+
+245
+00:17:40,470 --> 00:17:43,490
+اللي هو قدامه أنه احنا بنعمل صفحة على الإنترنت
+
+246
+00:17:43,490 --> 00:17:47,510
+وصفحة على الفيسبوك اللي هو ننشر فيها التطبيق، وبعدين
+
+247
+00:17:47,510 --> 00:17:51,470
+تسويقنا على هذا التطبيق، وآخر حاجة بعد ما نسوقه
+
+248
+00:17:51,470 --> 00:17:55,510
+نعمله اللي هو يكون عندنا تطوير إضافات حسب التحديث
+
+249
+00:17:55,510 --> 00:18:00,430
+اللي بتوصلنا من الزبائن، إن هي هذه خطة العمل 
+
+250
+00:18:00,430 --> 00:18:05,930
+بتوضح بشكل تفصيلي اللي هي الخطوات اللي درسناها، و
+
+251
+00:18:05,930 --> 00:18:08,450
+الأنشطة الأساسية في التطبيق
+
+252
+00:18:10,980 --> 00:18:15,240
+كيف احنا هنسوق لخدماتنا؟ كيف هنعرف الزبون بهذه 
+
+253
+00:18:15,240 --> 00:18:18,060
+الخدمة؟ أول حاجة اللي هو عندنا نقابة محاسبين
+
+254
+00:18:18,060 --> 00:18:21,840
+ومراجعين فلسطينيين، تقريبًا حوالي 8000 عضو موجود 
+
+255
+00:18:21,840 --> 00:18:25,220
+فيها، فإحنا لو .. لو اخترنا هدف فيه أنه احنا كيف 
+
+256
+00:18:25,220 --> 00:18:28,600
+نشر تطبيقنا مع كل تجديد عضوية أو مع كل عضوية اللي
+
+257
+00:18:28,600 --> 00:18:32,020
+هو نعطي نسخة من هذا التطبيق، فهذا أنه هراح عامله
+
+258
+00:18:32,020 --> 00:18:35,830
+على القطار بشكل كامل، أيضًا اللي هو عندنا كمان اللي 
+
+259
+00:18:35,830 --> 00:18:39,510
+هي الجامعات اللي موجودة بتدرس التطبيقات، بتدرس اللي
+
+260
+00:18:39,510 --> 00:18:44,310
+هو التخصصات المحاسبية، لو احنا عملنا عقد دورات خاصة
+
+261
+00:18:44,310 --> 00:18:48,270
+بتطبيق نوع جديد لأول مرة، وبعد هيك كل مرة، فهذا 
+
+262
+00:18:48,270 --> 00:18:53,360
+هيزيد انتشار التطبيق، وبيـ .. بيخلينا أنه احنا نطور
+
+263
+00:18:53,360 --> 00:18:56,620
+برضه المحاسبين لإنهم كيف يتعاملوا مع هذه التطبيقات،
+
+264
+00:18:56,620 --> 00:18:59,660
+وبيزيد اللي هو الخبرة اللي هنا، وآخر حاجة هي
+
+265
+00:18:59,660 --> 00:19:02,880
+الوسائل التقليدية اللي هي مواقع التواصل الاجتماعي 
+
+266
+00:19:02,880 --> 00:19:08,420
+و البريد والمواقع الإلكترونية، أنه كان هو عرض جدول 
+
+267
+00:19:08,420 --> 00:19:14,670
+التكاليف اللي هو الأجهزة والمعدات والتطوير وكل
+
+268
+00:19:14,670 --> 00:19:18,610
+تكاليفنا، فكرة اللي هو تقريبًا 6000 دولار، عندنا برضه 
+
+269
+00:19:18,610 --> 00:19:21,210
+اللي هو جدول إيرادات المتوقعة، إحنا إيراداتنا
+
+270
+00:19:21,210 --> 00:19:24,630
+المتوقعة هتكون أول حاجة من الإعلانات الممولة، ثاني 
+
+271
+00:19:24,630 --> 00:19:27,470
+إيش الاشتراك بالتطبيق هيكون، هنعرف اللي هو اشتراك 
+
+272
+00:19:27,470 --> 00:19:31,990
+اللي هو التطبيقات اللي هو اشتراك بالتطبيق هيكون هنا
+
+273
+00:19:31,990 --> 00:19:35,550
+جانب فيه مجاني، ولكن جانب غير مجاني بده يكون هو 
+
+274
+00:19:35,550 --> 00:19:40,210
+اشتراك، فيه زاوية مميزة، فبيكون لازم اشتراك شهري
+
+275
+00:19:40,210 --> 00:19:43,110
+وممكن أفر .. اللي هي أفر حاجة بيه التطبيق .. 
+
+276
+00:19:43,110 --> 00:19:46,270
+التطبيقات الغير مجانية، في شركات بتحب تكون إليها
+
+277
+00:19:46,270 --> 00:19:50,250
+التطبيق اللي خاص بها، فإحنا بنعمل إليها زاوية معينة 
+
+278
+00:19:50,250 --> 00:19:54,370
+أنه .. بمميزاتها، إيش بدها إضافات على هذا ونبيعهم
+
+279
+00:19:54,370 --> 00:19:57,850
+هذا التطبيق، فكان اللي هو العقد في أول سنة لإن اللي 
+
+280
+00:19:57,850 --> 00:20:01,510
+هو ألف ومـ .. ألف ومئتين وثلاثين دولار، آخر حاجة 
+
+281
+00:20:01,510 --> 00:20:04,230
+اللي هو الأرباح المتوقعة كانت اللي هو وفق دراسات
+
+282
+00:20:04,230 --> 00:20:08,310
+موجودة على مدار ثلاث سنوات نلاحظ بالأول أنه ما فيش 
+
+283
+00:20:08,310 --> 00:20:11,590
+هذا الربح اللي كثير لأنه مش هيتولّى بعد هيك تبدأ
+
+284
+00:20:11,590 --> 00:20:14,510
+الأرباح اللي تزيد لإنه بأول سنة نحتاج اللي هو
+
+285
+00:20:14,510 --> 00:20:20,500
+تكاليف تأسيسية عالية بسم الله مشروعنا اليوم بعنوان
+
+286
+00:20:20,500 --> 00:20:24,420
+ذريف الطول هيكون معاكم أول issue  دعاء قش pair و
+
+287
+00:20:24,420 --> 00:20:28,340
+بعدين ريمة منصورة و نسمة صادر الـ outline تبعنا
+
+288
+00:20:28,340 --> 00:20:32,160
+هنتكلم أول شيء عن الـ problem and motivation about
+
+289
+00:20:32,160 --> 00:20:37,360
+us و الـ idea and objective الـ marketing analysis و
+
+290
+00:20:37,360 --> 00:20:40,180
+الـ strength و الـ weakness و الـ opportunity و الـ
+
+291
+00:20:40,180 --> 00:20:44,260
+receipt analysisو الـ product and service و الـ
+
+292
+00:20:44,260 --> 00:20:49,440
+promotion و الـ management ده و آخر شيء هنتكلم عن الـ
+
+293
+00:20:49,440 --> 00:20:53,720
+financial information about us احنا بنات هندسة
+
+294
+00:20:53,720 --> 00:20:58,160
+حاسوب سنة خامسة عندنا خبرة في تصميم و قدرة على
+
+295
+00:20:58,160 --> 00:21:02,580
+إدارة المشاكل أول شيء زريف الطول من سنة قبل هيك
+
+296
+00:21:02,580 --> 00:21:07,660
+ليش زريف الطول انتشر عندنا الاسم هذا؟ حد بيعرف
+
+297
+00:21:07,660 --> 00:21:08,100
+اسمه؟
+
+298
+00:21:13,720 --> 00:21:18,500
+زريف الطول إيش اسمه هذا .. هذا شاب في فلسطين هو
+
+299
+00:21:18,500 --> 00:21:23,240
+بسبب طوله انتشر الاسم هو عبارة عن مقاول صار في
+
+300
+00:21:23,240 --> 00:21:27,680
+معارك عدة و استشهدوا مجموعة الحين فتّشوا على زريف
+
+301
+00:21:27,680 --> 00:21:32,600
+الطول ما لقوا بينهم فما لقوا أثر فيه فتشوا على كل
+
+302
+00:21:32,600 --> 00:21:36,380
+القرية ما لقوا له أثر فضلت الأغنية منتشرة على اسمه
+
+303
+00:21:36,380 --> 00:21:43,320
+أنه زريف الطول أنه ما لقوا له أثر في القرية و هيك الـ
+
+304
+00:21:43,320 --> 00:21:48,760
+problem اللي عندنا الأساسية أكثر شيء عندنا أنه الـ
+
+305
+00:21:48,760 --> 00:21:54,460
+..محاولة العدوان الإسرائيلي سرقت التراث الفلسطيني
+
+306
+00:21:54,460 --> 00:21:58,620
+و تسجيله في المؤسسات الإنسانية بتسجيله بتراث
+
+307
+00:21:58,620 --> 00:22:03,360
+إسرائيلي و سرقت كمان الكوفية و تصنيعها بأشكال و
+
+308
+00:22:03,360 --> 00:22:08,040
+ألوان مختلفة و وضع إشارة استدلالية عليها عندنا
+
+309
+00:22:08,040 --> 00:22:12,880
+بالنسبة للـ survey 24.6% من الـ customer عندهم
+
+310
+00:22:12,880 --> 00:22:18,500
+قاربهم في الخارج و يقدمونهم خزائن مغلفة بطريقة
+
+311
+00:22:18,500 --> 00:22:25,030
+مميزة و عندنا كمان 26% من الـ customers عندهم اهتمام
+
+312
+00:22:25,030 --> 00:22:30,870
+بالـ old food من المجففة و المصنعة اه و احنا ذريف
+
+313
+00:22:30,870 --> 00:22:36,070
+الطول هيكون deal with all issue of this problem
+
+314
+00:22:36,070 --> 00:22:41,450
+فكرة المشروع الـ idea and objective للمشروع سبعنا
+
+315
+00:22:41,450 --> 00:22:46,190
+احنا شركتنا هتكون داعمة أو تدي فرصة
+
+316
+00:22:49,170 --> 00:22:56,410
+و قدرة على التصنيع وإنتاج المواد التراثية وحنعود
+
+317
+00:22:56,410 --> 00:23:03,190
+بأرباح 50% بالنسبة للـ objective فانا اربع عناوين الـ
+
+318
+00:23:03,190 --> 00:23:07,190
+objective هي الـ sale و الـ profit و الـ pricing و الـ
+
+319
+00:23:07,190 --> 00:23:11,290
+product الـ sale يكون عندنا المنتج بجودة عالية و
+
+320
+00:23:11,290 --> 00:23:15,850
+طريقة التغليف مميزة للـ customer الـ profit يكون
+
+321
+00:23:15,850 --> 00:23:19,490
+عندنا نسبة الأرباح العائدة للسنة الثانية نسبة
+
+322
+00:23:19,490 --> 00:23:24,390
+خمسين بالمئة السعر هيكون في داخل غزة مقارب بأسعار
+
+323
+00:23:24,390 --> 00:23:25,290
+المنافسين
+
+324
+00:23:30,990 --> 00:23:36,650
+المنتج نفسه الـ product objective آخر شيء هنبدأ من
+
+325
+00:23:36,650 --> 00:23:39,810
+حسب الـ survey تبعنا أنه 50% من الـ customer اللي
+
+326
+00:23:39,810 --> 00:23:43,330
+لهم رغبة يكون عندهم منتجات الـ top الفلسطيني و
+
+327
+00:23:43,330 --> 00:23:50,950
+التراثية و 25.7% الأكل التقليدي و الأكل الشعبي أو
+
+328
+00:23:50,950 --> 00:23:56,450
+هنبدأ مشروعنا بـ الـ top competition من هدول و
+
+329
+00:23:56,450 --> 00:24:02,270
+هتكمل معاكم في الـ market الأساسية بسم الله الرحمن الرحيم
+
+330
+00:24:02,270 --> 00:24:05,750
+أنا ريمو منصور طبعا زي ما حدد الدعاء المشكلة
+
+331
+00:24:05,750 --> 00:24:08,790
+الموجودة عندنا وإيش الفكرة اللي احنا طرحناها طبعا
+
+332
+00:24:08,790 --> 00:24:11,370
+عشان نتوسط للأخير لدراسة لمشروعنا احتاجنا نعمل
+
+333
+00:24:11,370 --> 00:24:14,310
+مجموعة من التحليل .. التحليل سواء كان تحليل
+
+334
+00:24:14,310 --> 00:24:17,870
+للمنافسين تبعنا أو تحليل للـ suppliers أو تحليل للـ
+
+335
+00:24:17,870 --> 00:24:20,730
+customers اللي احنا راح نقدم لهم المنتجات تبعتنا أول
+
+336
+00:24:20,730 --> 00:24:23,390
+شيء بالنسبة للـ competitor analysis كان في عندنا
+
+337
+00:24:23,390 --> 00:24:26,250
+مجموعة من الـ competitors أكثرهم في قسم المترازات
+
+338
+00:24:26,250 --> 00:24:29,210
+لأنه في قسم الأغذية تقريبا كلها بتنبع في الأسواق
+
+339
+00:24:29,210 --> 00:24:33,180
+العادية العامة لكن قصدا و طرزاتى أكثر شيء فيها
+
+340
+00:24:33,180 --> 00:24:37,360
+computers و أكثر .. أكبر منافسين كان أبو ديا، في
+
+341
+00:24:37,360 --> 00:24:40,240
+عندنا كررش و في عندنا سُلفا و في عندنا general
+
+342
+00:24:40,240 --> 00:24:43,400
+markets بصورة عامة و قارنّاهم بـ ذريف الطول من حيث الـ
+
+343
+00:24:43,400 --> 00:24:46,460
+location، من حيث الـ quality، الـ graphs، السمعة، الـ
+
+344
+00:24:46,460 --> 00:24:50,360
+.. الترويج، طريقة الترويج، احنا تقريبا في الثانية
+
+345
+00:24:50,360 --> 00:24:54,670
+مع كررش، لكن أبو ديا بظلّوا ..أكبر منافسينا
+
+346
+00:24:54,670 --> 00:24:57,690
+بالنسبة للـ demographic analysis بالنسبة للـ 
+
+347
+00:24:57,690 --> 00:25:00,510
+survey احنا عملناها شوفنا مجموعة من البيانات من الـ
+
+348
+00:25:00,510 --> 00:25:04,150
+customers اللي هم شاركوا في الـ survey الجنس كان 77
+
+349
+00:25:04,150 --> 00:25:09,550
+% منهم إناث و 22% ذكور بالنسبة للعمر كان 59% منهم
+
+350
+00:25:09,550 --> 00:25:14,330
+ما بين 20 و 25% و هذه فترة الفئة المستهدفة عندنا أو
+
+351
+00:25:14,330 --> 00:25:18,870
+قطاع السوق الأول اللي احنا راح نستهدفه 27% فوق 25
+
+352
+00:25:18,870 --> 00:25:24,430
+و 12% كان ما بين 18 و 25 ما بين 18 و 20، بالنسبة
+
+353
+00:25:24,430 --> 00:25:29,470
+لمستوى التعليمي أكثر من مستوى الجامعية 85%، 12%
+
+354
+00:25:29,470 --> 00:25:33,990
+فوق ماجستير ودكتوراه، أما المستوى الدخل أغلبهم ما
+
+355
+00:25:33,990 --> 00:25:37,830
+بين 1000 إلى 2000 دولار، من 1000 إلى 2000 شكل كان
+
+356
+00:25:37,830 --> 00:25:41,490
+الدخل أقل من ذلك كان plus 34 أكثر من ذلك كان plus
+
+357
+00:25:41,490 --> 00:25:48,030
+30% المنطقة السكانية حنساعد في المنطقتين، داخل قطاع
+
+358
+00:25:48,030 --> 00:25:51,090
+غزة و خارج قطاع غزة، خارج قطاع غزة فيه إقبال عليها
+
+359
+00:25:51,090 --> 00:25:55,610
+37.5 أما داخل قطاع غزة 62.5 و طبعا هنبدأ في داخل
+
+360
+00:25:55,610 --> 00:25:59,360
+قطاع غزة بالنسبة للـ suppliers، شوفنا مجموعة من الـ
+
+361
+00:25:59,360 --> 00:26:01,960
+suppliers اللي بإمكانهم يعطونا المواد الخامة اللي
+
+362
+00:26:01,960 --> 00:26:06,220
+احنا بنحتاجها، كمان الـ computers بالنسبة للمطرزات
+
+363
+00:26:06,220 --> 00:26:10,660
+كانوا بيستخدموا الدادر هو الـ supplier تبع .. تبعي
+
+364
+00:26:10,660 --> 00:26:13,140
+منهم فعلا هيكون الـ supplier تبعنا هو الدادر
+
+365
+00:26:13,140 --> 00:26:16,360
+بالنسبة لقسم المطرزات أما قسم القطع ما هيكون
+
+366
+00:26:16,360 --> 00:26:21,650
+المزارع العامة عملنا تحليل للمنطقة اللي فيه إمكانية
+
+367
+00:26:21,650 --> 00:26:24,450
+يكون فيها المشروع تبعناها كان في عدة مناطق فيها
+
+368
+00:26:24,450 --> 00:26:30,650
+مميزات فيها عيوب جنوب الرمال و شمال الرمال و الجلاء
+
+369
+00:26:30,650 --> 00:26:34,290
+.. الجلاء و فعلا قريب من الـ universities و فعلا من
+
+370
+00:26:34,290 --> 00:26:38,390
+مصر أفضل شيء تقريبا النصر لإنه جد من ناحية الـ cost
+
+371
+00:26:38,390 --> 00:26:42,530
+المساحة تبعته مميّزة 70 متر و كمان إنه على الشارع
+
+372
+00:26:42,530 --> 00:26:46,890
+فالمكان تبعه مميز و أبقانه تبعته مسبقا بس بابه فيه
+
+373
+00:26:46,890 --> 00:26:49,310
+disadvantage القريب من الـ universities بعد الساعة
+
+374
+00:26:49,310 --> 00:26:53,050
+3 إنك تتوقع إن كل منطقة ميتة ما فيش فيها حركة أما
+
+375
+00:26:53,050 --> 00:26:55,650
+بالنسبة للجلاء high cost كذلك الحال في شمال
+
+376
+00:26:55,650 --> 00:26:58,610
+الرمال high cost أما جنوب الرمال إن هي منطقة
+
+377
+00:26:58,610 --> 00:27:02,790
+داخلية مش على الشارع مش فيها حركة عملنا تحليل
+
+378
+00:27:02,790 --> 00:27:05,530
+..عملنا تدقيق للموديل تبعنا و تدقيق للشركة تبعنا
+
+379
+00:27:05,530 --> 00:27:07,870
+عشان نشوف نقاط القوة و نقاط الضعف و إيش الفرص و
+
+380
+00:27:07,870 --> 00:27:11,470
+التهديدات اللي بتواجهنا بالنسبة للـ product تبعنا
+
+381
+00:27:11,470 --> 00:27:14,350
+بيتميز بإنه appropriately packaging و اللي احنا
+
+382
+00:27:14,350 --> 00:27:17,570
+اعتبرنا ميزة نفسية موجودة في الـ .. في المشروع اللي
+
+383
+00:27:17,570 --> 00:27:21,010
+تبعنا لإنه طبعا الـ computers مش كتير في عملية الـ
+
+384
+00:27:21,010 --> 00:27:25,210
+packaging خاصة مثلا ما حكت بها إنها احنا راح نعمل
+
+385
+00:27:25,210 --> 00:27:28,710
+تغليف هدايا خارج طبع الغزايا، فيعني high quality،
+
+386
+00:27:28,710 --> 00:27:31,310
+high accuracy و experience بينا على الأجداد اللي
+
+387
+00:27:31,310 --> 00:27:34,770
+احنا راح نعمل بهم احتضان لـ .. بالنسبة للشركة
+
+388
+00:27:34,770 --> 00:27:38,530
+تبعتنا، في .. نستطيع أن يكون فيها strength ..
+
+389
+00:27:38,530 --> 00:27:40,970
+strong في serving في الـ marketing، في عملية
+
+390
+00:27:40,970 --> 00:27:45,030
+الترويج، في عملية البيع، في عملية التسويق، نصل
+
+391
+00:27:45,030 --> 00:27:48,890
+لرضى الـ customer و كذلك يكون في عندنا قوة فيه
+
+392
+00:27:48,890 --> 00:27:52,590
+الإدارة و قوة فيه الـ weakness و أكبر weakness احنا
+
+393
+00:27:52,590 --> 00:27:55,190
+ممكن نواجهها اللي هي الـ budget و الـ financial بكون
+
+394
+00:27:55,190 --> 00:27:58,270
+أن احنا شركة ناشئة فمن ناحية الميزانية هيكون فيه
+
+395
+00:27:58,270 --> 00:28:02,300
+ضعف الـ opportunity analysis في عندنا market
+
+396
+00:28:02,300 --> 00:28:04,880
+opportunities و في عندنا environment opportunities
+
+397
+00:28:04,880 --> 00:28:07,440
+الـ market فيه بناء على الـ survey تبعنا فيه interest
+
+398
+00:28:07,440 --> 00:28:10,560
+فيه اهتمام من الـ customers أنهم يكونوا يشرقوا
+
+399
+00:28:10,560 --> 00:28:15,860
+بمتاجرتنا و في كمان إقبال على المتاجر تبعنا درجة من
+
+400
+00:28:15,860 --> 00:28:19,100
+الإقبال على المتاجر تبعنا فهذه ممكن نستغلها فرصة
+
+401
+00:28:19,100 --> 00:28:22,280
+الـ environment analysis environment opportunities
+
+402
+00:28:22,280 --> 00:28:26,620
+أنه في عندنا لإنه وجهة مشروعنا بتقول أنه هو مش
+
+403
+00:28:26,620 --> 00:28:30,540
+شركات خاصة ممكن يشتغلوا في جامعات وكذا فالكل يمكن
+
+404
+00:28:30,540 --> 00:28:33,220
+الـ government instruction في عندنا weakness في ضعف
+
+405
+00:28:33,220 --> 00:28:35,360
+عملية التنمية مش احنا دائما بنلاقي مترازات أو
+
+406
+00:28:35,360 --> 00:28:40,260
+أطعمة منتشرة في الأسواق العامة في عندنا يعني مش
+
+407
+00:28:40,260 --> 00:28:42,960
+الكل دائما بيستخدم المترازات لإنه ممكن أعمل في
+
+408
+00:28:42,960 --> 00:28:45,700
+إحلال المنتج في عقول الأذهان المستهدفة
+
+409
+00:28:45,700 --> 00:28:50,360
+والمستفيدين مش الشجاعية بس احنا هنحاول نعمل إحلال
+
+410
+00:28:50,360 --> 00:28:53,560
+الميزة التنافسية في أذهانهم في عندنا weakness في
+
+411
+00:28:53,560 --> 00:28:54,040
+الـ marketing
+
+412
+00:28:57,120 --> 00:28:59,840
+التهديد اللي بتواجهنا و اللي بتواجه كل قطاع غزة أول
+
+413
+00:28:59,840 --> 00:29:02,020
+شيء الـ closed boundaries طبعا خاصة أن احنا نتعامل
+
+414
+00:29:02,020 --> 00:29:06,420
+مع خارج قطاع غزة في عندنا easy في طبيعة مشروعنا في عندنا
+
+415
+00:29:06,420 --> 00:29:08,420
+أنه أي حد ممكن يتعلمها في سنة سنتين و يصير خبرة
+
+416
+00:29:08,420 --> 00:29:13,780
+فيها هي كمان مش تهديد make ان نسمع علاقات مع
+
+417
+00:29:13,780 --> 00:29:16,920
+التجار طبعا هيكون كمان مش صعب شوية لأنه احنا شركة
+
+418
+00:29:16,920 --> 00:29:22,080
+ناشئة و كمان لازم نقاوم مساومة الـ suppliers بقينا
+
+419
+00:29:22,080 --> 00:29:24,800
+يكون عندنا أكثر من supplier لكل منتج من المنتجات
+
+420
+00:29:24,800 --> 00:29:26,900
+اللي لازم نحددهم و كمان الـ competitors بيكونوا
+
+421
+00:29:26,900 --> 00:29:30,180
+مهلّدين إيش الـ product اللي بنقدّمه في قسم
+
+422
+00:29:30,180 --> 00:29:33,860
+المطرزات؟ في عندنا الثوب الفلسطيني، المخدّات،
+
+423
+00:29:33,860 --> 00:29:36,540
+الأشنطة، الـ accessories  و أي شيء ممكن يطلبه الـ
+
+424
+00:29:36,540 --> 00:29:40,540
+customers بنقدّمه و الـ food services ممكن قمر
+
+425
+00:29:40,540 --> 00:29:43,840
+الدين، الشطة الأصلية اللي محدش فيها بيعملها، الـ
+
+426
+00:29:43,840 --> 00:29:50,450
+cheese، الـ dried tomato و المخلّلات أخلقوا معنا
+
+427
+00:29:50,450 --> 00:29:55,970
+اسمها و أكمّلوا في قرمشبالنسبة لعملية تسويق للمنتج
+
+428
+00:29:55,970 --> 00:30:00,150
+تبعنا طبعًا اخترنا أن يكون gift بسيطة عبارة عن
+
+429
+00:30:00,150 --> 00:30:05,590
+ميدالية مثلًا باسم الشركة أنها ذريف الطول بحيث أي أحد
+
+430
+00:30:05,590 --> 00:30:10,670
+ييجي على شركتنا نعطيه .. يعني يشتري من عندنا
+
+431
+00:30:10,670 --> 00:30:15,130
+نعطيه هذه الهدية بحيث تنتشر أكثر حوالين الناس
+
+432
+00:30:15,130 --> 00:30:18,890
+بقول الـ social media أكيد رح يكون عامل كثير مهم أن
+
+433
+00:30:18,890 --> 00:30:21,820
+نعرض منتجاتنا وأكثر التفكيرات اللي عليها الـ CD
+
+434
+00:30:21,820 --> 00:30:28,040
+طبعًا قررنا نعمل مثلًا movie بإخراج معيّن يبيّن مدى الـ
+
+435
+00:30:28,040 --> 00:30:31,460
+qualifications و الـ .. الـ quality تبعنا و تبع
+
+436
+00:30:31,460 --> 00:30:35,620
+المنتج تبعنا، رح نوزّع هذا الـ CD في الجامعات و
+
+437
+00:30:35,620 --> 00:30:40,450
+المناطق العامة والمعارض كمان سألنا .. كمان سألنا
+
+438
+00:30:40,450 --> 00:30:45,550
+الـ .. الـ competitors تبعنا، البوش مهندسة حليمة
+
+439
+00:30:45,550 --> 00:30:51,110
+صاحبة كرداش سألناها عن إيش أكثر شيء سوقنا تبعك
+
+440
+00:30:51,110 --> 00:30:55,430
+المنتج، حكتنا إنه نفسها .. هي نفسها بلسانها إنه
+
+441
+00:30:55,430 --> 00:31:01,700
+لما تروح على المعارض العامة بتحكي عن منتجاتها وهذا
+
+442
+00:31:01,700 --> 00:31:05,800
+الشيء فاحنا رح نستخدم هذا الشيء بأن أي معرض خلال
+
+443
+00:31:05,800 --> 00:31:10,340
+يوم النكبة أو غيره نسوقنا تبعنا ونحاول يعني نوصل
+
+444
+00:31:10,340 --> 00:31:15,380
+ لأكبر قدر من الناس بكلامنا و زي الحاجات بالنسبة
+
+445
+00:31:15,380 --> 00:31:18,620
+للخارج، قطاع غزة طبعًا رح إنه .. إنه المعارض اللي
+
+446
+00:31:18,620 --> 00:31:23,540
+راح تقام تقريبًا فيه كل يوم .. كل مرّة في سنة .. يوم
+
+447
+00:31:23,540 --> 00:31:27,300
+النكبة، يوم الأرض، اللي بتقام على .. برّا، طريق الـ
+
+448
+00:31:27,300 --> 00:31:30,200
+relations بتاعنا، راح نحاول أن نسوّق لاسمنا 
+
+449
+00:31:32,820 --> 00:31:36,300
+أما بالنسبة للـ management plan طبعًا راح يكون أكيد
+
+450
+00:31:36,300 --> 00:31:39,340
+في عندنا general manager الـ two sub managers اللي
+
+451
+00:31:39,340 --> 00:31:42,040
+هم رؤساء الأقسام لـ .. الأقسام اللي تبعنا اللي
+
+452
+00:31:42,040 --> 00:31:45,440
+هو المطرزات و الـ .. الـ .. الـ .. الـ financial
+
+453
+00:31:45,440 --> 00:31:49,920
+account driver و الـ grant balance و الـ .. الـ
+
+454
+00:31:49,920 --> 00:31:52,500
+cleaners و الـ reception طبعًا الـ general manager
+
+455
+00:31:52,500 --> 00:31:56,080
+أهم شيء إنه يتابع الـ .. الخطة المالية تبع الـ
+
+456
+00:31:56,080 --> 00:32:01,140
+financial وكمان إنه يحطّ خطّة للتطوير و .. و الجودة
+
+457
+00:32:02,300 --> 00:32:05,500
+و .. و يحاول كمان يتواصل و يعمل relationship كثير
+
+458
+00:32:05,500 --> 00:32:09,420
+منيحه مع الـ .. الـ suppliers و الـ .. و الناس اللي
+
+459
+00:32:09,420 --> 00:32:14,340
+خارج قطاع غزة وأكيد يتابع الـ .. المشاكل اللي راح
+
+460
+00:32:14,340 --> 00:32:18,300
+تنتج من كل قسم و .. و إيش .. إيش ممكن راح يعمل
+
+461
+00:32:18,300 --> 00:32:23,300
+لحتى يطوّر كل قسم وإيش الـ sales و الـ .. المنتجات
+
+462
+00:32:23,300 --> 00:32:28,240
+الجديدة اللي راح تنضم للسوقبالنسبة للـ financial
+
+463
+00:32:28,240 --> 00:32:31,400
+information طبعًا راجعنا بالـ start-up cost اللي هي
+
+464
+00:32:31,400 --> 00:32:36,120
+عبارة عن المعدّات والأجهزة وطبعًا الـ previous ..
+
+465
+00:32:36,120 --> 00:32:39,320
+اللي هي الـ previous operations اللي هي راح تشمل
+
+466
+00:32:39,320 --> 00:32:43,180
+الدعايات وغيرهم طبعًا المواد الخام والـ ring طبعًا
+
+467
+00:32:43,180 --> 00:32:48,040
+شوفنا أنه لازم لـ .. أول ست أشهر لازم ندفع فإن الـ
+
+468
+00:32:48,040 --> 00:32:52,520
+print راح يكون داخل مع الـ start-up cost لست أشهر و
+
+469
+00:32:52,520 --> 00:32:56,280
+طبعًا الـ UPS وغيره طلب تقريبًا 28 ألف دولار
+
+470
+00:32:59,000 --> 00:33:02,360
+أما الـ fixed و الـ variable فالـ fixed طبعًا الـ rent
+
+471
+00:33:02,360 --> 00:33:05,700
+الـ salaries تكون under الـ internet الـ deposit و
+
+472
+00:33:05,700 --> 00:33:09,220
+اللي هو الـ first aid كلها تقريبًا مقدار 75 ألف
+
+473
+00:33:09,220 --> 00:33:11,920
+دولار الـ variable cost طبعًا اللي هي الـ raw
+
+474
+00:33:11,920 --> 00:33:15,100
+material الـ transport و الـ overhead و الـ
+
+475
+00:33:15,100 --> 00:33:17,940
+maintenance و الـ gifts طبعًا بتشمل الـ gifts لأنه
+
+476
+00:33:17,940 --> 00:33:21,660
+ممكن يزيد عدد الـ customers تقريبًا 33 ألف دولار
+
+477
+00:33:24,390 --> 00:33:27,210
+في السنة الثانية طبعًا تقريبًا fixed cost أظل زي ما
+
+478
+00:33:27,210 --> 00:33:30,470
+هو الـ variable cost لأن مصر ناشطة بتعمل مال أما الـ
+
+479
+00:33:30,470 --> 00:33:33,590
+variable cost فتقريبًا زاد lot ضارف لإنه تقريبًا الـ
+
+480
+00:33:33,590 --> 00:33:37,250
+customers بتعملون بناء على الأساسيات تبعنا زاد و
+
+481
+00:33:37,250 --> 00:33:41,050
+lot ضارف بناء على المعدّل الشركاني والـ competitors
+
+482
+00:33:44,260 --> 00:33:48,260
+بالنسبة لـ الـ first year طبعًا في الـ revenues اهتمّ
+
+483
+00:33:48,260 --> 00:33:50,480
+الأول شيء على الـ competitors كم عدد الناس اللي
+
+484
+00:33:50,480 --> 00:33:53,560
+بيجوهم .. كم عدد الناس اللي بيجوهم لكل منتج مثلًا
+
+485
+00:33:53,560 --> 00:33:59,260
+الـ .. الثوب الفلسطيني كم .. كم الشهر بيجيكي زبائن
+
+486
+00:33:59,260 --> 00:34:03,100
+وأساسًا بدنا نحسب قدّ إيش اللي هي عدد الـ revenues
+
+487
+00:34:03,100 --> 00:34:08,580
+للسنة الأولى طبعًا قدرناها بـ 144 ألف دولار و
+
+488
+00:34:08,580 --> 00:34:13,690
+الـ net profit قريبًا 16 ألف دولارالسكان ديّار تقريبًا
+
+489
+00:34:13,690 --> 00:34:20,070
+مئة وأربعة وثمانين ألف دولار طبعًا بناء على الـ
+
+490
+00:34:20,070 --> 00:34:23,910
+computers ومعدل النمو السكاني زدنا عدد الناس
+
+491
+00:34:23,910 --> 00:34:26,810
+اللي راح يجونا وكمان حطينا مثلًا لإنه لشهر رمضان
+
+492
+00:34:26,810 --> 00:34:31,430
+مثلًا راح يزيد عدد الناس على القمر الدين فبالتالي
+
+493
+00:34:31,430 --> 00:34:36,420
+راح يزيد عملية الـ .. البيع عليه بالنسبة للـ cash
+
+494
+00:34:36,420 --> 00:34:39,820
+flow طبعًا من خلال ما احنا عملنا طبعًا السنة الأولى
+
+495
+00:34:39,820 --> 00:34:45,280
+الثانية عندنا loss لكن السنة الثانية حققنا الربح 62%
+
+496
+00:34:45,280 --> 00:34:49,200
+عملية اللي هي العائد من الاستثمار احنا كنا متوقعين
+
+497
+00:34:49,200 --> 00:34:54,200
+50% وطلع 62% أما الـ even point تقريبًا منا بس
+
+498
+00:34:54,200 --> 00:34:58,200
+ لمنتج واحد اللي هو محب فلسطيني 50 واحدة لازم نبيع
+
+499
+00:34:58,200 --> 00:35:05,500
+لحتى نحقق ربح الـ pay back period طلعت تقريبًا في
+
+500
+00:35:05,500 --> 00:35:09,920
+السنة الثانية، رح نحقق أربعة، بالنهاية بطمئنّ
+
+501
+00:35:09,920 --> 00:35:14,630
+تكونوا ضارفين طول جهدكمبسم الله الرحمن الرحيم
+
+502
+00:35:14,630 --> 00:35:19,030
+اليوم رح أتكلم عن خطّة عمل مشروع مركبة المعرفة
+
+503
+00:35:19,030 --> 00:35:22,090
+موضوعنا بيجمع على وجود مشكلة في القراءة في قطاع
+
+504
+00:35:22,090 --> 00:35:25,930
+غزة قلة وهي إحجام الناس أو عدم إقبال الناس بشكل
+
+505
+00:35:25,930 --> 00:35:30,010
+كبير على القراءة لو جينا .. لو جينا نبحث عن أسباب
+
+506
+00:35:30,010 --> 00:35:34,330
+هذه المشكلة رح نلاقي أنّ الأسباب هذه بتنحصر أو
+
+507
+00:35:34,330 --> 00:35:39,210
+بشكل عام أهم 3 أسباب هي التالية التطوّر الإلكتروني
+
+508
+00:35:39,210 --> 00:35:42,910
+اللي حاصل الآن بيصير حوالينا بالعالم قدّ أدّى لوجود
+
+509
+00:35:42,910 --> 00:35:48,010
+فجوة كبيرة بين الإنسان أو بين الفرد في قطاع غزة و
+
+510
+00:35:48,010 --> 00:35:51,510
+أيضًا بين القراءة السبب الثاني اللي .. الأوضاع
+
+511
+00:35:51,510 --> 00:35:54,190
+الاقتصادية السيئة اللي بيمرّ فيها المجتمع الغزّي
+
+512
+00:35:54,190 --> 00:35:59,310
+قدّ أدّت لإحجام الناس عن شراء الكتب لإنه الـ .. الـ ..
+
+513
+00:35:59,460 --> 00:36:02,860
+أدت إلى إحجام الناس عن شراء الكتب، هذه المشاكل
+
+514
+00:36:02,860 --> 00:36:06,860
+بتتمثل في انخفاض مستويات الدخل وأيضًا في انتشار
+
+515
+00:36:06,860 --> 00:36:10,740
+البطالة بشكل كبير السبب الثالث أنّ كلنا أو أغلبنا
+
+516
+00:36:10,740 --> 00:36:13,680
+بنلاقي حالنا أنّ دائمًا ما عندنا نحن وقت نقرأ، هاي
+
+517
+00:36:13,680 --> 00:36:17,520
+هي كانت أهم الأسباب اللي بتواجه القراءة طيب الحل
+
+518
+00:36:17,520 --> 00:36:20,760
+المطروح فكّرنا بالحل شو ممكن يكون الحل لهذه المشكلة
+
+519
+00:36:20,760 --> 00:36:24,340
+وجدنا أنّ الحل ممكن يكون عبارة عن إنشاء مكتبة
+
+520
+00:36:24,340 --> 00:36:28,760
+متنقلة تستهدف جميع أفراد المجتمع بشكل عام وتجمّعات
+
+521
+00:36:28,760 --> 00:36:32,280
+شبابية وطلّابية بشكل خاص هي المكتبة قادرة على
+
+522
+00:36:32,280 --> 00:36:38,510
+توفير أغلب أصناف الكتب وبأسعار مناسبة للجامعة كانت
+
+523
+00:36:38,510 --> 00:36:42,350
+.. كانت .. كان الحل هذا بيتمثّل فيه مشروع يعني اللي
+
+524
+00:36:42,350 --> 00:36:45,890
+هو عبارة عن مركبة المعرفة مركبة المعرفة هي عبارة
+
+525
+00:36:45,890 --> 00:36:50,410
+عن مكتبة في باص متنقّل في شوارع قطاع غزة الرئيسية
+
+526
+00:36:50,410 --> 00:36:55,170
+تشتمل المكتبة على كتب مختلفة في مجالات أو مواضيع
+
+527
+00:36:55,330 --> 00:37:00,890
+متنوعة، المكتبة بتقدّم بيع وإعارة الكتب المطبوعة،
+
+528
+00:37:00,890 --> 00:37:04,630
+بيع الكتب المسموعة بالإضافة إلى بعض الألعاب
+
+529
+00:37:04,630 --> 00:37:08,490
+الورقية اللي هيتم بيعها، هاي كلها المنتجات بتاعتنا
+
+530
+00:37:08,490 --> 00:37:12,650
+رح نقوم ببيعها بأسعار منافسة وأيضًا مناسبة لجميع
+
+531
+00:37:12,650 --> 00:37:16,010
+أفراد المجتمع الغزّي، بالإضافة إلى ذلك رح يكون
+
+532
+00:37:16,010 --> 00:37:19,970
+عندنا موقع إلكتروني خاص بالمكتبة على شبكة الإنترنت
+
+533
+00:37:20,370 --> 00:37:23,250
+طيب أكيد أحد بيسأل شو اللي راح يخلي مركبة المعرفة
+
+534
+00:37:23,250 --> 00:37:25,930
+حالها مبتكرة مميزة عن جميع المكتبات اللي موجودة في
+
+535
+00:37:25,930 --> 00:37:29,750
+قطاع غزة؟ الحل ببساطة أنّ إحنا شفنا وين المشاكل
+
+536
+00:37:29,750 --> 00:37:32,470
+اللي ممكن نتواجه أي إنسان بده يقرأ وعملنا على
+
+537
+00:37:32,470 --> 00:37:36,130
+حلها أول شيء بالنسبة للأشخاص اللي ما بيقرؤوا بسبب
+
+538
+00:37:36,130 --> 00:37:40,190
+بعد المكتبات بنسبة معيّنة عنهم وبالتالي هم
+
+539
+00:37:40,190 --> 00:37:43,330
+بيتكاسلوا عن شراء الكتب هذا اللي .. أو هاي المشكلة
+
+540
+00:37:43,330 --> 00:37:46,250
+رح تنحل بإنّ مكتبتنا رح تكون متنقلة، بالتالي
+
+541
+00:37:46,250 --> 00:37:51,310
+يغطّي أكبر .. أكبر منطقة ممكنة في قطاع غزة، الفئة
+
+542
+00:37:51,310 --> 00:37:53,950
+الثانية من الأشخاص هم اللي ما بيقرؤوا لعدم تمكّنهم
+
+543
+00:37:53,950 --> 00:37:57,330
+من شراء الكتب، لإنه زي ما احنا بنعرف الصراحة أسعار
+
+544
+00:37:57,330 --> 00:38:00,630
+الكتب شوي مرتفعة في المكتبات اللي موجودة عندنا،
+
+545
+00:38:00,630 --> 00:38:03,950
+وبالتالي هاي المشكلة حلّيناها بطريقتين، أول شيء إنّ
+
+546
+00:38:03,950 --> 00:38:07,290
+المكتبة بتوفّر خدمة إعارة الكتب مقابل أسعار رمزية
+
+547
+00:38:07,290 --> 00:38:09,970
+فبالتالي الشخص اللي ما بيقدر يشتري كتب هو
+
+548
+00:38:09,970 --> 00:38:13,730
+قادر على إعارة هذه الكتب مقابل مبلغ بسيط الطريقة
+
+549
+00:38:13,730 --> 00:38:17,370
+الثانية أنّ أسعار الكتب أساسًا في مكتبتنا احنا هنكون
+
+550
+00:38:17,370 --> 00:38:20,610
+جاهدين على أنّ نعمل .. أنّ نخلي هذه الأسعار أقل من
+
+551
+00:38:20,610 --> 00:38:24,390
+كلّ .. من أسعار كتب في كلّ المواقع .. المكتبات اللي
+
+552
+00:38:24,390 --> 00:38:27,370
+موجودة في قطاع غزة أما بالنسبة للفئة الثالثة
+
+553
+00:38:27,370 --> 00:38:30,330
+والأخيرة هي عبارة عن أشخاص اللي ما بيقرؤوا لعدم
+
+554
+00:38:30,330 --> 00:38:32,570
+توفّر عندهم من وقت كافي لذلك هذه المشكلة اللي احنا
+
+555
+00:38:32,570 --> 00:38:37,880
+نتغلب عليها بهذه الكتب رح تكون مسجّلة على ..
+
+556
+00:38:37,880 --> 00:38:41,620
+ومحفوظة على CD هات أو فلاشات بيتمّ بيعها للأفراد
+
+557
+00:38:41,620 --> 00:38:44,100
+بالتالي الشخص اللي ما بيقدر يمسك كتاب يقرأ فيه هو
+
+558
+00:38:44,100 --> 00:38:48,800
+بيقدر يسمع له في مثلًا سيارته أو هو رايح على شغله أو
+
+559
+00:38:48,800 --> 00:38:51,900
+بيعمل بأي شغل معيّنة بهذا الأسلوب احنا ممكن نحلّ
+
+560
+00:38:51,900 --> 00:38:55,440
+معظم أو أهمّ المشاكل اللي ممكن يتواجه أي شخص بده
+
+561
+00:38:55,440 --> 00:38:58,600
+يقرأ أما بالنسبة لفريق العمل ففريق العمل هو عبارة
+
+562
+00:38:58,600 --> 00:39:02,040
+عن ثلاثة أشخاص رنا أبوديا، غدير أبو كواكو، أنت
+
+563
+00:39:02,040 --> 00:39:06,660
+سمين الجماسي جميعنا خريجات من هندسة لدينا خبرة في
+
+564
+00:39:06,660 --> 00:39:10,420
+البرمجة بالإضافة لمهارات إدارية لدينا ومهارات
+
+565
+00:39:10,420 --> 00:39:13,780
+تسويقية لدى غدير و لدى رنا في علم المكتبات
+
+566
+00:39:13,780 --> 00:39:17,260
+أما الهيكل التنظيمي للمشروع تبعنا هيكون مدير 
+
+567
+00:39:17,260 --> 00:39:21,480
+المشروع أمين المكتبة سيكون مسؤول عن شراء الكتب
+
+568
+00:39:21,480 --> 00:39:26,180
+بالإضافة لبيعها وسيكون مسؤول عن تصنيفاتها لديه أصلا
+
+569
+00:39:26,180 --> 00:39:29,860
+خبرة في علم المكتبات المحاسب هو سيكون مسؤول عن
+
+570
+00:39:29,860 --> 00:39:34,330
+الأمور المالية سائق الـ bus للزبائن المحتملين لدينا
+
+571
+00:39:34,330 --> 00:39:37,370
+في المشروع أفراد المجتمع بمختلف الفئات العمرية
+
+572
+00:39:37,370 --> 00:39:42,850
+خاصة الفئة بين 18 إلى 50... 50 سنة وهذه الفئة سيكون
+
+573
+00:39:42,850 --> 00:39:47,660
+أمامها القدرة على شراء الكتب واستعارتها المؤسسات
+
+574
+00:39:47,660 --> 00:39:51,040
+المجتمعية التي ممكن تساعدنا بالإضافة للمؤسسات غير
+
+575
+00:39:51,040 --> 00:39:53,800
+الربحية الداعمة ممكن تساعدنا عن طريق أن هي
+
+576
+00:39:53,800 --> 00:39:58,640
+تستخدمنا في بعض الأنشطة وبالإضافة للمكتبات
+
+577
+00:39:58,640 --> 00:40:01,320
+التابعة التي احنا ممكن لاحقا نكون موزعين خاصة 
+
+578
+00:40:01,320 --> 00:40:03,960
+للكتب المسموعة التي هي الفكرة الجديدة التي احنا
+
+579
+00:40:03,960 --> 00:40:07,760
+نستهدفها بشكل أساسي بالنسبة لنموذج العمل أي طبيعة
+
+580
+00:40:07,760 --> 00:40:13,000
+العمل وكيف المشروع سوف يجني أرباحا أولا بالنسبة لبيع
+
+581
+00:40:13,000 --> 00:40:17,440
+الكتب المطبوعة الكتب المطبوعة الورقية تبعنا راح
+
+582
+00:40:17,440 --> 00:40:22,660
+نشتريها من تجار الجملة بسعر معين سوف نكون بـ بائعين
+
+583
+00:40:22,660 --> 00:40:27,500
+بسعر أعلى للحصول على هامش ربح مع مراعاة أن
+
+584
+00:40:27,500 --> 00:40:31,980
+السعر يكون قليل بالنسبة للمكتبات الأخرى بالإضافة
+
+585
+00:40:31,980 --> 00:40:37,190
+لإعادة الكتب التي راح تكون بمبلغ غير رمزي للفئات
+
+586
+00:40:37,190 --> 00:40:42,270
+التي غير قادرة على أن تشتري الكتب التي ممكن تكون
+
+587
+00:40:42,270 --> 00:40:46,530
+باهظة الثمن قليلا وسيكون لدينا وسائل لضمان استرجاع
+
+588
+00:40:46,530 --> 00:40:50,710
+الكتب من المستخدمين الكتب المسموعة ستم تسجيلها أو
+
+589
+00:40:50,710 --> 00:40:54,150
+بيعها على اسطوانات فلاشات بالإضافة إلى موقع
+
+590
+00:40:54,150 --> 00:40:57,990
+إلكتروني سيتوفر لدى المكتبة سيكون نقطة... نقطة
+
+591
+00:40:57,990 --> 00:41:01,890
+أساسية للوصول إلى الزبون سيعرض... سيكون لدى الموقع
+
+592
+00:41:01,890 --> 00:41:07,070
+قدرة على مناقشة الكتب وطلب الزبائن لكتب معينة هم
+
+593
+00:41:07,070 --> 00:41:10,730
+يحتاجونها وسائل الترويج في... بالنسبة لمشروعنا، راح
+
+594
+00:41:10,730 --> 00:41:13,290
+يكون عنها أكثر من وسيلة أو وسائل تواصل اجتماعي،
+
+595
+00:41:13,290 --> 00:41:16,490
+سنعتمد بشكل أساسي على الإعلانات المدفوعة... الممولة
+
+596
+00:41:16,490 --> 00:41:20,030
+لنشر فكرة المشروع، إعلانات الراديو، استقطاب وسائل
+
+597
+00:41:20,030 --> 00:41:23,670
+الإعلان خاصة في افتتاح المشروع، الموسيقى الترويجية
+
+598
+00:41:23,670 --> 00:41:26,420
+واللافتات الإعلانية في الشوارع الرئيسية أما بالنسبة
+
+599
+00:41:26,420 --> 00:41:29,760
+لمنافذ البيع فبالتأكيد أن رح يتم تغطية المناطق
+
+600
+00:41:29,760 --> 00:41:34,320
+الجغرافية الأكثر تواجد ل... لزبائن المشروع قسمنا
+
+601
+00:41:34,320 --> 00:41:39,040
+محافظات قطاع غزة على أيام الأسبوع بحيث يتم تغطيتها
+
+602
+00:41:39,040 --> 00:41:45,620
+خلال هذه ال... خلال ساعات معينة من النهار وهذا
+
+603
+00:41:45,620 --> 00:41:49,980
+الجدول رح يكون متوفر على موقع المكتبة الإلكتروني و
+
+604
+00:41:49,980 --> 00:41:52,860
+الـ brochureات التي راح ننشرها بحيث أن يكون في يد
+
+605
+00:41:52,860 --> 00:41:59,060
+الزبون يعرف المنطقة، العرب لإله عشان يقدر هو يعرف
+
+606
+00:41:59,060 --> 00:42:03,620
+أن هو من أي منطقة راح يشتري أما بالنسبة للأهداف
+
+607
+00:42:03,620 --> 00:42:07,740
+المشروع المالية يهدف المشروع على المستوى القريب
+
+608
+00:42:07,740 --> 00:42:12,280
+إلى تحقيق أرباح لا تقل عن ألف دولار شهريا خلال بعد
+
+609
+00:42:12,280 --> 00:42:16,400
+ثلاثة أشهر من افتتاح المشروع أما الأهداف المتوسطة
+
+610
+00:42:16,400 --> 00:42:20,600
+المدى يهدف المشروع إلى زيادة المبيعات بنسبة 12.5%
+
+611
+00:42:20,900 --> 00:42:25,220
+شهريا بالإضافة إلى حصولها على حصة سوقية لا تقل عن
+
+612
+00:42:25,220 --> 00:42:30,020
+20% بعد سنة من المشروع ويأمل المشروع على مستوى
+
+613
+00:42:30,020 --> 00:42:34,520
+بعيد على زيادة نطاق المناطق التي يغطيها خلال
+
+614
+00:42:34,520 --> 00:42:39,160
+الأسبوع زيادة التي هو دعم المكتبات الثابتة خاصة
+
+615
+00:42:39,160 --> 00:42:43,220
+التي نائية منها بحيث أن تزيد أرباحنا عن 8000
+
+616
+00:42:43,220 --> 00:42:50,900
+دولار شهريا للمشروع منافسين عدة منهم المباشرين
+
+617
+00:42:50,900 --> 00:42:54,380
+المتمثلة بالمكتبات الربحية أو المكتبات العامة
+
+618
+00:42:54,380 --> 00:42:58,640
+بالإضافة إلى بعض المنافسين غير المباشرين التي
+
+619
+00:42:58,640 --> 00:43:02,000
+أهمها هي الكتب الإلكترونية التي موجودة على ال
+
+620
+00:43:02,000 --> 00:43:06,440
+internet أما ما يميز مشروعنا أو الميزة التنافسية
+
+621
+00:43:06,440 --> 00:43:11,070
+التي يحتويها كون المشروع فكرة جديدة على مسامع
+
+622
+00:43:11,070 --> 00:43:14,570
+التي هو أفراد قطاع غزة بالإضافة إلى الكتب المسموعة
+
+623
+00:43:14,570 --> 00:43:18,730
+و استعارة الكتب خدمة استعارة الكتب التي... التي
+
+624
+00:43:18,730 --> 00:43:22,250
+... التي... التي يفتقر إليها كثير من المكتبات في قطاع غزة
+
+625
+00:43:22,250 --> 00:43:26,610
+خاصة الربحية منها بالإضافة إلى موقع المكتبة
+
+626
+00:43:26,610 --> 00:43:30,190
+الإلكتروني التي بي... راح يكون نقطة تواصل جيدة جدا
+
+627
+00:43:30,190 --> 00:43:34,390
+مع الزبائن بحيث أن احنا نعرف متطلباته ونلبي له
+
+628
+00:43:34,390 --> 00:43:40,030
+إياها أما بالنسبة للتمويل فاحنا وجدنا أن التمويل العام
+
+629
+00:43:40,030 --> 00:43:45,090
+من المشروع يحتاج إلى 9700 دولار شهريا الهدف
+
+630
+00:43:45,090 --> 00:43:50,170
+الإجمالي بتاعها، متمثلة بالمصاريف التأسيسية
+
+631
+00:43:50,170 --> 00:43:54,170
+بتاعته، راح نساهم احنا مساهمة ذاتية بقيمة 2700
+
+632
+00:43:54,170 --> 00:44:00,370
+دولار، وراح نحصل على أن... نحرص على أن يكون في
+
+633
+00:44:00,370 --> 00:44:07,450
+عندنا منحة أو حاضنة بقيمة 7000 دولار آخر شيء احنا
+
+634
+00:44:07,450 --> 00:44:11,210
+التي شجعنا على ال... على فكرة المشروع والاستمرار
+
+635
+00:44:11,210 --> 00:44:14,690
+فيها هي الدراسة السوقية التي احنا عملناها في بداية
+
+636
+00:44:14,690 --> 00:44:19,510
+المشروع متمثلة بزيارة ميدانية لبعض المكتبات في
+
+637
+00:44:19,510 --> 00:44:23,090
+قطاع غزة التي أعطونا ردود إيجابية جدا على صعيد
+
+638
+00:44:23,090 --> 00:44:27,790
+المبيعات التي يحققوها فإحنا تأملنا كون المكتبة
+
+639
+00:44:27,790 --> 00:44:32,350
+متنقلة يعني يمكن تقدر تصل لزبائن أكثر من المكتبات
+
+640
+00:44:32,350 --> 00:44:39,590
+الثابتة اتوقعنا لمستقبل جيد للأرباح لمشروعنا، ثاني
+
+641
+00:44:39,590 --> 00:44:44,390
+حاجة للاستبيان الذي عرفنا من خلاله تفضيل الناس لل
+
+642
+00:44:44,390 --> 00:44:48,150
+... لل... لل... للكتب المطبوعة عن الكتب الإلكترونية
+
+643
+00:44:48,150 --> 00:44:53,830
+التي هم كانوا بنسبة 73% غالب الذين... الذين من الذين
+
+644
+00:44:53,830 --> 00:44:57,530
+عبأوا الاستبيان كان بيفضله أغلبهم الكتب الورقية عن
+
+645
+00:44:57,530 --> 00:45:03,430
+الكتب الإلكترونية بالإضافة إلى ال... سألنا عن خدمة
+
+646
+00:45:03,430 --> 00:45:05,810
+التي هي الكتب المسموعة التي راح توفرها المكتبة
+
+647
+00:45:05,810 --> 00:45:10,870
+فـلاقينا أن الناس راح بتشجعها بنسبة 60% وهذه نسبة
+
+648
+00:45:10,870 --> 00:45:15,230
+بصراحة كثيرة ومباشرة وإيجابية للمشروع آخر حاجة كان
+
+649
+00:45:15,230 --> 00:45:18,970
+استبياننا بتضمن سؤال هل مكتبتنا كونها متنقلة و
+
+650
+00:45:18,970 --> 00:45:23,240
+بتقدر تصل رح تزيد من إقبالك على ال... على القراءة
+
+651
+00:45:23,240 --> 00:45:26,920
+فـوجدنا أن التي... التي هي النسبة كانت ب... التي هي
+
+652
+00:45:26,920 --> 00:45:33,840
+الـ 86% فاحنا هذا... عن طريق هذول شيئين الزيارات
+
+653
+00:45:33,840 --> 00:45:38,840
+والاستبيان لاقينا أن احنا يعني مستقبل قريب جدا
+
+654
+00:45:38,840 --> 00:45:43,890
+في السوق للمشروع بسم الله الرحمن الرحيم احنا راح
+
+655
+00:45:43,890 --> 00:45:46,850
+نحكي عن مشروعنا الذي هو هيكون تطبيق الهواتف الذكية
+
+656
+00:45:46,850 --> 00:45:51,710
+للمطاعم في قطاع غزة فريق العمل هيبرنامج إسراء مقبل
+
+657
+00:45:51,710 --> 00:45:55,350
+هديل مقداد إشراف الدكتور حاتم العادي المحتوى الذي
+
+658
+00:45:55,350 --> 00:45:58,430
+هتكون هنحكي وصف فكرة المشروع بشكل عام عن الدراسة
+
+659
+00:45:58,430 --> 00:46:01,630
+التسويقية والدراسة التمويلية والتكاليف التسويقية
+
+660
+00:46:01,630 --> 00:46:06,190
+للسنوات القادمة وصف فكرة المشروع هنتكلم عن المشكلة
+
+661
+00:46:06,190 --> 00:46:09,310
+والحل الذي وجدناها ووصف التكنولوجيا ونموذج العمل
+
+662
+00:46:09,310 --> 00:46:15,920
+وفريق العمل بالنسبة للمشكلة، عندنا في ازدياد وإقبال
+
+663
+00:46:15,920 --> 00:46:19,160
+كثير على المطاعم في قطاع غزة واحتياج الأفراد في
+
+664
+00:46:19,160 --> 00:46:23,900
+معرفة المأكولات والوجبات التي يقدموها وكمان تقييم
+
+665
+00:46:23,900 --> 00:46:27,200
+للوجبة، يعني أن هم تاخد يراجع عن جودة هذه
+
+666
+00:46:27,200 --> 00:46:31,760
+المطاعم، حيث أن مافيش جهات رسمية معنية تهتم
+
+667
+00:46:31,760 --> 00:46:36,540
+بتقييم المطاعم بالنسبة لهذا المشكلة أوجبنا الحل إن
+
+668
+00:46:36,540 --> 00:46:41,480
+احنا نعمل تطبيق بتوفر فيه دليل للمطاعم ومعلومات
+
+669
+00:46:41,480 --> 00:46:44,440
+بالنسبة للتواصل الخاصة بها مع إمكانية إتاحة
+
+670
+00:46:44,440 --> 00:46:49,680
+للمشاركين بإضافة تقييم الوجبات والخدمات المقدمة في
+
+671
+00:46:49,680 --> 00:46:55,070
+المطاعم أول شيء هيكون التطبيق بيشمل دليل للمطاعم،
+
+672
+00:46:55,070 --> 00:46:59,110
+هيشمل كمان إعلانات للعروض... إعلانات والعروض عن
+
+673
+00:46:59,110 --> 00:47:04,410
+المطاعم وهيكون هناك طلبات أن أي مستخدم بإمكانه
+
+674
+00:47:04,410 --> 00:47:10,350
+يطلب وجبات عن طريق التطبيق نموذج العمالي الزبائن
+
+675
+00:47:10,350 --> 00:47:13,210
+المحتملين أن هم هيكونوا أصحاب المطاعم المهتمين في
+
+676
+00:47:13,210 --> 00:47:16,150
+إدراج مطاعمهم في التطبيق المستهلك أن إيه؟ التي
+
+677
+00:47:16,150 --> 00:47:19,950
+هم الأشخاص مرتادي المطاعم المهتمين في وجود خدمة
+
+678
+00:47:19,950 --> 00:47:23,230
+راجعه عن المطاعم الربح هيكون في اشتراك... اشتراك
+
+679
+00:47:23,230 --> 00:47:28,610
+شهري للمطاعم عشان يتم إدراج مطبق مطعمهم في الدليل و
+
+680
+00:47:28,610 --> 00:47:31,930
+هيكون إعلان للمطاعم عن عروضهم ونسبة على الطلبات
+
+681
+00:47:31,930 --> 00:47:37,350
+التي ستم عن طريق التطبيقفريق العمل زي ما اتكلمنا
+
+682
+00:47:37,350 --> 00:47:39,950
+هي أجراءات حتكون مسؤلة الإدارة واسراء مقبل بالمبيعات
+
+683
+00:47:39,950 --> 00:47:45,010
+وهديل مقداد علاقات عامة نتكلم عن الدراسة
+
+684
+00:47:45,010 --> 00:47:49,750
+التسويقية في الدراسة التسويقية نحكي عن وصف السلعة
+
+685
+00:47:49,750 --> 00:47:54,410
+وعن الفئة المستهدفة وعوامل التي بتأثر على زيادة
+
+686
+00:47:54,410 --> 00:47:56,970
+الطلب على منتجات المشروع وتحليل البيئة السوقية
+
+687
+00:47:56,970 --> 00:48:00,350
+وتحليل المنافسين وتحليل نتائج الاستبيان أول شيء
+
+688
+00:48:00,350 --> 00:48:03,960
+وصف السلعة وصف السلعة عبارة عن تطبيق أندرويد، تطبيق
+
+689
+00:48:03,960 --> 00:48:06,840
+الاندرويد هذا فيه دليل شامل لكل مطعم وكيف تتواصلي
+
+690
+00:48:06,840 --> 00:48:10,020
+معها وأيضا فيه كمان كل الوجبات وأنت تقدر تقيميه
+
+691
+00:48:10,020 --> 00:48:12,780
+وفيه إمكانية تراجع أن يتفاعل الجمهور يقيم الوجبات
+
+692
+00:48:12,780 --> 00:48:16,040
+ويقيم المطعم نفسه وأيضا كمان في قسم لعروض مثلا
+
+693
+00:48:16,040 --> 00:48:19,160
+المطعم بيعرض أن في تخفيض لوجبة معينة فاحنا بنعرض
+
+694
+00:48:19,160 --> 00:48:22,440
+فيها هذا وفيه إشعارات وأيضا بيكون في... اه أن
+
+695
+00:48:22,440 --> 00:48:25,200
+تقدري مثلا أن أنت بدك وجبة معينة تتصلي على المطعم
+
+696
+00:48:25,200 --> 00:48:28,190
+نفسه وتجيبي الذي فيه المفروض بقى عن قطاع غزة هيكون
+
+697
+00:48:28,190 --> 00:48:30,590
+التطبيق موجود في Google Play تجي ده الفئة
+
+698
+00:48:30,590 --> 00:48:32,650
+المستهدفة وانحجزها بقى المحتملين يكونوا أصحاب
+
+699
+00:48:32,650 --> 00:48:35,770
+المطعم نفسهم الذين بيهتموا أن يكون مطعمهم موجود
+
+700
+00:48:35,770 --> 00:48:39,510
+جوا التطبيق المستهلك المباشر هو الشخص الذي بيستخدم
+
+701
+00:48:39,510 --> 00:48:42,410
+التطبيق نفسه، وهو الأشخاص يعني اللي بيروحوا على
+
+702
+00:48:42,410 --> 00:48:45,390
+المطعم اللي بيهتموا في الحصول على الدليل، وأيضًا 
+
+703
+00:48:45,390 --> 00:48:48,250
+حجم الطلب الكلي، عدد الأشخاص اللي بيستخدموا الهواتف 
+
+704
+00:48:48,250 --> 00:48:51,250
+الذكية اللي هم تقريبًا نسبة الأشخاص اللي بيستخدموا
+
+705
+00:48:51,250 --> 00:48:53,370
+الهواتف الذكية بقطاع غزة.
+
+706
+00:48:58,660 --> 00:49:01,120
+ماشي، العوامل اللي بتأثر على زيادة الطلب على 
+
+707
+00:49:01,120 --> 00:49:04,680
+التسويق، اللي هو تطوير التكنولوجي وزيادة الطلب
+
+708
+00:49:04,680 --> 00:49:06,860
+على المطاعم، لإن صار كتير مطاعم، والناس كمان
+
+709
+00:49:06,860 --> 00:49:11,440
+بتروح كتير على المطاعم، وسعر التسويق. نيجي للدراسة 
+
+710
+00:49:11,440 --> 00:49:14,040
+تحليل البيئة السوقية. أول حاجة في عندنا نقاط ضعف، 
+
+711
+00:49:14,040 --> 00:49:15,460
+في عندنا نقاط قوة، في عندنا فرص، وفي عندنا 
+
+712
+00:49:15,460 --> 00:49:18,660
+تهديدات. أول شيء نقاط القوة، أول شيء التطبيق مجاني، 
+
+713
+00:49:18,660 --> 00:49:22,260
+فبيستقطب عدد كبير من الزبائن. اثنين، تكلفة إنشاء
+
+714
+00:49:22,260 --> 00:49:26,210
+التطبيق بتكون عادة مش كتيرة، يعني تكلفة الضآئلة. أول 
+
+715
+00:49:26,210 --> 00:49:29,470
+شيء ما فيش ثقة لبعض.. لبعض الأفراد أنه يثقوا في 
+
+716
+00:49:29,470 --> 00:49:33,470
+تطبيقنا، فبيتجهوا مباشرة إما للمطعم أو بياخدوا من
+
+717
+00:49:33,470 --> 00:49:36,070
+أصد.. من أصدقائهم يعني فكرة عن المو.. عن المطعم
+
+718
+00:49:36,070 --> 00:49:39,810
+نفسه، وأيضًا فريق العمل، بما أنه احنا يعني هندسة
+
+719
+00:49:39,810 --> 00:49:42,650
+كهرباء، ما بنفهمش كتير كثير في البرمجة، فممكن ناخد دورة
+
+720
+00:49:42,650 --> 00:49:46,840
+لتحسين هذا الموضوع. الفرص، ما فيش منافس مباشر أو قلة
+
+721
+00:49:46,840 --> 00:49:49,780
+عدد المنافسين، يعني ما فيش تطبيقات بتعمل تقييم
+
+722
+00:49:49,780 --> 00:49:52,720
+للمطاعم، وأيضًا كمان في عندنا شريحة كبيرة من الناس
+
+723
+00:49:52,720 --> 00:49:55,500
+بتروح المطاعم بتستخدم برضه الهواتف الذكية. 
+
+724
+00:49:55,500 --> 00:49:59,700
+تهديدات، في عندنا ممكن يظهر منافسين جدد، وأيضًا كمان
+
+725
+00:49:59,900 --> 00:50:03,540
+احتمال أنه أصحاب المطاعم نفسهم ما يجوا يعرضوا يعني 
+
+726
+00:50:03,540 --> 00:50:05,840
+الوجبات في تطبيقنا، يقولوا احنا خلاص مكتفيين
+
+727
+00:50:05,840 --> 00:50:08,120
+بالحملات الترويجية اللي بنعملها اللي عن طريق ال
+
+728
+00:50:08,120 --> 00:50:10,860
+facebook أو عن طريق صفحاتهم على الـ internet أو شيء ثاني. 
+
+729
+00:50:10,860 --> 00:50:14,840
+تحليل المنافسين، احنا عملنا للمنافسين في عندنا
+
+730
+00:50:14,840 --> 00:50:16,780
+الأصدقاء، أو في عندنا صفحات المطاعم على الـ facebook
+
+731
+00:50:16,780 --> 00:50:19,500
+وموقع الدليل، واحنا فطبعًا احنا تقريبًا المرتبة 
+
+732
+00:50:19,500 --> 00:50:21,400
+الثانية بعد صفحات المطاعم على الـ facebook.
+
+733
+00:50:24,390 --> 00:50:27,410
+تحليل نتائج الاستبيان، احنا عاملنا اثنين استبيان، 
+
+734
+00:50:27,410 --> 00:50:29,550
+واحدة للاشخاص اللي بيروحوا المطاعم، والثانية 
+
+735
+00:50:29,550 --> 00:50:32,710
+لاصحاب المطاعم نفسهم. فـ 72% من مرتادي 
+
+736
+00:50:32,710 --> 00:50:35,650
+مطاعم آه، عجبهم فكرة التطبيق، بدهم حد أنه يشوفوا
+
+737
+00:50:35,650 --> 00:50:39,350
+كيف المطعم، ووين مكانه وكل شيء عنه، و91.6% من 
+
+738
+00:50:39,350 --> 00:50:41,550
+أصحاب المطاعم بيشجعوا هذه الفكرة، أنه بدهم حد
+
+739
+00:50:41,550 --> 00:50:44,710
+يقيمهم، بدهم يأخذوا يراجعوا إيش الناس بتحكي عنهم. راح
+
+740
+00:50:44,710 --> 00:50:48,470
+نحكي في الدراسة التمويلية عن إجمالي تكلفة رأس المال
+
+741
+00:50:48,470 --> 00:50:53,660
+للمشروع، وتكلفة التشغيلية، والإيرادات التقديرية اللي 
+
+742
+00:50:53,660 --> 00:51:00,540
+راح تيجي. تكلفة المشروع أو رأس المال اللي لازم له
+
+743
+00:51:00,540 --> 00:51:05,220
+راح يتمثل التكلفة هاي بمطور android، أو ممكن احنا
+
+744
+00:51:05,220 --> 00:51:09,920
+ناخد دورة تدريبية ونعمله بنفسنا، والاشتراك بمتجر 
+
+745
+00:51:09,920 --> 00:51:14,260
+الـ android، وشراء جهاز.. أجهزة laptop وجوال، و
+
+746
+00:51:14,260 --> 00:51:16,960
+مصروفات تشغيل أولية. 
+
+747
+00:51:19,600 --> 00:51:23,960
+التكلفة التشغيلية راح تكون عبارة عن رواتب.. رواتب 
+
+748
+00:51:23,960 --> 00:51:30,940
+الأجور للموظفين، واشتراك لإنترنت ومصاريف كهرباء 
+
+749
+00:51:30,940 --> 00:51:35,200
+وفواتير مكالمات ودعاية وإعلان. 
+
+750
+00:51:38,050 --> 00:51:42,630
+الإيرادات التقديرية في ال.. راح تيجي من 3 مصادر،
+
+751
+00:51:42,630 --> 00:51:49,190
+الاشتراك الشهري حوالي 9000$ point 8 اللي هي من 
+
+752
+00:51:49,190 --> 00:51:54,810
+النسبة الأكبر اللي هي من نسب الأرباح اللي هي 78.13
+
+753
+00:51:54,810 --> 00:52:00,690
+%، وفي من الإعلانات حوالي 12.5% من مجمل الإيرادات 
+
+754
+00:52:00,690 --> 00:52:03,090
+والطلبات 9.37%.
+
+755
+00:52:06,350 --> 00:52:10,390
+التكلفة التسويقية للسنة الأولى راح تتمثل بمسألة
+
+756
+00:52:10,390 --> 00:52:15,310
+النقل والإعلانات والترويج، حوالي راح تكلف ألف و
+
+757
+00:52:15,310 --> 00:52:22,370
+خمسمئة دولار. بالمجمل راح تكون التكاليف كلها خمسة آلاف
+
+758
+00:52:22,370 --> 00:52:27,350
+، وراح نستعيدها في السنة.. بداية السنة الثانية إن
+
+759
+00:52:27,350 --> 00:52:34,990
+شاء الله. هاي مثل نموذج لكيف ممكن نعمل التطبيق في ال
+
+760
+00:52:34,990 --> 00:52:39,970
+.. في الترويج، رح يكون الترويج يعني عبارة عن أصحاب
+
+761
+00:52:39,970 --> 00:52:43,290
+المطاعم ذات أنفسهم يعملوا لنا ترويج للتطبيق أو
+
+762
+00:52:43,290 --> 00:52:50,210
+الإعلانات عن طريق موقع التواصل الاجتماعي. بسم الله
+
+763
+00:52:50,210 --> 00:52:54,710
+الرحمن الرحيم، مشروعنا عبارة عن شركة اسمها VR games.
+
+764
+00:52:54,710 --> 00:52:59,970
+أعضاء الفريق: إسراء، إحسان، مرفة العالمي، وشروق 
+
+765
+00:52:59,970 --> 00:53:00,490
+ربيع.
+
+766
+00:53:04,750 --> 00:53:08,350
+بداية نحكي لكم شوية عن الشركة، عن الخدمات اللي
+
+767
+00:53:08,350 --> 00:53:12,010
+بنقدمها، عن الأسباب اللي أدت إلى انتشار وروج 
+
+768
+00:53:12,010 --> 00:53:15,750
+المنتجات بين الناس، عن المخاطر اللي واجهتنا زي ما
+
+769
+00:53:15,750 --> 00:53:20,050
+بتواجه أي شركة ناشئة، هنشوف المبيعات المتوقعة
+
+770
+00:53:20,050 --> 00:53:24,050
+والتدفق النقدي، والطلبات رأس المال، والخصائص
+
+771
+00:53:24,050 --> 00:53:26,590
+الشخصية للقيادة، وأهداف الخدمة.
+
+772
+00:53:31,430 --> 00:53:36,130
+شركة VR Games هي شركة ناشئة، تختص بالواقع الافتراضي
+
+773
+00:53:36,130 --> 00:53:40,390
+كل ما يتعلق بهذا المجال من ألعاب وأفلام وغيرها.
+
+774
+00:53:40,390 --> 00:53:45,090
+موقعها إن شاء الله رح يكون في شارع جلال في خان يونس،
+
+775
+00:53:45,090 --> 00:53:50,230
+واحنا اخترناه لإنه شارع حيوي. الخدمات اللي رح
+
+776
+00:53:50,230 --> 00:53:54,790
+نقدمها: مكان للعب الفردي والجماعي، تأجير معدات 
+
+777
+00:53:54,790 --> 00:53:58,810
+العروض والألعاب ثلاثية الأبعاد، بيع معدات العروض و
+
+778
+00:53:58,810 --> 00:54:04,830
+الألعاب ثلاثية الأبعاد. أولًا توفير مكان للعب طبعًا
+
+779
+00:54:04,830 --> 00:54:10,170
+احنا راح نوفر خدمة، مكان واسع ومريح بيقدروا فيه
+
+780
+00:54:10,170 --> 00:54:14,330
+الناس يتمتعوا بالخدمات اللي بنقدمها من ألعاب و
+
+781
+00:54:14,330 --> 00:54:19,010
+أفلام سواء كان هذا شيء بشكل فردي أو شكل جماعي. في
+
+782
+00:54:19,010 --> 00:54:23,770
+هذه الخدمة عروض وحملات، منها إنه احنا بنعمل
+
+783
+00:54:23,770 --> 00:54:27,410
+تخفيضات في كل عام على المنتجات تبعتنا، ممكن إنها
+
+784
+00:54:27,410 --> 00:54:32,730
+توصل لثلاثة أشهر، بنقدم بطاقة عضوية للزبائن
+
+785
+00:54:32,730 --> 00:54:36,870
+الدائمين. هذه بتخليهم يستفيدوا من الخدمات والعروض 
+
+786
+00:54:36,870 --> 00:54:42,270
+المقدمة للزبائن، زي أننا نعمل سحب على جوائز، هذا
+
+787
+00:54:42,270 --> 00:54:47,210
+السحب هيكون حسب رقم العضوية، والفائز راح نديه
+
+788
+00:54:47,210 --> 00:54:52,030
+جائزة تتفق مع أقدمية هذا الزبون. وكل زبون بيجيب لنا 
+
+789
+00:54:52,030 --> 00:54:59,480
+زبون طبعًا راح يكون له جائزة رمزية. ثانيًا التأجير، 
+
+790
+00:54:59,480 --> 00:55:04,120
+طبعًا أوضاع الناس بتختلف، الأوضاع المادية تبعهم، 
+
+791
+00:55:04,120 --> 00:55:07,600
+في ناس أحيانًا بيكون وضعهم المادي صعب أو مش قادرين 
+
+792
+00:55:07,600 --> 00:55:11,960
+أنهم يشتريوا هذه الألعاب، فاحنا بنوفر لهم هذه الخدمة
+
+793
+00:55:11,960 --> 00:55:17,360
+عشان يقدروا يتمتعوا بهذه الألعاب، والكل يستفيد
+
+794
+00:55:17,360 --> 00:55:23,750
+منها. إيش المعدات اللي احنا ممكن نأجرها؟ نظارات 3D
+
+795
+00:55:23,750 --> 00:55:29,130
+لأكثر استخدام وأكثر من مرة، ألعاب 3D، أفلام 3D
+
+796
+00:55:29,130 --> 00:55:30,710
+وذراع التوجيه.
+
+797
+00:55:33,590 --> 00:55:37,870
+ثالثًا البيع، طبعًا في ناس بتفضل أن بدل ما تظلها 
+
+798
+00:55:37,870 --> 00:55:41,350
+تروح على الشركة تلعب بالألعاب أو الأفلام، تفضل أنها
+
+799
+00:55:41,350 --> 00:55:45,610
+تحتفظ بهذه الألعاب وتشتريها وتقدر تلعبها وقت ما
+
+800
+00:55:45,610 --> 00:55:50,290
+بدها. وهذول بيكونوا شاملين كل الخدمات اللي احنا 
+
+801
+00:55:50,290 --> 00:55:55,590
+بنقدمها. إيش الأشياء اللي احنا ممكن نبيعها؟ نظارات 3D
+
+802
+00:55:55,590 --> 00:55:59,730
+تستخدم مرة واحدة، وهذه طبعًا بيكون سعرها رخيص، ما
+
+803
+00:55:59,730 --> 00:56:03,320
+يتجاوز الدولار، وعشان هيك احنا بنأجرها. شو نظارة الـ
+
+804
+00:56:03,320 --> 00:56:09,720
+3D تستخدم أكثر من مرة، الألعاب 3D، أفلام الـ 3D، و
+
+805
+00:56:09,720 --> 00:56:13,520
+ذراع التوجيه، وشاشة تدعم تقنية ثلاثية الأبعاد، وطبعًا 
+
+806
+00:56:13,520 --> 00:56:16,740
+هذه احنا بنبيعها، ما بنأجرهاش، لإنها.. ال.. هذه
+
+807
+00:56:16,740 --> 00:56:20,480
+أجهزة حساسة وبتحتاج صيانة، وبدها خبراء يتعامل
+
+808
+00:56:20,480 --> 00:56:24,520
+معها، فبالتالي ما بنأجرهاش. وهنكمل معاملة. بعد هيك
+
+809
+00:56:24,520 --> 00:56:28,160
+لو بنرجع نحكي الكلام هذا كله على طريق.. نحكي عن 
+
+810
+00:56:28,160 --> 00:56:31,480
+روج المنتجات، إيش اللي خلانا نختار الـ 3D والعرض اللي هكذا بعد؟ أول حاجة هي هو الناس دائمًا 
+
+811
+00:56:31,480 --> 00:56:33,800
+بتطلع لتقنيات جديدة، ودائمًا بتحب تحدث وتجيب أشياء
+
+812
+00:56:33,800 --> 00:56:38,640
+جديدة، فهذا المجال جديد ومش واصل كتير لقطاع غزة.
+
+813
+00:56:38,640 --> 00:56:42,680
+الأسعار للبيع و لل.. اللي عاملين للبيع وللتأجير
+
+814
+00:56:42,680 --> 00:56:46,540
+فهي هتتناسب مع الكل، اللي ما عندهوش يشتري ممكن
+
+815
+00:56:46,540 --> 00:56:48,880
+يتأجر أو يلعب في أسعار مناسبة. 
+
+816
+00:56:48,880 --> 00:56:53,560
+غير هيك أنه في المكان اللي احنا.. احنا بنفتحه هنا نفسنا ما فيش شيء للـ
+
+817
+00:56:53,560 --> 00:56:57,160
+.. للـ 3D، يعني في محلات لبيع ألعاب الكمبيوتر أو
+
+818
+00:56:57,160 --> 00:57:00,780
+الأدوات للحاسوب، أو شيء زي هيك، ما فيش للـ 3D، نظارات و
+
+819
+00:57:00,780 --> 00:57:04,980
+الأفلام. المشروع كأي شركة ناشئة هو كإن واجهنا شوية
+
+820
+00:57:04,980 --> 00:57:10,660
+مخاطر وتحديات منها الإغلاق المستمر للمعابر. هذه
+
+821
+00:57:10,660 --> 00:57:14,340
+المشكلة هتواجه كل المشاريع اللي ممكن تنفتح في قطاع 
+
+822
+00:57:14,340 --> 00:57:16,700
+غزة. غير ذلك الجمارك والضرائب المتزايدة، لإن احنا
+
+823
+00:57:16,700 --> 00:57:20,020
+هندخل أجهزة ونظارات وشاشات عرض، فإيه اللي هيكون 
+
+824
+00:57:20,020 --> 00:57:23,960
+عليها ضرائب. قلة الخبراء في هذا المجال لإن ما فيش 
+
+825
+00:57:23,960 --> 00:57:27,260
+كتير شركات تتعلق بالـ 3D أساسًا في القطاع. بعد ذلك في 
+
+826
+00:57:27,260 --> 00:57:32,200
+تحدي أن حاجة الزبون مجلد لحالة تحديث، مثلًا أجرب مثال
+
+827
+00:57:32,200 --> 00:57:37,060
+اللي هو الجوالات، لو بده الواحد يلاحظ قناة 
+
+828
+00:57:37,060 --> 00:57:39,700
+الجوالات، كل شهر هيغير جوال، فممكن أنا عشان أتماشى
+
+829
+00:57:39,700 --> 00:57:43,220
+مع مطالبات الزبائن وأحصل على رضاهم، يمكن أجدد
+
+830
+00:57:43,220 --> 00:57:46,920
+أشياء ما خربتش بس لإن صارت قديمة، أجددها عشان أقلب 
+
+831
+00:57:46,920 --> 00:57:50,640
+برغبات الزبائن ويبقى لهم إيه شوية. لو نحكي الأشياء 
+
+832
+00:57:50,640 --> 00:57:55,320
+بشكل رقمي، أنا أعتقد متوقعة مبيعات ذراع التوجيه بناء
+
+833
+00:57:55,320 --> 00:57:59,800
+على دراسات عملناها وإحصائيات، أنه ذراع التوجيه
+
+835
+00:57:59,800 --> 00:58:03,740
+بتكلف التجارب السياسية الوحدة 300 دولار. المهم
+
+836
+00:58:03,740 --> 00:58:06,860
+بتطلع بالآخر إجمالي المبيعات 46955 دولار سنويًا.
+
+837
+00:58:06,860 --> 00:58:11,240
+المبيعات دراع التوجيه تقريبًا 20.9%، ونظارات شرح 
+
+838
+00:58:11,240 --> 00:58:16,600
+الأبعاد اللي لأكثر.. لأكثر استخدام أكثر من مرة 4%.
+
+839
+00:58:16,600 --> 00:58:20,960
+نظارات استخدام 1.33%، والعاب واقعي افتراضي وأفلا
+
+840
+00:58:20,960 --> 00:58:26,990
+م 3D تقريبًا 15%. بعد هيك التدفق المالي. 
+
+841
+00:58:32,150 --> 00:58:35,270
+عملنا دراسة شهرية بناء على حجم الطلب في السوق و
+
+842
+00:58:35,270 --> 00:58:42,230
+الأسعار اللي درسناها لكل قطعة وفيش كمان محل للبيع 
+
+843
+00:58:42,230 --> 00:58:45,910
+أو للتأجير بيخدم الديون فعملنا مبيعات مقدمة ممكن
+
+844
+00:58:45,910 --> 00:58:49,950
+تدفقات بييجي يعني كسيولة وتحسين الديون كمان
+
+845
+00:58:49,950 --> 00:58:53,030
+بختلف حسب دخل الناس بتراوح بين 40 دولار لـ 500 
+
+846
+00:58:53,030 --> 00:58:56,590
+دولار كل شهر بتفاوت في الآخر بطلع نحصل على جمعية
+
+847
+00:58:56,590 --> 00:58:59,310
+إيرادات، المصاريف بتسري مع ذلك، إعلانات ممولة على ال
+
+848
+00:58:59,310 --> 00:59:02,450
+casebook أو البروشورات اللي ممكن نطبعها، الأيام 
+
+849
+00:59:02,450 --> 00:59:05,710
+العاملة، رواتب العمال بتكلف تقريباً ألفين دولار في
+
+850
+00:59:05,710 --> 00:59:09,290
+الشهر، إيجار محل كل أربع شهور، حندفع إيجار مرة
+
+851
+00:59:09,290 --> 00:59:12,830
+واحدة حيكون تلت مرات في السنة، بتكلف تشغيلية زي
+
+852
+00:59:12,830 --> 00:59:17,590
+ممكن أجارات الشحن الـ .. الـ .. بتكلف تشغيلية، يعني 
+
+853
+00:59:17,590 --> 00:59:20,250
+المصاريف، المصاريف الإدارية ممكن زي القرطاسية،
+
+854
+00:59:20,250 --> 00:59:24,690
+البيافة، أشياء بنتاجها المدير مجموعة مصاريف من
+
+855
+00:59:24,690 --> 00:59:27,590
+الإدارة، بالآخر لو نعيش لكل شهر نحسب التطبيق المالي
+
+856
+00:59:27,590 --> 00:59:31,670
+نطرح المصاريف من مجموعة الإيرادات بالنهاية فعلاً 
+
+857
+00:59:31,670 --> 00:59:35,690
+المحصلة السنة الأولى عشر آلاف وأربعمائة وثمانية
+
+858
+00:59:35,690 --> 00:59:42,780
+دولار، مطلبات رأس المال حالياً، يعني قادرين أنه نقدر
+
+859
+00:59:42,780 --> 00:59:46,720
+نساهم في المشروع بالـ 3500 دولار تقريباً، لكن
+
+860
+00:59:46,720 --> 00:59:50,740
+المتطلبات الأصلية كله هتكون 60300 دولار، يعني
+
+861
+00:59:50,740 --> 00:59:57,560
+هنحتاج منها أو تمويل المقدار 56800 دولار تكاليف 
+
+862
+00:59:57,560 --> 00:59:59,880
+ثابتة ومتغيرة إذا المحل ثابت سواء أنا اللي روحت 
+
+863
+00:59:59,880 --> 01:00:03,260
+أو صرف دفعها، أجور العمال نفس الشيء، بطلع 28 ألف
+
+864
+01:00:03,260 --> 01:00:06,880
+ثلاثمائة دولار ثابتين لازم أدفعهم في كل سنة تكلفة
+
+865
+01:00:06,880 --> 01:00:10,060
+متغيرة ثالثة، طبعاً فيه ضرائب تفرض على كل المحلات
+
+866
+01:00:10,060 --> 01:00:13,100
+اللي عندها بضاعة أو اللي بتكون بتجيب أرباح، ضريبة
+
+867
+01:00:13,100 --> 01:00:16,640
+الدخل، سألنا يعني طبعاً على المحلات التجارية وعند 
+
+868
+01:00:16,640 --> 01:00:21,000
+الحكومة أنه الـ 17% بكون ضريبة دخل تتنسب مع أرباحك 
+
+869
+01:00:21,000 --> 01:00:25,980
+وضريبة على البضاعة الموجودة 16% بعد حسابكم تطلع
+
+870
+01:00:25,980 --> 01:00:31,000
+معناه فترة استرداد تلت سنين ونص و عائد 625.4%
+
+871
+01:00:31,000 --> 01:00:33,700
+وهذه مثلاً بيبقى تيرم جيد في المشروع، تلت تيرم
+
+872
+01:00:33,700 --> 01:00:36,520
+المعنى شغال؟ الصفات الشخصية للقيادة أول شيء يدرك 
+
+873
+01:00:36,520 --> 01:00:39,700
+الأهداف العامة للشركة اللي هي تحقيق رضا وترفيه
+
+874
+01:00:39,700 --> 01:00:44,260
+للزبائن لجانب تحقيق الأهداف الربحية للشركة، تحلى
+
+875
+01:00:44,260 --> 01:00:46,960
+بقدرة على ضبط النفس في التعامل مع الزبائن و
+
+876
+01:00:46,960 --> 01:00:51,400
+الموظفين، إن يكون حاضر البديهة وسريع الفهم، يكون
+
+877
+01:00:51,400 --> 01:00:55,880
+دايماً عنده حلول سريعة وجديدة ويستغل الفرص دايماً،
+
+878
+01:00:55,880 --> 01:00:59,100
+بيبرع في إيجاد حلول المشاكل مشان كل مشكلة إنه 
+
+879
+01:00:59,100 --> 01:00:59,560
+يوجه
+
+880
+01:01:02,870 --> 01:01:05,930
+المؤهلات الفريق، طبعاً الشركة ما عندها فريق متكامل،
+
+881
+01:01:05,930 --> 01:01:08,030
+بالذات بكل احتياجات الشركة، أول شيء أنه مدير
+
+882
+01:01:08,030 --> 01:01:12,190
+الشركة، مهندس حاسوب، لأن المهندسين أقدر على حل
+
+883
+01:01:12,190 --> 01:01:15,890
+المشاكل، كمان المشروع تقني فبيحتاج مهندس أكثر من
+
+884
+01:01:15,890 --> 01:01:19,310
+إنه يكون إدارة، المهندس يتعامل مع أمور الشبكة
+
+885
+01:01:19,310 --> 01:01:23,010
+والإنترنت والأمور التقنية وممكن يشد الناس لطريقة 
+
+886
+01:01:23,010 --> 01:01:27,900
+استخدام أجهزة العالم، نحتاج محاسب لأمور المالية،
+
+887
+01:01:27,900 --> 01:01:32,200
+نحتاج فني أو تقني لأمور الصيانة وكمان نحتاج مصمم
+
+888
+01:01:32,200 --> 01:01:36,680
+Graphic لتحسين دقة الألعاب اللي بتتعامل معاها
+
+889
+01:01:39,570 --> 01:01:42,730
+الفريق اللي جاء بتكون من ميرفت العالمي، مدير
+
+890
+01:01:42,730 --> 01:01:46,510
+الشركة وبكالوريوس هندسة حسون، إسراء إحسان، مهندس
+
+891
+01:01:46,510 --> 01:01:50,450
+.. مهندس حسون، نائب المدير، شوق ربيع، مصمم الـ
+
+892
+01:01:50,450 --> 01:01:55,730
+Graphic، هندسة حسون، عمر العالمي، فني تقني لصيانة،
+
+893
+01:01:55,730 --> 01:01:59,770
+وأحمد أنور محاسب،بسم الله الرحمن الرحيم، طبعاً احنا 
+
+894
+01:01:59,770 --> 01:02:03,390
+طلبة من كلية هندسة قسم الحاسوب أنا أه يا عنان
+
+895
+01:02:03,390 --> 01:02:07,990
+وصديقاتي سندس ولبنى وخلود وناهد، طبعاً مشروعنا 
+
+896
+01:02:07,990 --> 01:02:11,710
+بيحكي .. مشروعنا اسمه Ladies Cafe، فكرة المشروع هي
+
+897
+01:02:11,710 --> 01:02:15,730
+عبارة عن مكان خاص بالسيدات فقط، المكان رح يكون طبعاً
+
+898
+01:02:15,730 --> 01:02:20,170
+قريب من الجامعة، نقطة التقاء لطالبات الجامعات الأزهر
+
+899
+01:02:20,170 --> 01:02:26,310
+والإسلامية والأقصى، طبعاً فكرة المشروع استمدناها لما
+
+900
+01:02:26,310 --> 01:02:30,250
+كنا طالبات، كنا دائماً نحتاج لمكان هادئ قريب من
+
+901
+01:02:30,250 --> 01:02:34,370
+الجامعة حيث نلتقي مع صديقاتنا، نكون هذا المكان نشتغل
+
+902
+01:02:34,370 --> 01:02:37,670
+فيه، فترة في المشاريع الجامعية كانت ينقصها هذا
+
+903
+01:02:37,670 --> 01:02:41,410
+الأشياء، أنه دائماً كنا المكتبة دائماً كانت مليانة
+
+904
+01:02:41,410 --> 01:02:44,810
+طالبات طبعاً ما كناش نقدر نتناقش في هذه المشاريع
+
+905
+01:02:44,810 --> 01:02:47,910
+كافتيريا الجامعة طبعاً غير مناسبة أنه نشتغل فيها
+
+906
+01:02:47,910 --> 01:02:51,670
+ففكرنا أنه من وين بدنا نلاقي أنه مكان نقعد فيه
+
+907
+01:02:51,670 --> 01:02:57,290
+نشتغل فيه، طبعاً حيكون بيوفر الـ Internet للطالبات،
+
+908
+01:02:57,290 --> 01:03:00,130
+مكان هادئ، بيقدروا يلتقوا بصديقاتهم
+
+909
+01:03:03,950 --> 01:03:08,130
+طبعاً عندنا الأهداف والاستراتيجيات، أول ما درسنا
+
+910
+01:03:08,130 --> 01:03:10,990
+المشروع حددنا إيش هي الأهداف اللي إحنا بدنا إياها
+
+911
+01:03:10,990 --> 01:03:13,270
+وإيش كمان هي الاستراتيجيات اللي راح نمشي عليها
+
+912
+01:03:13,270 --> 01:03:16,350
+بحيث أنه نصل لهذه الأهداف، طبعاً عندنا .. عندنا الـ
+
+913
+01:03:16,350 --> 01:03:20,610
+Short Goals أنه بدنا نوصل اسم المكان لأكبر قدر
+
+914
+01:03:20,610 --> 01:03:24,650
+ممكن من خلال الجامعات، الجامعة الإسلامية والأقصى
+
+915
+01:03:24,650 --> 01:03:29,950
+وجامعة الأزهر، طبعاً عندنا Long Goals اللي هو إنه
+
+916
+01:03:29,950 --> 01:03:33,410
+نقدر من خلال فترة العمل بهذا المشروع إنه نوسع هذا
+
+917
+01:03:33,410 --> 01:03:36,210
+الـ Business، وايضاً كمان بدنا نقلل قد ما نقدر 
+
+918
+01:03:36,210 --> 01:03:40,330
+التكلفة بحيث إنه نزيد الربح ويكون كمان ملائم 
+
+919
+01:03:40,330 --> 01:03:45,230
+لجميع الطالبات، أما الـ Strategies اللي اخترناها إنه 
+
+920
+01:03:45,230 --> 01:03:51,430
+نمشي عليها لنصل لهذه الأهداف كانت إنه جميع الطالبات
+
+921
+01:03:51,430 --> 01:03:54,810
+تُحبّ المكان، رح يكون هادئ، موفر فيه الـ Internet،
+
+922
+01:03:54,810 --> 01:03:58,950
+بيقدم أجود الخدمات، استكمال اللي .. اللي حكت زميلتي
+
+923
+01:03:58,950 --> 01:04:05,440
+Ayah فيه إن احنا نقاط ضعف وقوة وفيه إن احنا فرص ومخاطر 
+
+924
+01:04:05,440 --> 01:04:10,540
+بالنسبة لي نقاط الضعف إنه مشروعنا رح يقدم أسعار 
+
+925
+01:04:10,540 --> 01:04:14,100
+مناسبة للجميع يعني الكل رح يقدر ييجي على هذا
+
+926
+01:04:14,100 --> 01:04:17,900
+المكان ورح يقدر كمان خدمات متنوعة من الأصناف
+
+927
+01:04:17,900 --> 01:04:23,340
+متنوعة من كافة من المشروبات ومن الكيك كمان، أما 
+
+928
+01:04:23,340 --> 01:04:26,660
+بالنسبة لي الضعف إنه تكلفة إنه رح نبدأ مشروعنا من 
+
+929
+01:04:26,660 --> 01:04:31,080
+البداية، فتكلفة البداية هي صعبة كثير لإنّها وكمان 
+
+930
+01:04:31,080 --> 01:04:34,460
+الاقتصاد تبع قطاع غزة متردد، أحيان بيكون كبير و
+
+931
+01:04:34,460 --> 01:04:39,760
+أحيان بيكون قليل فهذا بيكون صعب بالنسبة لإنّها أو
+
+932
+01:04:39,760 --> 01:04:46,340
+بحساب الضعف للمشروع، الفرص لإنّها إنه رح احنا نقدم
+
+933
+01:04:46,340 --> 01:04:50,640
+فرص عمل أولاً لخمس من الطالبات، يعني خلاص بكرا لما 
+
+934
+01:04:50,640 --> 01:04:55,340
+نخلص جامعة راح نكون احنا بردو كعباً على المجتمع، فرح
+
+935
+01:04:55,340 --> 01:04:59,080
+نوفر فرص عمل لإلنا وكمان رح نوفر فرص عمل لغيرنا
+
+936
+01:04:59,080 --> 01:05:01,480
+لما نوفق .. لما نكبر مشروعنا
+
+937
+01:05:04,080 --> 01:05:09,920
+أما بالنسبة للمخاطر لإلنا، المخاطر هو الحصار،
+
+938
+01:05:09,920 --> 01:05:15,020
+اقتصاد غزة .. غزة محاصرة فرح يقلل من الموارد، رح
+
+939
+01:05:15,020 --> 01:05:20,420
+يقلل من المنتجات، الأسعار رح تكون .. تغلى الأسعار
+
+940
+01:05:20,420 --> 01:05:25,320
+وكمان رح يكونوا يواجه .. يكونوا كعائق أمامي لإلنا
+
+941
+01:05:25,320 --> 01:05:27,540
+اللي هو ثقافة المجتمع وعاداته 
+
+942
+01:05:31,700 --> 01:05:35,480
+اللي زي ما ذكرت زميلتي قايلة، راح يكون المكان في
+
+943
+01:05:35,480 --> 01:05:39,520
+غزة حوالين الجامعات، راح يكون هذا السبب اللي لنا 
+
+944
+01:05:39,520 --> 01:05:46,500
+فرصة .. فرصة كبيرة لقبل الطالبات علينا، راح يكون
+
+945
+01:05:46,500 --> 01:05:50,880
+مشروعنا ملكية فردية، الملكية الفردية ملك لإلنا 
+
+946
+01:05:50,880 --> 01:05:54,600
+احنا اللي قايمين على المشروع، رح ي .. في إلنا
+
+947
+01:05:54,600 --> 01:05:57,900
+سلبيات وفي إلنا Advantages، بالنسبة لي لهذا الموضوع،
+
+948
+01:05:57,900 --> 01:06:01,960
+إنه مش راح تنضعف أي ضريبة دخل لإلنا تانية غير
+
+949
+01:06:01,960 --> 01:06:06,280
+الضريبة اللي .. الضريبة الدخل للمشروع، إن الربح رح
+
+950
+01:06:06,280 --> 01:06:11,420
+يكون خاص فينا إلنا، وأما بالنسبة لي السلبيات إنه
+
+951
+01:06:11,420 --> 01:06:15,740
+كمان السلبيات هي تكون الخسائر علينا، إحنا
+
+952
+01:06:15,740 --> 01:06:19,200
+ماركتنا ناساس، بتكون فكرة المشروع إنه على استخدام 
+
+953
+01:06:19,200 --> 01:06:22,740
+فئة الفئات من الـ 18 سنة وفوق، والتركيز بشكل 
+
+954
+01:06:22,740 --> 01:06:27,320
+أساسي على طالبات الجامعات، حيث إن موجودة نسبة 
+
+955
+01:06:27,320 --> 01:06:31,430
+طالبات الجامعة دي 110,000 طالبة، والأزهر تمام 10 آلاف
+
+956
+01:06:31,430 --> 01:06:38,330
+طالبة، والأقصى تقريباً سبع آلاف طالبة، وكان سوق طب
+
+957
+01:06:38,330 --> 01:06:42,530
+سيدات الأعمال، بالنسبة الـ Marketing للجمهور السوق
+
+958
+01:06:42,530 --> 01:06:47,010
+إحنا بنخطط إنه نضع سعر مناسب مع مراعاة الجودة
+
+959
+01:06:47,010 --> 01:06:52,050
+العالية، ايضاً حيكون مكان للتقاء الطالبات ووجود
+
+960
+01:06:52,050 --> 01:06:57,890
+أطعمة ومشروبات متنوعة، بالنسبة للـ Competition، عندنا
+
+961
+01:06:57,890 --> 01:07:00,790
+نوعين من المنافسين، عندنا المنافسة المباشرة و
+
+962
+01:07:00,790 --> 01:07:04,870
+منافسة غير مباشرة، بالنسبة للنوع الأول، عندنا لطعم
+
+963
+01:07:04,870 --> 01:07:08,870
+Break، الـ .. الـ Competition اللي بنافسنا فيه إنه
+
+964
+01:07:08,870 --> 01:07:11,950
+قربه من الجامعة، لكن ما بيميزنا عنه إن العاملين
+
+965
+01:07:11,950 --> 01:07:16,180
+حيكونوا إحنا نفسنا، يعني في أسفريات بيخليهم يشربوا 
+
+966
+01:07:16,180 --> 01:07:19,360
+الراحة أكثر، أما بالنسبة للنوع الثاني، النوع غير 
+
+967
+01:07:19,360 --> 01:07:23,500
+المباشر إنه مطاعم لكن بيشكلش خطر كبير علينا نفسنا
+
+968
+01:07:23,500 --> 01:07:26,680
+بقعد المكان عامل، يعني هو في الشارع نفسه ماركتها
+
+969
+01:07:26,680 --> 01:07:29,800
+استراتيجية، إن بالاستراتيجية اللي حنستخدمها إن بتوفر
+
+970
+01:07:29,800 --> 01:07:34,420
+التالي، إن توفر راحة نفسية للطالبة ودرجة بـ .. بس
+
+971
+01:07:34,420 --> 01:07:38,500
+إنها تخليها سيدات فقط وإنها حنستخدم أساليب ترويج
+
+972
+01:07:38,500 --> 01:07:41,220
+متعددة إنّه نُروّج لها على الـ Social Media 
+
+973
+01:07:43,970 --> 01:07:47,490
+وفجأة كمان هنستخدم إن نقلل الأسعار عشان نعمل جذب
+
+974
+01:07:47,490 --> 01:07:51,810
+لـ .. للبنات بشكل كبير وإنهم كمان نقول للناس في
+
+975
+01:07:51,810 --> 01:07:56,430
+الجامعات إنّه حيكون في عندك كثير من الإقبال عليا 
+
+976
+01:07:56,430 --> 01:07:59,230
+لإنه خاصة إنّه المكان بيتوفر راحة نفسية لإلهم
+
+977
+01:08:02,200 --> 01:08:05,800
+تكلفة البداية، حيكون عندنا المعدات والأجهزة حتكون
+
+978
+01:08:05,800 --> 01:08:10,540
+16695، عندنا إنما عندك تكلفة التشغيل حيكون عندنا 
+
+979
+01:08:10,540 --> 01:08:18,840
+35144، عندنا إنما عندك المواد الخام حيكون 1800 .. 18544
+
+980
+01:08:18,840 --> 01:08:21,740
+وحيكون عندك إيجار المحل 6000 دولار وبالتالي
+
+981
+01:08:21,740 --> 01:08:28,290
+هتكون عندنا تكلفة البداية 73383 دولار هذه الأكثر
+
+982
+01:08:28,290 --> 01:08:30,410
+فاعلية، رح نحكي عن التمويل اللي بيجيبنا في
+
+983
+01:08:30,410 --> 01:08:33,050
+مشروعنا، في البداية رح يكون في عندنا تمويل شخصي لكن
+
+984
+01:08:33,050 --> 01:08:36,450
+أكيد ما بيقدر أنه يكفينا لإنه نفتح مشروع فرح نرجع 
+
+985
+01:08:36,450 --> 01:08:39,470
+للتمويل الخارجي، في عندنا كان في البداية الحاضنات و
+
+986
+01:08:39,470 --> 01:08:42,470
+بنقدر أنه نستفيد من البنوك لكن أكيد البنوك رح ترتب
+
+987
+01:08:42,470 --> 01:08:44,890
+عليها فوائد، فإحنا مش راح نكون في البداية قادرين،
+
+988
+01:08:44,890 --> 01:08:47,930
+إحنا مش عارفين أنه مشروعنا رح ينجح أو رح يفشل،
+
+989
+01:08:47,930 --> 01:08:52,520
+فبالبداية إنه بنركز على الحاضنات، بالنسبة للمنتجات
+
+990
+01:08:52,520 --> 01:08:55,400
+اللي بقدمها مشروعنا، بقدم مشروبات، كافة، كابتشينو
+
+991
+01:08:55,400 --> 01:08:59,620
+ولا تان، بقدم ممكن أنه حلويات، كيك، ممكن يقدم طبعا
+
+992
+01:08:59,620 --> 01:09:03,320
+المعجنات، المخبزات، ما علينا، بالنسبة بالنهاية
+
+993
+01:09:03,320 --> 01:09:06,340
+للأرباح المتوقعة في مشروعنا كانت على مدار سنتين،
+
+994
+01:09:06,340 --> 01:09:10,980
+بالنسبة للسنة الأولى كانت عبارة عن 890 دولار،
+
+995
+01:09:10,980 --> 01:09:15,470
+بالنسبة للسنة الثانية كانت عبارة عن 1336 دولار، و في
+
+996
+01:09:15,470 --> 01:09:18,730
+النهاية طبعا بنشكر دكتورنا لأنه ما لا يشكر الناس
+
+997
+01:09:18,730 --> 01:09:21,950
+لا يشكر الله، فإحنا بنقدم شكرنا للدكتور حاتم لأنه
+
+998
+01:09:21,950 --> 01:09:24,750
+طبعا معانا كتير و ساعدنا أنه نكون رياضيين، شكرا
+
+999
+01:09:24,750 --> 01:09:28,250
+سلام عليكم و رحمة الله، Sam Yaswerki و Mariam
+
+1000
+01:09:28,250 --> 01:09:31,650
+Salah و ده مسعون مشروعنا اليوم the e-learning school
+
+1001
+01:09:31,650 --> 01:09:36,170
+بس قبل ما نبدأ بدنا نسأل سؤال، هل احنا عندنا خريجين
+
+1002
+01:09:36,170 --> 01:09:39,650
+اثنين طلاب، واحد معاه package كاملة من الدورات
+
+1003
+01:09:39,650 --> 01:09:43,290
+التدريبية وال... والكورسات اللي بتأهله للوظيفة
+
+1004
+01:09:43,290 --> 01:09:46,330
+اللي بتتعلق بتخصصه، والآخر مش حامل غير شهادته
+
+1005
+01:09:46,330 --> 01:09:49,390
+الثاني، نقدموا ال CV تبعهم، مين راح ينقبل في الوظيفة؟
+
+1006
+01:09:49,390 --> 01:09:53,050
+طبعا بديهيا احنا راح نجاوب أنه الطالب اللي...اللي
+
+1007
+01:09:53,050 --> 01:09:55,150
+معاه package كاملة من الدورات التدريبية اللي
+
+1008
+01:09:55,150 --> 01:09:59,420
+بتأهله للوظيفة، عشان هيك احنا حبينا أن كطلاب مقبلين
+
+1009
+01:09:59,420 --> 01:10:02,740
+على التخرج نعمل مشروع بتعلق بالخريجين أو بيفيد
+
+1010
+01:10:02,740 --> 01:10:05,780
+الطالب اللي...اللي مقبل على ورحلة التخرج وعلى
+
+1011
+01:10:05,780 --> 01:10:09,400
+الإقبال على سوق العمل، حكينا أنه احنا بدنا نعمله
+
+1012
+01:10:09,400 --> 01:10:12,820
+دورات تدريبية، بس احنا اذا بدنا نكون منافسين أقوياء
+
+1013
+01:10:12,820 --> 01:10:15,780
+لازم يكون في عندنا شيء بيميزنا، عشان هيك راح نعرف
+
+1014
+01:10:15,780 --> 01:10:19,280
+أكثر شيء معهود، شيء بيميزنا the e-learning هي عبارة عن
+
+1015
+01:10:19,280 --> 01:10:21,980
+مدرسة إلكترونية بتقدم الخدمات...الخدمات اللي
+
+1016
+01:10:21,980 --> 01:10:27,200
+بتقدمها هي عبارة عن دورات تدريبية في مجلة...في مجالات
+
+1017
+01:10:27,200 --> 01:10:31,920
+متعددة حسب طلب الزبائن، وحسب الطلب اللي هم بتلبوه،
+
+1018
+01:10:31,920 --> 01:10:37,100
+إيش الدورات احنا بنعدها، الميزة كمان أنه الدورات و
+
+1019
+01:10:37,100 --> 01:10:41,180
+المحاضرات والدروس تبث مباشرة من خلال الإنترنت
+
+1020
+01:10:41,180 --> 01:10:46,060
+والـ e-learning هي مش مجرد مدرسة بتعرض دروس و
+
+1021
+01:10:46,060 --> 01:10:50,220
+محاضرات ودورات للطلاب، ميزة مميزة كمان، شغلة مهمة
+
+1022
+01:10:50,220 --> 01:10:54,370
+شغلة أنه التواصل والتفاعل بين الطالب وال...و
+
+1023
+01:10:54,370 --> 01:10:59,130
+المدرب هيكون باستمرار، لأنه بعد كل محاضرة وبعد كل
+
+1024
+01:10:59,130 --> 01:11:03,050
+درس، مش إنه مجرد ما الطالب يطلق المحاضرة أو الدرس
+
+1025
+01:11:03,050 --> 01:11:05,410
+أنه هيمشي من المكان أو هيغادر المكان وينتهي
+
+1026
+01:11:05,410 --> 01:11:09,430
+علاقته بالمدرب، لأ، بعد كل محاضرة هيكون في task معين
+
+1027
+01:11:09,430 --> 01:11:14,750
+أو واجب يحله الطالب، المدرب هيعطيله...هيعطيله
+
+1028
+01:11:14,750 --> 01:11:19,030
+يعني والطالب حيكون على تواصل مستمر فأي سؤال، أي...
+
+1029
+01:11:19,030 --> 01:11:22,430
+أي مناقشة أو أي استفسار عنده بيقدر يتواصل مع
+
+1030
+01:11:22,430 --> 01:11:28,030
+المدرب ويحل هذه الإشكالية، وكمان شغلة إن ال video
+
+1031
+01:11:28,030 --> 01:11:32,670
+هيتم عرضه في ساعة محددة أو معاد محدد على ال
+
+1032
+01:11:32,670 --> 01:11:37,380
+internet، ما بضبط، لكن ممكن يكون الناس أنه عندهم
+
+1033
+01:11:37,380 --> 01:11:39,780
+مشغل بهذه الساعة وبهذا الوقت، فعشان نحل هذه
+
+1034
+01:11:39,780 --> 01:11:44,400
+الإشكالية، الفيديو هيتم تفعيله لمدة 24 ساعة، الطالب
+
+1035
+01:11:44,400 --> 01:11:48,300
+يعني بأي وقت بيكون فاضي فيه بيقدر يفتح على الموقع
+
+1036
+01:11:48,300 --> 01:11:54,330
+ويحضر المحاضرة وي...و يستفيد من الدراسة، الأهداف
+
+1037
+01:11:54,330 --> 01:11:59,970
+طبعا هدف شركتنا بالأول ك...زي أنه...أنه نقدر
+
+1038
+01:11:59,970 --> 01:12:05,770
+نوصل لكمناسب من الربح وأنه نحقق أرباح جيدة، لكن
+
+1039
+01:12:05,770 --> 01:12:08,310
+عشان نقدر نحافظ على هذه الأرباح، وعشان تكون
+
+1040
+01:12:08,310 --> 01:12:12,410
+أرباح مستمرة إن شاء الله، فإحنا لازم نقدم خدمات
+
+1041
+01:12:12,410 --> 01:12:16,190
+جيدة للزبائن ونقدر نحافظ عليهم، علشان نقدر نحافظ
+
+1042
+01:12:16,190 --> 01:12:20,540
+على هذه الأرباح، من أهدافنا اللي بنوفرها للزبائن أنه
+
+1043
+01:12:20,540 --> 01:12:24,900
+هنوفر عليهم وقت وجهد كبير، لأن الطالب مش محتاج أنه
+
+1044
+01:12:24,900 --> 01:12:28,380
+...غير أنه يفتح ال laptop تبعه الجهاز في أي وقت
+
+1045
+01:12:28,380 --> 01:12:31,360
+بنسبة ويحضر الدورة في الوقت اللي بنسبة وفي
+
+1046
+01:12:31,360 --> 01:12:36,100
+المكان اللي برتاح فيه، كمان شغلة أنه قضينا على قصة
+
+1047
+01:12:36,100 --> 01:12:39,240
+المسافات والمواصلات، يعني طيب لو كان في مسافة
+
+1048
+01:12:39,240 --> 01:12:43,500
+بعيدة أو في بلد آخر ممكن أنه يقدر من خلال الموقع
+
+1049
+01:12:43,500 --> 01:12:46,200
+يسجل في الدورة ويحضر الدروس كلها ويتواصل مع
+
+1050
+01:12:46,200 --> 01:12:49,820
+المدرب سواء...أي سواء كان في نفس البلد أو مكان
+
+1051
+01:12:49,820 --> 01:12:54,700
+آخر أو مكان بعيد، كمان اتغلبنا أنه هيضل مستمر يعني
+
+1052
+01:12:54,700 --> 01:13:00,060
+دايما مع المدرب، شغلة كمان مهمة أنه الطالب مش كل
+
+1053
+01:13:00,060 --> 01:13:05,200
+وقت يكون مثلا عقله حاضر أو صافي لإنه يتلقى دورة
+
+1054
+01:13:05,200 --> 01:13:09,460
+تدريبية، فإتاحة الفيديو أربعة وعشرين ساعة بتخلي
+
+1055
+01:13:09,460 --> 01:13:13,880
+أنه يختار الوقت المناسب، يكون عقله فيه صافي وقادر
+
+1056
+01:13:13,880 --> 01:13:19,020
+على التركيز فيه أكثر، كمان الشغلة أنه هننوع في أساليب
+
+1057
+01:13:19,020 --> 01:13:21,920
+التدريب والأساليب اللي بنعرض فيها المحاضرات علشان
+
+1058
+01:13:21,920 --> 01:13:25,320
+الطالب ما يمل، وهنستخدم أساليب التدريس الحديثة
+
+1059
+01:13:25,320 --> 01:13:30,320
+علشان يكون في اهتمام أكثر يعني، والطالب بيستفيد
+
+1060
+01:13:30,320 --> 01:13:33,740
+أكثر، هنحكي عن الفئة اللي تستهدفها المشروع...
+
+1061
+01:13:33,740 --> 01:13:36,880
+المشروع...المشروع بي...بيستهدف فئة الطلاب
+
+1062
+01:13:36,880 --> 01:13:41,000
+والخريجين، ليش؟ إن هم المقبلين على سوق العمل، كل
+
+1063
+01:13:41,000 --> 01:13:44,080
+طالب أو خريج بيكون متخرج من الجامعة، بيحتاج إنه
+
+1064
+01:13:44,080 --> 01:13:47,100
+يربط ما بين الجانب النظري اللي أخذه في الجامعة، ما
+
+1065
+01:13:47,100 --> 01:13:50,190
+بين...أنه بيحس إنه فيه gap ما بين الجانب النظري
+
+1066
+01:13:50,190 --> 01:13:53,630
+اللي كان...اللي أخذه بالجامعة وما بين سوق العمل
+
+1067
+01:13:53,630 --> 01:13:57,230
+فالطالب والخريج...الطالب الطلاب والخريجين هم
+
+1068
+01:13:57,230 --> 01:13:59,550
+أكثر الناس اللي بيسعوا على أنهم ياخدوا دورات لحد
+
+1069
+01:13:59,550 --> 01:14:02,750
+يكتسبوا فيها قدرات وزيادة في قدراتهم ومهارات
+
+1070
+01:14:02,750 --> 01:14:08,260
+المهارية...المهارية، يعني ليهم زيادة الثقافة سواء
+
+1071
+01:14:08,260 --> 01:14:13,380
+كانت لغات أو سواء كانت في التخصص، ووجدنا أنه في
+
+1072
+01:14:13,380 --> 01:14:16,180
+وزارة التربية والتعليم كانت عاملة إحصائيات لعدد
+
+1073
+01:14:16,180 --> 01:14:20,060
+الخريجين، لو تلاحظ إنه عدد الخريجين بيكون هائل في
+
+1074
+01:14:20,060 --> 01:14:24,660
+كل سنة، بالمقابل الفرص اللي بتتواجد بتكون قليلة، فالفرص
+
+1075
+01:14:24,660 --> 01:14:27,260
+اللي بتتواجد في سوق العمل بيحتاج إلى كفاءة، بيحتاج إلى
+
+1076
+01:14:27,260 --> 01:14:33,320
+تميز، فلهيك الكل لازم يسعى ويدور على...على دورات
+
+1077
+01:14:33,320 --> 01:14:38,030
+لزيادة الخبرة في المجال اللي...اللي هتساعدنا إنه
+
+1078
+01:14:38,030 --> 01:14:44,270
+احنا نعمل هذا المشروع، بالبداية التطور التكنولوجي
+
+1079
+01:14:44,270 --> 01:14:48,070
+الكبير إنه كل الناس صار في عندهم laptop، بات كل
+
+1080
+01:14:48,070 --> 01:14:50,850
+الناس صار في عندهم internet في البيت، فأصبح من
+
+1081
+01:14:50,850 --> 01:14:54,070
+السهل إنه أي حد بدل ما يقعد مثلا ضايع وقته على ال
+
+1082
+01:14:54,070 --> 01:14:57,310
+internet، لأ، ياخد دورة يتطور فيها حاله وهو قاعد في
+
+1083
+01:14:57,310 --> 01:14:57,630
+بيته
+
+1084
+01:15:01,020 --> 01:15:05,220
+الجانب الاقتصادي the economic factor، الجانب الاقتصادي
+
+1085
+01:15:05,220 --> 01:15:08,740
+أنه زي ما حكينا بالأول قلة فرص العمل، بالمقابل
+
+1086
+01:15:08,740 --> 01:15:12,240
+زيادة عدد الخريجين، سوق العمل صار بده الإنسان اللي
+
+1087
+01:15:12,240 --> 01:15:16,940
+عنده خبرة كمهندس حاسوب، أول ما بيطلع بده يقدم على...
+
+1088
+01:15:16,940 --> 01:15:22,020
+على مثلا وظيفة لازم يكون مثلا معاه برمجة web، برمجة
+
+1089
+01:15:22,020 --> 01:15:25,660
+android، كل...كل...خبرة بكل شيء بالمقابل هو يكون
+
+1090
+01:15:25,660 --> 01:15:29,860
+ماخد في الجامعة أساسيات أو يعني نقطة من بحر،
+
+1091
+01:15:29,860 --> 01:15:35,720
+فالكل لازم أنه يسعى يتطور نفسه عشان يلحق فرص العمل
+
+1092
+01:15:35,720 --> 01:15:41,040
+اللي في السوق، وزي ال...الجانب ده الثقافة، زيادة
+
+1093
+01:15:41,040 --> 01:15:44,240
+طبعا ثقافة بشكل عام، اللي مش بس دورات في التخصص
+
+1094
+01:15:44,240 --> 01:15:50,100
+كمان دورات مثلا في اللغة، في التنمية البشرية، العامل
+
+1095
+01:15:50,100 --> 01:15:54,740
+الجغرافي هيساعدنا لإنه مش هيحتاج الطالب لإنه يطلع
+
+1096
+01:15:54,740 --> 01:15:59,180
+مواصلات أو يبعد عن المكان، لكن هو في بيته بيقدر...
+
+1097
+01:15:59,180 --> 01:16:02,640
+تغلبنا يعني عن البعد جغرافيًا، والتطور التكنولوجي
+
+1098
+01:16:02,640 --> 01:16:06,480
+ساعدنا أول شيء، أي انسان لما بده يقدم يعمل مشروع
+
+1099
+01:16:06,480 --> 01:16:09,440
+بده يشوف المنافسين في السوق، المنافسين الأساسيين
+
+1100
+01:16:09,440 --> 01:16:12,400
+لاقينا هي الدورات العادية اللي بتعطى بأي مركز، و
+
+1101
+01:16:12,400 --> 01:16:14,460
+الثاني شيء اليوتيوب، الدورات اللي هو ال self
+
+1102
+01:16:14,460 --> 01:16:17,980
+learning، عملنا استبيانات وعملنا إحصائيات فلاقينا
+
+1103
+01:16:17,980 --> 01:16:21,760
+هم هدول أكثر اثنين منافسين، لكن احنا بنتميز عنهم
+
+1104
+01:16:21,760 --> 01:16:26,160
+مثلاً، الدورات التدريبية فيها مشكلة أن هي بتضيع في
+
+1105
+01:16:26,160 --> 01:16:31,470
+وقت وفي مكان، ممكن الطالب في هذا الوقت مش هيقدر
+
+1106
+01:16:31,470 --> 01:16:34,610
+يتلقى course أو صار عنده ظرف راح تروح عليه الدورة، و
+
+1107
+01:16:34,610 --> 01:16:38,450
+خلاص، مع إنه دفع...دفع حقها، فإحنا اتغلبنا عليها
+
+1108
+01:16:38,450 --> 01:16:41,950
+المشكلة، أن إحنا بنعيدي الدورة خلال ال 24 ساعة،
+
+1109
+01:16:41,950 --> 01:16:44,810
+بيضل ينعاد نفس ال course، بقى الوقت هو بفضة بيفتح
+
+1110
+01:16:44,810 --> 01:16:48,250
+بيتلقى هذه المحاضرة، ثاني شيء ال youtube courses
+
+1111
+01:16:48,250 --> 01:16:51,630
+المشكلة كانت الأساسية فيها أنه ما بتعطي شهادات
+
+1112
+01:16:51,630 --> 01:16:55,350
+معتمدة، يعني الطالب لما بده يعبي ال CV تبعه ما بيقدر
+
+1113
+01:16:55,350 --> 01:16:58,630
+يحكي، ومعناه صرف learning، تعلمت شيء معين، لازم يكون
+
+1114
+01:16:58,630 --> 01:17:02,370
+فيه شيء معتمد، فإحنا بنعطي شهادات معتمدة، وبنريح
+
+1115
+01:17:02,370 --> 01:17:07,450
+الطالب أنه ما بنقيده لا في وقت ولا في مكان، وهو
+
+1116
+01:17:07,450 --> 01:17:10,590
+بالوقت اللي هو بيحس إن عقله مستعد أنه يتقبل
+
+1117
+01:17:10,590 --> 01:17:16,470
+المعلومة بيفتح وبيحضر، the human resources فريق اللي
+
+1118
+01:17:16,470 --> 01:17:20,050
+عمل عندنا أربعة أشخاص، the team leader، the team leader هو
+
+1119
+01:17:20,050 --> 01:17:26,250
+القائد والإداري، وظيفته التخطيط والميزانية كاملة،
+
+1120
+01:17:26,250 --> 01:17:29,690
+هو اللي بيقدر يديرها ويتصرف فيها، the trainer هو 
+
+1121
+01:17:29,690 --> 01:17:32,110
+الإنسان اللي بيعطي الدورات هو اللي بيعدّي المادة
+
+1122
+01:17:32,110 --> 01:17:36,030
+التدريبية، الـ programmer هو اللي بيبرمجي للموقع و
+
+1123
+01:17:36,030 --> 01:17:40,450
+بيخليه قادر إنه يبث live الـ video Quality
+
+1124
+01:17:40,450 --> 01:17:43,970
+Controversy هو اللي بيفحص لنا جودة الخدمات اللي
+
+1125
+01:17:43,970 --> 01:17:48,890
+احنا بنقدمها المالية، رح نشوفها بعملية، في البداية
+
+1126
+01:17:48,890 --> 01:17:52,790
+عشان ندرس الجانب المالي للمشروع، فيه استراتيجية
+
+1127
+01:17:52,790 --> 01:17:58,850
+بتتساعد لأي دورة إحنا هنعطيها، هتكون حسب الصعوبة ..
+
+1128
+01:17:58,850 --> 01:18:01,330
+أو حسب الـ level تبع الدورة تبعتنا، مثلًا في برمج
+
+1129
+01:18:01,330 --> 01:18:05,490
+واحد، برمج اتنين يعني، فتساعدة الدورة بتكون حسب الـ
+
+1130
+01:18:05,490 --> 01:18:08,550
+level أو صعوبة الدورة، تاني شيء حسب تكلفة المدرب،
+
+1131
+01:18:08,550 --> 01:18:11,510
+لو كان المدرب مهندس، غير لما يكون مدرب تلميذ
+
+1132
+01:18:15,840 --> 01:18:19,640
+عملنا توقعات للسنة الأولى، فكانت التوقعات عبارة عن
+
+1133
+01:18:19,640 --> 01:18:23,800
+مئة وخمس .. مئة وخمس آلاف تقريبًا، حسب كل شهر كان
+
+1134
+01:18:23,800 --> 01:18:26,580
+من دورة، سواء كانت لغة، دورات لغة أو برمجة أو 
+
+1135
+01:18:26,580 --> 01:18:27,020
+تصميم
+
+1136
+01:18:29,670 --> 01:18:32,830
+التكاليف اللي أنا بحتاجها قبل ما أقيم المشروع أول 
+
+1137
+01:18:32,830 --> 01:18:36,850
+شيء نحتاج تكلفة في الترخيص، أي مركز تعليمي بده ينشط
+
+1138
+01:18:36,850 --> 01:18:39,790
+خصوصًا في قطاع غزة لازم أعمل ترخيص لوزارة التابعة
+
+1139
+01:18:39,790 --> 01:18:44,410
+والتربية والتعليم لإنه بده يعطينا شهادة معتمدة و .. و
+
+1140
+01:18:44,410 --> 01:18:47,870
+الترخيص اللي بتكلفنا، نحتاج كمان نروح لوزارة ..
+
+1141
+01:18:47,870 --> 01:18:51,830
+لوزارة الداخلية لكل شخص بده يشتغل في المركز لازم
+
+1142
+01:18:51,830 --> 01:18:55,130
+يكون له شهادات حسن سيرة وسلوك كل هذه الأشياء
+
+1143
+01:18:55,130 --> 01:19:00,020
+ممكن تكلفنا في تقريبًا كل تكلفة بنحتاجها على الترخيص
+
+1144
+01:19:00,020 --> 01:19:04,400
+خمسمئة دولار، منحتاج لكاميرات، سماعات، microphone،
+
+1145
+01:19:04,400 --> 01:19:09,760
+LCD و laptops، التكلفة .. التكلفة كلّه تقريبًا أقل
+
+1146
+01:19:09,760 --> 01:19:16,390
+عن سبعة آلاف، بعد ما نبني المشروع هيكون في عنا تكاليف
+
+1147
+01:19:16,390 --> 01:19:21,050
+لترويج المشروع عبارة عن ألفين دولار و .. وتكاليف
+
+1148
+01:19:21,050 --> 01:19:24,650
+إيجار اللي .. هنحتاج غرفة واحدة لحتى نصور فيها الـ
+
+1149
+01:19:24,650 --> 01:19:28,830
+.. الدورات اللي بنعطيها live تقريبًا ألفين و
+
+1150
+01:19:28,830 --> 01:19:34,290
+أربعمئة دولار وبنحتاج كل فترة صيانة ألفين دولار و
+
+1151
+01:19:34,290 --> 01:19:37,690
+بنحتاج كمان أجور للمدربين ولكل اللي بيشتغلوا
+
+1152
+01:19:37,690 --> 01:19:43,400
+بيبقى تقريبًا سبعين ألف دولار ولو احنا حسبنا الربح
+
+1153
+01:19:43,400 --> 01:19:48,220
+ما بين اللي احنا حصلناه في السنة الأولى لحد .. لكل
+
+1154
+01:19:48,220 --> 01:19:51,300
+التكلفة اللي احنا احتجناها هيكون صفر في عشر آلاف و
+
+1155
+01:19:51,300 --> 01:19:54,680
+هيك بنكون إن شاء الله نحكي المخاسر، اه طبعًا طبعًا
+
+1156
+01:19:54,680 --> 01:19:59,880
+بده أحكي آخر شيء عن المخاطر للمشروع أول .. أول ما
+
+1157
+01:19:59,880 --> 01:20:02,840
+بدينا نعمل CPI للمشروع ما كناش عاملين في حسابنا
+
+1158
+01:20:02,840 --> 01:20:06,180
+قطع الكهرباء اللي بيصير في غزة، فهذا المشكلة إن أنتَ
+
+1159
+01:20:06,180 --> 01:20:09,470
+تحدد الطالب في ساعة معينة يكون فيها online ممكن
+
+1160
+01:20:09,470 --> 01:20:12,370
+تكون هذه الساعة بتناسبه وممكن تكون ما بتناسبه بسبب
+
+1161
+01:20:12,370 --> 01:20:16,590
+قطع الكهرباء، حلّنا هذه المشكلة عن طريق بث الفيديو
+
+1162
+01:20:16,590 --> 01:20:19,430
+خلال 24 ساعة، في الوقت اللي هو بيكون فيه فاضي أو
+
+1163
+01:20:19,430 --> 01:20:23,430
+في الوقت اللي هو بتريح له إنه يحضر الـ .. الـ .. الـ
+
+1164
+01:20:23,430 --> 01:20:26,570
+.. الفيديو ومن طول ما يتواصل مع الدكتور أو المدرب
+
+1165
+01:20:26,570 --> 01:20:30,050
+بأي وقت، فإن إحنا نكون حلّينا أكبر مشكلة ممكن يعاني
+
+1166
+01:20:30,050 --> 01:20:34,970
+منها الطالب في مشكلة الـ online بسم الله الرحمن
+
+1167
+01:20:34,970 --> 01:20:39,070
+الرحيم، علوان مشروع Book Chino، أنا عارفة البطّة، أي
+
+1168
+01:20:39,070 --> 01:20:40,390
+عشور هي للبطة
+
+1169
+01:20:43,480 --> 01:20:46,440
+بنلاحظ في الآونة .. في الآونة الأخيرة إنّه ارتفاع
+
+1170
+01:20:46,440 --> 01:20:49,640
+عدد الطلاب الجامعيين وزيادة عددهم بشكل ملحوظ
+
+1171
+01:20:49,640 --> 01:20:53,440
+وبالتالي أصبحت الجامعات غير قادرة على تلبية احتياجات
+
+1172
+01:20:53,440 --> 01:20:56,840
+هدول الطلاب سواء من توفير مساحات أو من توفير أماكن
+
+1173
+01:20:56,840 --> 01:21:01,220
+خاصة للدراسة في المكتبات العامة أو حتى خدمات
+
+1174
+01:21:01,220 --> 01:21:04,780
+الإنترنت لإنّ هذه أعداد كبيرة فالجامعات أصبحت غير
+
+1175
+01:21:04,780 --> 01:21:08,620
+قادرة على مواكبة هذه الأعداد، مشكلة ثانية ظهرت هي
+
+1176
+01:21:08,620 --> 01:21:12,080
+نظام المكتبات الحالي، نظام المكتبات الحالي بيعتمد
+
+1177
+01:21:12,080 --> 01:21:15,160
+على نظام الـ shift والـ part-time أو النظام إنّ
+
+1178
+01:21:15,160 --> 01:21:17,820
+الطلاب اللي لهم مواعيد والطلبات اللي لها مواعيد حتى لو
+
+1179
+01:21:17,820 --> 01:21:21,180
+في طالب موجود عندي أنا ومحتاج إنّه يدرس يوم كامل
+
+1180
+01:21:21,180 --> 01:21:25,500
+من الصباح تمامًا مثلًا للصبح أو لفترة، هيدور في ..
+
+1181
+01:21:25,500 --> 01:21:28,280
+في نظام المكتبات ممنوع نظام الأكل، ممنوع نظام
+
+1182
+01:21:28,280 --> 01:21:31,560
+الشرب، وبالتالي إنّه بيستلزم على الطالب إنّه ياخد
+
+1183
+01:21:31,560 --> 01:21:36,550
+دراسته كاملة في مكتبة، بالإضافة إلى ذلك إنّ الطلاب
+
+1184
+01:21:36,550 --> 01:21:39,550
+بيواجهوا مشكلة كبيرة واللي هي إنّه كيف يوافقوا بين
+
+1185
+01:21:39,550 --> 01:21:43,450
+course خارجي برا الجامعة ومحاضراتهم، فهم محتاجين
+
+1186
+01:21:43,450 --> 01:21:46,590
+مكان قريب من الجامعات بحيث إنّه فوق الفراغ يروح
+
+1187
+01:21:46,590 --> 01:21:51,890
+يحضر الـ course الخارجي ويرجع لمحاضراته، فكان الحل
+
+1188
+01:21:51,890 --> 01:21:56,080
+إنّه ننشئ الـ Book Chino، الـ Book chain هو عبارة عن
+
+1189
+01:21:56,080 --> 01:21:59,740
+cultural café بيجمع ما بين القراء والمثقفين و
+
+1190
+01:21:59,740 --> 01:22:04,400
+الطلاب الجامعات، بيجمع ما بين المؤلفين والكتاب،
+
+1191
+01:22:04,400 --> 01:22:08,680
+مكان بيوفر للطلاب المكان يدرسوا فيه بأوقات غير ..
+
+1192
+01:22:08,680 --> 01:22:13,000
+يعني غير محددة، بيوفر لهم كتب، عملية استعارة الكتب
+
+1193
+01:22:13,000 --> 01:22:17,280
+و روايات موجودة، updated على يعني حسب التواريخ
+
+1194
+01:22:17,280 --> 01:22:23,240
+الموجودة، بيوفر أيضًا قاعة تدريب للمدربين بحيث إنهم
+
+1195
+01:22:23,240 --> 01:22:27,000
+يستقبلوا فيها طلاب دورات لمكان قريب من الجامعات
+
+1196
+01:22:27,000 --> 01:22:32,200
+بناءً على هالـ الإحصائية حصلنا عليها من موقع وزارة
+
+1197
+01:22:32,200 --> 01:22:36,100
+التربية والتعليم لعام 2016-2015، بنلاحظ ارتفاع عدد
+
+1198
+01:22:36,100 --> 01:22:38,620
+الطلاب الجامعيين، خاصة عند الجامعة الإسلامية جامعة
+
+1199
+01:22:38,620 --> 01:22:42,850
+الأزهر وجامعة الأقصى، وبالتالي كان الـ underlining
+
+1200
+01:22:42,850 --> 01:22:47,010
+message  قيلنا واللي هو بناء عليه اخترنا الموقع الاستراتيجي
+
+1201
+01:22:47,010 --> 01:22:50,030
+بالقرب من الجامعة الإسلامية وجامعة
+
+1202
+01:22:50,030 --> 01:22:53,530
+الأقصى والأزهر زي ما أنتم شايفين بالصورة هذه من
+
+1203
+01:22:53,530 --> 01:22:54,190
+Google Earth
+
+1204
+01:22:57,820 --> 01:23:01,940
+وأيضًا الفكرة نفسها اللي إحنا بنقدمها هي فكرة
+
+1205
+01:23:01,940 --> 01:23:06,520
+بتجمع مباني، توفير .. توفير الـ .. توفير الكتب،
+
+1206
+01:23:06,520 --> 01:23:11,000
+توفير القاعات وأيضًا بتسمح للطلاب إنهم يعني
+
+1207
+01:23:11,000 --> 01:23:15,220
+يوافقوا ما بين الـ .. أوقات الجامعة وأوقات .. و
+
+1208
+01:23:15,220 --> 01:23:19,660
+أوقاتهم في خارج المقهى .. في المقهى، الفكرة اللي
+
+1209
+01:23:19,660 --> 01:23:23,880
+إحنا بنوصلها إنّ إحنا ما بنسوقش لكتاب معين، لخدمة
+
+1210
+01:23:23,880 --> 01:23:28,080
+معينة، إحنا بنسوق أو بنكون فكرة القراءة درجة في
+
+1211
+01:23:28,080 --> 01:23:32,300
+المجتمع وفعّالة، الفئة المستهدفة هتكون للمقهى
+
+1212
+01:23:32,300 --> 01:23:35,360
+بالأول طلاب وطالبات الجامعة .. الجامعات زي الجامعة
+
+1213
+01:23:35,360 --> 01:23:38,480
+الإسلامية والأزهر والأقصى، هنكون برضه مستهدفين اللي
+
+1214
+01:23:38,480 --> 01:23:41,880
+هو الناس المثقفين في المجتمع وبرضه هنستهدف القراء
+
+1215
+01:23:41,880 --> 01:23:44,460
+وهنستهدف برضه الناس اللي ما بتقرا عشان نشجعهم عن
+
+1216
+01:23:44,460 --> 01:23:46,680
+القراءة، لإنّه زي ما حكت علينا إحنا بدنا نسوق
+
+1217
+01:23:46,680 --> 01:23:50,540
+للقراءة مش بس بدنا نسوق لخدمات معينة برضه هن ..
+
+1218
+01:23:50,540 --> 01:23:54,480
+هنسوق لـ .. اللي هو للناس الكتاب، مؤلفين الكتب لإنّ
+
+1219
+01:23:54,480 --> 01:23:58,380
+المقهى هيكون بيوفر اللي هو إمكانية عمل حفلات توقيع
+
+1220
+01:23:58,380 --> 01:24:04,180
+للكتب .. للكتب داخل المقهى، هلأ الـ profit اللي هو
+
+1221
+01:24:04,180 --> 01:24:07,400
+المقهى هيكون بيحقق .. بيحقق أرباحه من خلال الخدمات
+
+1222
+01:24:07,400 --> 01:24:10,800
+اللي بقدمها، هيكون في تقديم لوجبات خفيفة، وهيكون
+
+1223
+01:24:10,800 --> 01:24:13,540
+في برضه تقديم لمشروبات ساخنة أو باردة، ويتم
+
+1224
+01:24:13,540 --> 01:24:17,280
+تقديم برضه اللي هو كتب للقراءة مع هذه الـ .. مع
+
+1225
+01:24:17,280 --> 01:24:20,960
+المشروبات، برضه هيكون فيه اللي هو إمكانية إعارة لـ
+
+1226
+01:24:20,960 --> 01:24:25,080
+.. إعارة للكتب وبرضه توفير أماكن لتبادل الكتب ما
+
+1227
+01:24:25,080 --> 01:24:29,000
+بين اللي هو زوار المقهى، وبرضه هيكون في مكان مخصص
+
+1228
+01:24:29,000 --> 01:24:32,600
+لإقامة دورات تدريبية في مجالات معينة أو حسب طلب
+
+1229
+01:24:32,600 --> 01:24:36,940
+الزبائن، وهيكون فيه برضه اشتراكات شهرية، هيكون إيه
+
+1230
+01:24:36,940 --> 01:24:40,840
+لها ميزات معينة اللي هو زي إنّه يعني نوفر خدمات
+
+1231
+01:24:40,840 --> 01:24:45,200
+مثلًا internet أعلى، إعارة للكتب برضه بشكل مجاني،
+
+1232
+01:24:45,200 --> 01:24:48,480
+ممكنة برضه توفير حواسيب إنهم يشتغلوا عليها داخل
+
+1233
+01:24:48,480 --> 01:24:51,840
+المقهى، الـ market plan اللي هو إذا ما سوقنا
+
+1234
+01:24:51,840 --> 01:24:55,940
+للمشروع صح، مش هنقدر نصل للفئة المستهدفة بتاعتنا و
+
+1235
+01:24:55,940 --> 01:24:58,700
+بالتالي ممكن إنّ المشروع يفشل، فبالتالي هنسوق
+
+1236
+01:24:58,700 --> 01:25:02,680
+للمشروع بأكثر من طريقة، اللي هنسوق له عن طريق موقع
+
+1237
+01:25:02,680 --> 01:25:05,980
+التواصل الاجتماعي عشان نقدر نصل لفئة كبيرة وهنستخدم
+
+1238
+01:25:05,980 --> 01:25:09,020
+برضه الراديو عشان نصل برضه لفئة الناس اللي هو
+
+1239
+01:25:09,020 --> 01:25:12,740
+الغير قراء، هنكون بتوزيع برضه بروشورات تعريفية
+
+1240
+01:25:12,740 --> 01:25:16,460
+للمقهى وبرضه هنستخدم اللي هي لوحة إعلانات كبيرة
+
+1241
+01:25:16,460 --> 01:25:21,400
+هيتم استئجارها عند مفترق الأزهر وهنخصص برضه رجل
+
+1242
+01:25:21,400 --> 01:25:24,760
+اللي هو موظف يعني للتسويق عشان إدارة العملية
+
+1243
+01:25:24,760 --> 01:25:30,620
+التسويقية كاملة للمقهى، طبعًا في عندنا منافسين ..
+
+1244
+01:25:30,620 --> 01:25:34,600
+منافسين زي Gaza Sky Geeks مثلًا، الـ Gaza Sky Geeks
+
+1245
+01:25:34,600 --> 01:25:38,860
+بتقدم خدمات .. بتقدم .. بتوفر يعني مكان مناسب
+
+1246
+01:25:38,860 --> 01:25:42,920
+للعمل و .. للعمل .. يعني مكان مهيأ للعمل لكن
+
+1247
+01:25:42,920 --> 01:25:46,860
+مشكلتها إن هي بس متخصصة في مجال معين يعني ما ..
+
+1248
+01:25:46,860 --> 01:25:52,060
+يعني مش لـ .. مش لكافة الطلاب أو لكافة فئات الجامعة
+
+1249
+01:25:56,930 --> 01:25:59,130
+لأ ليه مش complete؟ المادة تبقى تبقى complete لإن
+
+1250
+01:25:59,130 --> 01:26:02,210
+هو أصلًا مش profit entity وليه يعني يجلسوا من حالهم
+
+1251
+01:26:02,210 --> 01:26:05,370
+يجلسوا .. يعني ما بيمشي دخله، كل التمثل لإني مش
+
+1252
+01:26:05,370 --> 01:26:08,970
+لغاية اللي هيبقى أرجع للتمثل بتاعي لإنها بتوفر
+
+1253
+01:26:08,970 --> 01:26:12,130
+أماكن .. يعني ممكن أشخاص ييجوا يشتغلوا فيها في
+
+1254
+01:26:12,130 --> 01:26:14,130
+خدمة، هلأ who working this place
+
+1255
+01:26:21,060 --> 01:26:24,940
+أماكنهم يعني مناسبة وقريبة من الجامعة لكن بس
+
+1256
+01:26:24,940 --> 01:26:28,680
+بتركز على خدمات اللي هو تقديم الطعام، ما بتركز على
+
+1257
+01:26:28,680 --> 01:26:31,560
+اللي هو تهيئة أماكن مناسبة لطلبة الجامعة وهم
+
+1258
+01:26:31,560 --> 01:26:35,300
+يقدروا يشتغلوا فيها، حاسكمت، هلأ أهلاً وأهلاً؟ بنسبة
+
+1259
+01:26:35,300 --> 01:26:37,860
+الطريقة العامة إحنا طلبنا طلبات من كلية هندسة
+
+1260
+01:26:37,860 --> 01:26:41,560
+الحاسوب، عندنا experience في عدة مجالات، عندنا 
+
+1261
+01:26:41,560 --> 01:26:44,440
+experience في الـ .. في الرياضة، أخدنا كورسات في
+
+1262
+01:26:44,440 --> 01:26:48,000
+الجامعة زي الـ course الاقتصاد الهندسي، اتعلمنا فيه
+
+1263
+01:26:48,000 --> 01:26:51,180
+كيف ننشأ مشاريع و كيف نعمل دراسة جدوى للمشاريع،
+
+1264
+01:26:51,180 --> 01:26:53,940
+وكمان زي الـ course اللي احنا فيه حاليًا هو
+
+1265
+01:26:53,940 --> 01:26:56,860
+course الإدارة الهندسية، اتعلمنا فيه كيف ننشأ
+
+1266
+01:26:56,860 --> 01:27:01,510
+مشاريع و نديرها، بالنسبة لجانب المادة للمشروع أول
+
+1267
+01:27:01,510 --> 01:27:06,750
+شيء عندنا التكلفة التأسيسية هتكلفنا تقريبًا حوالي
+
+1268
+01:27:06,750 --> 01:27:12,710
+يعني 83 ألف دولار، الـ marketing expense أن التكلفة
+
+1269
+01:27:12,710 --> 01:27:18,290
+التسويق هتكلفنا برضه بحوالي 717 ألف دولار، هتبين
+
+1270
+01:27:18,290 --> 01:27:21,950
+للواحدة الأولى أنه رقم كبير بس احنا يعني معنيين أن
+
+1271
+01:27:21,950 --> 01:27:26,170
+.. يعني مهتمين كثير بجانب التسويق عشان تصل فكرتنا
+
+1272
+01:27:26,170 --> 01:27:31,230
+بصورة جيدة للـ .. للزبون، وعشان يحصل مشروعنا على
+
+1273
+01:27:31,230 --> 01:27:35,710
+brand name قوي، بعد كده عادة الزبائن المتوقعين في
+
+1274
+01:27:35,710 --> 01:27:40,730
+السنة الأولى حوالي عشرين ألف زبون، بالنسبة للّي أنا
+
+1275
+01:27:40,730 --> 01:27:43,910
+حابة أحصلها أو اللي أنا بديها من .. من الـ toil أو
+
+1276
+01:27:43,910 --> 01:27:47,230
+من المنحة هي خمسين ألف دولار، المساهمة الشخصية
+
+1277
+01:27:47,230 --> 01:27:51,630
+هتكون بنسبة ثلاثين ألف دولار، الـ pay back period
+
+1278
+01:27:51,630 --> 01:27:55,170
+هترجع الدراسة المال بعد .. يعني بعد الحسابات اللي
+
+1279
+01:27:55,170 --> 01:27:59,830
+احنا عملناها، بعد ثلاث سنين، نسبة الفائدة واحد و
+
+1280
+01:27:59,830 --> 01:28:00,650
+ثلاثين بالمئة
+
+1281
+01:28:03,610 --> 01:28:07,170
+بالنسبة للـ current status احنا زرنا على الجامعات و
+
+1282
+01:28:07,170 --> 01:28:10,670
+عملنا استفتاء و زي هيك، لإنه في قبول كثير على فكرة
+
+1283
+01:28:10,670 --> 01:28:15,150
+مشروعنا، هدأوا وعملنا جوجل questionnaire برضه لإنه
+
+1284
+01:28:15,150 --> 01:28:19,190
+في قبول على الفكرة بنسبة 77%، بالنسبة لإن احنا و
+
+1285
+01:28:19,190 --> 01:28:22,610
+أنا حاليًا مشروعنا، و أنا وصلنا فيه لروحنا عن مهندس
+
+1286
+01:28:22,610 --> 01:28:26,790
+معماري، عملنا تخطيط يعني أولية أو طريقة أولية عن كيف
+
+1287
+01:28:26,790 --> 01:28:30,630
+هيكون المقهى تبعنا، فيه عندنا مهندس الدخول فيه
+
+1288
+01:28:30,630 --> 01:28:35,100
+عندنا قاعة للزبائن و للطلاب فيه، عندنا مهندس قاعة
+
+1289
+01:28:35,100 --> 01:28:38,160
+الدورات .. قاعة الدورات و المؤتمرات، يعني احنا بنجيب
+
+1290
+01:28:38,160 --> 01:28:42,180
+المدرب حسب طلب الزبائن و طلب الطلاب ويكون موفر لهم
+
+1291
+01:28:42,180 --> 01:28:47,100
+قاعة و مرفق آه
+
+1292
+01:28:47,100 --> 01:28:49,900
+و الـ use of funds أنا بانتظار طبعًا التمويل أو بانتظار
+
+1293
+01:28:49,900 --> 01:28:55,420
+الفلوس علشان أبدأ أطبّق فعليًا المشروع على أرض
+
+1294
+01:28:55,420 --> 01:28:57,980
+الواقع، نشتري المعدات نشتري الطاولات نشتري كل
+
+1295
+01:28:57,980 --> 01:29:01,770
+اللوازم اللازمة لإنشاء المشروع، الـ risk اللي بتواجه
+
+1296
+01:29:01,770 --> 01:29:06,390
+مشروعنا أنه يتم سرقة الفكرة تبعاتنا وانتشارها بشكل
+
+1297
+01:29:06,390 --> 01:29:10,730
+واسع، ثاني شيء طبعًا اللي هو كل البنات هتقول هو رح
+
+1298
+01:29:10,730 --> 01:29:13,430
+يُصْرَف، ويُخطِر الكهرباء، يخطر الكهرباء هو ما بتأثر
+
+1299
+01:29:13,430 --> 01:29:16,690
+على المعدات و على الـ .. على الآلات، ممكن تقلل من
+
+1300
+01:29:16,690 --> 01:29:20,330
+العمر الافتراضي للمعدات والآلات بتاعتنا، ثاني شيء
+
+1301
+01:29:20,330 --> 01:29:23,430
+اللي هو رح يصرف ويُغنِق المعابر، بما أن أنا هستضيف
+
+1302
+01:29:25,050 --> 01:29:29,410
+مستضيف كتاب وقراء وشعراء من .. من برا موظفين أو
+
+1303
+01:29:29,410 --> 01:29:32,910
+من أي مكان، وطبعًا مسكين المعبر هتأثر على إنهم يجمعوا
+
+1304
+01:29:32,910 --> 01:29:36,130
+.. يجمعوا على الـ .. الواقع، وطبعًا الـ fans بتبقى و
+
+1305
+01:29:36,130 --> 01:29:39,430
+أنا أيضًا هو صغير، شغال على إيمان كتاب يدخل الجواب
+
+1306
+01:29:39,430 --> 01:29:44,110
+بسم الله الرحمن الرحيم، اليوم مشروعنا اسمه مشروع
+
+1307
+01:29:44,110 --> 01:29:48,980
+مدرستي في بيتي، مشروعنا رح يكون حلّ لمشكلة حقيقية
+
+1308
+01:29:48,980 --> 01:29:52,680
+بتعاني قطاع غزة منها وبتعاني العالم منها وهي
+
+1309
+01:29:52,680 --> 01:29:56,600
+مشكلة تلوث الماء والهواء والتربة، هذه المشكلة
+
+1310
+01:29:56,600 --> 01:30:00,860
+بينتج عنها محاصيل غير صالحة للاستخدام البشري و
+
+1311
+01:30:00,860 --> 01:30:04,700
+بتسبب للإنسان الأمراض، خاصة مرض الـ cancer حسب
+
+1312
+01:30:04,700 --> 01:30:08,360
+إحصاءات، نسبة عدد الناس المصابة بهذا المرض تزداد كل
+
+1313
+01:30:08,360 --> 01:30:12,100
+سنة بسبب التلوث، خاصة بعد الحروب اللي تعرض لها قطاع غزة
+
+1314
+01:30:12,100 --> 01:30:15,000
+نسبة التلوث الموجودة في التراب وفي الماء وفي
+
+1315
+01:30:15,000 --> 01:30:19,330
+الهواء بتزيد، في مشاكل ثانية هي زيادة عدد السكان في
+
+1316
+01:30:19,330 --> 01:30:22,090
+القطاع، زيادة في عدد السكان، ده بيؤدي إلى إزالة مساحات
+
+1317
+01:30:22,090 --> 01:30:25,990
+الخضراء وبناء بدلها مباني، حتى هذه المباني مابتتم
+
+1318
+01:30:25,990 --> 01:30:29,930
+استخدام المساحات فيها بشكل أمثل، بتكون مساحات مش
+
+1319
+01:30:29,930 --> 01:30:33,870
+مستخدمة، مشاكل مثالي .. مش مستخدمة، مشاكل مثالية في
+
+1320
+01:30:33,870 --> 01:30:37,910
+مشاكل ثانية منها ارتفاع درجة الحرارة، ارتفاع درجة
+
+1321
+01:30:37,910 --> 01:30:40,930
+الحرارة بتأثر على الإنسان، سبب ضرر للإنسان، بتأثر
+
+1322
+01:30:40,930 --> 01:30:44,760
+كمان على المباني وبتقلل العمر الافتراضي للمباني، هي
+
+1323
+01:30:44,760 --> 01:30:48,500
+مشاكل ممكن يكون لها أكثر من حل، الحل اللي بيقدمه
+
+1324
+01:30:48,500 --> 01:30:53,300
+مشروعنا هو زراعة الأسطح في هذه المغامرة، زراعة
+
+1325
+01:30:53,300 --> 01:30:58,340
+الأسطح هيقدم أكثر من هدف على حسب الفئة المستهدفة
+
+1326
+01:30:58,340 --> 01:31:02,260
+أو الزبون اللي بيجي يحصل على هذه الخدمة، بشكل عام إيش
+
+1327
+01:31:02,260 --> 01:31:05,740
+راح تعمل؟ راح تعمل على تحديد .. راح تعمل على توفير
+
+1328
+01:31:05,740 --> 01:31:10,360
+المحاصيل، هذه المحاصيل راح تبقى طازجة، ما فيها
+
+1329
+01:31:10,360 --> 01:31:14,300
+سموم، طبعًا بتأثير سلبي على صحة الإنسان، مش بس
+
+1330
+01:31:14,300 --> 01:31:17,960
+ممكن تكون محاصيل، ممكن تكون يعني زينة أو ممكن تكون
+
+1331
+01:31:17,960 --> 01:31:21,300
+نباتات عطرية، كمان فوائدها إنها راح تعمل على تلطيف
+
+1332
+01:31:21,300 --> 01:31:23,780
+الجو وراح تقلل الـ metal oxide الكربون إلى حد ما
+
+1333
+01:31:23,780 --> 01:31:27,300
+يعني فوائدها كمان أيضًا إنها راح تعمل على استخدام
+
+1334
+01:31:27,300 --> 01:31:30,020
+المواد .. راح تعمل لها recycling لأن المشروع بيَهدف
+
+1335
+01:31:30,020 --> 01:31:32,220
+إلى استخدام المواد اللي متوفرة موجودة زي الخشب أو
+
+1336
+01:31:32,220 --> 01:31:34,820
+الحديد أو إطارات و .. إطارات السيارات والأعجاز
+
+1337
+01:31:34,820 --> 01:31:37,820
+فراح تعمل على استخدامها في بناء الـ .. أو في بناء
+
+1338
+01:31:37,820 --> 01:31:41,400
+الـ structure الكامل للأسطح، وتعمل تنفذ المشروع
+
+1339
+01:31:42,010 --> 01:31:46,330
+بالنسبة للرؤية للمشروع تبعنا، مشروعنا خدمات ربحي
+
+1340
+01:31:46,330 --> 01:31:50,090
+هدفه أنه يوصل لأكبر قدر من السكان ويقنعهم بأهمية
+
+1341
+01:31:50,090 --> 01:31:53,150
+هذا المشروع وفائدته، لأن فائدته للناس وكمان
+
+1342
+01:31:53,150 --> 01:31:58,130
+للبيئة، هدفه كمان أنه يعمل على كسب ثقة هؤلاء الزبائن
+
+1343
+01:31:58,130 --> 01:32:02,430
+ويقنعهم وكمان يوفر لهم أحسن خدمة بحيث أنه نستقطبهم
+
+1344
+01:32:02,430 --> 01:32:05,490
+من بين المنافسين والآخرين، لأنه في منافسين لهذا
+
+1345
+01:32:05,490 --> 01:32:08,580
+المشروع سواء مباشرين أو غير مباشرين، بالنسبة للفئات
+
+1346
+01:32:08,580 --> 01:32:11,940
+المستهدفة، مشروعنا أول سنة راح يكون بيستهدف فقط
+
+1347
+01:32:11,940 --> 01:32:16,680
+أصحاب الدخل المرتفع والمتوسط، والجامعات، المؤسسات
+
+1348
+01:32:16,680 --> 01:32:19,500
+لأن الـ price اللي راح يستخدم في مشروعنا schema
+
+1349
+01:32:19,500 --> 01:32:24,130
+فإحنا بحاجة إن إحنا نغطي تكاليف الإنتاج، فبالتالي
+
+1350
+01:32:24,130 --> 01:32:28,210
+راح يكون .. راح يكون السعر مرتفع، وبعدين كده ما ننطلق
+
+1351
+01:32:28,210 --> 01:32:31,230
+تكاليف الإبتدائية، بسير المشروع ويُفِد أكبر ناس و
+
+1352
+01:32:31,230 --> 01:32:34,430
+الناس وواثقة فيه وخدماته، راح نعمل على تقديم السعر
+
+1353
+01:32:34,430 --> 01:32:37,670
+فبنقدر نوصل لأصحاب الدخل أو المقافض، أهلاً وسهلاً
+
+1354
+01:32:37,670 --> 01:32:40,870
+يا حبيبي زي ما حكت لنا سلام إن شركتنا شركة .. شركة
+
+1355
+01:32:40,870 --> 01:32:44,350
+خدماتية بتقدم لنا خدمة زراعة أسطح المنازل،
+
+1356
+01:32:44,350 --> 01:32:48,400
+فبيجي لنا الزبون بيجي لشركتنا فبنعمله مقابلة مع الـ
+
+1357
+01:32:48,400 --> 01:32:52,220
+.. مع المهندس المعماري، فهذا المعماري بيصمم الـ
+
+1358
+01:32:52,220 --> 01:32:54,700
+structure والـ design اللي هو عاوزه يعمله في الباب
+
+1359
+01:32:54,700 --> 01:32:58,320
+بعد هيك بنروح نوجهه للمهندس الزراعي، هذا المهندس
+
+1360
+01:32:58,320 --> 01:33:02,380
+الزراعي هو اللي بيحدد له، يعني المهندس الزراعي بيوجهه
+
+1361
+01:33:02,380 --> 01:33:05,820
+أنه إيش .. إنه نوعية النباتات اللي هي يزرعها على
+
+1362
+01:33:05,820 --> 01:33:08,840
+سطح منزله، بعد ما يتم الاتفاق مع المهندس الزراعي و
+
+1363
+01:33:08,840 --> 01:33:12,140
+المهندس المعماري على الـ design المصمم لسطح المنزل
+
+1364
+01:33:12,140 --> 01:33:15,260
+بيروحوا احنا نتوجه لمنزل هذا الشخص و لهذا الزبون
+
+1365
+01:33:15,260 --> 01:33:18,340
+مع عامل البناء وعامل النظافة وعامل الدهان
+
+1366
+01:33:18,340 --> 01:33:22,800
+عامل البناء بيقوم بـ .. ببناء الأحواض الزراعية و ..
+
+1367
+01:33:24,710 --> 01:33:27,690
+طيب إحنا حكينا إنه الزبون هو اللي هيجي لشركتنا، طب كيف
+
+1368
+01:33:27,690 --> 01:33:31,090
+هو هيعرف عن شركتنا؟ أو كيف هيصل لهذه الشركة؟ فمن
+
+1369
+01:33:31,090 --> 01:33:33,350
+خلال أولًا وسائل التواصل الاجتماعي، الـ Facebook،
+
+1370
+01:33:33,350 --> 01:33:37,290
+ممكن نعمل صفحة عن أهمية زراعة .. عن شركتنا وعن
+
+1371
+01:33:37,290 --> 01:33:41,170
+رؤية شركتنا وعن الأهداف اللي احنا راح نوصلها، الشغل
+
+1372
+01:33:41,170 --> 01:33:44,710
+الثاني ممكن من خلال جرائد، بس يعني مش كثير هذه
+
+1373
+01:33:44,710 --> 01:33:48,210
+الجرائد، ممكن من خلال إذاعات .. إذاعات الـ radio
+
+1374
+01:33:49,090 --> 01:33:53,150
+نحكي عن فكرتنا، عن أهمية الزراعة في مجتمعنا، برضه
+
+1375
+01:33:53,150 --> 01:33:56,410
+ممكن من خلال منشورات ورقية، بروشورات، ممكن آخر شيء
+
+1376
+01:33:56,410 --> 01:33:59,910
+إنّه نعمل دورات وورشات توعية للناس، وممكن كمان
+
+1377
+01:33:59,910 --> 01:34:03,410
+بأهمية الزراعة وإنه في عندنا توعيتهم بقضية ..
+
+1378
+01:34:03,410 --> 01:34:06,890
+بقضية التغير المناخي عندنا في قطاع غزة، وممكن كمان
+
+1379
+01:34:06,890 --> 01:34:10,490
+ننزل على المدارس عشان نُوعّي الطلاب والأطفال منذ
+
+1380
+01:34:10,490 --> 01:34:13,690
+الصغر على أهمية الزراعة، أهمية إنه كيف نُوعّيهم على
+
+1381
+01:34:13,690 --> 01:34:18,740
+القضاء على المشكلة في التغير المناخي، طيب عندنا
+
+1382
+01:34:18,740 --> 01:34:21,920
+أكيد .. لأي مشروع أكيد عنده منافسين، فإحنا في
+
+1383
+01:34:21,920 --> 01:34:24,620
+البداية أكيد هنواجه كثير منافسين، لإنه أول شيء المنافس
+
+1384
+01:34:24,620 --> 01:34:27,360
+الأول عندنا المحل اللي بيبيع الخضار والفواكه و
+
+1385
+01:34:27,360 --> 01:34:32,180
+المشاتل، فالبداية عندنا إحنا كيف بنواجه هي .. ننافس
+
+1386
+01:34:32,180 --> 01:34:35,340
+محلات اللي بيبيع الخضار والفواكه، احنا عملنا سبينات
+
+1387
+01:34:35,340 --> 01:34:39,340
+ونزلنا على منازل المواطنين، لقينا إن في ناس معظم
+
+1388
+01:34:39,340 --> 01:34:43,290
+يعني أغلب .. في ..مجموعة من الناس إنهم بدأوا فعليًا
+
+1389
+01:34:43,290 --> 01:34:45,970
+من تلقاء أنفسهم إنهم يزرعوا أسطح بيوتهم
+
+1390
+01:34:45,970 --> 01:34:48,750
+فزرعوا البندورة، زرعوا الفراولة، أشياء بسيطة خالية
+
+1391
+01:34:48,750 --> 01:34:54,150
+من السموم وصحية، وضعوها بأسعار يعني مناسبة للـ ..
+
+1392
+01:34:54,150 --> 01:34:57,430
+للزبون، الشغلة الثانية، عندنا شركة مُحتضنة من حضرة
+
+1393
+01:34:57,430 --> 01:35:02,050
+اليوكاس، هذه الشركة برضه يعني بدأت إنها تزرع نفس
+
+1394
+01:35:02,050 --> 01:35:04,590
+فكرة مشروع زراعة أسطح المنازل، وفي كمان عندنا
+
+1395
+01:35:04,590 --> 01:35:07,650
+المهندسة ريهام أبو هيبة كانت مشروعها عن زراعة أسطح
+
+1396
+01:35:07,650 --> 01:35:10,030
+المنازل، نفذت هذا المشروع على جامعتين، جامعة
+
+1397
+01:35:10,030 --> 01:35:12,570
+الصوم للأطفال، هذه جامعة الصوم للأطفال كانت
+
+1398
+01:35:12,570 --> 01:35:15,590
+تستهدف إنها تعطي دورات ورش .. كانت لمدة مرحلة ..
+
+1399
+01:35:15,590 --> 01:35:19,500
+شهرين، مدتها كانت على .. مقسّمة يعني لمرحلتين، المرحلة
+
+1400
+01:35:19,500 --> 01:35:22,040
+الأولى أنها تعطي إرشادات توعية لموظفي هذه 
+
+1401
+01:35:22,040 --> 01:35:25,420
+الجامعية ولطلبة هذه الجامعة والمرحلة الحالية
+
+1402
+01:35:25,420 --> 01:35:29,820
+أنها بدأت في زراعة سطح المنزل على .. زراعة سطح هذه
+
+1403
+01:35:29,820 --> 01:35:33,360
+الجامعية مائة متر من مساحتها فكانت مركزّة على أنهم
+
+1404
+01:35:33,360 --> 01:35:36,860
+يستغلوا مخلفات البيئية من إطارات سيارات وخشب أنهم
+
+1405
+01:35:36,860 --> 01:35:39,860
+يعملوا أحواض زراعية والجامعية الثانية جامعة نطوف
+
+1406
+01:35:39,860 --> 01:35:46,510
+للبيئية ضمن مشروع قيادات بيئية بالاشتراك مع فريق
+
+1407
+01:35:46,510 --> 01:35:51,290
+شبابي والتمويل من الأمم المتحدة والاتحاد الأوروبي
+
+1408
+01:35:51,290 --> 01:35:55,630
+نتكلم معاكم فريق العمل احنا عندنا خمسة عندنا
+
+1409
+01:35:55,630 --> 01:35:57,690
+المدير هو اللي هيعمل الـ human resource عليهم
+
+1410
+01:35:57,690 --> 01:36:01,150
+وهيكون يتخذ القرارات عندنا مهندس معماري ومهندس
+
+1411
+01:36:01,150 --> 01:36:04,070
+زراعي المهندسين يبقوا عندهم أقل شيء يكون عندهم 
+
+1412
+01:36:04,070 --> 01:36:07,030
+خبرة سنتين بحيث المهندس المعماري يكون عنده خبرة في
+
+1413
+01:36:07,030 --> 01:36:10,090
+الرسم والتصميم واستخدام البرامج احنا لجينا عندهم
+
+1414
+01:36:10,090 --> 01:36:13,360
+برنامج بيستخدموه اسمه SketchUp هذا بيستخدموه 
+
+1415
+01:36:13,360 --> 01:36:16,740
+لزراعة .. كيفية تصميم الزراعة وكتير المسافات و
+
+1416
+01:36:16,740 --> 01:36:19,640
+الأبعاد هذا بيستخدموه .. يعني بيستخدموه في الجامعة
+
+1417
+01:36:19,640 --> 01:36:23,160
+جناهم و .. و شوفناها ومهندس زراعي لازم يكون عنده 
+
+1418
+01:36:23,160 --> 01:36:25,500
+خبرة في أنواع الشتلات اللي لازم تنزرع على الأسطح
+
+1419
+01:36:25,500 --> 01:36:28,580
+لإن مش كل شيء بظبط إنه نزرع على الأسطح وطريقة
+
+1420
+01:36:28,580 --> 01:36:30,620
+السقي يعني كم مرة يسقي في اليوم وكم مرة ما
+
+1421
+01:36:30,620 --> 01:36:34,900
+يسقيش ويعلم الناس يعني ومن عامل بناء حيث إنه بعد
+
+1422
+01:36:34,900 --> 01:36:41,180
+ما نتفجّع على كل شيء بنجيب عامل بناء أنا بابل خلاط 
+
+1423
+01:36:41,180 --> 01:36:43,880
+الماء وعامل دهان ممكن هذا وما قامش ده، مانجيبي
+
+1424
+01:36:43,880 --> 01:36:47,380
+يعني مثلا للمؤسسات إذا بدها منظر جمال يدهن .. يدهن
+
+1425
+01:36:47,380 --> 01:36:52,160
+جدران أو شيء بيزيد جمال يعني المنظر فلجينا للاتجاه 
+
+1426
+01:36:52,160 --> 01:36:55,180
+المالي طبعاً احنا بداية المشروع هيكون من تكاليف
+
+1427
+01:36:55,180 --> 01:36:59,340
+تأسيسية كبيرة كتير ثابتة ومتغيرة مثل أجور 
+
+1428
+01:36:59,340 --> 01:37:00,060
+للموظفين
+
+1429
+01:37:03,710 --> 01:37:07,470
+من هنا نعمل قاعة تدريبية وورشات عمل للطلاب ومن 
+
+1430
+01:37:07,470 --> 01:37:10,530
+هنا قاعة .. من هنا .. مش قاعة وغرفة يعني مثلا 
+
+1431
+01:37:10,530 --> 01:37:14,490
+للمدير إنه يجتمع .. المكتب لإله يجتمع هو والموظفين
+
+1432
+01:37:14,490 --> 01:37:17,830
+اللي بيتخذ القرارات وراح يكون فيه تأمين وإعلانات 
+
+1433
+01:37:17,830 --> 01:37:20,990
+وفيه مواد أولية لازمة للزراعة ومن هنا نختار
+
+1434
+01:37:20,990 --> 01:37:25,760
+الشتلات ونزرع حسب الموسم هلأ أكيد أول سنة هتكون
+
+1435
+01:37:25,760 --> 01:37:29,820
+عندنا كتير رُقْص .. رُقْص مال محتاجين فاحنا حسبنا
+
+1436
+01:37:29,820 --> 01:37:32,700
+المبيعات وحسبنا رُقْص المال فهي .. تقريباً يعني إن
+
+1437
+01:37:32,700 --> 01:37:36,420
+شاء الله بنصد أول شيء آخر السنة بنكون صدينا الـ ..
+
+1438
+01:37:36,420 --> 01:37:39,520
+صدينا كل التكاليف ورُقْص المال وطلعنا بهامش ربح بسيط 
+
+1439
+01:37:39,520 --> 01:37:44,190
+جدا هلّأ احنا كتير كان فيه مشاريع بيمكننا نختار أي
+
+1440
+01:37:44,190 --> 01:37:46,930
+مشروع نختار بس احنا اخترنا هذا المشروع لعدة أسباب 
+
+1441
+01:37:46,930 --> 01:37:50,950
+مهمة أولاً كان إنه احنا لاحظنا القطاع غزة ككل إنه
+
+1442
+01:37:50,950 --> 01:37:55,170
+تغير المناخ كتير وإنه سوق .. سوق المناخ في القطاع 
+
+1443
+01:37:55,170 --> 01:37:59,790
+غزة فالتاني احنا .. احنا أول سبب اخترنا إنه لما 
+
+1444
+01:37:59,790 --> 01:38:02,870
+نزرع أسطح ومنازل هتزيد نسبة الـ oxygen وتقل نسبة
+
+1445
+01:38:02,870 --> 01:38:06,250
+ثاني أكسيد الكربون ولجينا لدراسة علمية بتحكي إن 
+
+1446
+01:38:06,250 --> 01:38:10,100
+الزراعة شتلة واحدة في سطح المنزل خلال مدة سنة كاملة
+
+1447
+01:38:10,100 --> 01:38:15,480
+تكفي لشخص واحد تكفي للاستهلاك لمدة سنة وكمان 
+
+1448
+01:38:15,480 --> 01:38:18,560
+اخترناها ليش؟ لإنه لما نزرع أسطح المنازل بتيجي من 
+
+1449
+01:38:18,560 --> 01:38:22,580
+كمية الـ .. بتيجي من كمية الرطوبة المتصاعدة في السطح
+
+1450
+01:38:22,580 --> 01:38:26,200
+خصوصاً في فصل الصيف فبالتالي إنه الـ .. الـ .. الري 
+
+1451
+01:38:26,200 --> 01:38:29,420
+بشكل عام بتيجي اللي اللي هو كمية المتصاعدة من الحرارة 
+
+1452
+01:38:29,860 --> 01:38:32,780
+و .. وكمان اللي لاحظنا إن استغلال المساحات
+
+1453
+01:38:32,780 --> 01:38:35,920
+المهملة بدل ما احنا نترك السطح زي ما هو بس للأشياء
+
+1454
+01:38:35,920 --> 01:38:38,700
+اللي بنُنشّيها نرمي فيها وشيء لأ نستغلها في .. في
+
+1455
+01:38:38,700 --> 01:38:41,300
+الزراعة وبالتالي بتعود علينا وعلى المجتمع كله 
+
+1456
+01:38:41,300 --> 01:38:45,520
+يعني بفوائد كتيرة وتوفير مكان استجمامي ومتنفس
+
+1457
+01:38:45,520 --> 01:38:48,600
+لسكان المبنى حيث إنه يعني إنه ممكن هار في الجامعة 
+
+1458
+01:38:48,600 --> 01:38:51,900
+متى نعرف متى ممكن نزرع أسطح ومنازل ويكون منظر 
+
+1459
+01:38:51,900 --> 01:38:56,500
+حضري وأحلى المخاطر، هلّأ أكيد أي مشروع بيكون أولاً
+
+1460
+01:38:56,500 --> 01:38:58,980
+فيه مخاطر، احنا المخاطر الأساسية يعني كانت رأس 
+
+1461
+01:38:58,980 --> 01:39:02,320
+مال إنها كبيرة، بداية تأسيس كتيرة كبيرة والمخاطر
+
+1462
+01:39:02,320 --> 01:39:05,140
+إنّه خوف الناس يعني احنا لما لفّ لفينا أنا وصاحباتي و
+
+1463
+01:39:05,140 --> 01:39:07,500
+طلعنا أصلاً على المنازل كنا نحكي لهم عن الفكرة،
+
+1464
+01:39:07,500 --> 01:39:09,880
+كانوا كله لأ وغلّبوا ولسّه بتكونوا تناظفوا السطح 
+
+1465
+01:39:09,880 --> 01:39:11,920
+وبتكونوا تجيبوا وبتكونوا تعملوا فهم ماكانوش 
+
+1466
+01:39:11,920 --> 01:39:14,740
+مقتنعين بالفكرة كتير عشان هيك احنا بدنا نعمل دورات
+
+1467
+01:39:14,740 --> 01:39:17,840
+تدريبية ونزول و .. وعمل ميداني مقصد
+
+1468
+01:39:21,970 --> 01:39:25,390
+بحالها بتكون بتبني وبتزرع لحالها بدون ما حد
+
+1469
+01:39:25,390 --> 01:39:28,130
+يدعمها أو حد يوجهها و .. و .. و .. يعني مش ده 
+
+1470
+01:39:28,130 --> 01:39:31,370
+مانسقي ومهتموش كتير فبالتالي لجينا عندهم تشقّق ولـ
+
+1471
+01:39:31,370 --> 01:39:33,990
+جينا عندهم مشاكل كتيرة وطـ .. وطلع التحالب 
+
+1472
+01:39:33,990 --> 01:39:39,170
+بالنتيجة هذه بنحب ننجحها وطبعاً حسب كل سطح بيحتاج 
+
+1473
+01:39:39,170 --> 01:39:42,130
+مثلاً كل سطح وكل منزل بيختلف عن منزل تاني إيش ممكن
+
+1474
+01:39:42,130 --> 01:39:45,170
+نزرع فيها وإيش ممكن نزرع فيها وتزايد على المنافسين 
+
+1475
+01:39:45,170 --> 01:39:48,210
+يعني كتير احنا فينا منافسين طبعاً فبالتالي احنا كيف
+
+1476
+01:39:48,210 --> 01:39:51,980
+نحن نحتفظ بالزبائن الطريق ممكن نقدم لهم .. نقدم لهم
+
+1477
+01:39:51,980 --> 01:39:55,880
+خدمات مثل زيارة ربحية، نقدم لهم أشياء أو .. أو مثلا 
+
+1478
+01:39:55,880 --> 01:40:00,520
+تكون علاقتنا معهم مديّة، بس شكراً مشروع إن هو Gaza 
+
+1479
+01:40:00,520 --> 01:40:06,960
+Child Care Sympath G3C هو حضانة أطفال، أنا وغدير 
+
+1480
+01:40:06,960 --> 01:40:10,020
+عبد النبي وأنغام وغدير الإسراء نصر 
+
+1481
+01:40:18,150 --> 01:40:22,750
+هجّت فكرتنا إنه مشروع الحضانة للأطفال هو مشروع قوم
+
+1482
+01:40:22,750 --> 01:40:27,510
+ي برّغ الأهمية بيأثر على الطفل في المرحلة .. في
+
+1483
+01:40:27,510 --> 01:40:32,790
+المرحلة المبكرة من حياته بيكتسب في هذه المرحلة طفل
+
+1484
+01:40:32,790 --> 01:40:37,610
+أخلاقيات وسلوكيات، وبتكبر معاهم هذه السلوكيات 
+
+1485
+01:40:37,610 --> 01:40:41,590
+والأخلاقيات وبالتالي بتأثر على مستقبله وعلى
+
+1486
+01:40:41,590 --> 01:40:46,560
+مستقبل الحضارة معه طبعاً حكينا إنه اللي بتتعلم و
+
+1487
+01:40:46,560 --> 01:40:49,480
+بتتعلم من الأسرة وبعدين ابحضانه في الروضة هو 
+
+1488
+01:40:49,480 --> 01:40:52,140
+بيطبّقها بحياته لما يكبر وبالتالي بيكونوا يعني أما
+
+1489
+01:40:52,140 --> 01:40:58,280
+مجتمع رقيق أما مجتمع خشن فشتّت فكرتنا من إنه كتير
+
+1490
+01:40:58,280 --> 01:41:01,380
+من الأمهات .. هو فكرتنا مطبقة للطلاب وطالبات ..
+
+1491
+01:41:01,380 --> 01:41:05,560
+لطالبات وموظفين موظفات الجامعة الإسلامية في مكان
+
+1492
+01:41:05,560 --> 01:41:08,600
+برضه داخل الجامعة الإسلامية فشتّت فكرتنا من إنه
+
+1493
+01:41:08,600 --> 01:41:12,630
+كتير من الطالبات .. هم أمهاتهم .. أو الموظفات في
+
+1494
+01:41:12,630 --> 01:41:17,510
+الجامعة، عدم وجود بديل للأم أنها وين تحط طفلها
+
+1495
+01:41:17,510 --> 01:41:21,110
+لما .. كمان الدوام بيكون بشكل كبير، تقريباً من ساعة 
+
+1496
+01:41:21,110 --> 01:41:24,190
+ثمانية لساعة اثنتين، كتير من أم عايزة في هذا الدوام، 
+
+1497
+01:41:24,190 --> 01:41:27,470
+وبالتالي أنت هتقلق تقول وين .. وين أنا أحط طفلي وين
+
+1498
+01:41:27,470 --> 01:41:31,070
+أ .. وين أأمل على طفلي، وكتير من الناس إنه بترفض
+
+1499
+01:41:31,070 --> 01:41:34,390
+إنه مثلاً أنت هتخلي عندهم الأطفال، هددهم شوية في
+
+1500
+01:41:34,390 --> 01:41:35,010
+المرحلة هذه
+
+1501
+01:41:38,670 --> 01:41:44,490
+هدفنا في الـ .. في الدراسة إنه كان هنا حضانة بسيطة،
+
+1502
+01:41:44,490 --> 01:41:50,110
+قريباً هي إنها تكون في طابق سفلي أو أرضي مكوّن من
+
+1503
+01:41:50,110 --> 01:41:53,070
+ثلاثة فصول دراسية، غالباً تكون الفصول فيه خمسة عشر
+
+1504
+01:41:53,070 --> 01:41:58,410
+طفل كحد أقصى، قد .. يعني هدفنا إنه نستوعب خمسين 
+
+1505
+01:41:58,410 --> 01:42:02,580
+طفل في الحضانة وبالتالي إذا حصلنا على خمسين طفل 
+
+1506
+01:42:02,580 --> 01:42:05,420
+نحط الهدف، حكينا كل فصل فيه خمسة عشر طفل وبالتالي
+
+1507
+01:42:05,420 --> 01:42:08,400
+مساحة الفصل .. الفصل الواحد هتكون صغيرة تقريباً 
+
+1508
+01:42:08,400 --> 01:42:11,400
+ثلاثة متر وأربعة متر الفئة المستهدفة كانت فكرة
+
+1509
+01:42:11,400 --> 01:42:14,480
+المشروع هي تستهدف الجامعة لساكنيها بشكل عام لإنه
+
+1510
+01:42:14,480 --> 01:42:17,820
+عندها نسبة عالية من الموظفين والموظفات لهم أطفال، و
+
+1511
+01:42:17,820 --> 01:42:19,960
+ونسبة عالية من الموظفين الأطفال كذلك الجامعة أصلاً 
+
+1512
+01:42:19,960 --> 01:42:23,320
+بتحتوي على طالبات متزوجات داخل الجامعة، نوع اللي 
+
+1513
+01:42:23,320 --> 01:42:26,200
+عندي .. نوع الرعاية .. نوع الرعاية عندي نوعين،
+
+1514
+01:42:26,200 --> 01:42:26,500
+عندي
+
+1515
+01:42:29,550 --> 01:42:33,210
+نقرر المقدمة إنه عندي فئة أولى وفئة ثانية، نحن
+
+1516
+01:42:33,210 --> 01:42:36,650
+نوضحها في الجدول، عمر الأطفال من أربع .. من أربع 
+
+1517
+01:42:36,650 --> 01:42:40,670
+أشهر لحد عمر أربع سنوات، قيمة كل فرد حسب الفئة
+
+1518
+01:42:40,670 --> 01:42:43,070
+اللي ينتمي إليها، ممكن عند الطفل نفسه ثمانين
+
+1519
+01:42:43,070 --> 01:42:46,510
+دولار، وإذا كان ينتمي للفئة الثانية عنده مائة 
+
+1520
+01:42:46,510 --> 01:42:50,470
+دولار، طبعاً مش عامل للبناء مصادرة في حالة الغياب، في
+
+1521
+01:42:50,470 --> 01:42:52,970
+حالة غياب الأهل، الأرباح اللي بنحصل عليها مقابل 
+
+1522
+01:42:52,970 --> 01:42:58,800
+خدمات الأطفال الجدول مقدّم .. الخدمات مقدّمة، الفئة
+
+1523
+01:42:58,800 --> 01:43:01,120
+الأولى والفئة الثانية بتمشي مع بعضها .. مع .. مع 
+
+1524
+01:43:01,120 --> 01:43:04,120
+بعض، عندي الفئة الأولى مثلاً عندي مثلاً في تغيير
+
+1525
+01:43:04,120 --> 01:43:07,720
+الملابس والفطور، عندي ممكن الـ .. الـ .. اللعب
+
+1526
+01:43:07,720 --> 01:43:11,060
+بتتضمن جميع الأنواع، بالغذاء بالغداء، هذا الفئة 
+
+1527
+01:43:11,060 --> 01:43:14,660
+الأولى، الفئة الثانية بـ .. بتمّ .. بتم إضافة 
+
+1528
+01:43:14,660 --> 01:43:17,740
+الخدمات لخدمات أخرى، مثل عنديش تعليم الشغل الأساسي
+
+1529
+01:43:17,740 --> 01:43:18,220
+للطفل 
+
+1530
+01:43:21,290 --> 01:43:24,750
+لما احنا عملنا دراسة للسوق لإنه في الأمور الأكبر 
+
+1531
+01:43:24,750 --> 01:43:28,490
+نسبة اللي هي لأطفال من عمر سن لـ .. من ستة أشهر
+
+1532
+01:43:28,490 --> 01:43:32,190
+لسنة، النسبة للداخل كانت مناسبة عندي جدا للدراسات ومن 
+
+1533
+01:43:32,190 --> 01:43:38,670
+ألف ومئة لألفين شركة المنافسين 
+
+1534
+01:43:38,670 --> 01:43:42,170
+كان عندي أكبر منافس هي روضة ألوان وبعدين تيجي
+
+1535
+01:43:42,170 --> 01:43:47,130
+الحضانة الخاصة بالكلية الجامعية وبعدين الحضانة 
+
+1536
+01:43:47,130 --> 01:43:50,690
+الخاصة بالجامعة الإسلامية في الجنوب روضة ألوان
+
+1537
+01:43:50,690 --> 01:43:53,790
+عندها منافسة عالية جدا ليه روضة استثمارية مدعومة من 
+
+1538
+01:43:53,790 --> 01:43:58,970
+أكثر من جهة بتعمل على ضرب الساعة بالسوق مدعومة من
+
+1539
+01:43:58,970 --> 01:44:01,710
+الجهة الخارجية استثمارية درجة أولى وبالتالي أكثر
+
+1540
+01:44:01,710 --> 01:44:07,370
+شيء من المنافسين اللي عنديش بتنهج الساعة مواصفات موقع
+
+1541
+01:44:07,370 --> 01:44:11,070
+الحضانة لازم يكون في عندي مبنى آمن لأن طبعا المكان
+
+1542
+01:44:11,070 --> 01:44:16,250
+هيكون فيه أطفال لازم الحضانة تكون في الطابق الأرضي
+
+1543
+01:44:16,250 --> 01:44:20,330
+و علشان أحقق هذه الدراسة لازم يكون في عندي المكان 
+
+1544
+01:44:20,330 --> 01:44:22,930
+اللي أنا بديه لازم يكون في عندي ثلاث غرف لأن كل
+
+1545
+01:44:22,930 --> 01:44:26,770
+غرفة بدها تستوعب خمسة عشر طفلاً لازم يكون في عندي غرفة
+
+1546
+01:44:26,770 --> 01:44:30,090
+للإدارة ولازم طبعا يكون في عندي .. يكون في عندي 
+
+1547
+01:44:30,090 --> 01:44:33,490
+مرافق عامة زي حمامات مطبخ يكون في عندي ساحة خارجية
+
+1548
+01:44:33,490 --> 01:44:39,320
+للأنشطة وللألعاب المرافق والمستلزمات الضرورية اللي
+
+1549
+01:44:39,320 --> 01:44:41,500
+لازم تكون موجودة في الحضانة لازم الحضانة تكون
+
+1550
+01:44:41,500 --> 01:44:45,400
+تحتوي على حديقة جميلة لأن طبعا المكان هيكون فيه
+
+1551
+01:44:45,400 --> 01:44:49,560
+أطفال لازم لو ما قدرت أوفر حديقة جميلة يكون في
+
+1552
+01:44:49,560 --> 01:44:54,640
+عندي مكان للألعاب المحببة للأطفال زي الأرجوحة لو
+
+1553
+01:44:54,640 --> 01:44:59,140
+أنا كمان برضه ما قدرت أوفر مكان للألعاب لازم أوفر
+
+1554
+01:44:59,140 --> 01:45:03,430
+ذلك أن أنشر الخضرة في كل مكان أو أوفر ألعاب فيديو 
+
+1555
+01:45:03,430 --> 01:45:07,190
+محببة للأطفال طبعا لازم يتم اختيارها بدقة وبعناية
+
+1556
+01:45:07,190 --> 01:45:11,150
+لأن طبعا اللي هيشاهدها يكونوا أطفال لازم الحضانة 
+
+1557
+01:45:11,150 --> 01:45:15,490
+تحتوي على إسعافات أولية ولازم يكون المعلمون
+
+1558
+01:45:15,490 --> 01:45:18,710
+والمسؤولون عن الحضانة يكونوا على علم بكيفية استخدام 
+
+1559
+01:45:18,710 --> 01:45:23,050
+هذه الإسعافات لازم يكون في عندي مكان غرفة للإدارة
+
+1560
+01:45:23,050 --> 01:45:28,280
+مجهزة بكافة الأدوات المكتبية زي كراسي، مكتب، خزانة، 
+
+1561
+01:45:28,280 --> 01:45:33,440
+جهاز حاسوب لازم غرفة الإدارة أيضا تحتوي على مكتبة 
+
+1562
+01:45:33,440 --> 01:45:38,380
+صغيرة بتحتوي على كتب تعليمية ومناهل حضانات لتعزيز
+
+1563
+01:45:38,380 --> 01:45:41,680
+قدرة المعلمين واطلاعهم على كل جديد يعني يشوفوا إيش 
+
+1564
+01:45:41,680 --> 01:45:46,060
+بيصير في الحضانات المختلفة أيضا لازم يكون في عندي
+
+1565
+01:45:46,060 --> 01:45:49,960
+في الحضانة ألعاب تنمي قدرات الطفل العقلية و
+
+1566
+01:45:49,960 --> 01:45:55,320
+البدنية وأيضا ألعاب للترفيه أشهر فوائد العائدة على
+
+1567
+01:45:55,320 --> 01:45:59,200
+الطفل من وجوده في الحضانة تنمية ثقة الطفل بنفسه
+
+1568
+01:45:59,200 --> 01:46:02,360
+اكتشاف ذوي الاحتياجات الخاصة مبكراً  بالتالي توفير
+
+1569
+01:46:02,360 --> 01:46:05,320
+البيئة المناسبة لهم أيضا اكتشاف الموهوبين من
+
+1570
+01:46:05,320 --> 01:46:10,540
+الأطفال تزويد الأطفال بثروة لغوية كبيرة أيضا يمكن
+
+1571
+01:46:10,540 --> 01:46:13,620
+اعتبار الحضانة على أنها منزل العائلة الثاني للطفل
+
+1572
+01:46:13,620 --> 01:46:18,900
+يتعلم فيه كل ما يمكن تعلمه من معلومات مفيدة لبنائه
+
+1573
+01:46:18,900 --> 01:46:23,910
+لمستقبله طبعا فريق العمل كان أغم واسراء وغدير عبد 
+
+1574
+01:46:23,910 --> 01:46:27,750
+النبي، شكرا، أول حاجة السلام عليكم، إحنا مشروعنا 
+
+1575
+01:46:27,750 --> 01:46:32,290
+هو عبارة عن مطعم متنقل، the take a break، طبعا أنا نور
+
+1576
+01:46:32,290 --> 01:46:36,030
+الغمري، صديقاتي حنين أبو سلمية، دعاء عبد 
+
+1577
+01:46:39,170 --> 01:46:42,610
+راح نحكي عن introduction، راح نحكي عن ال .. ال
+
+1578
+01:46:42,610 --> 01:46:46,210
+product اللي راح يعملوا مطعمنا، راح ينتجوا مطعمنا، 
+
+1579
+01:46:46,210 --> 01:46:49,250
+راح نحكي عن marketing plan، راح نحكي عن عمليات ال
+
+1580
+01:46:49,250 --> 01:46:53,070
+company، راح نحكي عن المخاطر، راح نحكي عن حل
+
+1581
+01:46:53,070 --> 01:47:00,310
+المبيعات، وراح نحكي عن احتياج السوق للمطعم. في 
+
+1582
+01:47:00,310 --> 01:47:05,150
+البداية طبعا إحنا كان عندنا كثير أفكار لمشاريع، ف
+
+1583
+01:47:05,150 --> 01:47:10,790
+..في البداية كان في كثير أفكار لمشاريع، لاقينا إنه
+
+1584
+01:47:10,790 --> 01:47:14,390
+أكثر حاجة بتتوجه لها خصوصا إحنا يعني في غزة أكثر 
+
+1585
+01:47:14,390 --> 01:47:19,590
+حاجة المطاعم بتتوجه لها، النفا، حبينا إنه نعمل
+
+1586
+01:47:19,590 --> 01:47:23,570
+مطعم طيب، هلقيتها؟ في كثير مطاعم في غزة، إحنا
+
+1587
+01:47:23,570 --> 01:47:27,510
+حابين إن نتميز هذا المطعم بشيء جديد ونادر 
+
+1588
+01:47:27,510 --> 01:47:31,590
+تكون هي عبارة عن مطعم متنقل طبعا هو بالنسبة لنا
+
+1589
+01:47:31,590 --> 01:47:35,790
+كغزة هي جديدة ونادرة بس طبعا المطعم المتنقل برا
+
+1590
+01:47:35,790 --> 01:47:39,370
+كثير وعدديدة 
+
+1591
+01:47:41,710 --> 01:47:45,430
+المطعم شو بيقدم؟ بيقدم ساندويشات طبعا في كل
+
+1592
+01:47:45,430 --> 01:47:51,410
+الأصناف، شبات، مشروبات وإذا كانت باردة، ساخنة،
+
+1593
+01:47:51,410 --> 01:47:54,570
+أهم حاجة في المطعم أنا عندي يكون عندي ال quality
+
+1594
+01:47:54,570 --> 01:47:59,190
+عالية و price مخفضة يعني عشان إنها تناسب كل ..
+
+1595
+01:48:00,010 --> 01:48:03,390
+المجتمع خصوصا إنه إحنا مطعم متنقل يعني بيروح لل ..
+
+1596
+01:48:03,390 --> 01:48:07,030
+بيروح للزبون وإحنا كمان مش بس .. يعني مش هنبيع 
+
+1597
+01:48:07,030 --> 01:48:10,730
+مثلا في منطقة مثلا معينة أو راقية لا ممكن بيع في
+
+1598
+01:48:10,730 --> 01:48:14,430
+مدارس ممكن بيع في جامعات فيعني كل الأسعار لازم
+
+1599
+01:48:14,430 --> 01:48:18,010
+تتلاقم هدول يعني الطلاب المدارس مثلا مصروفهم قليل
+
+1600
+01:48:18,010 --> 01:48:25,130
+لازم يكون في أسعار تتناسب معهم طبعا أهم عملية في
+
+1601
+01:48:25,130 --> 01:48:29,900
+.. عملية مراحل نجاح أي مشروع هي التسويق التسويق 
+
+1602
+01:48:29,900 --> 01:48:34,080
+الناجح هو اللي بنجح المشروع، طبعا إحنا عملنا عدة 
+
+1603
+01:48:34,080 --> 01:48:37,640
+معايير لهذا التسويق، أول حاجة طبعا الدعاية، 
+
+1604
+01:48:37,640 --> 01:48:41,580
+الدعايات طبعا عملنا حملة .. راح نعمل حملة إعلانية، 
+
+1605
+01:48:41,580 --> 01:48:47,300
+راح نعمل منشورات، راح نوزع كثير منشورات، كمان حتى 
+
+1606
+01:48:47,300 --> 01:48:50,900
+يوم الافتتاح لازم يكون حاجة يعني كبيرة، إنه تجذب 
+
+1607
+01:48:50,900 --> 01:48:55,160
+انتباه الناس، إنه شو فيه هامةده .. الثانية حاجة ..
+
+1608
+01:48:55,160 --> 01:48:58,060
+يعني الثانية حاجة أهم حاجة يعني .. كلنا بنستخدم ال
+
+1609
+01:48:58,060 --> 01:49:01,140
+internet فلازم يكون عندنا على الأقل صفحة على facebook، 
+
+1610
+01:49:01,140 --> 01:49:06,720
+على twitter إنه .. تعرف .. تعرف مطعمنا .. مش بس
+
+1611
+01:49:06,720 --> 01:49:09,340
+هيك إحنا عندنا في غزة كمان مشكلة .. يعني صار عندنا
+
+1612
+01:49:09,340 --> 01:49:12,620
+مشاكل كثير في المطاعم ونظافتها فممكن إنه نعمل
+
+1613
+01:49:12,620 --> 01:49:17,000
+video بوضح مثلا ال chef مثلا إنه لابس uniform لابس
+
+1614
+01:49:17,000 --> 01:49:22,180
+دي رسمي بالنظافة .. يعني نظافة المكان .. هذا أهم
+
+1615
+01:49:22,180 --> 01:49:28,860
+حاجة كمان إنه ممكن يتعقد مع مثلا شركة جوال إنهم 
+
+1616
+01:49:28,860 --> 01:49:34,080
+يبعتوا رسائل في موقع الافتتاح إنه .. يعني زي زي
+
+1617
+01:49:35,040 --> 01:49:40,560
+كمان إحنا كمهندسين حاسوب ممكن نعمل موقع .. موقع
+
+1618
+01:49:40,560 --> 01:49:46,000
+لمطعمنا بيعرض كل خدمات مطعمنا وإحنا قبل هيك عملنا
+
+1619
+01:49:46,000 --> 01:49:50,080
+مشروع تخرجنا بالنسبة
+
+1620
+01:49:50,080 --> 01:49:55,960
+للعروض التجارية طبعا الكثير من الناس طبعا بتتوجه للعروض
+
+1621
+01:49:55,960 --> 01:50:00,520
+أكثر حاجة يعني لو بنعمل مثلا كل خمسين وجبة فيه
+
+1622
+01:50:00,520 --> 01:50:07,770
+جوائز كل مثلا .. كل ما تأخذ وجبة إلكابون تدخل على سحب
+
+1623
+01:50:07,770 --> 01:50:12,730
+فهذا الشيء كثير بساعد في الترويج كمان إنه مثلا كل
+
+1624
+01:50:12,730 --> 01:50:18,670
+شهر إحنا راح نقدم مثلا وجبة جديدة مميزة ممكن كمان
+
+1625
+01:50:18,670 --> 01:50:21,910
+إنه إحنا راح نبيع عند .. عند مدارس ممكن نعمل 
+
+1626
+01:50:21,910 --> 01:50:25,250
+ساندويشات بطريقة معينة تجذب الانتباه زي مثلا إنه 
+
+1627
+01:50:25,250 --> 01:50:30,290
+يكون وجه مثلا بضحك نجمة فهذا كله ب .. بساعد على
+
+1628
+01:50:30,290 --> 01:50:35,390
+الترويج في إطار اللي حكته زميلتي نور إنه محتاجين
+
+1629
+01:50:35,390 --> 01:50:40,790
+عمليات وخطط معينة للتسويق، قبل ما نعمل أو نبدأ
+
+1630
+01:50:40,790 --> 01:50:44,850
+بتنفيذ هذه الخطط، محتاجين إنه نبدأ بعمليات أساسية 
+
+1631
+01:50:44,850 --> 01:50:49,450
+بتحتاجها أي شركة اللي هي في البداية إنه عملية تجهيز 
+
+1632
+01:50:49,450 --> 01:50:53,430
+المعدات اللي بنحتاجها لإنشاء هذه الشركة اللي هي 
+
+1633
+01:50:53,430 --> 01:50:57,910
+عبارة عن المطعم المتنقل الخاص فينا هتتمثل اللي هي
+
+1634
+01:50:57,910 --> 01:51:02,210
+من خلال شراء اللي هو ال bus أو الشاحنة وتجهيزه بحيث
+
+1635
+01:51:02,210 --> 01:51:06,190
+يكون مطبخ اللي هو ويكون بمثابة مطعم متنقل 
+
+1636
+01:51:06,190 --> 01:51:10,210
+بالإضافة إلى اللي هو تجهيز المعدات اللي هي أو
+
+1637
+01:51:10,210 --> 01:51:14,830
+أدوات اللي هي المطبخ اللازمة لل chef اللي هيعمل 
+
+1638
+01:51:14,830 --> 01:51:19,590
+اللي هو المنتجات الخاصة فينا نيجي للجزء الآخر من
+
+1639
+01:51:19,590 --> 01:51:23,530
+العمليات الخاصة بالشركة اللي هي عملية التوظيف إحنا 
+
+1640
+01:51:23,530 --> 01:51:28,090
+هنحتاج عدد يعني بسيط من الموظفين أهمهم اللي هو ال
+
+1641
+01:51:28,090 --> 01:51:32,050
+manager ال manager هيكون المشرف على عملية اللي هي 
+
+1642
+01:51:32,050 --> 01:51:36,020
+المحاسبة والجزء المالي بالإضافة إلى إنه يغطي اللي
+
+1643
+01:51:36,020 --> 01:51:39,940
+هي المؤونة أو المخزن أو النقص يعني اللي هي .. ياخد 
+
+1644
+01:51:39,940 --> 01:51:45,240
+اللي هو اللي هي المعطيات اللي هي الناقصة في المخزن
+
+1645
+01:51:45,240 --> 01:51:48,940
+أو المؤونة من خلال اللي هو الطباخ بالإضافة إلى إنه
+
+1646
+01:51:48,940 --> 01:51:53,160
+مسؤول عن الإدارة يعني عملية المراقبة وأداء اللي 
+
+1647
+01:51:53,160 --> 01:51:56,600
+هو الموظفين بالإضافة إلى ال manager اللي هو المدير
+
+1648
+01:51:56,600 --> 01:52:01,980
+أن اللي هو ال chef أو اللي هو الطباخ يعني هو دور 
+
+1649
+01:52:01,980 --> 01:52:06,270
+الأساسي في العملية هو اللي هينتج المنتجات وهو اللي
+
+1650
+01:52:06,270 --> 01:52:10,230
+هيصنع الأشياء فإحنا هناخده بالإعتبار إن يكون فيه 
+
+1651
+01:52:10,230 --> 01:52:13,710
+مميزات يعني خاصة في إنه أنده المهارة والكفاءة
+
+1652
+01:52:13,710 --> 01:52:18,030
+العالية إنه ينتج منتجات عالية الجودة بالإضافة إلى
+
+1653
+01:52:18,030 --> 01:52:20,630
+اللي هو ال waiter، النادل، النادل هنا هيكون
+
+1654
+01:52:20,630 --> 01:52:23,750
+بدورين، اللي هو عملية توصيل الطلبات بالإضافة إلى 
+
+1655
+01:52:23,750 --> 01:52:27,460
+التنظيف، لأنهم مش محتاجين يعني إنه .. عمليات تنظيف
+
+1656
+01:52:27,460 --> 01:52:31,960
+عالية، هنحتاج اللي هو لشخصه، اللي هي أهم المخاطر
+
+1657
+01:52:31,960 --> 01:52:37,040
+اللي ممكن نواجهها كمطعم متنقل، اللي هي نقص في
+
+1658
+01:52:37,040 --> 01:52:40,340
+الغاز أو البنزين، لإنه إحنا في إطار اللي هو المطعم
+
+1659
+01:52:40,340 --> 01:52:43,480
+المتنقل محتاجين لعملية تشغيل اللي هي أدوات
+
+1660
+01:52:43,480 --> 01:52:47,410
+كهربائية مولدة كهرباء أو محولة وبناء على ذلك إحنا 
+
+1661
+01:52:47,410 --> 01:52:50,810
+محتاجين للبنزين اللي لازم نتشغيله وبما إنه إحنا 
+
+1662
+01:52:50,810 --> 01:52:54,650
+في قطاع غزة فالظروف اللي هي والحصار بتؤدي إلى 
+
+1663
+01:52:54,650 --> 01:52:58,510
+اللي هو شوية إعاقات في هذه الأشياء من احتياطات
+
+1664
+01:52:58,510 --> 01:53:02,770
+اللي هو الغاز والبنزين الخاص فينا فإحنا كحل 
+
+1665
+01:53:02,770 --> 01:53:06,810
+المشكلة هو طبعا حل جزء .. يعني حل هيك مش إنه 
+
+1666
+01:53:06,810 --> 01:53:10,830
+أساسي أو جذري للأشياء إنه هيكون ال .. هنعمل
+
+1667
+01:53:10,830 --> 01:53:14,670
+احتياطنا مخزون احتياطي يعني من باب إنه مستقبلاً
+
+1668
+01:53:14,670 --> 01:53:18,530
+يعني يغطي مثلا لمدة سنة أو سنتين احتياطا ما هو هيكون 
+
+1669
+01:53:18,530 --> 01:53:22,250
+إن المشكلة الثانية اللي هو المنافسين في إطار اللي
+
+1670
+01:53:22,250 --> 01:53:25,370
+هو عملنا إنه إحنا مثلا هروح على .. هنستهدف الأماكن 
+
+1671
+01:53:25,370 --> 01:53:28,950
+اللي بتجذب الناس يعني في ناس وفيه ازدهار وخصوصا 
+
+1672
+01:53:28,950 --> 01:53:31,270
+من كافة الفئات على صعيد اللي هو 
+
+1673
+01:53:35,320 --> 01:53:39,240
+على صعيد اللي هو يعني من الأطفال مروراً بالبالغين
+
+1674
+01:53:39,240 --> 01:53:43,220
+والكبار فيعني مثلا على سبيل المثال عندنا منطقة
+
+1675
+01:53:43,220 --> 01:53:47,140
+الجندي المجهول مزدحمة وفي ناس كثير وعائلات بتروح 
+
+1676
+01:53:47,140 --> 01:53:50,180
+عليها لكن في نفس الوقت في عندنا اللي هي مطاعم
+
+1677
+01:53:50,180 --> 01:53:55,300
+ثابتة وها دي اللي هي زبائنها الدائمون فهدول بمثابة
+
+1678
+01:53:55,300 --> 01:53:59,480
+بالنسبة لنا شوية يعني من باب اللي هو الخطورة إنه
+
+1679
+01:53:59,480 --> 01:54:04,050
+يعني كيف نفرض أنفسنا وإنه يعني نجلب اللي هو الزبائن 
+
+1680
+01:54:04,050 --> 01:54:06,870
+اللي إحنا محتاجينه عشان نغطي اللي هي نسبة الأرباح
+
+1681
+01:54:06,870 --> 01:54:10,490
+الخاصة فينا فهذا بيتمن خلاله اللي هو إثبات اللي هو
+
+1682
+01:54:10,490 --> 01:54:14,810
+جودتنا جودة المنتجات الخاصة فينا بالإضافة إلى اللي 
+
+1683
+01:54:14,810 --> 01:54:18,610
+هو الأسعار يعني في مطاعم في هذه المنطقة تستهدف 
+
+1684
+01:54:18,610 --> 01:54:22,430
+يعني فئات معينة من الدخل معين احنا لأ هنحاول قدر
+
+1685
+01:54:22,430 --> 01:54:25,690
+الإمكان نستهدف كافة الأفراد يعني تكون مناسبة لكافة
+
+1686
+01:54:25,690 --> 01:54:30,760
+الأفراد بغض النظر عن اللي هو نوع الدخل تبعهم في
+
+1687
+01:54:30,760 --> 01:54:35,800
+قطاع ذلك اللي هو .. هتحكي معنا اللي هو دعاء تحليل
+
+1688
+01:54:35,800 --> 01:54:38,880
+المبيعات والتوقعات الخاصة في المطعم ثانية طبعا أهم
+
+1689
+01:54:38,880 --> 01:54:42,560
+حاجة احنا في أي شركة أو في أي مشروع هو رأس المال
+
+1690
+01:54:42,560 --> 01:54:46,740
+أو الأرباح أو اللي هو عنصر المال علشان هيك قبل ما
+
+1691
+01:54:46,740 --> 01:54:49,440
+الواحد يفكر في أي مشروع لازم يكون عنده دراية كاملة
+
+1692
+01:54:49,440 --> 01:54:52,980
+أو كبيرة أو عميقة في كيفية إدارة هذه الأموال بشكل
+
+1693
+01:54:52,980 --> 01:54:57,000
+سليم علشان يقدر انه يحقق الأرباح بشكل سليم و علشان
+
+1694
+01:54:57,000 --> 01:55:00,760
+كمان يشوفوا قد إيش بده معطيات يعني علشان ينفذ مشروعه
+
+1695
+01:55:00,760 --> 01:55:04,440
+و قد إيش كمان هيرجعله الدخل تبعه عشان لازم يكون عامل
+
+1696
+01:55:04,440 --> 01:55:07,400
+دراسة جدوى دقيقة و مظبوطة علشان يحدد إذا هالمشروع
+
+1697
+01:55:07,400 --> 01:55:11,890
+هذا هيكون ناجح ولا لأ احنا في البداية عملنا دراسات
+
+1698
+01:55:11,890 --> 01:55:15,410
+لـ اللي هو التكلفة الأساسية أو السابت اللي احنا
+
+1699
+01:55:15,410 --> 01:55:19,030
+هنحتاجها كمطعم متنقل احنا أهم حاجة هيكون عندنا
+
+1700
+01:55:19,030 --> 01:55:21,830
+اللي هو الـ bus الـ bus هذا اللي هيكون مجهز بكل 
+
+1701
+01:55:21,830 --> 01:55:25,370
+الأجهزة اللازمة علشان احنا ننفذ مشروعنّا نطلعنا
+
+1702
+01:55:25,370 --> 01:55:28,610
+على أسعار الباصات لقيناها أنها متفاوتة بشكل يعني 
+
+1703
+01:55:28,610 --> 01:55:32,010
+تبدأ من عشرين ألف دولار لعند متين ألف دولار فاحنا 
+
+1704
+01:55:32,010 --> 01:55:34,650
+حاولنا أنه نطلع على المميزات و ناخد الشي اللي 
+
+1705
+01:55:34,650 --> 01:55:38,550
+بنسبنا بالسعر المعقول فلقينا أنه الـ .. أنه الـ cost
+
+1706
+01:55:38,550 --> 01:55:41,390
+تبعها هيكون الـ تسعين ألف دولار هيكون المميزات
+
+1707
+01:55:41,390 --> 01:55:45,100
+تبعها كتير ملائمة لإنا كمان احنا هنحتاج شوية 
+
+1708
+01:55:45,100 --> 01:55:48,980
+إعدادات أخرى، هنحتاج شوية لمسات بسيطة كمان ثانية و
+
+1709
+01:55:48,980 --> 01:55:51,860
+أدوات في المطبخ زيادة، فهذا الشي احنا حسبناه
+
+1710
+01:55:51,860 --> 01:55:55,280
+فاطلع كإجمالي بيطلع يعني أقل من الف دولار تقريبا
+
+1711
+01:55:55,280 --> 01:55:59,120
+هيكلفناه، فعشان هيك التكلفة الأساسية ثابتة بتاعتنا
+
+1712
+01:55:59,120 --> 01:56:03,750
+هتكون واحد و تسعين ألف دولار بس و هيكون كمان عندنا
+
+1713
+01:56:03,750 --> 01:56:07,610
+أكيد اللي هو تكلفة متغيرة بناء على الرواتب، بناء
+
+1714
+01:56:07,610 --> 01:56:10,230
+على الغاز، بناء على تكلفة الـ sandwiches اللي احنا 
+
+1715
+01:56:10,230 --> 01:56:12,610
+هنعملها، كل هذا الشي لازم الواحد ياخدوا بعين الاعتبار
+
+1716
+01:56:12,610 --> 01:56:15,890
+احنا روحنا حسبنا بشكل شهري، بناء على 
+
+1717
+01:56:15,890 --> 01:56:19,430
+التوقعات اللي احنا عملناها في المبيعات، فلاقينا
+
+1718
+01:56:19,430 --> 01:56:22,810
+أنه احنا في الأول بدنا نوظف مجموعة من العمال، مش
+
+1719
+01:56:22,810 --> 01:56:25,710
+عددهم مش كبير، يعني ثلاثة، فهنحتاج تقريبا 800
+
+1720
+01:56:25,710 --> 01:56:31,130
+دولار للي هو راتبهم هنحتاج كمان أنه نجهز تجهيز 
+
+1721
+01:56:31,130 --> 01:56:35,050
+السندوتشات و تجهيز العصائر هيكلفنا مبلغ بس بناء
+
+1722
+01:56:35,050 --> 01:56:38,530
+على التوقعات المبيعات اللي احنا عملناها فبيكلفنا
+
+1723
+01:56:38,530 --> 01:56:43,190
+3900 دولار و المشروبات هتكلفنا 3000 دولار بالنسبة
+
+1724
+01:56:43,190 --> 01:56:46,150
+للغاز هيكلفنا تقريبا 50 دولار و بالنسبة للبنزين
+
+1725
+01:56:46,150 --> 01:56:49,810
+150 دولار و بالنسبة للمياه هتكلفنا تقريبا 20 دولار
+
+1726
+01:56:49,810 --> 01:56:53,630
+عشان هيك بيطلع التكلفة الشهرية لإنا هتكون 8000
+
+1727
+01:56:53,630 --> 01:56:59,450
+دولار تقريبا يعني ما يقارب 31 ألف شكل هذا الكلام
+
+1728
+01:56:59,450 --> 01:57:02,690
+بناء على اللي هو المبيعات المتوقعة لنا، احنا
+
+1729
+01:57:02,690 --> 01:57:05,970
+سألناه، سألنا المطاعم، سألنا حوالين الجامعة،
+
+1730
+01:57:05,970 --> 01:57:08,730
+حاولنا أن نستفسر عن اللي هو قد إيش بيبيعوا في اليوم
+
+1731
+01:57:08,730 --> 01:57:13,250
+معدلات، كانت الأرقام يعني .. يعني .. يعني مختلفة
+
+1732
+01:57:13,250 --> 01:57:16,190
+.. يعني في كان رجج كبير يعني، في ناس كانوا يعطونا
+
+1733
+01:57:16,190 --> 01:57:18,910
+أرقام صغيرة، في ناس أعطونا أرقام كتير كبيرة، احنا
+
+1734
+01:57:18,910 --> 01:57:22,540
+برضه حاولنا ناخد الوسط و .. يعني لاقينا أن الوسط
+
+1735
+01:57:22,540 --> 01:57:25,840
+تقريبا 150 لـ 200 ساندوش في اليوم هذا طبعا لإن احنا 
+
+1736
+01:57:25,840 --> 01:57:29,040
+هنكون متجولين هنكون حوالين منطقة الجامعة عدد
+
+1737
+01:57:29,040 --> 01:57:31,520
+الطلاب تعون الجامعين .. الجامعيين اللي بيفطروا
+
+1738
+01:57:31,520 --> 01:57:34,060
+كتير كبير ف .. يعني لما سألنا حوالين الجامعة
+
+1739
+01:57:34,060 --> 01:57:36,980
+أعطونا أرقام كبيرة فاحنا حاولنا أن ناخدوا الوسط
+
+1740
+01:57:36,980 --> 01:57:40,560
+فلاقينا أنه 150 وشبه و ساندوش في اليوم بيبيعوا هذا
+
+1741
+01:57:40,560 --> 01:57:44,660
+هو الوسط طبعا هتكون أسعارنا من 1 شيكل لـ 10 شيكل
+
+1742
+01:57:44,660 --> 01:57:48,100
+تقريبا يعني هيكون معدل .. يعني يبيعنا اليوم 900
+
+1743
+01:57:48,100 --> 01:57:52,060
+شيكل يعني و في الشهر بتطلع تقريبا .. بس الـ
+
+1744
+01:57:52,060 --> 01:57:55,320
+sandwiches تطلع تقريبا سبعة آلاف دولار اللي هي سبعة
+
+1745
+01:57:55,320 --> 01:57:59,920
+و عشرين ألف شيكل تقريبا هذا الشي طبعا احنا حسبناها أنه 
+
+1746
+01:57:59,920 --> 01:58:03,600
+هتكلفنا 3900 دولار طبعا حاولنا أنه نعمل أرقام 
+
+1747
+01:58:03,600 --> 01:58:06,640
+تقريبية في التكلفة من ناحية الخبز طبعا هيكون عندنا
+
+1748
+01:58:06,640 --> 01:58:09,720
+أنواع مختلفة فحاولنا أنه نعمل يعني شيء تقريبي و
+
+1749
+01:58:09,720 --> 01:58:13,760
+range تقريبي فتقريبا طبعا عندنا 4000 دولار تقريبا
+
+1750
+01:58:13,760 --> 01:58:17,120
+تكلفتهم هيكون لنا هذا بالنسبة للواجبات بالنسبة 
+
+1751
+01:58:17,120 --> 01:58:20,500
+للمشروبات فاحنا قلنا أنه بمعدل مشروبات باردة و
+
+1752
+01:58:20,500 --> 01:58:25,210
+ساخنة بمعدل 100 لـ 150 من تقريبا من نصف دولار لثلاثة
+
+1753
+01:58:25,210 --> 01:58:28,570
+دولار يعني من شيكل لعشرة شيكل تقريبا هتكون مشروباتنا
+
+1754
+01:58:28,570 --> 01:58:32,230
+باردة وساخنة بيطلع تقريبا يعني بالمعدل اللي احنا
+
+1755
+01:58:32,230 --> 01:58:36,530
+نبيع من 100 لـ 150 بيطلع تقريبا 4500 دولار 17000
+
+1756
+01:58:36,530 --> 01:58:41,270
+شيكل يعني كإجمال مبيعات مشروبات وواجبات احنا لاقينا
+
+1757
+01:58:41,270 --> 01:58:48,330
+أنه هيطلع 44000 شيكل واحنا لما حسبنا التكلفة اللي
+
+1758
+01:58:48,330 --> 01:58:55,360
+هي المتغيرة لنا لاقينا إنه تكلفتنا المتغيرة تكلفتنا 
+
+1759
+01:58:55,360 --> 01:58:59,500
+المتغيرة كانت 8000 دولار فـ و اللي احنا وصلناله
+
+1760
+01:58:59,500 --> 01:59:02,740
+أنه هيكون تقريبا .. تبعنا هيكون تقريبا بـ 11000
+
+1761
+01:59:02,740 --> 01:59:06,440
+دولار مبيعاتنا و تكلفتنا هتكون بـ 8000 دولار لاقينا
+
+1762
+01:59:06,440 --> 01:59:09,320
+أنه الربح تبعنا هيكون تقريبا 3000 دولار في الشهر
+
+1763
+01:59:09,320 --> 01:59:13,580
+فاحنا .. يعني أنه تقريبا النسب كانت واقعية يعني مش
+
+1764
+01:59:13,580 --> 01:59:16,800
+إنها مش غير واقعية لإن احنا بناء على الأسئلة و
+
+1765
+01:59:16,800 --> 01:59:19,460
+الاستفسارات اللي سألنا فيها المطاعم المجاورة تماما
+
+1766
+01:59:19,720 --> 01:59:22,980
+فأنه 3000 دولار لاقينا أنه هذا هيرجعنا رأس المال
+
+1767
+01:59:22,980 --> 01:59:26,440
+تقريبا خلال سنتين، هيكون رأس المال رجعه، طبعا
+
+1768
+01:59:26,440 --> 01:59:29,060
+السنة الأولى هتكون زي هيك، السنة الثانية طبعا إلا
+
+1769
+01:59:29,060 --> 01:59:32,280
+هيكون فيه اختلافات في راتب العاملين اللي عندنا،
+
+1770
+01:59:32,280 --> 01:59:35,100
+يعني إنما يصير تغيرات في التكلفة المتغيرة في
+
+1771
+01:59:35,100 --> 01:59:38,520
+السنين الجاية، بس إنه .. إنه احنا هنرجع رأس المال
+
+1772
+01:59:38,520 --> 01:59:41,860
+خلال سنتين، فلاقينا إن هذا الشيء هيكون كويس يعني
+
+1773
+01:59:41,860 --> 01:59:43,220
+عنصر تفاؤل بالنسبة لنا
+
+1774
+01:59:47,420 --> 01:59:50,480
+قيمنا يعني تقريبيا بشكل منطقي وبشكل واقعي بناء على
+
+1775
+01:59:50,480 --> 01:59:54,900
+التجربة والأسئلة اللي احنا سألناها طبعا الفكرة هذه
+
+1776
+01:59:54,900 --> 01:59:58,320
+يعني الفكرة الجديدة على غزة هي فكرة عالمية بس هي
+
+1777
+01:59:58,320 --> 02:00:01,980
+جديدة على غزة اللي هي مميزات كتير يعني أنه الفكرة
+
+1778
+02:00:01,980 --> 02:00:04,660
+الجديدة الناس دائما بتحبوا يجربوا شيء جديد فهيكون
+
+1779
+02:00:04,660 --> 02:00:07,680
+هذا الشيء كويس لهم أنه في البداية ممكن يقولوا أنه
+
+1780
+02:00:07,680 --> 02:00:10,800
+خلونا نجرب أنه نشتري من الـ bus هذا يعني سندوتشات
+
+1781
+02:00:10,800 --> 02:00:13,980
+أو شيء خصوصا أنه احنا هنكون متنقلين، يعني هنكون عند
+
+1782
+02:00:13,980 --> 02:00:17,480
+الجامعة، هنكون الصبح مثلا عند الجامعة، في العصر
+
+1783
+02:00:17,480 --> 02:00:20,620
+هنروح عند الميناء، هنروح عند جندي، يعني هنحاول أنه 
+
+1784
+02:00:20,620 --> 02:00:23,320
+نغطي في المناسبات، في الأعياد، في هذه الأماكن
+
+1785
+02:00:23,320 --> 02:00:26,540
+كلها، هنحاول نغطي، فهذا الشيء يعني هيكون إيجابي و
+
+1786
+02:00:26,540 --> 02:00:29,340
+كويس بالنسبة لنا يعني، و شكرا يعني، عطيكم العافية
+
+1787
+02:00:29,340 --> 02:00:30,500
+عطيكم العافية